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i
4 th INTERNATIONAL CONFERENCE ON
RECENT ADVANCES IN PURE AND APPLIED
MATHEMATICS, KUSADASI, TURKEY
11-15 MAY 2017
Abstract Book
ii
4th INTERNATIONAL CONFERENCE ON RECENT
ADVANCES IN PURE AND APPLIED
MATHEMATICS, KUSADASI, TURKEY
11-15 MAY 2017
Abstract Book
List of Major Sponsors
Istanbul Commerce University
The Turkish Academy of Sciences
Republic of Turkey Prime Ministry Turkish Cooperation and Coordination Agency
Albaraka Turk
Simurg
iii
4th INTERNATIONAL CONFERENCE ON RECENT ADVANCES IN PURE AND APPLIED
MATHEMATICS, KUSADASI, TURKEY, 11-15 MAY 2017
Honorary Chairs of Scientific Committee
Prof. Dr. B. E. Rhoades, USA Prof. Dr. H. M. Srivastava, Canada Prof. Dr. Ljubisa Kocinac, Serbia Prof. Dr. Mubariz Tapdigoglu Garayev, Saudi Arabia Prof. Dr. Sadek Bouroubi, Algeria Prof. Dr. Ali M. Akhmedov, Azerbaijan Prof. Dr. Werner Varnhorn, Germany Prof. Dr. Emine Mısırlı, Turkey Prof. Dr. Huseyin Cakalli, Turkey Prof. Dr. G. Das, India Prof. Dr. M. Perestyuk, Ukraine Prof. Dr. O. Boichuk, Ukraine Prof. Dr. I. Shevchuk, Ukraine Prof. Dr. Anatoliy M. Samoilenko, Ukraine Prof. Dr. V. Guliyev, Turkey Prof. Dr. M. Abbas, S.Africa Prof. Dr. M. Mursaleen, India Prof. Dr. W. Sintunavarat, Thailand Prof. Dr. V. Kalantarov, Turkey Prof. Dr. Cihan Orhan, Turkey Prof. Dr. Metin Basarir, Turkey
Organizing Committee
Prof. Dr. Ekrem Savas, Istanbul Commerce University Prof. Dr. Richard Patterson, North Florida University Prof. Dr. Mehmet Gürdal, Suleyman Demirel University Prof. Dr. Martin Bohner, Missouri S&T Prof. Dr. Ram Mohapatra, Uni. of Central Florida Prof. Dr. Fairouz Tchier, King Saud University Prof. Dr. Mehmet Dik, Rockford University Prof. Dr. Lubomira Softova, Second University of Naples Prof. Dr. Agron Tato, Polytechnic Uni. of Tirana Prof. Dr. Debasis Giri, Haldia Institute of Technology Prof. Dr. Naim Braha, Uni. of Prishtina Assoc. Prof. Dr. Yusuf Zeren, Yildiz Technical University Assoc. Prof. Dr. Rahmet Savas, Istanbul Medeniyet University Assoc. Prof. Dr. Erhan Deniz, Kafkas University Assoc. Prof. Dr. Mahpeyker Ozturk, Sakarya University Assoc. Prof. Dr. Esra Duman, Gazi University Assist. Prof. Dr. Sukran Konca, Bitlis Eren University Assist. Prof. Dr. Gokhan Cuvalcioglu, Mersin University Assist. Prof. Dr. Emel Asici, Karadeniz Technical University Assist. Prof. Dr. Arzu Akgul, Kocaeli University Assist. Prof. Dr. Hafize Gumus, Necmettin Erbakan University Dr. Veli Capali, Süleyman Demirel University Dr. Lakhdar Ragoub, Alyammah University Dr. Nora Mahloul, University of Scien. and Tech. Houari Boumedien
iv
4th INTERNATIONAL CONFERENCE ON RECENT ADVANCES IN PURE AND APPLIED
MATHEMATICS, KUSADASI, TURKEY, 11-15 MAY 2017
Local Organizing Committee
Rabia Savas, Sakarya University Sefa Anil Sezer, Istanbul Medeniyet University Dr. Ulas Yamanci, Suleyman Demirel University Sevim Ertug, Ankara University A. Buyukkaya, Sakarya University Oya Mert, Kemerburgaz University Gulsemay Yigit, Kemerburgaz University
Scientific Committee Prof. Dr. Huseyin Cakalli, Turkey Prof. Dr. Jeff Connor, USA Prof. Dr. Lubomira Softova, Italy Prof. Dr. Reza Langari, USA Prof. Dr. Mikail Et, Turkey Prof. Dr. S. A. Mohiuddine, S. Arabia Prof. Dr. Narendra Kumar Govil, USA Prof. Dr. T. A. Chishti, India Prof. Dr. Ayhan Serbetci, Turkey Prof. Dr. Bilal Altay, Turkey Prof. Dr. Ismail Ekincioglu, Turkey Prof. Dr. A. Sinan Cevik, Turkey Prof. Dr. Leiki Loone, Estonia Prof. Dr. Akbar B. Aliyev, Azerbaijan Prof. Dr. Vali M. Gurbanov, Azerbaijan Prof. Dr. Faqir M. Bhatti, Pakistan Prof. Dr. Said Melliani, Morocco Prof. Dr. Abdalah Rababah, Jordan Prof. Dr. Radouane Yafia, Morocco Prof. Dr. Sudarsan Nanda, India Prof. Dr. Seyit Temir, Turkey Prof. Dr. Halit Orhan, Turkey Prof. Dr. Vatan Karakaya, Turkey Prof. Dr. Amir Khosravi, Iran Prof. Dr. Seifedine Kadry, Kuwait Prof. Dr. Ali M. Akhmedov, Azerbaijan Prof. Dr. Ziyatkan Aliyev, Azerbaijan Prof. Dr. Poom Kumam, Thailand Prof. Dr. Agacik Zafer, Kuwait Prof. Dr. Tunay Bilgin, Turkey Prof. Dr. Gangaram S. Ladde, USA Prof. Dr. Claudio Cuevas, Brazil
Prof. Dr. Reza Saadati, Iran Prof. Dr. Salih Aytar, Turkey Prof. Dr. Charles Swartz, USA Prof. Dr. Yagub A. Sharifov, Azerbaijan Prof. Dr. Niyazi A. Ilyasov, Azerbaijan Prof. Dr. Aref Jeribi, Tunisia Prof. Dr. Husamettin Coskun, Turkey Prof. Dr. Maria Zeltser, Estonia Prof. Dr. Kamalmani Baral, Nepal Prof. Dr. Ants Aasma, Estonia Prof. Dr. Ismail N. Cangul, Turkey Prof. Dr. Murat Tosun, Turkey Prof. Dr. Yilmaz Simsek, Turkey Prof. Dr. Harry Miller, Bosnia Prof. Dr. Ali Fares, France Prof. Dr. Ibrahim Canak, Turkey Prof. Dr. Naim Braha, Kosova Prof. Dr. Mustapha Cheggag, Algeria Prof. Dr. Fahrettin Abdullayev, Kırgizistan Prof. Dr. Praveen Agarwal, India Prof. Dr. P. D. Srivastava, India Prof. Dr. Naila Rozi, Pakistan Prof. Dr. Emine Can, Turkey Prof. Dr. Hemen Dutta, India Assoc. Prof. Dr. Bayram Ali Ersoy, Turkey Assoc. Prof. Dr. Ayhan Aydın, Turkey Asst. Prof. Vishnu Narayan Mishra, India Dr. Lejla Miller Van-Wieren, Bosnia Dr. Mayssa Alqurashi, S. Arabia Dr. Fardous Taoufic, S. Arabia Dr. Ammar Edress Mohamed, Iraq
v
Dear Collogues;
First of all I wish to offer you a warm welcome to the fourth International Conference on
Recent Advances in Pure and Applied Mathematics (ICRAPAM 2017).
The last conference of this series was organized in Bodrum, Turkey, during 19-23 May
2016 and it was attended by 350 scientists from 48 different countries, contributing 300 oral
presentations and 50 posters.
As the past conference, the aim of this conference is to provide a platform for
mathematicians to present their recent Works, exchange ideas and new methods in several
important areas of Mathematics and to provide an opportunity to improve collaboration
between local and international participants in the wonderful historic city of Istanbul. Further
we believe that, the development in various fields of Mathematics lead to new research areas in
Mathematics and the richness of the new results can also provide basis for interdisciplinary
collaborations. That is why; we have planned to provide a common forum for scientists to
communicate their original results in various fields of analysis and applied mathematics.
We would like to thank all the invited speakers who have kindly accepted our invitation
and have come to spend their precious time by sharing their ideas during the conference.
Finally, we would also like to thank all of the members of the Scientific Advisory Committee
and the Organizing Committee of this conference.
Again we would like to convey our heartiest welcome to each of you who have come to
attend this conference and we wish for an enjoyable high scientific level conference and hope
to meet you again in the future.
With our best wishes and warm regards,
Prof. Dr. Ekrem SAVAS
Chair of the Conference
vi
4th INTERNATIONAL CONFERENCE ON RECENT ADVANCES IN PURE AND APPLIED
MATHEMATICS, KUSADASI, TURKEY, 11-15 MAY 2017
INVITED TALKS
The Sturm-Liouville Theory and Fourier Analysis Prof. Dr. Mohammed Al-Gwaiz
1 1
Topological Spaces with an -base Prof. Dr. Taras Banakh
2
Schwarz Problem for Higher-order Equations in a Polydisc Prof. Dr. A. Okay Celebi
3
Gelfand Theory Unplugged Prof. Dr. Robin Harte
4
Decision Models for Autonomous Vehicles Prof. Dr. Reza Langari
5
Summation and Quadrature Processes for Slowly Convergent Series Prof. Dr. Gradimir V. Milovanović
6
vii
4th INTERNATIONAL CONFERENCE ON RECENT ADVANCES IN PURE AND APPLIED MATHEMATICS, KUSADASI, TURKEY, 11-15 MAY 2017
LIST OF TALKS
New Iterative Methods for Solving Non-Linear Equations
Osama Y. Ababneh
7
Solution of Animplicit Complementarity Problem on Isotone Projection Cones
Mujahid Abbas
Analysis and Modeling the Drought Hydrologic by the Copulas in North Algeria
Rassoul Abdelaziz
8
9
Rayleigh-Marangoni Convection in a Layer of Nanofluid
Abdullah A. Abdullah
10
On the Properties of the Orthogonal Polynomials along a Contour
Fahreddin.G.Abdullayev and Gülnara.A.Abdullayev
11
Modeling and Classifying by using Binary Logistic Regression Analysis Application on Hepatitis Disease
Data
Qais Mustafa Abdulqader
13
Residual Power Series Approach to Handle a Class of Fractional Differential Equations
Ayed H. Adamat
14
On the Existence and Uniqeness of Positive Solution for a Fractional Boundary Value Problem with New
Fractional Derivative
Asghar Ahmadkhanlu
15
On Derivation of a Subclasses of Filiform Leibniz Algebras
AL-Nashri AL-hossain Ahmed
Global Existence and Uniqueness of Weak Solution to a Chemotaxis Model
N. Aïssa and A. Balehouane
16
17
A Generalization of Hereditary Noetherian Prime Rings
Evrim Akalan
On Some Inequalities of Analytic and Biunivalent Functions Given by Subordination
Arzu Akgul
18
19
Compact Finite Differences Method for Burgers-Huxley Equation
Canan Akkoyunlu
Approximation Solution of System of Volterra Integro Differential Using Finite Element Method
Adel Alamarashi
20
21
Fixed Point Theorem in FM-Spaces
Rateb AlBtoush 22
viii
Bounds for the Zeros of Polynomials by Using Similar Matrices
Mohammad. Al-Hawari
23
An Application of Decision Tree for Evaluating a Classroom Teaching Practice
Sadri Alija and Halil Snopce
24
Existence of Positive Solution of Boundary Value Fractional Quadratic Differential Equations
Youssef Allaoui, Khalid Hilai and Guida Karimi
25
Some Applications of Cozero Sets in Topological Spaces
Ahmad Al-Omari
26
An Efficient Analytical-Numerical Technique for Handling Model of Fuzzy Differential Equations of
Fractional-Order
Mohammad Aloroud, Mohammed Al-Smadi, Rokiah Rozita Ahmad, Ummul Khair Salma Din
Adaptation of Fractional Power Series Method for Solving Fuzzy BVPs
Mohammad Alaroud, Rokiah Rozita Ahmad, Mohammed Al-Smadi and Ummul Khair Salma
Din
27
29
Solving Fuzzy Mixed Integral Equations of Second Kind in Hilbert Spaces
Mohammed Al-Smadi
Numerical Algorithm for Solving Time-Fractional Bvps in a Simplified Reproducing Kernel Space
Mohammed Al-Smadi
31
33
Semiregularization of Almost Countably Compact Spaces
Zuhier Altawallbeh
Generalization on Countably Compact Spaces via Hereditary Classes
Zuhier Altawallbeh
35
36
Hybrid Master Equation of the Jump Diffusion Approximation
Derya Altintan and Heinz Koeppl
37
Coefficient Bounds for a Subclass of Analytic Functions with Respect to Symmetric Points
Osman Altintas and Oznur Ozkan Kilic
On The Relationship Between A Family of Fibonacci And Lucas Numbers
Ipek Altun, Ali Aydogdu and Engin Ozkan
39
40
Convergence, Consistency and Stability in Intuitionistic Fuzzy Differential Equations
Bouchra Ben Amma, Said Melliani and Lalla Saadia Chadli
41
SQCQP Descent Scheme for Multi-objective Optimization Problem
Md Abu Talhamainuddin Ansary and Geetanjali Panda
42
On Gauss Balancing and Gauss Cobalancing Numbers
Mustafa Asci and Mustafa Yilmaz
43
An Overview of Ordering Based on Nullnorms
Emel Asici
44
Analytical-Numerical Solutions for a class of Systems of Differential Equations Using Reproducing Kernel
Method
Ali Mahmud Ateiwi
A Fuzzy Project Scheduling with Constrained Resources
Lyazzat Atymtayeva, Ardakbek Kungaliyev and Daniyar Artykov
45
47
ix
A Convergent Two-Level Linear Scheme for the Generalized Rosenau-Kdv-RLW Eqution
Ayhan Aydin
Fuzzy Soft Metric and Fuzzifying Soft Topology Induced by Fuzzy Soft Metric
Ebru Aydogdu, Abdulkadir Aygunoglu, Halis Aygun
Some Identities Associated With Hecke Operators
Aykut Ahmet Aygunes
48
49 50
Some Rough Convergence Criteria for the Sequences of Intervals of Fuzzy Numbers
Salih Aytar
Modified Simple Equation Method and its Applications to Some Nonlinear Physical Equations
Gizel Bakicierler and Emine Misirli
51
52
Jacobi Elliptic Function Solutions of the Space-Time Fractional Symmetric Regularized Long Wave
Equation
Dilek Varol Bayram, Sevil Çulha and Ayşegül Daşcıoğlu
53
Functional Quadratic Integral Equations in the L1loc (R+) space
Latifa Benhamouche and Smail Djebali
Suborbital Graphs for a Non-Transitive Action of the Normalizer
Murat Besenk, Bahadır Ozgur Guler and Abdurrahman Buyukkaya
54 55
On Spherically Symmetric Solutions of the Einstein-Maxwell Field Equations
Rashida Bibi and Azad A. Siddiqui
56
A Numerical Approximation Based on Collocation Method for the Solutions of Telegraph Equation
Kübra Erdem Bicer
57
Rotating Disk Cryptosystem: RDC
Sadek Bouroubi and Louiza Rezkallah
58
Free Convection inside a Porous Enclosure
Canan Bozkaya
59
Tauberian Theorems for the Cesáro Second Order Operators for Sequences of Fuzzy Numbers
Naim L. Braha
60
Estimating the Distortion Parameter of the Proportional Hazards Premium for Heavy-Tailed Losses
Brahimi Brahim
On Some Fixed Point Results Related to Almost Generalized (α,β)-(ψ,ϕ)-Weakly Contractive Mappings in
S Metric Spaces
Abdurrahman Buyukkaya and Mahpeyker Ozturk
61
62
Beyond statistical quasi Cauchy sequences
Huseyin Cakalli
63
A Study on Strongly Lacunary Ward Continuity
Huseyin Cakalli and Huseyin Kaplan
64
A Study on Abel Statistical Quasi Cauchy Sequences
Huseyin Cakalli and Iffet Taylan
65
Graph Theoretical Applications of Molecular Graphs
Ismail Naci Cangul
66
x
A Study on Public Transit Users’ Route Choice and Assignment Function
Buket Capali and Halim Ceylan
67
A New Developed Semi–Empirical Formula for Nuclear Reaction Cross–Section Calculations
Veli Capali, Mert Sekerci, Hasan Ozdogan and Abdullah Kaplan
68
On Uninorms on Bounded Lattices
Gül Deniz Cayli and Funda Karacal
69
On Statistical Dunford and Pettis Integration
Anita Caushi
71
On The Cardinality of Category Spaces
Bahaettin Cengiz and Banu Gunturk
72
Remarks and Observations on Some Special Arithmetical Sums
Elif Cetin and Yilmaz Simsek
73
S-Generalized Mittag-Leffler Function
Aysegul Cetinkaya, I. Onur Kiymaz and M. Baki Yagbasan
74
Jacobi elliptic function solutions of time-fractional KdV-Zakharov-Kuznetsov equation
Sevil Culha, Dilek Varol Bayram and Aysegul Dascioglu
75
A Fix-And-Optimize Heuristic for the Integrated Fleet Sizing and Replenishment Planning Problem with
Predetermined Delivery Frequencies
Niousha Karimi Dastjerd and Kadir Ertogral
76
Catalogue of Degree Sequences of Molecular Graphs
Sadik Delen and Ismail Naci Cangul
77
Streamline Topology of Vortex Breakdown Bubbles near the Re-Entrant Corner
Ali Deliceoglu and Ebutalib Celik
78
Optimality Conditions for a Linear Differential System with Two Delays
Hanna Demchenko
α-Convexity of Some Struve and Lommel Functions
Erhan Deniz, Halit Orhan and Murat Çağlar
79
80
Fuzzy Soft Topolical Spaces and the Related Category FST
Tugbahan Simsekler Dizman and Naime Tozlu
Fuzzy Soft Ditopological Spaces
Tugbahan Simsekler Dizman, Naime Tozlu and Şaziye Yüksel
On The Difference Method for Approximating of Second Order Derivatives of a Solution of Laplace's
Equation in a Rectangular Parallelepiped
Adiguzel A. Dosiyev and Hediye Sarıkaya
81
82
83
Kolmogorov Inequality on Variable Exponent Lebesgue Spaces
Ismail Ekincioglu, Esra Kaya
An Application of Functional Variable Method For Semi-Analytical Solutions of Nonlinear Evolution
Equations
Berfin Elma and Emine Misirli
84
85
New Types of Soft Separation Axioms and Soft Compactness in Soft Topological Spaces
M. E. El-Shafei, M. Abo-Elhamayel and T. M. Al-shami
86
xi
On Quaternion n-Spaces
Fatma Ozen Erdogan and Atilla Akpinar
87
Decomposition of Soft Continuity via Soft Locally b-Closed Set
Zehra Guzel Ergul, Naime Tozlu and Saziye Yuksel
Periodic Solutions for a Third-Order Delay Differential Equation
Nouioua Farid and A. Ardjuoni
88
89
Copula Conditional Tail Expectation for Multivariate Financial Risks
Benatia Fatah and Brahim Brahimi
90
New Properties of Fractional Derivatives Defined Using Mittag Leffler Kernel
Arran Fernandez and Dumitru Baleanu
Nodal Solutions for Indefinite Robin Problems
Michael Filippakis
91
92
On Slowly Oscillating Double Sequences
Goksen Findik, Ibrahim Canak and Umit Totur
93
A Bayes Minimax Result for a Large Class of Distributions
Dominique Fourdrinier, Fatiha Mezoued and William E. Strawderman
94
A Search for Designs with the Same Parameters as 2-(256,64,21) Design with 2-Rank 25
Mustafa Gezek
95
Compact and Matrix Mappings on the Space |Afθ|k
Fadime Gokce and G.Canan Hazar Gulec
On Some Classes of Fractional Differential Equations of Parabolic Type
Dilovar Guljonov
Some Results about ΔI-Statistically Pre-Cauchy Sequences with an Orlicz Function
Hafize Gumus, Omer Kisi and Ekrem Savas
96
97
98
A Numerical Analysis of FLMM for Semilinear Time Fractional Schrödinger Equations
Betul Hicdurmaz
On Modified FLMM Methods for Fractional Population Equations
Betül Hicdurmaz and Emine Can
99
100
Coincidence Best Proximity Points for Geraghty Type Proximal Cyclic Contractions
Azhar Hussain
Estimation of a Loss Function for Spherically Symmetric Distribution with Constraints on the Norm
Ouassou Idir
101
102
An overview on Fuzzy AHP and Its Priority Derivation
Iftikhar and Musheer Ahmad
103
Solutions of (n) (n 1)od od When n 1 Has Three Distinct Odd Primes
Nazli Yildiz Ikikardes, Daeyeoul Kim and Lianrong Ma
104
Hypersurfaces of a Kenmotsu Space Form
Mohammad Ilmakchi
105
On Some Classes of Fractional Integrodifferential Equations in Hilbert Space
Mamadsho Ilolov 106
xii
The Generators of Regular, Quasi-regular Representations and Casimir Operator
Yasemin Isik and Mehmet Sezgin
108
Some Properties of Cartan Null Curves in Semi-Euclidean 4-space with index 2
Esen Iyigün
Proximal Point Algorithms Involving Cesaro Type Mean of Total Asymptotically nonexpansive Mappings
in CAT(0) Spaces
Amna Kalsoom and Hafiz Futhar ud Din
Semi–Empirical Systematic Development for Photon Induced Nuclear Reaction Cross–Section Calculations
Abdullah Kaplan, Hasan Ozdogan, Mert Sekerci and Veli Capali
Positive Solutions for Fractional-Order Boundary Value Problems
Ilkay Yaslan Karaca
The Existence of Positive Solutions of Boundary Value Problems with P-Laplacian on the Half-Line
Ilkay Yaslan Karaca and Aycan Sinanoglu
The Dimension of Digital Khalimsky Manifolds
Ismet Karaca and Gokhan Temizel
Some Properties of Persistent Homology Groups
Ismet Karaca and Hatice Sevde Denizalti
On Digital Cohomology Groups
Ismet Karaca and Ozgur Ege
Some Common Fixed Point Theorems on Complex Valued Gb-Metric Spaces
Ismet Karaca and Ozgur Ege
109
110 111
112
113
114 115 116 118
On Some Deddens Subspaces of Banach Algebras
Mubariz Karaev, Mehmet Gurdal and Havva Tilki
Duhamel Operator and Existence of Invariant Subspace
Mubariz Karaev, Mehmet Gurdal and Mualla Birgul Huban
119
120
On Extended Eigenvalues and Extended Eigenvectors of Toeplitz Operators
Mubariz Karaev, Mehmet Gurdal and Mualla Birgul Huban
121
A generalization on the Incidence Energy and Laplacian-Energy-Like Invariant
Ezgi Kaya and A. Dilek Maden
A Data Mining Approach: Application to the Extraction of the Characteristics of IARD Products in the
Insurance Sector
Sadi Khadidja and Lounici Mosbah Nora
122
123
The Le Corbusier Approach in the Relationship between Architecture and Mathematics
Murat Kilic and Melih Kurnali
124
The Absolute Möbius Divisor Function and Euler function
Daeyeoul Kim, Umit Sarp and Sebahattin Ikikardes
126
S-Generalized Lauricella’s Hypergeometric Functions
I. Onur Kiymaz, M. Baki Yagbasan and Aysegul Cetinkaya
127
Some Remarks on Fuzzy Anti-Normed Spaces
Ljubiša D.R. Kočinac 128
xiii
On Asymptotically f-Statistical Equivalent Sequences
Sukran Konca and Mehmet Kucukaslan
Some Permanents of Hessenberg Matrices
Sibel Koparal, Nese Omur and Cemile Duygu Sener
Best Proximity Points for Generalized Geraghty Proximal Contraction Mapping in Elliptic Valued
Metric Space
Isil Arda Kosal, Hidayet Huda Kosal and Mahpeyker Ozturk
129 130
131
Characterizations of , ,p q - Convex Sequences
Xhevat Z. Krasniqi
132
A Note on the Numbers Yn(Λ) and the Polynomials Yn(X;Λ) and Their Generating Functions
Irem Kucukoglu and Yilmaz Simsek
133
Modelling Worldwide CO2 Emissions and Oil Consumption based on the L1, L2 and L∞-norm Regressions
Pranesh Kumar and Mohamadtaghi Rahimi
134
Some Symmerty Identities for Modified Degenerate Apostol-Bernoulli and Modified Degenerate Apostol-
Euler Polynomials Related to Multiplier Sums
Burak Kurt
135
Univalency Conditions of a General Nonlinear Integral Operator of Analytic Functions with Different
Domains
Shuhai Li and Huo Tang
136
Certain Subclasses of Harmonic Univalent Functions Defined By Convolution and Subordination
Shuhai Li and Huo Tang
137
Refinement of Some Inequalities Concerning to Bn-Operator of Polynomials with Restricted Zeros
A. Liman
138
Gaussian Approximation to the Estimator of the Mean of a Heavy-Tailed Distribution under Random
Censoring
Djamel Mearghni
139
Industrial Application of Fuzzy Logic Control for Torque-ripple Minimization in Electricals Machines
Zineb Mekrini and Seddik Bri
140
On Optimal Control of Stochastic Mean Field Systems
Brahim Mezerdi
141
Ring Theory Approaches to Solve Cauchy-Euler Differential Equations of Several Variables
Assal Miloud
142
Subgradient Method of Solving the Problem of Linear Stochastic Programming with Bifurcation Effect
Fakhriddin Mirzoahmedov
143
Modelling Asymmetric Magnetic Recording Heads with an Underlayer Using Superposition
Ammar Edress Mohamed
144
G-compactness for Topological Groups with Operations
Osman Mucuk and Huseyin Cakalli
145
Topological Aspects of Monodromy Groupoids for Group-Groupoids
Osman Mucuk and Serap Demir
147
xiv
A Characterization of the Two-Weight Inequality for Riesz Potentials on Cones of Radially Decreasing
Functions
Ghulam Murtaza
149
On The Fourth Geometric-Arithmetic Index of Graphs
Y. Nacaroglu and A. Dilek Maden
150
Laplace Transform of Fractional Differential Equations
Khaled I. Nawafleh
151
Gaussian Approximation of a New Tail Index Estimator for Right-Censored Pareto-Type Distributions
Abdelhakim Necir
On Residual Algebraic Free Extensions of Valuations
Figen Oke
152
153
Statistically (C,1,1) Summable Double Sequences of Fuzzy Numbers and a Tauberian Theorem
Zerrin Onder, Ibrahim Canak and Umit Totur
154
The Sheffer Stroke Basic Algebras on the Intervals
Tahsin Oner and Tugce Katican
155
A Reduction of Basic Algebras: Sheffer Stroke Basic Algebras
Tahsin Oner and Ibrahım Senturk
156
Applications on Weak and Strong Forms of Fuzzy α-Open (Closed) Sets
Hakeem A. Othman
157
Code Verification Using Method of Manufactured Solutions for CFD Problems
Hatice Ozcan
158
On the Existence of Einstein Weyl Manifold with a Special Metric Connection
F. Ozdemir and M. D. Turkoglu
159
Repeat Codes, Even Codes, Odd Codes and Their Equivalence
Mustafa Ozkan and Figen Oke
160
Tauberian Theorems for the Weighted Mean Summability Methods of Integrals
Firat Ozsarac and Ibrahim Canak
161
On Lifting Polynomials and Distinguished Pairs
Burcu Ozturk, Figen Oke
On Some Fixed Point and Common Fixed Theorems in b-Metric-Like Spaces
Mahpeyker Ozturk
162
163
Experimental Evidence of Landau Damping in a Fluid at a Macroscopic Scale
Eric Padilla, William Cody Wilson and Andrei Ludu
A Boundary Value Problem for an Irrational Order Partial Equation
A.A. Pashavand, N.A. Aliyev and A.Y. Delshad Gharegheshlaghi
164
165
Generalized Close to Convex Functions with q-Properties
Yasar Polatoglu, Oya Mert and Asena Cetinkaya
Steady-State Modeling of the Biological Network via Long-tailed Symetric Distribution
Vilda Purutcuoglu and Melih Agraz
166
167
xv
Quadrature Formula with High Degree of Exactness
Abedallah Rababah
Best Cubic Spline Interpolation Based on Minimizing the Error
Abedallah Rababah and Mohammed Bani Khalid
169
170
On Chebyshev Collocation Method and Applications to Nonlinear Integral Equations Abdalah Rababah, Benferhat Leila, Hichem Ramoul and Nora Mahloul
171
The Treatment of Fractional Singular Lagrangian
Eqab Rabei
172
MHD Convective Flow due to a Curved Surface with Thermal Radiation and Chemical Reaction
Madiha Rashid
173
On The Isolated Points of the Spectrum of M-Paranormal Operators
Mohammad Rashid
174
Existence of Homoclinic Orbit in Generalized Planar System of Lienard Type
Vahid Roomi
175
Some Results of the Picard-Krasnoselskii Hybrid Iterative Process
Aynur Sahin and Metin Basarir
176
Optimal Coincidence Best Proximity Point Results in Fuzzy Metric Spaces
Naeem Saleem
177
New Concept of Determinants with Three Indexes (3D Determinants) and Possibilities of Use
Armend Salihu
Boundedness Properties of Some Operators on M (P, Q) ( d)
Ayse Sandikci
178
179
On Approximate Biprojectivity of Banach Algebras
M. H. Sattari
On Some New Sequence Spaces Defined By Almost Lacunary Bounded Variation Ekrem Savas
On Filter Convergence of Nets in Uniform Spaces
Ekrem Savas and Ulas Yamanci
180
181 182
On E-J Hausdorff Transformations for Double Sequences
Rabia Savas and Hamdullah Sevli
Double Lacunary Statistical Boundedness of Order α
Rabia Savas and Mahpeyker Ozturk
Statistical Convergent Functions Via Ideals With Respect To The Intuitionistic Fuzzy 2-Normed Spaces
Rahmet Savas
183
184 185
Submanifolds in 1
2H ( 1)m with Finite Type Pseudo-Hyperbolic Gauss Map
Ruya Yegin Sen and Ugur Dursun
186
On the Determination of Validity of Categorical Syllogisms by Using a Mathematical Model
Ibrahım Senturk and Tahsin Oner
187
xvi
Converse Theorems for Statistical Convergence
Sefa Anil Sezer, Rahmet Savas and Ibrahim Canak
188
Cesàro Summability of Sequences in 2-Normed Spaces
Sefa Anil Sezer and Rahmet Savas
189
Applications of the Schwarz Lemma to Inequalities for Polynomials with Restricted Zeros
Lubna Wali Shah
190
Growth of Maximum Modulus of Polynomials and Rational Functions in the Complex Domain
Wali Mohammad Shah
Trace Formula for Witt Vector Rings
Mokhfi Siham
191
192
On Parametrization of the q-Bernstein Basis Functions
Yilmaz Simsek
Control of the Performance of the Panel of Judge in Sensory Analysis by a Functinal Principal Component
Analysis of Probability Densities Function
Yousfi Smail
193
194
Optimization of an Execution Time for Parallel Matrix Multiplication by adding a New Set of Processors
on the Array
Halil Snopce, Sadri Alija, Azir Aliu and Artan Luma
195
From Dido to Morrey: Variational Problems and Regularity Theory!
Lubomira G. Softova
196
A Publicly Verifiable Authenticated Encryption Scheme Based on Chaotic Maps and Factoring Problems
Nedal Tahat
197
Third-Order Differential Sandwich-type Results Involving the Liu-Owa Operator
Huo Tang, M. K. Aouf, Shigeyoshi Owa and Shu-Hai Li
198
Second-Order Differential Superordination for Analytic Functions in the Upper Half-Plane
Huo Tang, H. M. Srivastava, Guan-Tie Deng and Shu-Hai Li
199
Capacity Sizing and Pricing with Heterogeneous Products and Flexible Resources
Salih Tekin
201
A New Class of the r-Stirling Numbers and the Generalized Bernoulli Polynomials
Meriem Tiachachat
202
Degree Sequences and Inverse Problem on Graphs
Muge Togan, Aysun Yurttas and Ismail Naci Cangul 203
Notes on Permuting tri-derivations on Prime and Semi-prime Rings
Seda Oguz Unal, Hasret Durna
204
Weakly Invariant Subspaces for Multivalued Linear Operators on Banach Spaces
Gerald Wanjala
205
Speech Quality Analysis with Respect to Noise Corruption by a Kalman Filter to Estimation the Parameters
of the SWLP Method
Ervenila Xhaferraj (Musta)
206
S-Generalized Srivastava’s Triple Hypergeometric Functions
M. Baki Yagbasan, Aysegul Cetinkaya and I. Onur Kiymaz 207
xvii
Berezin Number Inequality for Convex Function in Reproducing Kernel Hilbert Space
Ulas Yamanci, Mehmet Gurdal and Mubariz T. Garayev
208
On Power Inequalities for Berezin Number of Operators and Convex Functions
Ulas Yamanci, Mehmet Gurdal and Ceren Celik
209
Spectral Properties of Discrete Klein-Gordon Equations
Nihal Yokus and Nimet Coskun
210
On the Inverse Problem on Graphs
Aysun Yurttas, Muge Togan and Ismail Naci Cangul
211
Summability of Subsequences of Divergent Sequences
Maria Zeltser and Johann Boss
212
Many to one Embedding Crossed Cube into Pancake Mohamed Faouzi Zerarka
213
______________________________________________________
1
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
The Sturm-Liouville Theory and Fourier Analysis
Mohammed Al-Gwaiz
Department of Mathematics,
King Saud University, Riyadh
Abstract: According to the Sturm-Liouville Theory, the eigenfunctions of a self
adjoint linear differential operator of second order form an infinite sequence
which is orthogonal and complete in L^2. Thus, depending on the choice of the
differential operator and the boundary conditions, we obtain an assortment of
bases for L^2. This provides a convenient approach for expanding any function
in L^2 in terms of these eigenfunctions. It turns out that the classical Fourier
series expansion on (-pi,pi) in terms of sin nx and cos nx is the result of choosing
the differential operator to be d^2 /dx^2, with appropriate boundary conditions.
For other choices we arrive at a more generalized theory of Fourier series based
on other orthogonal bases
______________________________________________________
2
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Topological Spaces with an -base
Taras Banakh
Jan Kochanowski University in Kielce (Poland) and
Ivan Franko National University of Lviv (Ukraine),
Kielce-Lviv, Poland-Ukraine
Abstract: Given a partially ordered set P we shall discuss properties of
topological spaces X admitting a P-base, i.e., an indexed family (U)P of
subsets of XX such that U U for all in P and for every x X the
family (U[x])P of balls U[x]=yX:(x,y) U is a neighborhood base at x.
A P-base (U[x])P for X is called locally uniform if the family of entourages
(UU-1U)P remains a P-base for X. A topological space is first-countable if
and only if it has an -base. By Moore's Metrization Theorem, a T0-space is
metrizable if and only if it has a locally uniform -base.
In the talk we shall discuss topological spaces possessing a (locally uniform) -
base. Our results show that spaces with an -base share some common
properties with first countable spaces, in particular, many known upper bounds
on the cardinality of first-countable spaces remain true for countably tight -
based topological spaces. On the other hand, topological spaces with a locally
uniform -base have many properties, typical for generalized metric spaces.
Also we study Tychonoff spaces whose universal (pre- or quasi-) uniformity has
an -base and show that such spaces are close to being -compact.
More information can be found in the paper-book [1].
Keywords: generalized metric space, partially ordered set, neighborhood base.
References:
[1] T. Banakh, “Topological spaces with an -base”, 105 pp. preprint
(https://arxiv.org/abs/1607.07978).
______________________________________________________
3
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Schwarz Problem for Higher-order Equations in a Polydisc
A. Okay Celebi
Department of Mathematics, Yeditepe University
Istanbul, Turkey
Abstract: In this presentation, we discuss the Schwarz boundary value problem
for higher order linear complex differential equations in the unit polydisc. Firstly
we state the results obtained in ℂ (see for example [1]). Secondly the integral
representation for functions in ℂ𝑛[2,3,4] is improved. Then we give the solution
of the model equation with homogeneous Schwarz conditions posed in a
polydisc, which enables us to define an integral operator. Thus we can convert
the linear complex differential equations into an integral equation. The solution
is obtained via Fredholm theory.
Keywords: Schwarz problem, Polydisc,
P.S: This is a joint work with Umit Aksoy; Atilim University, Department of
Mathematics, Ankara, Turkey
References:
[1] U. Aksoy, A. O. Celebi; A survey on the boundary value problems for
complex partial differential equations, Adv. Dyn. Syst. Appl., 5(2010), 133-158.
[2] Begehr, H. and Dzhuraev, A., An Introduction to several complex variables
and partial differential equations, Pitman Monographs and Surveys1 in Pure and
Applied Mathematics, Addison Wesley Longman Limited
(1997).
[3] Begehr, H., Boundary value problems in C and C^n, Acta Mathematica
Vietnamica, 22(1997), 407-425.
[4] Begehr, H., Dai, D.-Q. and Li, X., Integral representation formulas in
polydomains, Comp. Var., 47(2002), 463-484
______________________________________________________
4
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Gelfand Theory Unplugged
Robin Harte
Trinity College, Dublin, Ireland
Abstract: It was Norbert Wiener who observed that whenever a periodic
continuous function which never vanishes has an absolutely convergent Fourier
series, then so does its reciprocal. Pointwise multiplication generates
“convolution” of their coefficient sequences, with a homomorphism from
sequences to functions; according to Wiener, if the function is pointwise
invertible then also the sequence is “convolution invertible”. When Israel
Gelfand looked at these sequences he saw for the first time what would come to
be known as a commutative “Banach algebra”. He went on to extend Wiener’s
observation from absolutely summable sequences to these Banach algebras, with
a completely different and abstract proof. The electricity that powers this
“Gelfand theory” is Zorn’s lemma and “maximal ideals”, together with the
Gelfand-Mazur lemma, which says that maximal ideals are always generated by
bounded multiplicative linear functionals. The “unplugged” version bypasses
maximal ideals, and proceeds via the superficially more concrete spectral
mapping theorem for finite and infinite systems of Banach algebra elements.
Keywords: Fourier series, Banach algebra, maximals ideals, Gelfand characters,
several variable spectral mapping theorem.
References:
[1] Robin Harte, Invertibility and singularity, Dekker (New York) 1988.
[2] Robin Harte, Spectral mapping theorems - a bluffer’s guide, Springer Briefs
in Mathematics, 2014.
[3] R,E. Harte, Non-commutative Taylor invertibility, Operators and Matrices (to
appear).
[4] Vladimir Mu¨ller, Spectral theory of linear operators, Birkh¨auser Basel,
2007.
______________________________________________________
5
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Decision Models for Autonomous Vehicles
Reza Langari
Engineering Technology and Industrial Distribution
Texas A&M University
Abstract: The market for autonomous vehicles (Level 4+ autonomy, or L4+) is
expected to reach $42B by 2025 (Bloomberg) and upwards of $85B by 2030.
The key issues in this context are i) localization, ii) perception, ii) decision logic,
iv) control execution as well as v) validation/verification. These are central to
effective functioning of autonomous vehicles and remain both research topics as
well as subjects of significant development effort by industry.
The presentation provides an overview of the issues listed above and the outlook
for future development in the relevant areas. In particular, we focus on decision
and control for autonomous vehicles where matters of expediency and safety
have to be balanced in a sensible manner in view of uncertainty in the behavior
of other vehicles. We present approaches based on classical optimization as well
as game theory, which offers a unique means of dealing with multi-player
decision processes. The benefits and drawbacks of this approach and future
outlook for its use in autonomous driving will also be discussed.
______________________________________________________
6
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Summation and Quadrature Processes for Slowly Convergent
Series
Gradimir V. Milovanović
Serbian Academy of Sciences and Arts, Belgrade, Serbia
Abstract: An account on summation/integration methods for computation of
slowly convergent series and finite sums, as well as some new results on this
subject and new applications, are presented. Methods are based on Gaussian
quadrature formulas with respect to some non-classical weight functions over the
real line or the halfline. For constructing such quadrature rules we use recent
progress in symbolic compuation and variableprecision arithmetic, implemented
through our Mathematica package “OrthogonalPolynomials” [1], [2]. Some
details on these methods can be found in [3], [4], [5].
Keywords: Summation, Gaussian quadrature rules, weight function,
convergence, orthogonal polynomials.
References:
[1] A. S. Cvetković and G. V. Milovanović, “The Mathematica Package
OrthogonalPolynomials”, Facta Univ. Ser. Math. Inform. 19 (2004), 17-36.
[2] G. V. Milovanović and A. S. Cvetković, “Special classes of orthogonal
polynomials and corresponding quadratures of Gaussian type”, Math. Balkanica
26 (2012), 169-184.
[3] G. V. Milovanović, “Summation of series and Gaussian quadratures”, In:
Approximation and Computation (R.V.M. Zahar, ed.), ISNM Vol. 119, pp. 459-
475, Birkhäuser Verlag, Basel-Boston-Berlin, 1994.
[4] G. Mastroianni and G. V. Milovanović, Interpolation Processes - Basic
Theory and Applications, Springer Monographs in Mathematics, Springer
Verlag, Berlin - Heidelberg - New York, 2008.
[5] G. V. Milovanović, “Summation formulas of Euler-Maclaurin and Abel-
Plana: old and new results and applications”, In: Progress in Approximation
Theory and Applicable Complex Analysis – In the Memory of Q,I. Rahman
(N.K. Govil, R.N. Mohapatra, M.A. Qazi, G. Schmeisser, eds.), Springer, 2017
(to appear).
______________________________________________________
7
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
New Iterative Methods for Solving Non-Linear Equations
Osama Y. Ababneh
Department of Mathematics, Zarqa University, Zarqa, Jordan
Abstract: Solving the non-linear equation f(x) = 0 has nice applications in
various branches of physics and engineering. Sometimes the applications of the
numerical methods to solve non-linear equations depending on the second
derivatives are restricted in physics and engineering. The purpose of this paper is
to propose new modified Newton’s method for solving non-linear equations and
free from second derivative. Convergence results show that the order of
convergence of the proposed iterative methods is four. Finally, several numerical
examples are given to illustrate that the new iterative algorithms are effective.
Keywords: non-linear equations, Newton’s method.
______________________________________________________
8
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Solution of Animplicit Complementarity Problem on Isotone
Projection Cones
Mujahid Abbas
Department of Mathematics, University of Management and Technology,
C-II Johar Town, Lahore, Pakistan,
and
Department of mathematics and applied mathematics,
University of Pretoria, South Africa
Abstract: In this talk an iterative algorithm is presented in connection with an
implicit complementarity problem. It is shown that if the sequence generated
through the defined algorithm is convergent, then its limit is a solution of the
coincidence point equation and thus solves the implicit complementarity
problem. Sufficient conditions are discussed for this sequence to be convergent
for implicit complementarity problems defined by isotone projection coneses.
______________________________________________________
9
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Analysis and Modeling the Drought Hydrologic by the Copulas
in North Algeria
Rassoul Abdelaziz
Department of Irrigation and Drainage, National High School of Hydraulics,
Blida, Algeria
Abstract: In this work, we use the three dimensional copula for modeling the
dependence of the drought variables, severity–duration–frequency (S–D–F).
Drought is a natural event, which has huge impact on both the society and the
natural environment. Drought events are mainly characterized by their severity,
duration and intensity. The study adopts standardized precipitation index (SPI)
for drought characterization, and copula method for multivariate risk analysis of
droughts. The Beni-Behdel River basin was selected as an example to illustrate
the copulas. Results indicates that the Student copula was more appropriate for
drought analysis in the selected area. Drought probabilities and return periods
were calculated and analyzed based on the three dimensional.
Keywords: Copula, Drought, SPI index, return period.
References:
[1] C. Genest, K. Ghoudi, L.P. Rivest (1995) A semiparametric estimation
procedure of dependence parameters in multivariate families of distributions.
Biometrika 82(3):543–552
[2] H. Joe (1997) Multivariate models and dependence concepts, vol 73.
Monographs on statistics and applied probability. Chapman and Hall, London, p
399
[3] W.C. Palmer WC (1965) Meteorological drought. Research paper no. 45, US
Weather Bureau, Washington, DC.
[4].A. Tawn (1988) Bivariate extreme value theory: models and estimation.
Biometrika 75(3):397–415
[5] A. Sklar (1959) Fonctions de répartition à n dimensions et leurs marges.
Publications de l’Institut de Statistique de l’Université´ de Paris 8:229–231
______________________________________________________
10
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Rayleigh-Marangoni Convection in a Layer of Nanofluid
Abdullah A. Abdullah
Department of Mathematical Sciences, Umm Al-Qura University,
Makkah, Saudi Arabia
Abstract: A linear stability analysis for the onset of Rayleigh-Marangoni
convection in a horizontal layer of a nanofluid heated from below is investigated.
The model employed for the nanofluid incorporates the effects of Brownian
motion and thermophoresis. The lower boundary of the layer is assumed to be a
rigid surface at fixed temperature while the top boundary is assumed to be a non-
deformable free surface cooled by convection to an exterior region at a fixed
temperature. The boundaries of the layer are assumed to be impenetrable to
nanoparticles with their distribution being determined from a conservation
condition. The linear analysis uses spectral methods based on the expansion of
eigenfunctions as Chebyshev series. Stability boundaries for Rayleigh number
and temperature and nanofraction Marangoni numbers are obtained for several
nanofluids.
Keywords: Rayleigh-Marangoni convection, Nanofluid, Linear stability,
Brownian motion, Thermophoresis.
______________________________________________________
11
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
On the Properties of the Orthogonal Polynomials along a
Contour
Fahreddin.G.Abdullayev1, 2, Gülnara.A.Abdullayev²
¹Kyrgyz-Turkish Manas University, Bishkek, KYRGYZSTAN,
[email protected]; [email protected]
²Mersin University, Mersin, TURKEY
Abstract: Let be a complex plane; L be a closed rectifiable Jordan
curve: Let ( )h z be a non-negative, summable on L and non-zero except
possible on a set of measure zero function. The systems of polynomials
( )nK z ; ( ) ...n
n nK z z ; deg nK n ; n ; satisfying the
orthonormality condition:
,( ) ( ) ( )n m n m
L
h z K z K z dz ,
are called orthonormal polynomials for the pair ( , )L h . These polynomials are
determined uniquely if the major coeficient 0n . These polynomials were
first studied in [6]. Some properties of the polynomials ( )nK z under the various
conditions on the weight function ( )h z and contour L were investigated in [1]-
[5], [7]-[9] and others (also, references in therein).
In this work, we investigated the order of growth of the modulus of ( )nK z
polynomials in the weighted space, where the contour and the weight functions
have some singularities on the finite points on the contour. Exact estimations for
the growth of the modulus of orthogonal polynomials were obtained.
Keywords: Orthogonal Polynomial, Quasiconformal Curve, Coformal Mapping.
______________________________________________________
12
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
References:
[1] F.G. Abdullayev.,G.A. Abdullayev, On the Sharp Inequalities for
Orthonormal Polynomials Along a Contour, Complex Analysis and Operator
Theory, 1, 2017, DOI: 10.1007/s11785-017-0640-1.
[2] G. Fauth, Über die Approximation analytischer Funktionen durch
Teilsummenihrer Szegö-Entwicklung, Mitt. Mathem. Semin. Giessen, No:67,
(1966), pp.1-83.
[3] Ya.L. Geronimus, Polynomials Orthogonal on a Circle and Interval. IX + 210
S. m. 9 Tafeln. Oxford/London/New York/Paris 1960.
[4] P.P. Korovkin, Sur les polynomes orthogonaux le long d.un contour recti.able
dans le cas de la présence d.unpoids, Rec. Math. [Mat. Sbornik] N.S., (1941) ,
Vol. 9(51), No: 3, pp. 469.485.
[5] A.L Kuz.mina, Asymptotic representation of polynomials orthogonal on a
piecewise-analytic curves, Proc. "Functional Analysis and theory of Functions",
I,.Kazan., (1963), pp. 42-50.
[6] G. Szegö, Über orthogonale Polynome, die zu einer gegebenen Kurve der
komplexen Ebene gehören, Mathem. Zeitschr. 9 (1921), pp.218-270.
[7] G. Szegö, Orthogonal Polynomials, Fizmatgis,1962, (in Russian).
[8] P.K. Suetin, Main properties of the orthogonal polynomials along a circle.
Uspekhi Math. Nauk, Vol.21, No:2 (128), (1966), pp.41-88.
______________________________________________________
13
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Modeling and Classifying by using Binary Logistic Regression
Analysis Application on Hepatitis Disease Data
Qais Mustafa Abdulqader
Department of Information Technology, Duhok Polytechnic University,
Dohuk, Zakho, Iraq
Abstract: Logistic Regression Analysis analyze the relationship between
multiple explanatory variables and a single binary response variable, a
categorical variable with two categories [1]. Many medical applications have
been done in this area such as [2,3,4 and 5]. In this paper, the binary logistic
regression analysis technique has been used and applied for building a suitable
model for hepatitis disease data using stepwise procedure and depending on
some laboratory tests which represents explanatory variables. Also, the technique
has used for classifying persons into two groups which are infected and
uninfected with viral hepatitis disease. The evaluation was depending on some
statistical criteria. The results of the analysis have been discussed and mentioned.
Keywords: Binary logistic regression, Hepatitis, Stepwise procedure, statistical
criteria.
References:
[1] S. Sweet, and K. Martin, "Data Analysis with SPSS: A First Course in
Applied Statistics," 4th ed., Pearson publisher, 2011.
[2] S. Javali, and P. Pandit, " Multiple logistic regression model to predict risk
factors of oral health diseases," Romanian statistical review journal, 5(2012), 73-
86.
[3] P. Reeda, and Y. Wub, " Logistic regression for risk factor modelling in
stuttering research," Journal of Fluency Disorders, 38 (2013), 88-101.
[4] M. T., Dev Mukherji, N. Padalia, and A. Naidu, " A heart disease prediction
model using SVM-decision trees-logistic regression (SDL)," International
Journal of Computer Applications, 68 (2013), 11-14.
[5] W. M. Amir et al., " Association of Hypertension with Risk Factors Using
Logistic Regression, " Applied Mathematical Sciences, 8(2014), 2563 – 2572.
______________________________________________________
14
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Residual Power Series Approach to Handle a Class of
Fractional Differential Equations
Ayed H. Adamat
Department of Mathematics, Faculty of Science, Al-Hussein Bin Talal
University, P.O. Box 20, Ma'an, Jordan
Abstract: In this paper, we present a computational algorithm to find the
coefficients of the fractional power series solutions for linear and nonlinear
differential equations of fractional order. This approach provides the solution in
the form of a rapidly convergent series with easily computable components using
symbolic computation software [1-5]. The proposed method based on the
generalized Taylor's formula that involving Caputo fractional derivative which
constructs an analytical solution in the series form and reproduces the exact
solution when the solution is a finite series. This technique is applied to a few
test examples to illustrate the accuracy, efficiency and applicability of the
method. The results reveal that the method is very effective, straightforward, and
simple.
Keywords: Fractional differential equations; Fractional power series method;
Initial value problems; Generalized Taylor series approximation.
References:
[1] A. El-Ajou, O. Abu Arqub, M. Al-Smadi, A general form of the generalized
Taylor’s formula with some applications, Applied Mathematics and
Computation, 256 (2015), 851-859.
[2] Z. Odibat, N. Shawagfeh, Generalized Taylor’s formula. Appl. Math.
Comput., 186 (2007), 286-293.
[3] K. Moaddy, M. Al-Smadi, I. Hashim, A Novel representation of the exact
solution for differential algebraic equations system using residual power-series
method, Discrete Dynamics in Nature and Society, 2015 (2015), Article ID
205207, pp.1-12.
[4] I. Komashynska, M. Al-Smadi, A. Ateiwi, S. Al-Obaidy, Approximate
analytical solution by residual power series method for system of fredholm
integral equations. Applied Math. Inform. Sci., 10 (2016) 975-985.
[5] I. Komashynska, M. Al-Smadi, O. Abu Arqub, S. Momani, An efficient
analytical method for solving singular initial value problems of nonlinear
systems. Applied Math. Inform. Sci., 10 (2016), 647-656. DOI:
10.18576/amis/100224
______________________________________________________
15
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
On the Existence and Uniqeness of Positive Solution for a
Fractional Boundary Value Problem with New Fractional
Derivative
Asghar Ahmadkhanlu
Department of Mathematics, Azarbaijan Shahid Madani University,
Km 35 Tabriz-Maragheh rod, Tabriz, Iran
Abstract: We are concerned with the existence and uniqueness of positive
solutions for the following nonlinear fractional boundary value problem:
𝐷𝑡𝐴𝐵𝑅
0𝛼𝑢(𝑡) + 𝑓(𝑡, 𝑢(𝑡)) = 0 0 < 𝑡 < 1, 1 < 𝛼 < 2
𝐷𝑡𝐴𝐵𝑅
0𝛼−1𝑢(0) = 𝑢(1) = 0
where 𝐷𝑡𝐴𝐵𝑅
0𝛼 denotes the Atangana-Baleano fractional derivative in sense of
Reimman-liouville. Our analysis relies on a fixed point theorem in partially
ordered sets. Some examples are also given to illustrate the results
Keywords: Boundary value problem, Positive solution, fixed point theorems
References:
[1] A. Atangana, “On the new fractional derivative and application to nonlinear
Fisher’s reaction-diffusion equation”, App. Math. Comp., 273(2016) 948-956.
[2] N. Al-Salti, E. Karimov and S. Kerbal, “Boundary-value problems for
fractional heat equation involving Caputo-Fabrizio derivative”, NTMSCI, 4.4
(2016), 79-89.
[3] T. Salat, “Atangana-Baleanu derivative with fractional order applied to the
model of groundwater within an
unconfined aquifer”, J. Nonlinear Sci. Appl., 9 (2016), 3647-3654.
[4] D. Baleanu1, B. Agheli, M. M. Al Qurashi, “Fractional advection differential
equation within Caputo and Caputo–Fabrizio derivatives”, Advances in
Mechanical Engineering
8.12(2016), 1–8.
______________________________________________________
16
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
On Derivation of a Subclasses of Filiform Leibniz Algebras
AL-Nashri AL-hossain Ahmed
Department of Mathematics, AL-Qunfudhah University college, Umm
Al-Qura University, KSA.
Abstract: In this paper, dimension the derivations of a Third class of Leibniz
algebras are studied and discussed. For 𝐿 ∈ 𝑇𝐿𝑏𝑛 , we have 𝑛 + 1 ≤
dim 𝐷𝑒𝑟(𝐿) ≤ 2𝑛 + 1, are deduced.
Keywords: Filiform Leibniz algebra, numerical validation, gradation,
derivation..
References
[1] Albeverio, S.; Ayupov, Sh. A.; Omirov, B. A., On nilpotent and simple
Leibniz algebras, Comm. in Algebra Vol. 33(2005), 159-172.
[2] Albeverio, S., Omirov, B. A., Rakhimov, I. S., (2006), Classi_cation of 4-
dimensional nilpotent complex Leibniz algebras, Extracta Math., 3(2006), 197-
210.
[3] AL-hossain, A. A.; Khiyar, A. A.,Derivations of some Filiform Leibniz
algebras. Pure and Applied mathematics Journal.Vol. 3,No.6,(2014), 121-125.
[4] Alnashri. A. A., Derivations of one type of algebra of First class Filiform
Leibniz algebras of Dimension Derivation (n+1), International Journal of
Advanced Scienti_c and Technical Research,Vol. 1,No.5,(2015), 41-55.
[5] Alnashri. A. A., Derivations of Second type of algebra of _rst class Filiform
Leibniz algebras of Dimension Derivation (n+1), International Journal of
Advanced Scientific and Technical Research,Vol. 3,No.5,(2015), 29-43.
[6] Ayupov, Sh. A.; Omirov, B. A., On Leibniz algebra, Algebra and Operator
Theory. Proceeding of the Colloquium in Tashkent (1997), Kluwer (1998),
Doi 10.1007/978-94-011-5072-9-1 Springer, p 1-13.
[7] Ayupov, Sh. A.; Omirov, B. A., On 3-dimensional Leibniz algebra, Uzbek
Math. J. (1999), 9-14.
[8] Dixmier. J. and Lister. W. G. , Derivations of nilpotent Lie algebras, Proc.
Amer. Math. Soc. 8(1957), 155-158.
[9] Jacobson. N. , A note on automorphisms and derivations of Lie algebras,
Proc. Amer. Math. Soc. 6(1955), 281283.
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17
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Global Existence and Uniqueness of Weak Solution to a
Chemotaxis Model
N. Aïssa and A. Balehouane
Laboratoire AMNEDP, Faculté de Mathematiques
USTHB
BP 32, El Alia, Bab Ezzouar,
16111 Alger, Algeria.
Abstract: We prove global existence and uniqueness of weak solutions to a
chemotaxis model with nonlinear diffusion.
First, we use a fixed point theorem to prove local in time existence of a weak
solution.
In order to prove that the solution is global in time, we provide a priori estimates
of the solution in an appropriate Lebesgue space by adapting the method of [3].
Then, we obtain uniform bounds of the solution by using the result [1] based on
Moser's iterative method.
KeyWords: Quasilinear Parabolic Systems, Reaction-Diffusion Systems,
Chemotaxis.
References:
[1] N. D. Alikakos, Lp bounds of solutions of reaction-diffusion equations.
Comm. Partial Differential Equations 4, (1979), 827-868.
[2]R. Kowalczyk, Z. Szymanska, On the global existence of solutions to an
aggregation model, J. Math. Anal. Appl. 343 (2008), 379-398.
[3] L. Wang, C. Mu, P. Zheng, Q. Zhang, Global existence and boundedness of
classical solutions to a parabolic-parabolic chemotaxis system, Nonlinear Anal.
Real. World. Appl 14, 1634-1642 (2013).
______________________________________________________
18
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
A Generalization of Hereditary Noetherian Prime Rings
Evrim Akalan
Department of Mathematics, Hacettepe University,
Ankara, Turkey
Abstract: In this talk, we will introduce generalized hereditary noetherian prime
rings (G-HNP rings for short) which generalizes the class of hereditary
noetherian prime (HNP rings for short) rings. We will describe the structure of
projective ideals of G-HNP rings and some over rings of G-HNP rings.
Examples will be given to illustrate and delimit the theory.
Keywords: HNP Rings, projective ideals, invertible ideals.
References:
[1] D. Eisenbud, J. C. Robson, “Hereditary Noetherian Prime Rings”, J. Algebra
16 (1), (1970), 86-104.
[2] H. Marubaysahi, “A Krull type generalization of HNP rings with enough
invertible ideals”, Comm.
in Algebra 11 (5) (1983), 469-499.
______________________________________________________
19
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
On Some Inequalities of Analytic and Biunivalent
Functions Given by Subordination
Arzu Akgul
Department of Mathematics, Kocaeli University,
Kocaeli, Turkey
Abstract: In the present investigation, the subclass MΣ𝜑
(𝛾, 𝜆, 𝛿)_ of analytic
biunivalent functions is defined and established bounds for the coefficients for
this subclass. Also several related classes are considered and connections to
earlier known results are made.
Keywords: Analytic and bi-univalent functions, subordination, coefficient
estimate
References:
[1] R. M. Ali, S. K. Lee, V. Ravichandran and S. Supramaniam, Coefficient
estimates for bi-univalent Ma-Minda starlike and convex functions, Appl. Math.
Lett., 25, (2012), 344-351.
[2] D.A. Brannan, T.S. Taha, On some classes of bi-univalent functions, in: S.M.
Mazhar, A. Hamoui, N.S. Faour (Eds.), Math. Anal. and Appl., Kuwait; February
18.21, 1985, in: KFAS Proceedings Series, vol. 3, Perg-
amon Press, Elsevier Science Limited, Oxford, 1988, pp. 53.60. see also Studia
Univ. Babe¸s-Bolyai Math. 31 (2) (1986) 70.77.
[3] D. A. Brannan and J. G. Clunie, Aspects of comtemporary complex analysis,
(Proceedings of the NATO Advanced Study Instute Held at University of
Durham:July 1-20, 1979). New York: Academic Press, (1980).
[4] S. Bulut, Faber polynomial coe¢ cient estimates for a subclass of analytic bi-
univalent functions, Filomat, Vol. 30, No. 6, (2016),1567-1575 .
[5] S. S. Ding, Y. Ling, and G. J. Bao, Some properties of a class of analytic
functions, Journal of Mathematical Analysis and Applications, vol. 195, no. 1,
pp. 71.81, 1995
[6] B. A. Frasin and M. K. Aouf, New subclasses of bi-univalent functions,
Applied Mathematics Letters, 24, (2011), 1569-1573.
[7] E. Deniz, Certain subclasses of bi-univalent functions satisfying subordinate
conditions, Journal of Classical analysis, 2, 1, (2013), 40-60.
[8] J. M. Jahangiri and S. G. Hamidi, Coe¢ cient estimates for certain classes of
bi-univalent functions, Int. J. Math. Sci., ArticleID 190560, (2013), 4 pp.
______________________________________________________
20
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Compact Finite Differences Method for Burgers-Huxley
Equation
Canan Akkoyunlu
Department of Mathematics and Computer Sciences, Istanbul Kultur University,
Bakırkoy, Istanbul, Turkey
Abstract: In this paper, a numerical solution for the Burgers-Huxley equation is
presented by using compact finite differences method. In the solution of the
problem, finite differences discretization along the time, and fifth-order compact
finite differences scheme along the spatial coodinate are applied. Dispersive
properties for the compact finite difference method are investigated for the
linearized equations to examine the nonlinear dynamics after discretization. The
result shows that the applied method in this study is an applicable tecnique and
approximates the exact solution very well.
Keywords: Burger-Huxley equation, compact finite differences method,
dispersion analysis.
References:
[1] AG. Bratsos, “A fourth order improved numerical scheme for the generalized
Burgers-Huxley equation’’, J. Comput Math, 1(2011), 152-158.
[2] B. Batiha, MSM. Noorani and I. Hashim, “Application of variational iteration
method to the generalized Burgers-Huxley equation’’, Chaos Solitons Fractals,
36(2008), 660-663.
[3] HNA, Ismail, K. Raslan, AAA. Rabboh, “Adomain decomposition method
for Burgers-Huxley and Burgers-Fisher equation’’, Appl Math Comput,
159(2004), 291-301.
[4] I. Hashim, MSM. Noorani and MRS. Al-Hadidi, “Solving the generalized
Burgers-Huxley equation using the adomain decomposition method’’, Math
Comput Model, 43(2006), 1404-1411.
[5] M. Javidi, “A numerical solution of the generalized Burgers-Huxley equation
by pseudospectral method and darvishi’s preconditioning’’, Appl Math Comput,
175(2006), 1619-1628.
[6] M. Javidi, “A numerical solution of the generalized Burgers-Huxley equation
by spectral collocation method’’, Appl Math Comput, 178(2006), 338-344.
______________________________________________________
21
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Approximation Solution of System of Volterra Integro
Differential Using Finite Element Method
Adel Alamarashi*
*Department of Mathematics, College of Science
Jazan University, KSA.
*Department of Mathematics, College of Education,
Thamar University, Yemen.
[email protected] ; [email protected]
Abstract: In the present paper, we first obtain variational form of the problem,
and then, finite element method and basis functions will be used. Also, the error
analysis of the method is considered. Furthermore, we give numerical
computational example to test and validate the proposed method.
Keywords: System Of Volterra Integro-Differential; Finite element method-
error analysis.
References:
[1] Adel. Al-Marashi and Al-Faour.O.M. "Approximate solution for system of
multi- term initial value problem of Fractional Differential Equations by Spline
functions". Sana'a University Journal of Science & Technology, (2008), 1,
pp.251-264.
[2] Adel A. Al-Marashi ,” Approximate Solution of the System of Linear
Fractional Integro-Differential Equations of Volterra Using B- Spline Method”,
American Review of Mathematics and Statistics December 2015, Vol. 3, No. 2,
pp. 39-47
[3] Adel Al-Marashi. “Numerical Solution For Multi-term Fractional Orders
Differential Equations By Splin Functions”, Journal Focuses on Human
Knowledge and Applied Sciences, Issue no 9,June (2008),pp.170 – 187
[4] Z. Mahmoodi , J. Rashidinia & E. Babolian, B-Spline collocation method for
linear and nonlinear Fredholm and Volterra integro-differential equations, pp.
1787-1802, Journal Applicable Analysis An International Journal Volume 92,
2013 - Issue 9.
[5] Hermann Brunner, The numerical treatment of Volterra integro-differential
equations with unbounded delay, Journal of Computational and Applied
Mathematics, Volume 28, December 1989, Pages 5-23.
______________________________________________________
22
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Fixed Point Theorem in FM-Spaces
Rateb AlBtoush
Department of Mathematics& Statistics
Faculty of Science P.O. Box (7)
Mu'tah University
Al-Karak-Jordan
Abstract: The goal of this section is to study the existence problems of fixed
points or common fixed points for some varieties of single-valued mappings in
non-Archimedean probabilistic fuzzy metric space.
Keywords: Fixed Point, Compatible mappings, Non-Archimedean Menger
probabilistic normed spaces.
References:
[1] Y. J. Cho, Fixed points in fuzzy metric spaces, J. Fuzzy Math. 5(1997), 949-
962.
[2] S. S. Chang, On the theory of probabilistic metric spaces with applications,
Acta Math. Sinica, New Series, 1(4) (1985), 366-377.
[3] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Set Syst. 27(1998),
385-390.
[4] V. Gregori, S. Morillas and A. Sapena, Examples of fuzzy metrics and
applications, Fuzzy Sets Syst. 170(2011), 95111.
[5] P.J. He, The variational principle in fuzzy metric spaces and its applications,
Fuzzy Sets and Systems, 45 (1992), 389394.
[6] M. Hegedus and T. Szilagyi, Equivalence conditions and a new _xed point
theorem in the theory of contraction mappings, Math. Japonica, 25 (1) (1980),
147-157.
______________________________________________________
23
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Bounds for the Zeros of Polynomials by Using Similar Matrices
Mohammad. Al-Hawari
Department of Mathematics, Irbid National University,
Irbid, Jordan
Abstract: We apply several matrix inequalities to the similar Frobenius
companion matrices of monic polynomials to derive new bounds for the zeros of
these polynomials which are better than other bounds.
Keywords: Bounds for the zeros of polynomials; Companion matrix; Spectral
norm; Spectral radius
References:
[1] Horn, R.A. and Johnson, C.R., 1985, Matrix Analysis (Cambridge:
Cambridge University Press).
[2] Hou, J.C. and Du, H.K., 1995, Norm inequalities of positive operator
matrices. Integral Equations Operator Theory, 22, 281–294.
[3] Kittaneh, F. and Shebrawi, K .,2007,Bounds for the zeros of polynomials
from matrix inequalities – II, Linear and Multilinear Algebra., 55:2, 147-158.
[4] Kittaneh, F., 2003, Bounds for the zeros of polynomials from matrix
inequalities. Archiv des Mathematik, 81, 601–608.
[5] Kittaneh, F., 2003, A numerical radius inequality and an estimate for the
numerical radius of the Frobenius companion matrix. Studia Mathematica, 158,
11–17.
[6] Linden, H., 2000, Bounds for zeros of polynomials using traces and
determinants. Seminarberichte Fachbereich Mathematik FeU Hagen., 69, 127–
146.
[7] Mohammad H. Al-Hawari.,2016, ZEROS OF POLYNOMIALS BY USING
SOME INEQUALITIES. Far East Journal of Mathematical Sciences (FJMS).,
Volume 100, Number 10, 2016, Pages 1545-1550.
______________________________________________________
24
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
An Application of Decision Tree for Evaluating a Classroom
Teaching Practice
Sadri Alija and Halil Snopce
Faculty of Business and Economics,
South East European University,
Tetovo, Macedonia
Faculty of Contemporary Sciences and Technologies,
South East European University,
Tetovo, Macedonia
Abstract: The aim of this research is to use the decision-making tree in order to
give the meaning for the classification of some activities done during the
realization of the math subject lesson. Actually, the aim is to identify which
activity is more important in achieving the objective of the lesson and at the
same time, which one has bigger impact in achieving the final results on the
math course.
In total we have used 22 variables divided into three different groups: The first
one is about some activities concerning the beginning of the lesson, the second
groups are the variables about the continuation of the lesson and the third groups
are the variables concerning the exercises and assessment. For all of these three
activities we have chosen the averages of the answers for every group separately.
In this research are shown the results gathered from 48 randomly chosen students
of the Faculty of Business Economics at the SEE-University in Macedonia, who
have attended the math subject on the winter semester of the year 2016.
For the construction of the decision making tree, we have used the ID3 algorithm
by using the Weka software.
We have found that the root of the decision-making tree is the attribute
concerning the activities taken at the beginning of the lesson. This attribute at the
same time is the most important attribute from all 4 attributes.
Key words: Teaching practice, decision tree, ID3 algorithm, Weka software
______________________________________________________
25
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Existence of Positive Solution of Boundary Value Fractional
Quadratic Differential Equations
Youssef Allaoui1, Khalid Hilai2 and Guida Karimi3
Laboratory of Applied Mathematics and Scientific Computing 1,2,3
Faculty Of Sciences and Technologies1,2,3
Sultan Moulay Slimane University, PO Box 523, 23000 Beni Mellal,
Morocco1,2,3
[email protected],[email protected],
Abstract: In this work, we prove the existence as well as approximate of the
positive solutions for boundary value problem of nonlinear fractional quadratic
differenrtial equations. We use some porprieties of the Mittag-Leffler functions
and its relationship with fractional calculus. Also we obain some results
regarding the existence of positive solutions using the Dhage iterative method
enbodied in a recent hybrid fixed point theorem of Dhage in partially ordered
normed lineair spaces.
Keywords: Fractional quadratic differential equation, Mittag-leffler equation,
Dhage iterative method, Approximate positive solution.
References:
[1] Bapurao C.Dhage, Lakshmikantham.V, Basic results on hybrid differential
equations, Nonlinear Anal. Hybrid syst. 4, 414-424 (2010).
[2] Bapurao C.Dhage, Lakshmikantham, Quadratic perturbations of periodic
boundary value problems of second order ordinary differential equations. Differ.
Equ. Appl. 2, 465-486 (2010).
[3] Bapurao C.Dhage and Shyam B. Dhage: Approximating positive solutions of
nonlinear first order ordinary quadratic differential equations: Applied and
Interdisciplinary Mathematics, Cogent Mathematics 2,1023671(2015).
[4]Rudolf Gorenflo, Anatoly A. Kilbas, Francesco Mainardi, Sergi V. Rogostin:
Mittag-Leffler functions, Related Topics and Applications. Springer-Verlag
Berlin Heidelberg 2014.
[5]K.Hilal, A. Kajouni: Boundary value problems for hybrid differential
equations. Mathematical Theory and modeling. 2224-5804 (2015).
______________________________________________________
26
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
z
Some Applications of Cozero Sets in Topological Spaces
Ahmad Al-Omari
Al al-Bayt University, Faculty of Sciences, Department of Mathematics
P.O. Box 130095, Mafraq 25113, Jordan
Abstract: An ideal on a set X is a nonempty collection of subsets of X with
heredity property which is also closed finite unions. The concept of ideal
topological spaces via cozero sets was introduced by Al-Omari [10]. In this
paper, we introduce and study some an operator via cozero sets and we construct
a topology τ∗ for X by using the cozero sets and an ideal I on X. Moreover, we
obtain characterizations and preserving theorems of quasi compact spaces.
Keywords: cozero set, zero set, quazi compact space, ideal topological space. References:
[1] S. Bayhan and I. L. Reilly, On some variants of compactness, Hacettepe
Journal of Mathematics and Statistics 43 (6) (2014), 891–898.
[2] S. Bayhan, A. Kanibir, A. McCluskey, and I. L. Reilly, On almost z-
supercontinuity, Filomat 27(6) (2013), 965–969.
[3] Z. Frolik, Generalizations of compact and Lindelof sppaces (Russian),
Czechoslovak Math. J. 9(84) (1959), 172–217.
[4] L. Gillman and M. Jerison, Rings of Continuous Functions, Van Nos- trand
Co., Inc., Princeton, N. J. 1960.
[5] J. K. Kohli and R. Kumar, Z-supercontinuous functions, Indian J. Pure Appl.
Math. 33 (7) (2002), 1097
[6] J. K. Kohli, D. Singh and R. Kumar, Generalizations of z-
supercontinuous functions and Dδ -supercontinuous functions, Appl. Gen.
Topology 9 (2008), 239-251.
[7] J. K. Kohli, D. Singh and J. Aggarwal, F-supercontinuous functions, Appl.
Gen. Topol. 10 (1) (2009)
[8] M. K. Singal and S. B. Niemse, z-continuous mappings, Math. Student 66
(1997), 193-210.
[9] W. T. Van Est and H. Freudenthal, Trennung durch stetige Funktionen in
topologischen Rau¨men, Indagationes Math. 15 (1951), 359-368.
[10] A. Al-Omari, On ideal topological spaces via cozero sets, Questions and
Answers in General Topology 34 (2) (2016), 83–91.
[11] D. Jankovic and T. R. Hamlett, New topologies from old via ideals, Amer.
Math. Monthly, 97 (4) (1990), 295-310.
______________________________________________________
27
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
An Efficient Analytical-Numerical Technique for Handling
Model of Fuzzy Differential Equations of Fractional-Order
Mohammad Aloroud1, Mohammed Al-Smadi2,*, Rokiah Rozita Ahmad1, Ummul
Khair Salma Din1
1School of Mathematical Sciences, Faculty of Science and Technology,
Universiti Kebangsaan Malaysia 2Department of Applied Science, Ajloun College, Al-Balqa Applied University,
Ajloun 26816, Jordan
Abstract: This paper proposes an efficient analytical numerical technique for
finding approximate solutions for a class of fuzzy fractional initial value
problems. The algorithm is based on the generalized Taylor series residual power
series (RPS), which is extended to handle such problems. The analytical solution
is calculated in the form of multiple fractional power series expansion of a
rabidly convergent series with easily computable components. In addition,
description of the RPS method is discussed [1-6]. In this sense, some numerical
examples are given to show the effectiveness and performance of the proposed
method. The results reveal that the method is quite accurate, simple,
straightforward, and convenient for exploring fuzzy fractional models.
Keywords: Generalized Taylor series, Residual power series method, Initial
value problem, Fuzzy fractional differential equations.
References:
[1] K. Moaddy, M. Al-Smadi and I. Hashim, A Novel Representation of the
Exact Solution for Differential Algebraic Equations System Using Residual
Power-series Method, Discrete Dynamics in Nature and Society, Vol. 2015
(2015), Article ID 205207, 1-12. http://dx.doi.org/10.1155/2015/205207
[2] M. Al-Smadi, Solving initial value problems by residual power series
method, Theoretical Mathematics & Applications 3(1), (2013) 199-210.
[3] I. Komashynska, M. Al-Smadi, O. Abu Arqub and S. Momani, An efficient
analytical method for solving singular initial value problems of nonlinear
systems, Applied Mathematics & Information Sciences, 10(2), (2016) 647-656.
______________________________________________________
28
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
[4] I. Komashynska, M. Al-Smadi, A. Ateiwi and S. Al-Obaidy, Approximate
Analytical Solution by Residual Power Series Method for System of Fredholm
Integral Equations, Applied Mathematics & Information Sciences 10 (3), (2016)
975-985.
[5] I. Komashynska, M. Al-Smadi, A. Al-Habahbeh, A. Ateiwi, Analytical
approximate Solutions of Systems of Multi-pantograph Delay Differential
Equations Using Residual Power-series Method, Australian Journal of Basic and
Applied Sciences 8 (10), (2014) 664-675.
[6] O. Abu Arqub, Series solution of Fuzzy differential equations under strongly
generalized differentiability. J. Adv. Res. Appl. Math. 5, (2013) 31–52.
______________________________________________________
29
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
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Kusadasi - Aydin, TURKEY www.icrapam.org
Adaptation of Fractional Power Series Method for Solving
Fuzzy BVPs
Mohammad Alaroud1, Rokiah Rozita Ahmad1, Mohammed Al-Smadi2,*,
Ummul Khair Salma Din1
1School of Mathematical Sciences, Faculty of Science and Technology,
Universiti Kebangsaan Malaysia 2Department of Applied Science, Ajloun College, Al-Balqa Applied University,
Ajloun 26816, Jordan
Abstract: In this paper, we propose a computational iterative technique, the
fractional power seies method (FPR) for finding numeric-analytic solutions for a
class of fuzzy BVPs. The approach constructs to express the solutions in form of
a series expansion in terms of elementary α-level representation [1-6]. By
linguistic of fuzzy terms, the fuzzy fractional equation is converted to system of
fractional equations in crisp case, whereas the crisp results are mapped to fuzzy
output using the membership functions. Further, numerical examples are
provided and discussed quantitatively and graphically to show the performance
features, generality and superiority of the FRP algorithm. The results reveal that
the method is quite accurate, simple, straightforward, and convenient for
exploring fuzzy fractional models.
Keywords: Generalized Taylor series, Residual power series method, Boundary
value problem, Fuzzy fractional differential equations.
References:
[1] K. Moaddy, M. Al-Smadi and I. Hashim, A Novel Representation of the
Exact Solution for Differential Algebraic Equations System Using Residual
Power-series Method, Discrete Dynamics in Nature and Society, Vol. 2015
(2015), Article ID 205207, 1-12. http://dx.doi.org/10.1155/2015/205207
[2] M. Al-Smadi, Solving initial value problems by residual power series
method, Theoretical Mathematics & Applications 3(1), (2013) 199-210.
[3] I. Komashynska, M. Al-Smadi, O. Abu Arqub and S. Momani, An efficient
analytical method for solving singular initial value problems of nonlinear
systems, Applied Mathematics & Information Sciences, 10(2), (2016) 647-656.
doi:10.18576/amis/100224.
[4] I. Komashynska, M. Al-Smadi, A. Ateiwi and S. Al-Obaidy, Approximate
Analytical Solution by Residual Power Series Method for System of Fredholm
______________________________________________________
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in
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Kusadasi - Aydin, TURKEY www.icrapam.org
Integral Equations, Applied Mathematics & Information Sciences 10 (3), (2016)
975-985. doi:10.18576/amis/100315
[5] I. Komashynska, M. Al-Smadi, A. Al-Habahbeh, A. Ateiwi, Analytical
approximate Solutions of Systems of Multi-pantograph Delay Differential
Equations Using Residual Power-series Method, Australian Journal of Basic and
Applied Sciences 8 (10), (2014) 664-675.
[6] O. Abu Arqub, Series solution of Fuzzy differential equations under strongly
generalized differentiability. J. Adv. Res. Appl. Math. 5, (2013) 31–52.
______________________________________________________
31
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Solving Fuzzy Mixed Integral Equations of Second Kind in
Hilbert Spaces
Mohammed Al-Smadi
Department of Applied Science, Ajloun College, Al-Balqa Applied University,
Ajloun 26816, Jordan [email protected]
Abstract: In this paper, we propose a computational iterative technique for
finding numeric-analytic solutions for a class of fuzzy mixed integral equations
of the second kind based on orthonormal basis sets derived from Gram-Schmidt
process in reproducing-kernel Hilbert spaces [1-6]. The approach constructs to
express the solutions in form of a series expansion in terms of elementary 𝛼-level
representation in the Sobolev space 𝜔2[𝑎, 𝑏]. By linguistic of fuzzy terms, the
fuzzy integral equation is converted to system of integral equations in crisp case,
whereas the crisp results are mapped to fuzzy output using the membership
functions. Further, numerical examples are provided and discussed quantitatively
and graphically to show the performance features, generality and superiority of
the reproducing-kernel algorithm.
Keywords: Fuzzy calculus, Reproducing-kernel theory, Fredholm-Volterra
integral equations, Fourier series expansion.
References:
[1] O. Abu Arqub, M. Al-Smadi and N. Shawagfeh, “Solving Fredholm integro-
differential equations using reproducing kernel Hilbert space method”, Applied
Mathematics and Computation, 219 (2013), 8938-8948.
[2] M. Al-Smadi, O. Abu Arqub and S. Momani, “A Computational Method for
Two-Point Boundary Value Problems of Fourth-Order Mixed Integrodifferential
Equations”, Mathematical Problems in Engineering, 2013 (2013), Article ID
832074, 1-10. http://dx.doi.org/10.1155/2013/832074
[3] O. Abu Arqub and M. Al-Smadi, “Numerical algorithm for solving two-
point, second-order periodic boundary value problems for mixed integro
differential equations,Applied Mathematics and Computation,243(2014)911-922
______________________________________________________
32
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
[4] O. Abu Arqub, M. Al-Smadi, S. Momani and T. Hayat, “Numerical Solutions
of Fuzzy Differential Equations using Reproducing Kernel Hilbert Space
Method”, Soft Computing, (2015), 1-20. http://dx.doi.org/10.1007/s00500-015-
1707-4
[5] M. Al-Smadi, O. Abu Arqub, N. Shawagfeh and S. Momani, “Numerical
investigations for systems of second-order periodic boundary value problems
using reproducing kernel method”, Applied Mathematics and Computation, 291
(2016) 137-148.
[6] O. Abu Arqub, M. Al-Smadi, S. Momani and T. Hayat, “Application of
reproducing kernel algorithm for solving second-order, two-point fuzzy
boundary value problems”, Soft Computing, 2016 (2016), 1-16.
doi:10.1007/s00500-016-2262-3
______________________________________________________
33
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Numerical Algorithm for Solving Time-Fractional Bvps in a
Simplified Reproducing Kernel Space
Mohammed Al-Smadi
Department of Applied Science, Ajloun College, Al-Balqa Applied University,
Ajloun 26816, Jordan
Abstract: In this paper, we propose a computational iterative technique for
finding numeric-analytic solutions for a class of of time-fractional boundary
value problem within favorable aspects of the reproducing kernel Hilbert space
in Caputo sense. The algorithm methodology is based on generating an
orthonormal basis sets derived from Gram-Schmidt process [1-6]. The approach
constructs to express the solutions in form of a series expansion in terms of
elementary representation in the Sobolev space. Error estimates are obtained as
well as numerical examples are provided and discussed quantitatively and
graphically to show the performance features, generality and superiority of the
reproducing-kernel algorithm. The numerical results indicate that the IRKA is a
significant development tool for handling such issues arising in computer,
physics and engineering fields.
Keywords: Fractional differential equations; Reproducing kernel theory; Inner
product spaces; Error estimation and error bound.
References:
[1] O. Abu Arqub, M. Al-Smadi and N. Shawagfeh, “Solving Fredholm integro-
differential equations using reproducing kernel Hilbert space method”, Applied
Mathematics and Computation, 219 (2013), 8938-8948.
[2] M. Al-Smadi, O. Abu Arqub and S. Momani, “A Computational Method for
Two-Point Boundary Value Problems of Fourth-Order Mixed Integrodifferential
Equations”, Mathematical Problems in Engineering, 2013 (2013), Article ID
832074, 1-10. http://dx.doi.org/10.1155/2013/832074
[3] O. Abu Arqub and M. Al-Smadi, “Numerical algorithm for solving two-
point, second-order periodic boundary value problems for mixed integro-
differential equations”, Applied Mathematics and Computation, 243 (2014), 911-
922.
______________________________________________________
34
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
[4] O. Abu Arqub, M. Al-Smadi, S. Momani and T. Hayat, “Numerical Solutions
of Fuzzy Differential Equations using Reproducing Kernel Hilbert Space
Method”, Soft Computing, (2015), 1-20. http://dx.doi.org/10.1007/s00500-015-
1707-4
[5] M. Al-Smadi, O. Abu Arqub, N. Shawagfeh and S. Momani, “Numerical
investigations for systems of second-order periodic boundary value problems
using reproducing kernel method”, Applied Mathematics and Computation, 291
(2016) 137-148.
[6] O. Abu Arqub, M. Al-Smadi, S. Momani and T. Hayat, “Application of
reproducing kernel algorithm for solving second-order, two-point fuzzy
boundary value problems”, Soft Computing, 2016 (2016), 1-16.
doi:10.1007/s00500-016-2262-3
______________________________________________________
35
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Semiregularization of Almost Countably Compact Spaces
Zuhier Altawallbeh
Department of Mathematics, Tafila Technical University,
Tafila 66110, Jordan
Abstract: Among various covering properties of topological spaces a lot of
attention has been made to those covers. Weakly Lindelöf spaces were
introduced by Frolik [1] and nearly compact spaces were defined by Singal and
Mathur [2]. Other generalizations of Lindelöfness and compactness are given by
many authors as Balasubramanian [3], and Altawallbeh and Al-Momany in [4].
Bonanzinga, Matveev and Pareek [5] defined almost countably compact spaces
as a generalization of countably compact spaces. In this paper, we investigate
this new class of spaces, almost countably compact spaces, also we study some
other properties in the view of regular cover notion and semiregularization
topology relating to this class of spaces.
Keywords: regularly open sets, regularly closed sets, countably compact, nearly
countably compact, semiregularization topology.
References:
[1] Z. Frolik, “Generalizations of compact and Lindelöf spaces”, Czechoslovak
Math. J., 9.84(1959), 172-217.
[2] M.K Singal and A. Mathur, “On nearly compact spaces”, Boll. Un. Mat Ital.,
2.4(1969), 702-710.
[3] G. Balasubramanian, “On some generalizations of compact spaces”, Glas.
Mat. Ser. III, 17.37(1982), 357-380.
[4] Z. Altawallbeh and A. Al-Momany, “Nearly countably compact spaces”,
International Electronic Journal of Pure and Applied Mathematics, 8.4(2014),
59-56.
[5] M. Bonanzinga, M.V Matveev and M. Pareek, “Some remarks on
generalizations of countably compact spaces and Lindelöf spaces”,
Rend.Circ.Mat.palermo, 2.51.1(2002), 163-174.
______________________________________________________
36
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Generalization on Countably Compact Spaces via Hereditary
Classes
Zuhier Altawallbeh
Department of Mathematics, Tafila Technical University,
Tafila 66110, Jordan
Abstract: A lot of work has been taken in account to generalize different
covering properties of spaces as compact and countably compact spaces in
different ways either by taking topologies with respect to an ideal as in [1] which
was presented by Hamlett and Jankovic or by giving weaker condition in the
definition as nearly countably compact spaces which is done by Altawallbeh and
Al-Momany in [2]. In this article, we use the notions of generalized topologies
and hereditary classes that was presented by Csa sza r in [3] and [4]. Here, we
define and characterize the countably compact spaces taking in account
generalized topologies in terms of hereditary classes. In particular, by setting a
generalized topology μ on a nonempty set X, we define new concept of
countably compactness, μԨ-countably compact space in generalized topology μ
in the sense of a hereditary class Ԩ, called ԨGTS. The space ԨGTS is μԨ-
countably compact if for every countable μ- covering of X there exists a finite
subset such that the complement, in X, of the union of sets of that subset belongs
to Ԩ.
Keywords: hereditary class, generalized topology.
References:
[1] T.R. Hamlett and D. Jankovic, “Ideals in general topology”, General
Topology and Applications, 1988, 115-125.
[2] Z. Altawallbeh and A. Al-Momany, “Nearly countably compact spaces”,
International Electronic Journal of Pure and Applied Mathematics, 8.4(2014),
59-56.
[3] Ả. Csẚszẚr, “Generalized topology, generalized continuity”, Acta Math.
Hungar, 96 (2002), 351-357.
[4] Ả. Csẚszẚr, “Modification of generalized topologies via hereditary classes”,
Acta Math. Hungar, 1-2. 115 (2007), 29-36.
______________________________________________________
37
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Hybrid Master Equation of the Jump Diffusion Approximation
Derya Altintan* and Heinz Koeppl**
*Department of Mathematics, Selcuk University,
Konya, Turkey
**Department of Electrical Engineering and Information Technology,
Technische Universitat Darmstadt,
Darmstadt, Germany
Abstract: Most often biochemical reactions are multi-scale processes because
of the differences in the abundance of species and the reaction rates. To exploit
this multi-scale nature, hybrid models which combine the deterministic and
stochastic approaches are needed. In [1], we propose a jump diffusion
approximation to model and simulate these types of systems. The idea of the
method is to partition the reactions into fast and slow subgroups and model the
fast group by Langevin equation while slow group is modelled by continuous
time Markov chains. In this study, we define a new vector whose components
represents the number of occurrences of reactions in the hybrid model given in
[1]. Similar to the idea of splitting the reactions into two different groups, we
consider this vector as a combination of random vectors represent the continuous
and discrete random processes which count the occurrence of reactions in the fast
group and the slow group, respectively. Based on the studies in [4], we prove
that the time derivative of the probability distribution of this new vector which is
called hybrid master equation is a summation of the Fokker-Planck equation
(FPE) [2] which represents the time evolution of the conditional probability
distribution of the continuous random variable given discrete random variable
and chemical master equation (CME) [3] which is the time derivative of the
marginal distribution of the discrete variable.
Keywords: Multi-Scale Processes, Jump-Diffussion Approximation, Fokker-
Planck Equation (FPE), Chemical Master Equation (CME).
______________________________________________________
38
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
References:
[1] A. Ganguly, D. Altintan, H. Koeppl, “Jump-diffusion approximation of
stochastic reaction dynamics: Error bounds and algorithms”, SIAM journal of
Multiscale Modeling and Simulations, 13. 4 (2015), 1390-1419.
[2] D. T. Gillespie, “The Chemical Langevin and Fokker-Planck Equations for
the Reversible Isomerization Reaction”, The Journal of Physical Chemistry A,
106.20 (2002), 5063-5071.
[3] D. T. Gillespie, “A rigorous derivation of the chemical master equation,”
Physica A, 188 (1992), 404–425.
[4] R. F. Pawula. “Generalizations and extensions of the fokker-planck-
kolmogorov equations”, IEEE Transactions on Information Theory , 13.1, 1967,
33-41.
Acknowledgments
This work is supported by the Scientific and Technological Research Council of
Turkey (TÜBİTAK) Program no:3501 Grant, no. 115E252.
______________________________________________________
39
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PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Coefficient Bounds for a Subclass of Analytic Functions with
Respect to Symmetric Points
Osman Altintas1, Oznur Ozkan Kilic2
1 Department of Mathematics Education, Baskent University,,
Ankara, Turkey
[email protected] 2 Department of Technology and Knowledge Management, Baskent University,,
Ankara, Turkey
Abstract: In this paper, we determine the coefficient bounds for a subclass of
analytic functions with respect to symmetric points which is introduced here
several corollaries are also considered.
Keywords: Analytic function, Close-to-convex function, Close-to-star function,
Symmetric points.
References:
[1] O. Altıntaş, “On a subclass of certain starlike functions with negative
coefficients”, Math. Japonica 36, No. 3, (1991), 489-495.
[2] O. Altıntaş, “Certain applications of subordination associated with
neighborhoods”, Hacettepe J.Math. Statist. 39, No. 4, (2010), 527-534.
[3] R. Bucur, D. Breaz and L. Georgescu, “Third hankel determinant for a class
of analytic functions with respect to symmetric points”, Acta Univer. Apulensis,
No.42, (2015), 79-86.
[4] R.N. Das, P. Sing, “On subclasses of schlicht mappings”, Indian. J. Pure
Appl. Math. 8 (1997), 864-872.
[5] K. Sakaguchi, “On certain univalent mappings”, J. Math. Soc. 11 (1959),
Japan, 72-75.
[6] C. Selveraj, N. Vasanthi, “Subclasses of analytic functions with respect to
symmetric and conjugate Points”, Tamkang J. Math. 42 (1) (2011), 87-94
[7] H. M. Srivastava, O. Altinta_s and S. K. Serenbay, “Coefficient bounds for
certain subclasses of starlike functions of complex order”, Appl. Math. Lett. 24
(2011), 1359-1363.
______________________________________________________
40
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
On The Relationship Between A Family of Fibonacci And
Lucas Numbers
Ipek Altun2, Ali Aydogdu1, Engin Ozkan2
1Department of Mathematics and Computing, Beykent University 2Department of Mathematics. Erzincan University
[email protected], [email protected], [email protected]
Abstract: In this work, we prove some properties of a family of Fibonacci
numbers. Also some relationship between the family of Fibonacci and Lucas
numbers are given.
Keywords: Fibonacci Numbers, Generalized Fibonacci Numbers, Lucas
Numbers.
References:
[1] V.E. Hoggatt, “Fibonacci and Lucas numbers”, Houghton Mifflin, 1969
[2]. J. lvie , “A General Q-Matrix”, Fibonacci Quarterly, Vol. 10, No. 3, April,
1972, 255-261
[3] T. Koshy, “Fibonacci and Lucas numbers with applications”, John Wiley &
Sons, Inc.; 2001.
______________________________________________________
41
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Convergence, Consistency and Stability in Intuitionistic Fuzzy
Differential Equations
Bouchra Ben Amma1, Said Melliani2 and Lalla Saadia Chadli3
Laboratory of Applied Mathematics and Scientific Computing 1,2,3
Faculty Of Sciences and Technologies1,2,3
Sultan Moulay Slimane University, PO Box 523, 23000 Beni Mellal,
Morocco1,2,3
[email protected] , [email protected],
Abstract: In this work, we consider first-order intuitionistic fuzzy differential
equations with initial value conditions. The convergence, consistency and
stability of difference method for approximating the solution of intuitionistic
fuzzy differential equations are studied. Then the local truncation error is defined
and sufficient conditions for convergence, consistency and stability of difference
method are provided and some examples are presented to illustrate the accuracy
of our proposed concepts.
Keywords: Intuitionistic fuzzy differential equations, Convergence,
Consistence, Stability, Local truncation error
References:
[1] K. Atanassov, Intuitionistic fuzzy sets. VII ITKR’s session, Sofia (deposited
in Central Science and Technical Library of the Bulgarian Academy of Sciences
1697/84) (1983)
[2] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1986),
pp. 87-96.
[3] K. Atanassov, Operators over interval valued intuitionistic fuzzy sets, Fuzzy
Sets Syst. 64(2) (1994), pp. 159-174.
[4] S. Abbasbandy, T. Allahviranloo, Numerical Solution of fuzzy differential
equations by Taylor method, J.of Comp.Methods in Appl. Math. 2 (2002), 113-
124.
[5] S. Abbasbandy, T. Allahviranloo, O. Lopez-Pouso, J.J. Nieto, Numerical
methods for fuzzy differential inclusions, Journal of Computer and Mathematics
With Applications 48 (2004), pp. 1633–1641.
______________________________________________________
42
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
SQCQP Descent Scheme for Multi-objective Optimization
Problem
Md Abu Talhamainuddin Ansary 1, Geetanjali Panda2
Department of Mathematics, Indian Institute of Technology Kharagpur
Kharagpur, India 1 [email protected], 2 [email protected]
Abstract: Developing numerical approximation techniques for multi-objective
programming problem (MOP): (f1, f2,…fm) , f: is a
growing research area in recent time. Some of these techniques for unconstrained
MOP include steepest descent scheme by Fliege and Svaiter [1] in 2000, Newton
scheme by Fliege, Drummond, and Svaiter [2] in 2009, Quasi-Newton scheme
by Qu, Goh and Chan [3] in 2011 and for constrained MOP include SQP scheme
by Fliege and Vaz [4] in 2015. The SQP scheme due to Fliege and Vaz
considers the linear approximation of the constraint functions and quadratic
approximation of all objective functions. This paper has focused on nonlinear
MOP with inequality constraints and developed a descent converging sequence
considering quadratic approximation of both constraints and all objective
functions at every iterating point. This method is follows the idea of sequential
quadratically constrained quadratic program (SQCQP) technique. A non-
differentiable penalty function l∞ is used to restrict the constraint violations. It is
proved that the descent sequence generated in this process converges to a critical
point under Slater constraint qualifications. Global convergence of this scheme is
justified with some mild assumptions. This process is free from any kind of
priori chosen parameters and ordering information of objective functions as in
scalarization processes. The proposed scheme is verified and compared with
existing methods using a set of test problems.
Keywords: Sequential quadratically constrained quadratic programing; Slater
constraint qualification; Penalty function, Critical point.
References:
[1] J .Fliege and B.F. Svaiter, “Steepest descent scheme for multicriteria
optimization”, Math. Methods Oper. Res., 51.3(2000), 479-494.
[2] J. Fliege, L. M. G. Drummond, and B.F. Svaiter, “Newton's method for
multiobjective optimization”, SIAM J. Optim, 20.2(2009), 602-626.
[3] S. Qu and M. Goh and F. T. S. Chan , “Quasi-Newton methods for solving
multiobjective optimization”, Oper. Res. Lett., 39(2011), 139-150.
[4] J. Fliege and A. I. F. Vaz, “A method for constrained multiobjective
optimization based on SQP techniques”, SIAM J.Optim., 24.4(2015), 2091-2119.
______________________________________________________
43
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
On Gauss Balancing and Gauss Cobalancing Numbers
Mustafa Asci and Mustafa Yilmaz
Department of Mathematics, Pamukkale University, Kınıklı, Denizli, Turkey
Abstract: A. Behera and G.K. Panda [1] defined new number sequence
Balancing numbers as following: They call a natural number 𝑛 a balancing
number if
1 + 2 + ⋯ + (𝑛 − 1) = (𝑛 + 1) + (𝑛 + 2) + ⋯ + (𝑛 + 𝑟)
for some natural number 𝑟, while they call 𝑟 the balancer corresponding to the
balancing number 𝑛.
According to Panda and Ray [2] the values of 𝑛 satisfying the Diophantine
equation
1 + 2 + ⋯ + 𝑛 = (𝑛 + 1) + (𝑛 + 2) + ⋯ + (𝑛 + 𝑟)
for some natural number 𝑟 are known as cobalancing numbers while 𝑟 is the
cobalancer corresponding to the cobalancing number 𝑛. Many authors study the
interesting properties of Balancing and Cobalancing numbers. In this paper we
define and study the Gaussian Balancing and Gaussian Cobalancing numbers.
We give many properties of these numbers and we prove these properties by
matrix methods.
Keywords: Balancing Numbers, Cobalancing Numbers, Gauss Fibonacci
Numbers.
References:
[1] A. Behera and G.K. Panda. On the square roots of triangular numbers. The
Fib. Quart, 49 (1)28-33,
[2] G.K. Panda and P.K. Ray Cobalancing Numbers and Cobalancers. Int. J.
Math. Sci., 2005 (8): 1189-1200.
[3] Liptai, K.; Panda, G. K.; Szalay, L. A balancing problem on a binary
recurrence and its associate. Fibonacci Quart. 54 (2016), no. 3, 235–241.
[4] Rout, S. S.; Panda, G. K. k-gap balancing numbers. Period. Math. Hungar.
70 (2015), no. 1, 109–121.
[5] Davala, R. K.; Panda, G. K. On sum and ratio formulas for balancing
numbers. J. Indian Math. Soc. (N.S.) 82 (2015), no. 1-2, 23–32.
[6]Panda, G. K.; Panda, A. K. Balancing-like sequences associated with integral
standard deviations of consecutive natural numbers. Fibonacci Quart. 52 (2014),
no. 5, 187–192.
[7] Panda, G.K.; Rout, S. S. Gap balancing numbers. Fibonacci Quart. 51
(2013), no. 3, 239–248.
______________________________________________________
44
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
An Overview of Ordering Based on Nullnorms
Emel Asici
Department of Software Engineering, Faculty of Technology,
Karadeniz Technical University,
Trabzon, Turkey
Abstract: Nullnorms and t-operators were introduced by Calvo and et all [1] and
Mas and et all [2], respectively, which are also generalizations of the notions of
t-norms and t-conorms. In [3] Mas and et all it is pointed out that nullnorms and
t-operators are equivalent since they have the same block structures in [0,1]2. In
[4] Asici was define and discuss an order induced by nullnorms on bounded
lattices. In this paper, we investigate some properties an order induced by
nullnorms on bounded lattices. We determine with the examples the relationship
between the order induced by a nullnorm and the order on the lattice. So, 𝑆-
partial order and 𝑇-partial order are extended to a more general form.
Keywords: Nullnorm, Bounded Lattice, Partial order.
References:
[1] T. Calvo, B. De Baets and J. Fodor, “The functional equations of Frank and
Alsina for uninorms and nullnorms”, Fuzzy Sets Syst., 120(2001), 385-394.
[2] M. Mas, G. Mayor and J. Torrens, “t-operators”, Int. J. Uncertain. Fuzz.
Knowl.-Based Syst., 7(1999), 31-50.
[3] M. Mas, G. Mayor and J. Torrens, “The distributivity condition for uninorms
and t-operators”, Fuzzy Sets Syst., 7(1999), 31-50.
[4] E. Aşıcı, “An order induced by nullnorms and its properties”, Inf. Sci., 267
(2014), 323-333.
[5] E. Aşıcı and F. Karaçal, “On the T-partial order and properties”, Fuzzy Sets
Syst.,
[6] E. P. Klement, R. Mesiar and E. Pap, “Triangular Norms ”, Kluwer
Academic Publishers, Dordrecht 2000.
[7] J. Drewniak, P. Drygas and E. Rak, “Distributivity between uninorms and
nullnorms”, Fuzzy Sets Syst., 159(2008), 1646-1657.
[8] J. Casasnovas and G. Mayor, “Discrete t-norms and operations on extended
multisets”, Fuzzy Sets Syst., 159(2008), 1165-1177.
______________________________________________________
45
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Analytical-Numerical Solutions for a class of Systems of
Differential Equations Using Reproducing Kernel Method
Ali Mahmud Ateiwi
Department of Mathematics, Faculty of Science, Al-Hussein Bin Talal
University, P.O. Box 20, Ma'an, Jordan
Abstract: This paper proposes an efficient numerical method to obtain
analytical-numerical solutions for a class of system of boundary value problems.
This new algorithm is based on a reproducing kernel Hilbert space method [1-6].
The analytical solution is calculated in the form of series in reproducing kernel
space with easily computable components. In addition, convergence analysis for
this method is discussed. In this sense, some numerical examples are given to
show the effectiveness and performance of the proposed method. The results
reveal that the method is quite accurate, simple, straightforward, and convenient
to handle a various range of differential equations.
Keywords: System of differential equations, Reproducing kernel method,
Boundary value problem, Gram-Schmidt process.
References:
[1] O. Abu Arqub, M. Al-Smadi, S. Momani and T. Hayat, “Application of
reproducing kernel algorithm for solving second-order, two-point fuzzy
boundary value problems”, Soft Computing, 2016 (2016), 1-16.
doi:10.1007/s00500-016-2262-3
[2] M. Al-Smadi, O. Abu Arqub and S. Momani, “A Computational Method for
Two-Point Boundary Value Problems of Fourth-Order Mixed Integrodifferential
Equations”, Mathematical Problems in Engineering, 2013 (2013), Article ID
832074, 1-10. http://dx.doi.org/10.1155/2013/832074
[3] M. Al-Smadi, O. Abu Arqub, N. Shawagfeh and S. Momani, “Numerical
investigations for systems of second-order periodic boundary value problems
using reproducing kernel method”, Applied Mathematics and Computation, 291
(2016) 137-148.
[4] O. Abu Arqub, M. Al-Smadi, S. Momani and T. Hayat, “Numerical Solutions
of Fuzzy Differential Equations using Reproducing Kernel Hilbert Space
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Method”, Soft Computing, (2015), 1-20. http://dx.doi.org/10.1007/s00500-015-
1707-4
[5] O. Abu Arqub and M. Al-Smadi, “Numerical algorithm for solving two-
point, second-order periodic boundary value problems for mixed integro-
differential equations”, Applied Mathematics and Computation, 243 (2014), 911-
922.
[6] O. Abu Arqub, M. Al-Smadi and N. Shawagfeh, “Solving Fredholm integro-
differential equations using reproducing kernel Hilbert space method”, Applied
Mathematics and Computation, 219 (2013), 8938-8948.
______________________________________________________
47
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
A Fuzzy Project Scheduling with Constrained Resources
Lyazzat Atymtayeva, Ardakbek Kungaliyev, Daniyar Artykov
Department of Computer Engineering, Satbayev Kazakh National Research
Technical University, Almaty, Kazakhstan
Abstract: The problems of project scheduling optimization in the conditions of
constrained resources have been researched by many authors including Arvind
Sathi et al. [1], Xiaoqing (Frank) Liu et al. [2], Wang [3], Herroelen, W. et al.
[4], Javad Nematian et al. [5] and others. They have been focused on the using of
fuzzy logic and systems as an intelligent component in project management tools
for scheduling. The main purpose for their researches was the development of an
algorithm for solving Fuzzy Random Resource-Constrained Project Scheduling
problem. This problem concerned the using of linear programming approach that
was proposed by Alvarez-Valdes and Tamarit in 1993 [6]. In this paper we use
the mentioned concepts for development of intelligent tools and algorithms in
fuzzy project scheduling and discuss the ways how to make it enabled the
converting of original complex scheduling model to a mixed integer
programming model. Keywords: fuzzy project random resource-constrained scheduling, linear
programming, mixed interger programming.
References:
[1] Arvind Sathi, Thomas E. Morton, and Steven F. Roth.Callisto: An Intelligent
Project Management System, Journal AI Magazine. 7(5), 34-52 (1986)
[2] Xiaoqing (Frank) Liu, Gautam Kane, Monu Bambroo. An intelligent early
warning system for software quality improvement and project management,
Journal of Systems and Software. 79(11), 15521564 (2006)
[3] Wang, J. A fuzzy project scheduling approach to minimize schedule risk for
product development. Fuzzy Sets andSystems, 127, 99116 (2002).
[4] Herroelen W., and R. Leus. Project Scheduling under Uncertainty: Survey
and Research Potentials. European Journal of Operational Research 165, 289306
(2005).
[5] Javad Nematian, Kourosh Eshghi, Abdolhamid Eshragh- Jahromi. A
Resource-Constrained Project Scheduling Problem with Fuzzy Random
Duration. Journal of Uncertain Systems Vol.4, No.2, pp.123-132, 2010
[6] Alvarez-Valdes, R. and J. Tamarit. The project Scheduling Polyhedron:
Dimension, Facets and Lifting Theorems. European Journal of Operational
Research 67, 1993, pp. 204-220
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48
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
A Convergent Two-Level Linear Scheme for the Generalized
Rosenau-Kdv-RLW Eqution
Ayhan Aydin
Department of Mathematics, Atilim University,
Incek, Istanbul, Turkey
Abstract: A new convergent two-level finite difference scheme is proposed for
the numerical solution of initial value problem of generalized Rosenau-KdV-
RLW equation. The new scheme is linear and conservative. It contains one free
parameter. The impact of the parameter to error of the numerical solution is
studied. The prior estimate of the finite difference solution is obtained. The
existence, uniqueness and convergence of the scheme are proved. Accuracy and
reliability of the scheme is tested by simulating the solitary wave graph of the
equation. Numerical experiments indicate the efficiency of the method..
Keywords: conservative scheme, convergence, solitary wave.
References:
[1] Wongsaijai, B., Poochinapan, K., A tree-level average implicit finite
difference scheme to solve equation obtained by coupling the Rosenau-KdV
equation and the Rosenau-RLW equation, Applied Mathematics and
Computation, 245, (2014), 289-304.
[2] Pan, X., Wang, Y., Zhang, L., Numerical analysis of a pseudo-compact C-N
conservative scheme for the Rosenau-KdV equation coupling with the Rosenau-
RLW equation, Boundary Value Problem, (2015):65.
[3] Y.L. Zhou, Application of Discrete Functional Analysis to the Finite
Difference Methods, International Academic Publishers, Beijing, 1990
______________________________________________________
49
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PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Fuzzy Soft Metric and Fuzzifying Soft Topology Induced by
Fuzzy Soft Metric
Ebru Aydogdu, Abdulkadir Aygunoglu, Halis Aygun
Department of Mathematics, Kocaeli University, Kocaeli, Turkey
[email protected] , [email protected] ,
Abstract: The aim of this study is to define fuzzy soft metric compatible to soft
theory and investigate fuzzifying soft topology induced by fuzzy soft metric. For
this, firstly we introduce a fuzzy soft metric on soft set and by using this we
construct a fuzzy metric on soft set. Then we investigate fuzzifying soft topology
characterized by this fuzzy metric and studied their properties.
Keywords: Soft metric, Fuzzy metric, Fuzzifying soft topology.
References:
[1] A. Aygünoğlu and H. Aygün, “Some notes on soft topological spaces”,
Neural Computing and Applications, 21.1(2012),113-119.
[2] A. Aygünoğlu, V. Cetkin and H. Aygün, “An introduction to fuzzy soft
topological spaces”, Hacettepe Journal of Mathematics and Statistics,
43.2(2014), 197-208.
[3] A. George and P. Veeramani, “On some results in fuzzy metric spaces”,
Fuzzy sets and systems, 64.3(1994), 395-399.
[4] A. Shostak, “Two decades of fuzzy topology: basic ideas, notions and
results”, Russ.Math.Surv., 44(1989), 125-186.
[5] B.P. Varol and H.Aygün, “Fuzzy soft topology”, Hacettepe Journal of
Mathematics and Statistics, 41.3(2012), 407-419.
[6] J.J. Minana and A. Šostak, "Fuzzifying topology induced by a strong fuzzy
metric." Fuzzy Sets and Systems 300 (2016), 24-39.
[7] M. Shabir and M. Naz, “On soft topological spaces” Comput. Math. Appl.”,
61(2011), 1786-1799.
[8] P.K. Maji, R. Biswas and A.R. Roy, “Soft set theory” Computers &
Mathematics with Applications, 45(2003), 555-562.
[9] S. Das and S.K. Samanta, “Soft real sets, soft real numbers and their
properties”, J. Fuzzy Math., 20.3(2012), 551-576.
[10] S. Das and S.K. Samanta, “Soft metric”, Annals of Fuzzy Mathematics and
Informatics, 6.1(2013), 77-94.
[11] S. Das and S.K. Samanta, “On soft metric spaces”, J. Fuzzy Math.,
21.3(2013), 707-734.
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50
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PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Some Identities Associated With Hecke Operators
Aykut Ahmet Aygunes
Department of Software Engineering, Faculty of Engineering and Architecture,
Antalya Akev University,
Antalya, Turkey
Abstract: In this paper, we introduce the Hecke operators and we give some
properties of these operators. Then we deal with a new approach, based on
Hecke operators, to study a large class of special polynomials including
Bernoulli and Euler polynomials. From this new approach we obtain some
identities associated with Hecke operators.
Keywords: Hecke operators, partial Hecke operators, Bernoulli and Euler
polynomials.
References:
[1] L. Euler, Methodus generalis summandi progressiones, Comment. acad. sci.
Petrop., v.6 (1738) 68-97.
[2] Y. Hellegouarch, Invitation aux mathématiques de Fermat-Wiles, Dunod.
(2001).
[3] T. Kim, Symmetry identities for the twisted generalized Euler polynomials ,
Adv. Stud. Contemp. Math. Vol 19 ( 2009 ), 111-118.
[4] T. Kim, Some identities of symmetry for the generalized Bernoulli numbers
and polynomials , ( 2009) Arxiv, http://arxiv.org/pdf/0903.2955.
[5] J. L. Raabe, Zurückführung einiger Summen and bestimmten Integrale auf
die Jacob Bernoullische Function, Journal für die reine and angrew. math., 42
(1851) 348-376.
[6] J-P. Serre, Cours d'arithmétique, PUF, 1970.
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51
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PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Some Rough Convergence Criteria for the Sequences of
Intervals of Fuzzy Numbers
Salih Aytar
Department of Mathematics, Süleyman Demirel University,
lsparta, Turkey
Abstract: An interval of fuzzy number is a set of fuzzy numbers with the
property that any fuzzy number that lies between two fuzzy numbers in the set is
also included in the set. In this talk, we examine the rough convergence relations
between a sequence of intervals of fuzzy numbers and a sequence of fuzzy
numbers included these intervals.
Keywords: Rough convergence; Fuzzy interval numbers
References:
[1] F.G. Akçay, S. Aytar (2015), Rough convergence of a sequence of fuzzy
numbers, Bulletin of Mathematical Analysis and Applications, 7(4): 17-23.
[2] S. Aytar (2008). Rough statistical convergence, Numer. Funct. Anal. and
Optimiz. 29(3-4):291-303.
[3] H.X. Phu (2001), Rough convergence in normed linear spaces, Numer. Funct.
Anal. and Optimiz., 22:201-224.
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52
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Modified Simple Equation Method and its Applications to
Some Nonlinear Physical Equations
Gizel Bakicierler and Emine Misirli
Department of Mathematics, Ege University,
Bornova, İzmir, Turkey
[email protected] , [email protected]
Abstract: The model of many problems encountered in various fields of
engineering and science such as plasma physics, mathematical physics and fluid
mechanics is expressed by nonlinear partial differential equations. Therefore, it is
very important to investigate the solutions of these equations. In this paper, wave
solutions of some nonlinear physical equations are obtained by Modified Simple
Equation Method and wave types are determined. This method have been applied
(2+1) dimensional Calogero-Bogoyavlenskii-Schiff (CBS) equation and (3+1)
dimensional Jimbo-Miwa equation as a result we obtained exact solution
functions. The graphics of solution functions have been drawn using the
Mathematica program and these solutions of equations are interpreted.
Key Words: nonlinear partial differential equations, evolution equations,
modified simple equation method
References:
[1] Ayati, Zainab, "Exact Solutions of Nonlinear (2+ 1)-Dimension Nonlinear
Dispersive Long Wave and Coupled Boiti–Leon–Pempinelli Equations by using
the Modified Simple Equation Method." World Applied Programming, WAP
journal, Vol (3), Issue (12), December 2013. 565-571.
[2] Jawad, Anwar Ja’afar Mohamad, Marko D. Petković and Anjan Biswas,
"Modified simple equation method for nonlinear evolution equations." Applied
Mathematics and Computation 217 (2010): 869-877.
[3] Khan, M. Ashrafuzzaman and M. Ali Akbar, "Exact and Solitary Wave
Solutions to the Generalized Fifth-order KdV Equation by Using the Modified
Simple Equation Method." Applied and Computational Mathematics 4,3 (2015)
[4] Zayed, Elsayed ME, and Hoda Ibrahim SA, "Modified simple equation
method and its applications for some nonlinear evolution equations in
mathematical physics." International Journal of Computer Applications 67, 6
(2013).
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53
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Jacobi Elliptic Function Solutions of the Space-Time Fractional
Symmetric Regularized Long Wave Equation
Dilek Varol Bayrama, Sevil Çulhab, Ayşegül Daşcıoğlua
aDepartment of Mathematics, Faculty of Science and Arts, Pamukkale
University, Denizli, 20070, Turkey bInstitute of Science, Pamukkale University, Denizli, 20070, Turkey
[email protected], [email protected], [email protected]
Abstract: In this work, new families of analytical exact solutions of the
fractional nonlinear symmetric regularized long wave (SRLW) equation are
presented by using the Jacobi elliptic function expansion method. By this
method, the solutions are found in general form containing the hyperbolic,
trigonometric, and rational functions. Also, the complex valued solutions and
soliton solutions are obtained.
Keywords: Jacobi elliptic function, fractional differential equation, SRLW
equation
References:
[1] S. Ahmadian, M.T. Darvishi, New exact traveling wave solutions for space-
time fractional (1+1)-dimensional SRLW equation, Optik 127 (2016)
10697–10704.
[2] R. Abazari, Application of 𝐺′ 𝐺⁄ -expansion method to traveling wave
solutions of three nonlinear evolution equations, Comput. Fluids 39
(2010)1957–1963.
[3] F. Xu, Application of exp-function method to symmetric regularized long
wave (SRLW) equation, Phys. Lett. A 372 (2008) 252–257.
[4] H. Jafari, N. Kadkhoda, C.M. Khalique, Travelling wave solutions of
nonlinear evolution equations using the simplest equation method,
Computers and Mathematics with Applications 64 (2012) 2084–2088.
[5] J.F.Alzaidy, The fractional sub-equation method and exact analytical
solutions for some nonlinear fractional PDEs, American Journal of
Mathematical Analysis, 1 (1) 2013 14-19.
[6] O. Guner, D. Eser, Exact Solutions of the Space Time Fractional
Symmetric Regularized Long Wave Equation Using Different Methods
Advances in Mathematical Physics, 2014 Article ID 456804.
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54
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
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Functional Quadratic Integral Equations in the L1loc (R+) space
Latifa Benhamouche and Smail Djebali
Department of Mathematics, Faculty of Sciences, Saad Dahlab University
Blida, Algeria
Abstract : In this work we study the existence of solutions of functional
quadratic integral equations of Volterra type in the space L1loc (R+) consisting of
all real functions locally integrable on the positive real half axis. The main result
of this paper is obtained by using the new concept of family of measures of weak
noncompactness recenlty introduced by Olszowy in [1] a 2014 paper, which is
applied here in conjection with the Schawder- Tychonov fixed point theorem.
In fact many authors studied the solvability of different types of integral
equations on the Banach space BC (R+) consisting of all real functions defined,
bounded and continuous on the positive real half axis, while in some practical
situations integral equations are well understood in 𝐿1 settings see for example
Taoudi [3].
Recently in a 2015 paper [2], Wang and Zhou developed some fixed point
theorems in locally convex spaces with Krein-Smulian property. As an
application authors gave existence result in the space L1loc (R+) to a general
Volterra integral equation. Unfortunately the quadratic case is not covered by
their result. The quadratic case was followed with interest in [4] but only on
bounded intervals. In the present paper we focus on the question of existence of
solutions of functional quadratic integral equations on unbounded intervals.
References:
[1] L. Olszowy, A family of measures of noncompactness in the space L1loc (R+)
and its application to some nonlinear Volterra integral equation,Mediterr. J.
Math. 11, 2014, no. 2, 687--701.
[2] F. Wang, H. Zhou,Fixed point theorems and the Krein-Smulian property in
locally convex spaces, Fixed Point Theory Appl. 2015, 2015:154.
[3] N. Salhi and M.A Taoudi, Existence of integrable solutions of an integral
equation of Hammerstein type on unbounded interval, M. J of mathemathiques,
[4] A. Bellour, D. O'Regan, M.A. Taoudi, On the existence of integrable
solutions for a nonlinear quadratic integral equation, J. Appl. Math. Comput.
2014, 46:67-77.
______________________________________________________
55
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Suborbital Graphs for a Non-Transitive Action of the
Normalizer
Murat Besenk, Bahadır Ozgur Guler, Abdurrahman Buyukkaya
Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey
[email protected], [email protected], [email protected]
Abstract: The notion of suborbital graphs was introduced by Sims[6]. We can
summarize Sims’theory as follows: a permutation group G act on a set H,
suborbital graphs formed by this action with vertex-set H on which G induces
automorphisms. After it was shown that this idea is also useful in the study of the
modular group whichis a finitely generated Fuchsian group[3], some other
finitely generated groups have been studied by suborbital graphs[1,2,4]. In most
of them, it has been emphasized the connection between elliptic elements in
group and circuits of the same order in graph closely related with the signature
problem. It is known that the graph of a group provides a method by which a
group can be visualized; in many cases it suggests an economical algebraic proof
for a result and it gives same information but in a much more efficient way [5].
In this view, the idea of suborbital graph has been used mainly by finite group
theorists. The aim of this paper is to examine the action of the normalizer which
produce some congruence equations with solutions. Actually, the suborbital
graphs of the normalizer were studied for some special cases[2]. In here, taking a
different case, we obtained new results.
Keywords: Normalizer, Imprimitive action, Suborbital graphs.
References:
[1] M. Beşenk, “Circuit lengths of graphs for the Picard group”. J Inequal Appl
(2013), 106:8.
[2] B.O. Güler et al., “Elliptic elements and circuits in suborbital graphs”, Hacet
J Math Stat 40(2) (2011), 203–210.
[3] G.A. Jones, D. Singerman, K. Wicks, “The modular group and generalized
Farey graphs”, Lond Math Soc Lect Note Ser 160(1991), 316–338.
[4] S. Kader, B.O. Güler (2013) “On suborbital graphs for the extended modular
group”, Gr Comb, 29(2013), 1813–1825.
[5] M. Magnus, A. Karrass, D. Solitar, “Combinatorial group theory”. Wiley,
New York, (1966).
[6] C.C. Sims, “Graphs and finite permutation groups”, Math. Z. 95(1967), 76–
86.
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56
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
On Spherically Symmetric Solutions of the Einstein-Maxwell
Field Equations
Rashida Bibi and Azad A. Siddiqui
Department of Mathematics, School of Natual Sciences, National University of
Science and Technology (NUST),
Islamabad, Pakistan
Abstract: In literature many solution of the Einstein-Maxwell equations have
been found [1-8]. We consider the spherically symmetric geometry and classify
the solutions of the Einstein-Maxwell equations by considering the null/non-null
electromagnetic field and isotropic/anisotropic mater with the help of Segre type
of the spacetime.
Keywords: Einstein-Maxwell Equations, null/non-null Electromagnetic Field,
Segre Type, and Isotropic/Anisotropic geometry.
References:
[1] H. Stephani, D. Kramer, M. MacCallum and C. Hoenselaers, Exact Solutions
to Einstein Field Equations, (2009).
[2] C. B. G. Mclntosh, J. M. Foyster and A. W. C. Lun, The classi_cation of the
Ricci and Plebanski Tensors in General Relativity using Newman-Penrose
Formalism, J. Math. Phys., 22 (1980).
[3] Tooba Feroze. Exact solutions of the Einstein-Maxwell equations with linear
equation of state, Can.J.Phys (2012). 90 1179-1183.
[4] G. S. Hall, and D. A. Negm, Physical structure of the energy-momentum
tensor in General Relativity, Int. J. Theo Phys. Volume 25, (1986).
[5] Rashida Bibi, Tooba Feroze, and Azad A. Siddiqui, Solution of the Einstein–
Maxwell equations with anisotropic negative pressure as a potential model of a
dark energy star, Canadian Journal of Physics 2016.
[6] S. Thirukkanesh and S. D. Maharaj, Charged Anisotropic Matter with Linear
Equation of State, Class. Quant. Grav., 25 (2008).
[7] M. K. Mak and T. Harko, Quark Stars Admitting a One Parameter Group of
Conformal Motions, Int. J. Mod. Phys. D, 13 (2004).
[8] J. M. Sunzu, S. D. Maharaj and S. Ray, Quark Star Model with Charged
Anisotropic Matter, Astrophysics and Space Science, 354 (2014).
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57
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
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A Numerical Approximation Based on Collocation Method for
the Solutions of Telegraph Equation
Kübra Erdem Bicer
Department of Mathematics, Manisa Celal Bayar University,
Manisa, Turkey
Abstract: In this paper, a numerical method based on Bernoulli polynomials is
developed to solve telegraph equations. By using Bernoulli polynomials and
collocation points, the main problem is reduced to the system of algebric
equations, after evaluating some matrix operations. By solving this system, we
obtain the coefficients of approximate solutions of the main problem. And also to
demonstrate the validity and applicability of this method, an error analysis based
on residual function is developed and this method is applied to some examples.
Keywords: Telegraph Equations, Partial Differential Equations, Numerical
Methods, Bernoulli Polynomials.
References:
[1] H. M Lieberstein, “Theory of Partial Differential Equations”, Academic
Press, New York (1972).
[2] G . Doetsch, “Introduction to the Theory and Application of the Laplace
Transformation”, Springer, Berlin (1974).
[3] D. R. Bland, “Wave Theory and Applications”, Oxford Clarendon press,
London (1988).
[4] V. H. Weston and S. He, “Wave splitting of the telegraph equation in R3 and
its application to inverse scattering”, InverseProblems, 9 (1993), 789–812.
[5] P. M. Jordan and A . Puri, “Digital signal propagation in dispersive media”,
Journal of Applied Physics, 85.3 (1999), 1273–1282.
[6] J. Banasiak and J. R. Mika, “Singular perturbed telegraph equations with
applications in the random walk theory” Journal of Applied Mathematics and
Stochastic Analysis, 11.1(1998), 9–28.
[7] P. R. Wallace, “Mathematical Analysis of Physical Problems”, Dover, New
York (1984).
[8] L. Debnath and P. Mikusinski, “Introduction to Hilbert Spaces with
Applications”, Elsevier Academic Press, London (2005).
______________________________________________________
58
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Rotating Disk Cryptosystem: RDC
Sadek Bouroubi and Louiza Rezkallah
Department of Mathematics, USTHB University,
Bab Ezzoua, Algier, Algeria
Abstract: Cryptography is a hot and active topic, it plays a crucial role in many
aspects nowadays, from internet banking and e-commerce to email and
webbased business processes. An important area of research today is to test the
security of cryptosystems, a cryptographic system is safe as long as no one could
not break it. Modern cryptographic algorithms are based on mathematical
problems, known to be difficult, so breaking the security of a cryptosystem
requires the solution of a such problem, as in the case of RSA [1] which is based
on the factorization problem in number theory. This paper proposes a symmetric-
key cryptosystem named Rotating Disk Cryptosystem and is denoted as RDC
used for encryption and decryption of text as well as images which is based on
chaotic function and the factorization problem.
Keywords: Rotating Disk, Symmetric-key Cryptosystem, Chaotic function,
Linear Congruential Generator Modified, Factorization Problem.
References:
[1] R. Rivest, A. Shamir and L. Adleman, « A Method for Obtaining Digital
Signatures and Public-Key Cryptosystems », Communications of the ACM, vol.
21, no 2, 1978, p. 120-126.
[2] Arjen K. Lenstra and H. W. Lenstra, Jr. (eds.). "The development of the
number field sieve". Lecture Notes in Math. (1993) 1554. Springer-Verlag.
[3] Laurence T. Yang, Li Xu, Sang-Soo Yeo, Sajid Hussain, An integrated
parallel GNFS algorithm for integer factorization based on Linbox Montgomery
block Lanczos method over GF(2). Computers Mathematics with Applications,
Volume 60, Issue 2, July 2010, Pages 338–346.
[4] Delfs, Hans Knebl, Helmut (2007). "Symmetric-key encryption".
Introduction to cryptography: principles and applications. Springer. ISBN
9783540492436
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Free Convection inside a Porous Enclosure
Canan Bozkaya
Department of Mathematics, Middle East Technical University,
Ankara, Turkey
Abstract: The steady free convection in a rectangular enclosure filled with a
fluid-saturated porous medium is numerically investigated in the present study.
The left vertical wall of the enclosure is maintained at a temperature greater than
the temperature of the right vertical wall. The top and bottom horizontal walls of
the enclosure are adiabatic. The incompressible, laminar flow inside the
homogeneous and isotropic porous medium is assumed to obey Darcy law. The
fluid physical properties are constant except the density in the body force term
which is treated according to Boussinesq approximation. The fluid and porous
medium are in thermal equilibrium, and the thermal radiation flux in y-direction
is considered negligible compared to that in x-direction. Thus, the temperature
gradient in x-direction is higher than that in y-direction. For this reason, the
thermo-diffusion velocity only in the x-direction is considered. The governing
equations, obtained under these assumptions, in non-dimensional stream function
and temperature formulation are solved using the dual reciprocity boundary
element method (DRBEM). Dual reciprocity BEM aims to transform the
differential equations into equivalent integral equations only on the boundary of
computational domain by treating the nonhomogeneity through a radial basis
function approximation. The stream function equation is solved by DRBEM in
the usual way, that is by using the fundamental solution of the Laplace equation.
On the other hand, the fundamental solution to the modified diffusion
(Laplacian) term in the energy equation (that is, the coefficients of the second
order derivatives in x- and y-directions are not equal due to higher thermal
radiation in x-direction) is used, and moreover the corresponding radial basis
functions for the modified diffusion equation are derived. The results of the
present numerical model is compared with previously published works. The
validated model is employed to investigate the effect of the physical parameters,
namely Rayleigh number and radiation parameter, on the flow and heat transfer
characteristics.
Keywords: Free convection, porous medium, thermal radiation, DRBEM.
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60
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Tauberian Theorems for the Cesáro Second Order Operators
for Sequences of Fuzzy Numbers
Naim L. Braha
Department of Mathematics and Computer Sciences
University of Prishtina, Avenue Mother Teresa, No-4, Prishtine, 10000, Kosova
Abstract: In this paper we define the Cesáro second order summability method
for fuzzy numbers and prove some theorems dealing with weighted statistical
converge of fuzzy numbers and their behaviors. In second section we prove
Tauberian theorems for this kind of summability method and in the end of the
paper we prove Tauberian theorems, related to the Cesáro second order mean-
level convergence.
Keywords: Cesáro second order summability method, Tauberian theorems.
References:
[1] Y. Altin; M. Mursaleen, H. Altinok, Statistical summability $(C,1)$ for
sequences of fuzzy real numbers and a Tauberian theorem, Journal of Intelligent
and Fuzzy Systems 21 (2010) 379-384.
[2]S. Aytar; M. A. Mammadov and S. Pehlivan, Statistical limit inferior and
limit superior for sequences of fuzzy numbers, Fuzzy Sets and Systems 157(7)
(2006), 976-985.
[3] B. Bede and S. G. Gal, Almost periodic fuzzy number valued functions,
Fuzzy Sets and Systems 147 (2004), 385-403.
[4] Braha, Naim L. Geometric properties of the second-order Ces\'aro spaces.
Banach J. Math. Anal. 10 (2016), no. 1, 1-14.
[5] N. L. Braha, Tauberian conditions under which $\lambda -$statistical
convergence follows from statistical summability $(V,\lambda ),$ Miskolc Math.
Notes 16(2) (2015), 695-703.
[6] N.L. Braha and Mikail Et, Tauberian theorems for the Euler-N\"orlund mean-
convergent sequences of fuzzy numbers, to appear in Iranian Journal of Fuzzy
Systems.
[7N.L. Braha, Tauberian Theorems under N\"orlund-Ces\'aro summability
methods (357-411), Current Topics in Summability Theory and Applications,
editors, Hemen Dutta and Billy E. Rhoades, Springer, 2016.
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61
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Estimating the Distortion Parameter of the Proportional
Hazards Premium for Heavy-Tailed Losses
Brahimi Brahim
Laboratory of Applied Mathematics, Mohamed Khider University, Biskra,
Algeria.
Abstract: Estimating the distorted parameter in the case of non negative heavy-
tailed losses has been treated in [1]. In this paper, we extend this work to the case
of the real heavy-tailed losses. We derive an asymptotic distribution of the
estimator. We construct a practically implemented confidence interval for the
distortion parameter and illustrate the performance of the interval in a simulation
study with application to real data.
Keywords: Proportional-hazard premium; Distortion risk measure; Distortion
parameter; Extreme value; Heavy tail; Risk aversion index; Lévy-stable
distribution.
References:
[1] Brahimi, B., Meraghni, D., Necir, A. and Zitikis, R., (2011). Estimating the
distortion parameter of the proportional-hazard premium for heavy-tailed losses.
Insurance Math. Econom. 49, 325-334.
[2] Brahimi, B; Abdelli, J., (2016). Estimating the distortion parameter of the
proportional hazards premium for heavy-tailed losses under Lévy-stable
regime.Insurance Math. Econom. 70 (2016), 135--143.
[3] Hill, B.M., (1975). A simple approach to inference about the tail of a
distribution. Ann. Statist. 3, 1136-1174.
[4] Necir, A. and Meraghni, D., (2010). Estimating L-functionals for Heavy-
tailed Distributions and Applications. Journal of Probability and Statistics.
Volume 2010, ID 707146.
[5] Necir, A., Rassoul, A., Zitikis, R., (2010). Estimating the conditional tail
expectation in the case of heavy-tailed losses. Journal of Probability and
Statistics 2010, ID 596839.
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62
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
On Some Fixed Point Results Related to Almost Generalized
(𝜶, 𝜷) − (𝝍, 𝝓) −Weakly Contractive Mappings in 𝑺 Metric
Spaces
Abdurrahman Buyukkaya1, Mahpeyker Ozturk2
1Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey 2Department of Mathematics, Sakarya University, Sakarya, Turkey
[email protected], [email protected]
Abstract: In this paper, we establish some fixed and common fixed point
theorems by using almost generalized (𝛼, 𝛽) − (𝜓, 𝜙) −weakly contractive
mappings in the settings of 𝑆 metric spaces, which given results are
generalizations of some existing literature.
Keywords: Fixed Point, Almost Contraction, Admissible Mappings, S Metric
Spaces.
References:
[1] L. Ciric, M. Abbas, R. Saadati and N. Hussain, Common fixed points of
almost generalized contractive mappings in ordered matric spaces , Appı. Math.
Comput. 217(2011), 5784-5789.
[2] M. Abbas, G. V. R. Babu, and G. N. Alemayehu, On common fixed of
weakly compatible mappings satisfying generalized condition (B), Filomat,
25(2) (2011), 9-19.
[3] S. Alizadeh, F. Moradlou, P. Salimi, Some fixed point results for
(Alpha,Beta)-(Psi,Phi)-conrtactive mappings, Filomat, 28(3) (2014) 635-647.
[4] S. Sedghi, N. Shobe, S. Aliouche, A generalization of fixed point theorems S
metric spaces, Matematicki Vesnik, 64(3) (2012), 258-266.
[5]O. Yamaod, W. Sintunavarat, Some Fixed Point Results for Generalized
Contraction with Cyclic (Alpha,Beta)-admissible Mapping in Multiplicative
Metric Spaces, Journal of Inequalities and Applications, 488 (2014), 1-15.
[6]S. Sedghi, N. V. Dung, Fixed point theorems on S metric spaces, Matematicki
Vesnik, 66(1) (2014), 113-124
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63
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Beyond Statistical Quasi Cauchy Sequences
Huseyin Cakalli
Maltepe University, Graduate School of Science and Engineering, Marmara
Egitim Koyu, TR 34857,Maltepe, Istanbul, Turkey
Abstract: A sequence (αk) is called -statistically downward quasi-Cauchy if
limn (1/n)|k≤n: k+1-k|=0 for every >0, where (n) is a non-decreasing
sequence of positive real numbers tending to such that limsupn (n) /n )<,
n =O(1), and αk =αk+1 – αk for each positive integer k. A real valued function
defined on a subset of the set of real numbers is -statistically downward
continuous if it preserves -statistically downward quasi-Cauchy sequences, i.e.
(f(k)) is -statistically downward quasi-Cauchy whenever (k) is. It turns out
that the set of -statistical downward continuous functions defined on an above
bounded set is a proper subset of the set of uniformly continuous fonctions.
Keywords: statistical convergence, -statistical downward quasi Cauchy
sequence,.
References:
[1] D. Burton, J. Coleman, “Quasi-Cauchy sequences”, Amer. Math. Monthly,
117 (2010), 328-333.
[2] H.Cakalli, “Forward continuity”,J. Comput. Anal. Appl.,13 2(2011),225-230.
[3] H. Cakalli, “Statistical ward continuity”, Appl. Math. Lett., 24 10 (2011),
1724-1728.
[4] H. Cakalli, “Statistical quasi-Cauchy sequences”, Math. Comput. Modelling,
54 (2011), 1620-1624.
[5] H. Cakalli, “A Variation on Statistical Ward Continuity”, Bull. Malays.
Math. Sci. Soc., DOI 10.1007/s40840-015-0195-0
[6] H.Cakalli,”Upward and downward statistical continuities”, Filomat, 29 10
(2015), 2265-2273.
[7] H.Cakalli, and H. Kaplan, “A study on N-theta-quasi-Cauchy sequences”,
Abstr. Appl. Anal, 2013 (2013), Article ID 836970, 4 pages.
[8] H. Cakalli, and H. Kaplan, “A variation on lacunary statistical quasi cauchy
sequences”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 66 2 (2017),1-9
[9] H. Cakalli, and M.K. Khan, “Summability in topological spaces”, Appl.
Math. Lett., 24 (2011), 348-352.
______________________________________________________
64
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
A Study on Strongly Lacunary Ward Continuity
Huseyin Cakalli*, Huseyin Kaplan**
* Maltepe University, GraduateSchool of Science and Engineering,
Marmara Egitim Koyu, Maltepe, Istanbul, Turkey
** Niğde University, Faculty of Science and Letters, Niğde, Turkey
Abstract: In this paper, the concept of a strongly lacunary 2-quasi-Cauchy
sequence is investigated. In this investigation, we proved interesting theorems
related to strongly lacunary 2-ward continuity, and some other kinds of
continuities, introducing strongly lacunary 2 ward continuity in the sense that a
real valued function f defined on a subset A of IR, the set of real numbers, is
strongly lacunary 2 ward continuous on A if it preserves strongly lacunary 2
quasi-Cauchy sequences of points in A, i.e. (f(αk)) is a strongly lacunary 2
quasi-Cauchy sequence whenever (αk) is a strongly lacunary 2 quasi-Cauchy
sequences of points in A, where a sequence (αk) is called strongly lacunary 2
quasi-Cauchy if (2 αk) is a strongly lacunary quasi-Cauchy sequence where 2
αk= αk+2 -2 αk+1 + αk for each positive integer k.
Keywords: Summability; series and sequences; continuity and related questions.
References: [1] D. Burton, and J. Coleman, “Quasi-Cauchy Sequences”, Amer. Math.
Monthly, 117 4 (2010), 328-333.
[2] Naim L. Braha, H. Cakalli, “A new type continuity for real functions”, J
Math. Analysis.7 6 (2016), 54-62.
[3] H. Cakalli, “On G-continuity”, Comput. Math. Appl., 61 (2011), 313-318.
[4] H. Cakalli, “N-theta-Ward continuity”, Abstr. Appl. Anal,. 2012 Article ID
680456 (2012), 8 pp.
[5] H. Cakalli, “A variation on arithmetic continuity”, Bol. Soc. Paran. Mat., 35
3 (2017), 195-202.
[6] H. Cakalli, C. Gunduz Aras and A. Sonmez, “Lacunary statistical ward
continuity”, AIP Conf. Proc. 1676, 020042 (2015)
______________________________________________________
65
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
A Study on Abel Statistical Quasi Cauchy Sequences
Huseyin Cakalli*, Iffet Taylan**
* Maltepe University, Graduate School of Science and Engineering, Marmara
Egitim Koyu, Maltepe, Istanbul, Turkey
** Maltepe University, Education Faculty, Maltepe, Istanbul, Turkey
Abstract: In this paper, we investigate the concepts of Abel statistical
convergence and Abel statistical quasi Cauchy sequences. We also study Abel
statistical continuity and Abel statistical ward continuity. A real valued function f
is Abel statistically continuous on a subset E of IR, the set of real numbers, if it
preserves Abel statistical convergent sequences, i.e. (f (pk)) is Abel statistically
convergent whenever (pk) is an Abel statistical convergent sequence of points in
E. Some other types of continuities are also studied and interesting results are
obtained.
Keywords: Statistical Convergence; Abel series method; continuity.
References:
[1] D. Burton, J. Coleman, “Quasi-Cauchy sequences”, Amer. Math. Monthly,
117 (2010), 328-333.
[2] H. Cakalli, “A study on statistical convergence”, Funct. Anal. Approx.
Comput.1 2 (2009) , 19–24.
[3] H. Cakalli, “Forward continuity”, J. Comput. Anal. Appl., 13 2 (2011), 225-
230.
[4] H. Cakalli, “Statistical ward continuity”, Appl. Math. Lett., 24 10 (2011),
1724-1728.
[5] H. Cakalli, “Statistical quasi-Cauchy sequences”, Math. Comput. Modelling,
54 (2011), 1620-1624.
[6] H. Cakalli, “On G-continuity”, Comput. Math. Appl. 61 (2011), 313-318.
[7] H. Cakalli, “A variation on arithmetic continuity”, Bol. Soc. Paran. Mat. 35 3
(2017), 195-202.
[8]H. Çakallı and M. Albayrak, “New Type Continuities via Abel Convergence”,
Scientific World Journal, 2014 (2014), Article ID 398379, 6 pages.
______________________________________________________
66
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Graph Theoretical Applications of Molecular Graphs
Ismail Naci Cangul
Department of Mathematics, Uludag University,
Bursa, Turkey
Joint work with Aysun YURTTAS, Muge TOGAN, Ahmet Sinan CEVIK
Abstract: Most of the papers on graph theory published recently deal with
molecular graphs due to their intensive applications in chemistry and
pharmacology. In this paper we give some applications of topological graph
indices in these two areas.
Keywords: Molecular graph, topological graph index.
References:
[1] K. Ch. Das, N. Akgunes, M. Togan, A. Yurttas, I. N. Cangul, A. S. Cevik, On
the first Zagreb index and multiplicative Zagreb coindices of graphs, Analele
Stiintifice ale Universitatii Ovidius Constanta 24 (1) (2016)
[2] K. C. Das, K., Xu, I. N., Cangul, A. S., Cevik, A., Graovac, On the Harary
Index of Graph Operations, Journal of Inequalities and Applications, SI: Recent
Advances in General Inequalities, DOI: 10.1186/1029-242X-2013-339, 2013,
[3] K. Ch. Das, A. Yurttas, M. Togan, I. N. Cangul, A. S. Cevik, The
multiplicative Zagreb indices of graph operations, Journal of Inequalities and
Applications, (2013), 1-14.
[4] I. Gutman, N. Trinajstic, Graph theory and molecular orbitals III, Total $\pi$-
electron energy of alternant hydrocarbons, \textitChem. Phys. Lett.,
\textbf17 (1972), 535-538.
[5] H. Hosoya, K. Kawasaki, K. Mizutani, 1972, Topological index and
thermodynamic properties: Empirical rules on the boiling point of saturated
hydrocarbons, Bull. of the Chem. Soc. of Japan, 45, 3415.
[6] H. Wiener, 1947, Correlation of heats of isomerization and differences in
heats of paraffin hydrocarbons, J. of the American Chemical Society, 69, 2636
[7] H. Wiener, 1947, Structural determination of parafin boiling points, J. of the
American Chemical Society, 69, 17
[8] N. Trinajsti?, Chemical graph theory, vols. I and II, CRC, Boca Raton, FL,
1983
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67
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
A Study on Public Transit Users’ Route Choice and
Assignment Function
Buket Capali1, Halim Ceylan2
1Department of Civil Engineering, Faculty of Engineering, Süleyman Demirel
University, Isparta, Turkey 2Department of Civil Engineering, Faculty of Engineering, Pamukkale
University, Denizli, Turkey
Abstract: Many passengers wants to travel between two points from point A to
point B, the next step is to determine the routes to reach their destination. This
determination relies on passenger behavior. When there are more than two routes
to travel, a rate representing the amount of interest in the travel assignment
process for the different transit routes is determined. In this study; a new formula
for transit users’ route choice and assignment, which includes travel demand and
waiting time, has been developed.
Keywords: Public transportation, route choice, transit assignment.
______________________________________________________
68
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
A New Developed Semi–Empirical Formula for Nuclear
Reaction Cross–Section Calculations
Veli Capali1, Mert Sekerci1, Hasan Ozdogan2, Abdullah Kaplan1
1Department of Physics, Süleyman Demirel University, Isparta, Turkey
2Department of Biophysics, Akdeniz University, Antalya, Turkey
Abstract: In this study; a new semi–empirical formula for reaction cross–section
calculations, which includes inelastic scattering and Coulomb effects, has been
developed. The cross–sections and asymmetry parameters are dependent on
target nuclei and the selected energies which are 10-11, 18-19 and 22-23 MeV.
The reaction cross–section calculations have been performed for (p,n) reaction
for sample materials. The cross–section values calculated from developed semi–
empirical formula have been compared with the experimental values exist in the
literature and nuclear reaction models’ computation results.
Keywords: Semi–Empirical Formula, Nuclear Cross–Section, Asymmetry
Parameter.
______________________________________________________
69
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
On Uninorms on Bounded Lattices
Gül Deniz Cayli and Funda Karacal
Department of Mathematics, Faculty of Sciences, Karadeniz Technical
University, 61080, Trabzon, Turkey
Abstract: The triangular norms (t-norms) with 1 as neutral element and
triangular conorms (t-conorms) with 0 as neutral element were introduced by
Schweizer and Sklar in [14]. Uninorms that were introduced by Yager and
Rybalov in [15] are generalization t-norms and t-conorms. These operators allow
the freedom for the neutral element e (sometimes called identity) to be an
arbitrary element from unit interval [0,1], which is 1 for t-norms and 0 for t-
conorms. In [11] the existence of uninorms on an arbitrary bounded lattice 𝐿 for
the neutral element e to be an arbitrary element from 𝐿 ∖ 0,1 has been shown.
As a by-product, it has been demonstrated that the existence of the smallest
uninorm and of the greatest uninorm on L with a fixed neutral element 𝑒 ∈ 𝐿 ∖
0,1. In [6] the existence of idempotent uninorms on given bounded lattice L for
any element 𝑒 ∈ 𝐿 ∖ 0,1 playing the role of a neutral element has been proved.
By this construction method, the smallest idempotent uninorm and the greatest
idempotent uninorm with the neutral element 𝑒 ∈ 𝐿 ∖ 0,1 is obtained. In this
paper, we study uninorms on bounded lattices and investigate some properties of
these operators. By considering the existence of t-norms and t-conorms on an
arbitrary bounded lattice L, we give methods of constructing uninorms with
given neutral element 𝑒 ∈ 𝐿 ∖ 0,1. And we consider some special classes of t-
norms and t-conorms by using the presence of uninorms on arbitrary bounded
lattice L with a fixed neutral element 𝑒 ∈ 𝐿 ∖ 0,1.
Keywords: Uninorm, Bounded lattice, T-norm, T-conorm.
References:
[1] E. Aşıcı, F. Karaçal, “On the T -partial order and properties”, Inf. Sci.
267(2014), 323-333.
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70
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
[2] E. Aşıcı, F. Karaçal, “Incomparability with respect to the triangular order”,
Kybernetika 52(2016), 15-27.
[3] G. Birkhoff, “Lattice Theory”, American Mathematical Society Colloquium
Publishers, Providence, RI, 1967.
[4] B. De Baets, “Uninorms: the known classes”, Third Internat FLINS
Workshop in Fuzzy Logic and Intelligent Technologic, 1998.
[5] S. Bodjanova, M. Kalina, “Construction of uninorms on bounded lattices”,
IEEE 12th International Symposium on Intelligent Systems and Informatics,
SISY 2014, September 1113, 2014, Subotica, Serbia.
[6] G.D. Çaylı, F. Karaçal, R. Mesiar, “On a new classes of uninorms on
bounded lattices”, Inf. Sci. 367–368(2016), 221-231.
[7] G. Deschrijver, “Uninorms which are neither conjunctive nor disjunctive in
interval-valued fuzzy set theory”, Inf. Sci. 244(2013), 48-59.
[8] P. Drygaś, “On properties of uninorms with underlying t-norm and t-conorm
given as ordinal sums”, Fuzzy Sets Syst. 161(2010), 149-157.
[9] P. Drygaś, D. Ruiz-Aguilera, J. Torrens, “A characterization of uninorms
locally internal in A(e) with continuous underlying operators”, Fuzzy Sets Syst.
287 (2016), 137-153.
[10] J.Fodor, R.R. Yager, A. Rybalov, “Structure of uninorms,” Internat J.
Uncertain Fuzziness Knowledge-Based Systems, 5(1997), .411-427.
[11] F. Karaçal, R. Mesiar, “Uninorms on bounded lattices”, Fuzzy Sets Syst.
261(2015), 33-43.
[12] J. Martin, G. Mayor, J. Torrens, “On locally internal monotonic operations”,
Fuzzy Sets Syst. 137(2003), 27-42
[13] R. Mesiar, E. Pap, “Different interpretations of triangular norms and related
operations”, Fuzzy Sets Syst. 96(1998), 183-189.
[14] B.Schweizer, A.Sklar, “Statistical metric spaces”, Pacific J. Math, 10(1960),
313-334.
[15] R.R. Yager, A. Rybalov, “Uninorms aggregation operators”, Fuzzy Sets
Syst. 80(1996), 111-120.
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71
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
On Statistical Dunford and Pettis Integration
Anita Caushi
Department of Mathematical Engineering, Polytechnic University of Tirana
Mother Teresa Square nr.4, Tirana, Albania
Abstract: Pettis and Dunford integrals are more important concepts with respect
to modern theory of probabilities. We can find them in the definitions of
mathematical expectation as well as dispersion. Some random probailitary
funktions take the value on vectorial spaces.In this paper we extend the usual
concept of Dunford and Pettis integration to a statistical form. We give some
essential properties of them and give an example where we find one function that
is statistical Dunford integrable but not Pettis integrable. We obtain some special
properties of statistical Pettis integration which are well known for usual the
Pettis integration.
References:
[1] Bhardwaj V., Balai., On Ëeakly Statistical Convergence, international
Journal of Mathematics and Mathematical Sciences, 2007, Article iD 38530, 9p
[2] Çakalli H., A study on statistical convergence. Functional analysis,
approximation and computation 1:2(2009), 19-24
[3] Caushi, A., Tato, A., A statistical integral of Bohner type on Banach space,
Hikari Ltd Appl. Math. Sci., Vol. 6, 2012, no. 137-140, 6857-6870.
[4] Connor J., Ganichev M., and Kadets V., “A characterization of Banach
spaces ëith separable duals via weakly statistical convergence,” Journal of
Mathematical Analysis and Applications, vol. 244, no. 1, pp. 251–261, 1989.
[5] Fast H., “Sur la convergence statistique,” ColloquiumMathematicum, 2,1951.
[6] Fridy J. A., “On statistical convergence,”Analysis, 5-4, 301-313, 1985.
[7] Fridy J. A., “Statistical limit points,” Proceedings of the American
Mathematical Society, vol. 118, no. 4, pp. 1187–1192, 1993.
[8] Schoenberg i. J., “The integrability of certain functions and related
summability methods,” The American Mathematical Monthly, 66, 5, 1959.
[9] Schëabik S., Guoju Y., Topics in Banach space integration, Series in
Analysis vol. 10. Ëorld Scientific Publishing Co. Singapore 2005.
[10] Steinhaus H., “Sur la convergence ordinaire et la convergence
asymptotique,” Colloquium Mathematicum, vol. 2, pp. 73–74, 1951.
[11] Zygmund A., Trigonometric Series, Cambridge University Press,
Cambridge, UK, 1979
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72
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
On The Cardinality of Category Spaces
Bahaettin Cengiz1, Banu Gunturk2
1Faculty of Engineering, Baskent University,
Ankara, Turkey
2Faculty of Engineering, Baskent University,
Ankara, Turkey
Abstract: We call a compact Hausdorff space Ω a category space if C(Ω), the
space of all scalar-valued continuous functions, is a dual space. Category spaces
are necessarily extremally disconnected, and on such a space there always exists
an essentially unique category (or perfect) Borel measure. If one of the category
measures on a category space is σ-finite, then so are the rest. These measures
play a crucial role in determining the greatest lower bound for the cardinalities of
infinite category spaces. In this paper, among other things, it is proved that for
any infinite category space Ω, card(Ω) ≥ 2c if the category measure is σ-finite,
and 22ℵ1 otherwise, where c is the cardinality of the continuum, ℵ1 is the first
uncountable cardinal number, and for any infinite cardinal number ℵ, 2ℵ denotes
the cardinality of the power set of a set of cardinality ℵ. Both of the above
mentioned cardinal numbers are actually attained.
Keywords: Category space, cardinality, dual space.
______________________________________________________
73
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Remarks and Observations on Some Special Arithmetical Sums
1Elif Cetin and 2Yilmaz Simsek
1Department of Mathematics, Faculty of Art and Science, University of Manisa
Celal Bayar, Manisa, Turkey, 2Department of Mathematics, Faculty of Science University of Akdeniz TR-
07058,
Antalya, Turkey. [email protected] , [email protected]
Abstract: In this talk, we investigate some properties of the Dedekind sums and
Hardy sums. These sums are used commonly not only in analytic number theory,
but also in other areas of mathematics. The Dedekind sums arise in the
behaviour of the Dedekind eta functions under the modular groups. On the other
hand, the Hardy sums arise in the behaviour of the Theta functions under the
subgroups of the modular groups. Recently, many authors give relation between
the Dedekind sums and geometry (lattice point enumeration in polytopes,
topology (signature defects of manifolds), algorithmic complexity (pseudo
random number generators), character theory, the family of zeta functions, the
Bernoulli and Euler functions. Moreover, we give some applications of the
special arithmetic sums related to the Hardy sums, the Dedekind sums and the
other special arithmetical sums.
Keywords: Dedekind sums, Hardy-Berndt sums, Generating functions,
Bernoulli numbers and polynomials.
References:
[1] T. M. Apostol, “Introduction to Analytic Number Theory”, Springer-Verlag,
New York, USA (1976), 340pp.
[2] B.C. Berndt, “Analytic Eisenstein series, Theta-functions, and series relations
in the spirit of Ramanujan”, J. Reine Angew. Math. 303/304(1978), 332-365.
[3] E. Cetin, Y. Simsek and I.N. Cangul, “Some special finite sums related to the
three-term polynomial relations and their applications”, Adv. Difference. Equ.,
283(2014), 1-18.
[4] E. Cetin, “A Note on Hardy type Sums and Dedekind Sums”, FILOMAT,
30.4(2016), 977-983.
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PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
S-Generalized Mittag-Leffler Function
Aysegul Cetinkaya, I. Onur Kiymaz, M. Baki Yagbasan
Department of Mathematics, Ahi Evran University,
Kırşehir, Turkey
Abstract: In this study, we introduced a new generalization of Mittag-Leffler
function by using S-generalized beta function. Furthermore, we investigated some
of its properties such as integral representations, recurrence formulas, derivative
formulas and Mellin transform.
Keywords: S-Generalized Beta function, Mittag-Leffler function, Mellin
transform.
Acknowledgement: This work was supported by Ahi Evran University Scientific
Research Projects Coordination Unit. Project Number: FEF.A3.16.035
References:
[1] Agarwal, P.,Choi, J.,Paris,R.B.“Extended Riemann-Liouville fractional
derivative operator and its applications”,J.Nonlinear Sci.Appl,8,(2015): 451-466.
[2]Chaudhry M. A., Qadir A., Rafique M., Zubair S. M., “Extension of Euler's
beta function”, J. Comput.Appl. Math., 78, (1997): 19-32.
[3] Luo, Min-Jie, Milovanovic, G. V., Agarwal, P., “Some results on the
extended beta and extended hypergeometric functions”, Applied Mathematics
and Computation, 248, (2014): 631-651.
[4] Prabhakar, T. R. “A singular integral equation with a generalized Mittag
Leffler function in the kernel”, Yokohama Math. J., 19, (1971): 7-15.
[5] Srivastava, H. M., Agarwal, P., Jain S., “Generating functions for the
generalized Gauss hypergeometric functions”, Applied Mathematics and
Computation, 247, (2014): 348-352.
[6] Srivastava, H. M., Jain, R., Bansal, M. K. “A Study of the S-Generalized
Gauss Hypergeometric Function and Its Associated Integral Transforms”,
Turkish Journal of Analysis and Number Theory, 3.5, (2015): 116-119.
[7] Srivastava, H. M., Manocha, H.L., “A Treatise on Generating Functions”,
Halsted, New York (Ellis Horwood, Chichester), (1984).
[8] Özergin, E., Özarslan, M. A., Altın, A., “Extension of gamma, beta and
hypergeometric functions”, Journal of computational and applied mathematics,
235.16 (2011): 4601-4610.
[9] Özarslan, M. A., Yılmaz, B. “The extended Mittag-Leffler function and its
properties”, Journal of Inequalities and Applications, 2014.1, (2014): 85.
______________________________________________________
75
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Jacobi Elliptic Function Solutions of Time-Fractional Kdv-
Zakharov-Kuznetsov Equation
Sevil Culha, Dilek Varol Bayram, Aysegul Dascioglu
Department of Mathematics, Faculty of Science and Arts, Pamukkale University
Denizli, Turkey [email protected]
Abstract: In this study, new analytical exact solutions of the nonlinear evolution
equation in mathematical physics, namely the conformable time-fractional KdV–
Zakharov–Kuznetsov (KdV–ZK) equation are presented by using the Jacobi
elliptic function expansion method.
Keywords: Jacobi elliptic function, fractional differential equation, KdV- ZK
equation.
References:
[1] R.L. Mace, M.A. Hellberg, The Korteweg–de Vries–Zakharov–Kuznetsov
equation for electron-acoustic waves, Phys. Plasmas 8 (6) (2001) 2649–
2656.
[2] M.H. Islam, K. Khan, M.A. Akbar, M.A. Salam, Exact traveling wave
solutions of modified KdV–Zakharov–Kuznetsov equation and viscous
Burgers equation, Springer Plus 3 (105) (2014) 1–9.
[3] T. Abdeljawad, On conformable fractional calculus, Journal of
Computational and Applied Mathematics 279 (2015) 57–66.
[4] H. Naher, F.A. Abdullah, M.A. Akbar, Generalized and improved (𝐺’/𝐺)-
expansion method for (3+1)-dimensional modified KdV–Zakharov–
Kuznetsov equation, PLoS One 8(5) (2013) 1–7.
[5] K. Khan, M. A. Akbar, Exact and solitary wave solutions for the Tzitzeica–
Dodd–Bullough and the modified KdV–Zakharov–Kuznetsov equations
using the modified simple equation method, Ain Shams Engr J 4(4) (2013)
903–909.
[6] S. T. Mohyud-Din, A. Irshad, On exact solutions of modified KdV-ZK
equation, Alexandria Engineering Journal (55) (2016) 3253-3265.
[7] E. M. E. Zayed, New traveling wave solutions for higher dimensional
nonlinear evolution equations using a generalized (𝐺′ 𝐺⁄ )-expansion
method Journal of Physics A: Mathematical and Theoretical (42) (2009).
______________________________________________________
76
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
A Fix-And-Optimize Heuristic for the Integrated Fleet Sizing
and Replenishment Planning Problem with Predetermined
Delivery Frequencies
Niousha Karimi Dastjerd, Kadir Ertogral
Department of Industrial Engineering, TOBB University of Economics and
Technology,
Sogutozu, Ankara, Turkey
[email protected], [email protected]
Abstract: We tackled an integrated fleet sizing and replenishment planning
problem in a vendor managed inventory system. There is a set of customers
which must be replenished based on a given set of predetermined frequencies.
The vehicle fleet consists of multiple types of heterogeneous vehicles which
differ in carrying capacity, cost per kilometer, and ownership costs. Customer
demands are taken as deterministic values. The main decision we make in this
problem is the triple asignment of vehicle-frequency-customer. As a result of
these assignment decisions, we obtain an annual costs consisting of vehichle
ownership cost, routing cost, inventory holding and fixed replenishment costs. A
key simplification in the model is the use of linear approxiamation for the
routing cost based on the number of customers visited in a tour. The developed
model, which is new in the literature, integrates fleet sizing and replenishment
planning decisions.
Our problem is NP-hard since it can be shown that a special case of our problem
is a bin packing problem. In order to solve large problems efficiently, we
suggested and applied a fix and optimize heuristic as a solution procedure. This
fix and optimize heuristic divides the problem into smaller problems in which
some variables are binaries and the others are linearly relaxed, and it fixes the
linear decision variable iteratively. We also showed the effectiveness of the
suggested heuristic solution procedure on a large set of randomly generated
problems.
Keywords: Fleet sizing, Replenishment planning, Predetermined frequencies,
Fix and Optimize
______________________________________________________
77
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Catalogue of Degree Sequences of Molecular Graphs
Sadik Delen, Ismail Naci Cangul
Department of Mathematics, Uludag University,
Bursa, Turkey
[email protected], [email protected]
Abstract: Molecular graphs are those graphs which are trees with vertex degrees
at most 4. They have applications in chemistry and pharmacology. In this paper
we give the catalogue of all molecular graphs and give results on their
classification.
Keywords: Molecular graph, degree sequences.
References:
[1] B. Bollobas, Degree sequences of random graphs, Discrete Mathematics 33
(1981), 1-19.
[2] Delen, S., Cangul, I. N., Algebraic Properties of Some Graph Operations in
Terms of Degree Sequences, (preprint)
[3] Delen, S., Cangul, I. N., Degree Sequences of Join and Corona Products of
Graphs, (preprint)
______________________________________________________
78
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Streamline Topology of Vortex Breakdown Bubbles near the
Re-Entrant Corner
Ali Deliceoglu 1 and Ebutalib Celik 2
1Erciyes University, Kayseri, Turkey,
[email protected] 2Erciyes University, Kayseri, Turkey,
Abstract: In this paper, topological bahavior of a viscous flow near a re-entrant
corner is studied. The method derived in this paper is intended to clarify the
understanding flow structures near the re-entrant corner. A numerical-asymptotic
matching solution for computing the local singular behavior of a viscous flow
around a re-entrant corner is developed. The theory is applied to the vortex
brakdown bubbles found numerically in an L-shaped cavity.
Keywords: Vortex Breakdown, Flow structure, Bifurcations.
Research supported by the TUBITAK under Grant No: 114F525
References:
[1] Deliceoğlu, A. and Aydın, S.H., “ Flow bifurcation and eddy genesis in an L-
shaped cavity” . Computers and Fluids, Vol. 73, pp. 24-46, 2013.
[2] Deliceoğlu, A. and Aydın, S.H., “Topological flow structures in an L-shaped
cavity with the vertical motion of the upper lid” . Journal of Computational and
Applied Mathematics, Vol. 259, pp. 937-943, 2014.
[3] Hawa T. And Rusak Z., Numerical-Asymptotic expansion matching for
computing a viscous flow around a sharp expansion corner, Theoret. and Comp.
Fluid Dyn., Vol. 15, pp. 265-281, 2002.
______________________________________________________
79
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Optimality Conditions for a Linear Differential System with
Two Delays
Hanna Demchenko
Department of Mathematics, Faculty of Electrical Engineering and
Communication, Brno University of Technology,
Brno,Czech Republic
Abstract: In the contribution, for linear differential system with two delays
𝑑𝑥(𝑡)
𝑑𝑡= 𝐴0𝑥(𝑡) + 𝐴1𝑥(𝑡 − 𝜏) + 𝐴2𝑥(𝑡 − 𝛿) + 𝑏𝑢(𝑡), (1)
where 𝐴0, 𝐴1 and 𝐴2are 𝑛 × 𝑛 constant matrices, 𝑏 ∈ 𝑅𝑛, 𝜏 > 0, 𝛿 > 0,
𝑢(𝑡) ∈ 𝑅 and 𝑢(𝑡) is a control function, a problem of minimizing a functional
𝐼 = ∫ (𝑥𝑇(𝑡)𝐶11𝑥(𝑡) + 𝑥𝑇(𝑡)𝐶12𝑥(𝑡 − 𝜏) + 𝑥𝑇(𝑡)𝐶13𝑥(𝑡 − 𝛿) + 𝑥𝑇(𝑡 −∞
𝑡0
𝜏)𝐶21𝑥(𝑡) + 𝑥𝑇(𝑡 − 𝜏)𝐶22𝑥(𝑡 − 𝜏) + 𝑥𝑇(𝑡 − 𝛿)𝐶31𝑥(𝑡) + 𝑥𝑇(𝑡 − 𝛿)𝐶33𝑥(𝑡 −𝛿) + 𝑑𝑢2(𝑡))𝑑𝑡 (2)
where integrand is a positive-definite quadratic form, is considered. To solve the
problem, Malkin’s approach and Lyapunov’s second method are utilized.
Theorem. Assume that there exists a positive-definite matrix 𝐻 satisfying the
matrix equation
𝐴0𝑇𝐻 + 𝐻𝐴0 + 𝐶11 + 𝐶22+𝐶33 −
1
𝑑𝐻𝑏𝑏𝑇𝐻 = 𝜃.
If, moreover, 𝐻𝐴1 = −𝐶12 and 𝐻𝐴2 = −𝐶13, then for problem (1)-(2) the
optimal stabilization control function exists and equals
𝑢0(𝑡) = −1
𝑑𝑏𝑇𝐻𝑢(𝑡).
Keywords: optimal control, delayed differential system, Lyapunov-Krasovskii
functional, integral quality criterion.
References:
[1] G.A. Dolenko, D.Ya Khusainov, “A partial inverse linear-quadratic
optimization problem”, Cybernetics and System Analysis, Vol.41, No.3 (2005),
473-478.
[2] F. R. Gantmacher, “The Theory of Matrices”, AMS Chelsea Publishing,
Providence, RI, USA (2002).
[3] I.G. Malkin, “Theory of Stability of Motion, Second revised edition”,
Moscow, Nauka Publisher (1966), 530.
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PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
α-Convexity of Some Struve and Lommel Functions
1Erhan Deniz,
2Halit Orhan,
1Murat Caglar
1Department of Mathematics, Kafkas University, Kars, Turkey
2Department of Mathematics, Atatürk University, Erzurum, Turkey
[email protected] (E.Deniz)
[email protected] (H.Orhan)
[email protected] (M. Çağlar)
Abstract: In this paper our first aim is to determine the radii of α-convexity of
some normalized Struve and Lommel different of the first kind. Moreover,
necessary and sufficient conditions are also given for the parameters such that
the these functions are α-convex in the open unit disk. The key tools in the proof
of our main results are the Mittag-Leffler expansion for Struve and Lommel
functions, properties of zeros of the Struve and Lommel functions and their
derivatives and some inequalities for complex and real numbers.
Keywords: Sruve function, Lommel function, convex functions, starlike
functions, α-convex functions, radii of α-convexity, zeros of Stuve and Lommel
functions.
Acknowledgements: The research of E. Deniz and M. Çağlar was supported by
the Commission for the Scientific Research Projects of Kafkas University,
project number 2016-FM-67.
References:
[1] Á. Baricz, P. A. Kupán, R. Szász, The radius of starlikeness of normalized
Bessel functions of the first kind. Proc. Amer. Math. Soc. 142(5) (2014), 2019-
2025.
[2] Á. Baricz, R. Szász, The radius of convexity of normalized Bessel functions
of the first kind. Anal. Appl. 12(5) (2014), 485-509.
[3] A. Baricz, D.K. Dimitrov, H. Orhan, N. Yağmur, Radii of starlikeness of
some special functions, Proc. Amer. Math. Soc. (in press)
doi:10.1090/proc/13120.
[4] A. Baricz, N. Yağmur, Geometric properties of some Lommel and Struve
functions, Ramanujan J. (in press) doi:10.1007/s11139-015-9724-6.
______________________________________________________
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Fuzzy Soft Topolical Spaces and the Related Category FST
Tugbahan Simsekler Dizman, Naime Tozlu
Department of Science and Mathematics Education, Gaziantep University
Sehitkamil, Gaziantep, Turkey
Abstract: Fuzzy set theory defined by Zadeh in 1968 as a new method for
vagueness. Certainly this theory became the most succesful theory for unprecise
concepts. Both in mathematics and in engineering a lot of papers based on this
theory were published. In 2001, Molodtsov defined soft set theory as a different
approach for vague concepts. Molodtsov searched the relations between this
theory with the fuzzy set theory and showed that soft set is more general than
fuzzy set. In a short time the researchers worked on soft set theory and its
applications. Also the hybrid models as fuzzy soft set were defined and studied
by several researchers.
In this paper we consider fuzzy soft sets with a different approach. We inspire of
Sostak’s fuzzy sets and generalize this idea for fuzzy soft sets. This allows us to
grade the openness and closedness of a fuzzy soft set in a fuzzy soft topological
space. The degree may range from 1 to 0 for each parameter. We define fuzzy
soft continuous mappings between two fuzzy soft topological spaces also we
define the category FST of fuzzy soft topological spaces and give some
properties of this category. Moreover we define the initial and the final fuzzy soft
topological spaces.
Keywords: fuzzy soft set, fuzzy soft topology, category FST
References:
[1] A.Aygunoğlu and H.Aygun, Some notes on soft topological spaces, Neural
Computing and Applications, doi: 10.1007/s00521-011-0722-3, 2011.
[2] A. Kharal and B.Ahmad, Mappings on fuzzy soft classes, Advances in Fuzzy
Systems, doi:10.1155/2009/407890, 2009.
[3] P. K. Maji, A. R. Roy, R. Biswas, Fuzzy soft sets, J. Fuzzy Math.9.3 (2001),
589-602.
[4] D. Molodtsov, Soft set theory-First results, Comput. Math. Appl. 37.45
(1999),19-31.
[5] T. Simsekler, S.Yuksel, Fuzzy soft topological spaces, Ann. Fuzzy Math.
Inform.,5.1(2013),87-96.
[6] A. Sostak, On a fuzzy topological structure, Proceedings of the 13thˇ Winter
School on Abstract Analysis, Section of Topology,11 (1985), 89103.
______________________________________________________
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Fuzzy Soft Ditopological Spaces
Tugbahan Simsekler Dizman, Naime Tozlu, Şaziye Yüksel
Department of Science and Mathematics Education, Gaziantep University,
Sehitkamil, Gaziantep, Turkey
Abstract: Fuzzy and soft sets are two different approaches for vague concepts.
Both of these theories took attention of researchers and were applied several
branches of mathematics. Also the hybrid models as fuzzy soft sets were defined
and searched by the mathematicians. The concept of a ditopology was introduced
by L.M. Brown and studied in a series of papers by L.M. Brown and co-authors.
Ditopologies are related to the concept of a bitopology introduced by J.L. Kelly.
In this paper we consider the case when two independent fuzzy soft structures on
a given set are defined – one of them is realizing the property of openness, and
the other is interpreting the property of closedness. Hence we define the concept
of a fuzzy soft ditopological space. Some properties of such spaces are studied.
Keywords: Fuzzy set, soft set, ditopology
References:
[1] L. M. Brown and M. Diker, Ditopological texture spaces and intuitionistic
sets, Fuzzy Sets and Systems 98 (1998), 217–224.
[2] L. M. Brown, R. Erturk, ¨ Fuzzy sets as texture spaces, I. Representation
theorems, Fuzzy Sets and Systems 110 (2) (2000), 227–236.
[3] J.L. Kelly, Bitopological spaces , Proc. Lond. Math.Soc., III Ser. 13 (1963),
71–89 .
[4] D. Molodtsov, Soft set theory-First results, Comput. Math. Appl. 37(4-5)
(1999), 19-31.
[5] A. Sostak, ˇ On a fuzzy topological structure, Suppl. Rend. Circ. Matem.
Palermo, Ser II 11 (1985), 89–103.
[6] A. Sostak, ˇ Two decades of fuzzy topology: basic ideas, notions and results,
Russian Math. Surveys 44:6 (1989), 125–186.
[7] S. Roy and T. K. Samanta, A note on fuzzy soft topological spaces, Ann.
Fuzzy Math. Inform. 3 (2012) 305–311
[8] L. A. Zadeh, Fuzzy sets, Inform. Control. 8 (1965) 338–353.
______________________________________________________
83
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
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On the Difference Method for Approximating of Second Order
Derivatives of a Solution of Laplace's Equation in a
Rectangular Parallelepiped
Adiguzel A. Dosiyev and Hediye Sarıkaya
Department of Mathematics, Near East University,
Nicosia, KKTC, Mersin 10, Turkey
Abstract: A 14-point averaging operator is used to construct finite difference
problems for the approximation on a cubic grid with step size h, of the pure and
mixed second order derivatives of a solution of the Dirichlet problem of
Laplace's equation on a rectangular parallelepiped. The boundary functions 𝜑𝑗 on
the faces 𝛤𝑗 , 𝑗 = 1,2, . . . ,6 belong to the Hölder classes 𝐶𝑝,𝜆, 0 < 𝜆 < 1, 𝑝 ∈
4,5, and on the edges their second and fourth order derivatives satisfy the
compatibility conditions.
It is proved that the solutions of the constructed difference problems converge of
orders 𝑂(ℎ𝑝−2+𝜆) and O(ℎ𝑝−2+𝜆) to the exact value of the second pure and
mixed derivatives, respectively.
Numerical experiments are illustrated to support the theoretical results.
Keywords: finite difference method, approximation of the derivatives, error
estimations, Laplace's equation on parallelepiped
______________________________________________________
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
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Kolmogorov Inequality on Variable Exponent Lebesgue Spaces
Ismail Ekincioglu, Esra Kaya
Dumlupinar University, Department of Mathematics, Kutahya, Turkey,
Dumlupinar University, Department of Mathematics, Kutahya, Turkey,
Abstract: In this study, it is considered the Riesz-Bessel transforms, The Riesz-
Bessel transforms are bounded on variable exponent Lebesgue
spaces for , but these operators are not bounded on variable exponent
Lebesgue spaces for . For this reason, it is necessary to work in
variable exponent Hardy spaces to get the boundedness of such operators for
. The most important method to show the boundedness of the Riesz-
Bessel transforms in variable exponent Hardy spaces is atomic
decomposition. The most important inequality used when atomic decomposition
is applied is Bessel type Kolmogorov inequality. Therefore, in this paper, Bessel
type Kolmogorov inequalities, which is necessary to demonstrate the
boundedness of Riesz-Bessel transforms in the variable exponent Hardy spaces,
will be proved in variable exponent Lebesgue spaces. We say that
is a convolution-type singular integral operator with regularity of order if the
distribution coincides with a function on and has the properties that
are hold and, for all multi-indices
and . Therefore, singular integrals that satisfy above
conditions are bounded on , . More importantly, the
pointwise smoothness conditions guarantee that they satisfy weighted norm
inequalities. In this work, we will obtain weighted Kolmogorov inequality.
Keywords: Generalized Shift Operator, Laplace-Bessel Operator, Kolmogorov
Inequality, Variable Exponent Lebesgue Spaces.
References:
[1] A. Osexkowski, “Sharp Inequalities for Riesz Transforms”, Stud. Math.,
222, (2014), 1-18.
[2] B. M. Levitan, “Generalized Shift Operators”, Moskow Nauva (1973).
______________________________________________________
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An Application of Functional Variable Method For Semi-
Analytical Solutions of Nonlinear Evolution Equations
Berfin Elma and Emine Misirli
Department of Mathematics, Ege University
Bornova, İzmir, Turkey
[email protected] , [email protected]
Abstract: In recent years, many powerful methods have been developed to
obtain exact solutions of partial differential equations. In this paper, we obtained
some semi-analytical solutions of the nonlinear Modified Benjamin-Bona
equation and nonlinear Coupled Klein-Gordon system which seems in the
various scientific and engineering fields such as fluid mechanics, chemical
kinematics, by using Functional Variable method. We specified wave types of
these equations. Also the physical behaviors of the obtained solution functions
are examined and three dimensional graphics are drawn using the Mathematica
program. It is shown that this method is used to solve the equations of evolution
in mathematical physics and engineering.
Key Words: evolution equations, nonlinear partial differential equations,
functional variable method.
References:
[1] Kamruzzaman K.H.A.N., and M. Ali AKBAR," Study of functional variable
method for finding exact solutions of nonlinear evolution equations." Walailak
Journal of Science and Technology (WJST) 12,11 (2014): 1031-1042.
[2] Zayed, Elsayed ME and S.A. Hoda Ibrahim, " The functional variable
method and its applications for finding the exact solutions of nonlinear PDEs in
mathematical physics." AIP Conference Proceedings. Eds. Theodore E. Simos, et
al.Vol.1479.No.1.AIP,2012.
[3] Zayed, Elsayed ME, Yaser A. Amer, and Ahmed H. Arnous, " Functional
variable method and its applications for finding exact solutions of nonlinear
PDEs in mathematical physics." Scientific Research and Essays 8,42 (2013):
2068-2074.
[4] Zerarka, A.S.Ouamane, and A. Attaf, " On the functional variable method
for finding exact solutions to a class of wave equations." Applied Mathematics
and Computation 217,7 (2010): 2897-2904.
______________________________________________________
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New Types of Soft Separation Axioms and Soft
Compactness in Soft Topological Spaces
M. E. El-Shafei1, M. Abo-Elhamayel1 and T. M. Al-shami2
1Department of Mathematics, Mansoura University, Egypt 2Department of Mathematics, Sana'a University
Abstract: In the present article, we define partial belong and total non belong
relations which are more e_ective to theoretical and application studies in soft
topological spaces. Many properties related to these two relations are studied and
discussed. We then introduce new soft separation axioms namely p-soft Ti-
spaces (i = 0; 1; 3; 4), depending on a totally non belong relation, and study their
characterizations in detail. with the help of examples, we illustrate the
relationships among these soft separation axioms and point out that p-soft Ti-
spaces are stronger than soft Ti-spaces, for i = 0; 1; 4. Also, we definedne a p-
soft regular space, which is weaker than a soft regular space ([1], Def.31), by
utilizing a total non belong relation instead of non belong relation (2.2) and
verify the equivalent between soft T2-spaces and p-soft T3-spaces when the
universe set is _nite. In the last section, we initiate a concept of soft locally
compact spaces and study main properties. We investigate under what conditions
a soft subset of a soft T2-space is soft compact. Moreover, we derive some
important results such that every soft compact T2-space is soft T3-space and a
_nite product of soft locally compact spaces is soft locally compact. we
illuminate that some _ndings obtained in general topology are not true
concerning softitopological spaces such as a _nite soft topological space need not
be soft compact.
Keywords: Partial belong (Total non belong) relation, Soft regular, p-soft Ti-
space (i = 0; 1; 3; 4), Soft T2-space, Soft compactness, Soft locally compactness
and soft topological spaces.
References:
[1] M. Shabir and M. Naz, On soft topological spaces, Computers and
Mathematics with Applications 61 (2011) 1786-1799.
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
On Quaternion n-Spaces
Fatma Ozen Erdogan, Atilla Akpinar
Department of Mathematics, Uludag University,
Bursa, Turkey
[email protected] , [email protected]
Abstract: In this presentation, we introduce some combinatorial results related
to points and lines of the quaternion n space P(J') defined by the special
Jordan matrix algebra ( , )n
J' H Α J , the set of n by n matrices, with
entries in an local ring :A Q Q (an quaternion division ring Q , Q
and 2 0 ), that are symmetric with respect to the canonical involution J .
Keywords: local ring, special Jordan matrix algebra; quaternion; quaternion 3-
space; quaternion n-space, projective Klingenberg plane, projective plane.
References:
[1] Akpinar, A. and Erdogan, F.O., “On Special Jordan Algebras of Dimension
2n²-n”, 2017 (under review)
[2] Akpinar, A. and Erdogan, F.O., “Collineations and Cross-Ratios in Octonion
Planes”, 2017 (under review)
[3] Baker C.A., Lane N.D., Lorimer J.W., “A coordinatization for Moufang-
Klingenberg Planes”, Simon Stevin, 65(1991), 3-22.
[4] Bix, R., “Octonion Planes over Local Rings”, Trans. Amer. Math. Soc.,
261(2), (1980), 417-438.
[5] Faulkner, J.R., “Octonion Planes Defined by Quadratic Jordan Algebras”,
Mem. Amer. Math. Soc., 104(1970), 1-71.
[6] Faulkner, J.R., “The Role of Nonassociative Algebra in Projective
Geometry”, Graduate Studies in Mathematics, Amer. Math. Soc., Providence,
R.I., 159(2014).
[7] Jacobson, N., “Structure and Representations of Jordan Algebras”, Colloq.
Publ., Amer. Math. Soc., Providence, R.I., 39(1968).
[8] Jacobson, N., “Basic Algebra I”, W. H. Freeman and Company, New York,
1985.
[9]McCrimmon,K., “The Freudenthal-Springer-Tits Constructions of
Exceptional Jordan Algebras”, Trans. of the Amer. Math. Soc.,139(1969), 495-
510.
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Decomposition of Soft Continuity via Soft Locally b-Closed Set
Zehra Guzel Ergul, Naime Tozlu, Saziye Yuksel
Department of Mathematics, Ahi Evran University, Kırsehir, Turkey
Department of Mathematics, Omer Halisdemir University, Nigde, Turkey
Department of Mathematics, Selcuk University, Konya, Turkey
Abstract: In this paper, we introduce soft locally b-closed sets in soft
topological spaces, which are defined over an initial universe with a fixed set of
parameters, and study some of their properties. We investigate their relationships
with different types of subsets of soft topological spaces with the help of
counterexamples. Also, the concept of soft locally b-closed continuous functions
is presented. Finally, some decompositions of soft continuity are obtained.
Keywords: Soft set, Soft topological space, Soft locally b-closed set, Soft
locally b-closed continuous function.
Acknowledgements: This work is supported by Ahi Evran University Scientific
Research Projects Coordination Unit. (Project Number: FEF. A3.16.020).
References:
[1] Acikgoz A. and Arabacioglu Tas N., “Some new soft sets and
decompositions of some soft continuities”, Annals of Fuzzy Mathematics and
Informatics, 9.1(2015), 23-35.
[2] Akdag M. and Ozkan A., “Soft α-open sets and soft α-continuous functions”,
Abstract and Applied Analysis, http://dx.doi.org/10.1155/2014/891341, (2014).
[3] Akdag M. and Ozkan A., “Soft b-open sets and soft b-continuous functions”,
Math. Sci., 8.124(2014).
[4] Akdag M. and Ozkan A., “On Soft preopen sets and soft pre separation
axioms”, Gazi University Journal of Science, 27.4(2014), 1077-1083.
[5] Akdag M. and Ozkan A., “On soft β-open sets and soft β-continuous
functions”,The Scientific World Journal, http://dx.doi.org/10.1155/2014/843456,
(2014).
[6] Ali M.I., Feng F., Liu X., Min W.K. and Shabir M., “On some new
operations in soft set theory”, Computers and Mathematics with Applications,
57(2009), 1547-1553.
______________________________________________________
89
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
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Periodic Solutions for a Third-Order Delay Differential
Equation
Nouioua Farid and A. Ardjuoni
Department of Mathematics, Souk-Ahras University,
Souk-Ahras, Algeria
Abstract: In this paper, the following third order nonlinear delay differential
equation with periodic coefficient
))(()()))((),(,()()()(')()('')()(''' ttxtcttxtxtftxtrtxtqtxtptx
is considered. By employing Green’s function, Krasnoselskii’s …fixed point
theorem and the contraction mapping principle, we state and prove the existence
and uniqueness of periodic solutions to the third-order delay differential
equation. Finally, an example is given to illustrate our results.
A. Ardjouni and A. Djoudi, Existence of periodic soluxions for a second-order
non-linear neuxral dixerentixl equation with variable delay, Palesx. J. Math.,
x(x014),191-197.
Keywords: Fixed point , positive periodic solutions, third-order delay
differential equations.
References:
[1] A. Ardjouni and A. Djoudi, Existence of periodic solutions for a second-
order nonlinear neutral differential equation with variable delay,Palesx. J. Math ,
3(2014), 191-197 .
[2] A. Ardjouni, A. Djoudi, and A. Rezaiguia, Existence of positive periodic
solutions for two types of third-order nonlinear neutral differential equation with
variable delay, Appl. Math. E-Notes, 14(2014), 86-96
[3] A. Ardjouni and A. Djoudi, Existence of positive periodic solutions for a
nonlinear neutral differential equation with variable delay, Appl. Math. E-Notes,
12(2012), 94-101 .
[4] A. Ardjouni and A. Djoudi, Existence of periodic solutions for a second-
order nonlinear neutral differential equation with functional delay, Electronic. J.
Qual. Theory Diff. Eq, 2012, No. 31,9 pp.
[5] T. A. Burton, Liapunov functionals, fixed point and stability by
Krasnoselskii’s theorem nonlinear stud, 9(2002), 181-190
______________________________________________________
90
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
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Copula Conditional Tail Expectation for Multivariate Financial
Risks
Benatia Fatah and Brahim Brahimi
Laboratory of Applied Mathematics,
Mohamed Khider University, Biskra, Algeria,
Abstract: Our goal in this paper is to propose an alternative risk measure which
takes into account the fluctuations of losses and possible correlations between
random variables. This new notion of risk measures, that we call Copula
Conditional Tail Expectation describes the expected amount of risk that can be
experienced given that a potential bivariate risk exceeds a bivariate threshold
value, and provides an important measure for right-tail risk. An application to
real financial data is given.
Keywords: Conditional Tail Expectation; Positive Quadrant Dependence;
Copulas; Dependence measure; Risk Management; Market Models.
References:
[1] Artzner, P. H., Delbaen, F., Eber, J. M., Heath, D., 1997. Thinking
Coherently, RISK 10, 68-71.
[2] Brahimi, B., Meraghni, D., Necir, A., 2010. Distortion risk measures for
sums of dependent losses. J. Afr. Stat. 5, 260-267.
[3] Joe, H., 1997. Multivariate Models and Dependence Concepts. Monographs
on Statistics and Applied Probability 73. Chapman and Hall, London.
[4] Nelsen, R. B., 2006. An Introduction to Copulas. second ed. Springer, New
York.
[5] Sklar, A., 1959. Fonctions de répartition à n dimensions et leurs marges,
Publ. Inst. Statist. Univ. Paris 8, 229-231.th. Econom. 21(2), 173-183.
______________________________________________________
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
New Properties of Fractional Derivatives Defined Using Mittag
Leffler Kernel
Arran Fernandez 1, Dumitru Baleanu 2,3
1 Department of Applied Mathematics & Theoretical Physics, University of
Cambridge, Wilberforce Road, Cambridge, United Kingdom 2 Department of Mathematics, Cankaya University, 06530 Balgat, Ankara,
Turkey 3 Institute of Space Sciences, Magurele-Bucharest, Romania
Abstract: Recent developments in the theory of fractional calculus have
included a new definition introduced by Atangana and Baleanu [1] for fractional
derivatives in terms of a Mittag-Leffler kernel function; the theory of such
derivatives has been further extended in other papers such as [2]. In this
presentation we prove a new formula for such fractional derivatives, in terms of
an infinite convergent series of standard Riemann-Liouville or Caputo fractional
derivatives. This enables us to extend various results from classical calculus,
such as the product rule and chain rule, much more easily than otherwise. We
also consider the semigroup property for derivatives and integrals and how it
applies to these new fractional differintegrals, and we show how to solve certain
fractional ODEs using the new definition.
Keywords: Fractional Derivatives, Fractional Integrals, Laplace Transforms,
Ordinary Differential Equations
References:
[1] A. Atangana and D. Baleanu, “New fractional derivatives with nonlocal and
non-singular kernel: theory and application to heat transfer model”, Therm. Sci.
20(2) (2016), 763–769.
[2] T. Abdeljawad and D. Baleanu, “Integration by parts and its applications of a
new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel”, J.
Nonlinear Sci. Appl. 10(3) (2017), 1098-1107.
______________________________________________________
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Nodal Solutions for Indefinite Robin Problems
Michael Filippakis
Department of Digital Systems
Univeristy of Piraeus
Piraeus 18536, Greece
Abstract: We consider a semilinear Robin problem driven by the negative
Laplacian plus an indefinite, unbounded potential. The reaction term is a
Caratheodory function of arbitrary structure outside an interval [−c, c] (c > 0),
odd on [−c, c] and concave near zero. Using a variant of the symmetric mountain
pass theorem, together with truncation, perturbation and comparison techniques,
we show that the problem has a whole sequence unn≥ 1 of distinct nodal
solutions converging to zero in C1 (Ω).
Keywords: Indefinite potential, Robin boundary condition, sequence of nodal
solution, regularity theory, strong maximum principle
______________________________________________________
93
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On Slowly Oscillating Double Sequences
Goksen Findik, Ibrahim Canak, Umit Totur
Department of Mathematics, Ege University, Bornova, Izmir, Turkey
Department of Mathematics, Ege University, Bornova, Izmir, Turkey
Department of Mathematics, Adnan Menderes University, Aydin, Turkey
[email protected]; [email protected] ;
Abstract: In this paper, we first examine the relationships between a double
sequence and its arithmetic means in different senses (i.e. (C,1,0), (C,0,1) and
(C,1,1) means) in terms of slow oscillation in certain senses and investigate
some properties of oscillatory behaviors of the difference sequence between the
double sequence and its arithmetic means in different senses. Next, we give an
alternative proof of the generalized Littlewood Tauberian theorem for Cesaro
summability method as an application of the results obtained in the first part.
Keywords: Tauberian conditions and theorems, convergence in Pringsheim's
Sense, slow oscillation, double sequences, summability (C, 1, 0), (C, 0, 1) and
(C, 1,1)
References:
[1] R. Schmidt, “Über divergente Folgen und lineare Mittelbildungen”, Math. Z.,
22 (1925), 89-152.
[2] E. Landau, “Über einen Satz des Herrn Littlewood”, Palermo Rend., 35
(1913), 265-276.
[3] T. Vijayaraghavan, “A Tauberian theorem”, J. Lond. Math. Soc., 1 (1926),
113-120.
[4] F. Móricz, “Tauberian theorems for Cesaro summable double sequences”,
Studia Math., 110 (1) (1994), 83-96.
______________________________________________________
94
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A Bayes Minimax Result for a Large Class of Distributions
Dominique Fourdrinier, Fatiha Mezoued and William E. Strawderman
Université de Rouen, France,
Ecole Nationale de Statistique et d'Economie Appliquée, Algiers, Algeria
Rudgers University, USA
[email protected], [email protected],
Abstract: We consider Bayesian estimation of the location parameter of a
random vector X having a unimodal spherically symmetric density (‖𝑥−𝜃‖2) for a
spherically symmetric superharmonic prior density ((‖𝜃‖2)). We consider
minimaxity of the Bayes estimator 𝛿𝜋(𝑋) = 𝑋 + 𝛻𝑀(∥𝑋∥2)/ 𝑚(∥𝑋∥2) under
quadratic loss, where m is the marginal associated to 𝑓(∥𝑥−𝜃 ∥2) and M is the
marginal with respect to 𝐹(∥𝑥−𝜃 ∥2)=1/2∫𝑓(𝑡)∞‖𝑥−𝜃‖2𝑑𝑡 . In this paper we
extend the results given by Fourdrinier, Strawderman in 2008 [3], and
Fourdrinier, Mezoued strawderman in 2012 [2].
Keywords: Bayesian estimation, Spherically symmetric density, Minimaxity,
Superharmonicity, proper and improper estimators.
References:
[1]J.O. Berger, “Minimax estimation of location vectors for a wide class of
densities”, Annals of Statistics, 3:13181328, (1975).
[2]D. Fourdrinier, F. Mezoued, and W. E. Strawderman, “Bayes minimax
estimators in the Berger class”, EJS, 6: 783-809, (2012).
[3]D. Fourdrinier and W. E. Strawderman, “Generalized bayes minimax
estimators of location vector for spherically symmetric distributions”, Journal of
Multivariate Analysis, 99(4): 735-750, (2008).
______________________________________________________
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A Search for Designs with the Same Parameters as 2-
(256,64,21) Design with 2-Rank 25
Mustafa Gezek
Department of Mathematical Sciences, Michigan Technological University, Houghton, MI, USA [email protected]
Abstract: Let D be a t − (v, k, λ) design with b blocks. One of the important
results in theory of combinatorial designs is that the number of blocks of a design
≥ the number of points, named as the Fisher inequality. This implies that the p-
rank of D is not greater than v. The researchers working in this area are
interested about the lower bound on the p-ranks of some certain designs and a
great amount of research is done on this problem. Let D_1 be a geometric design
having as blocks the d -subspaces of P G(n, q) or AG(n, q), and let m be the p-
rank of D_1 . Hamada [3] conjectured that if D_2 is a design with the same
parameters as D_1 , then the p-rank of D_2 is greater or equal m, and the
equality holds if and only if D_2 is isomorphic to D_1 . In [1, 2, 4, 5, 6], there
are some proven cases and as well as some counterexamples to the this
conjecture. Our work here is using the connection of known 2-(64,16,5) designs
with 2-rank 16 to find non-geometric designs with the same parameters as AG 3
(4, 4).
References:
[1] Clark D., Jungnickel D., Tonchev V.D., Affine geometry designs, polarities,
and Hamada’s conjecture, Journal of Combinatorial Theory, Series A 118 231-
239 (2011).
[2] Doyen J., Hubaut X., Vandensavel M., Ranks of incidence matrices of
Steiner Triple Systems, Math Z., Vol.163 (1978) 251 - 259.
[3] Hamada N., On the p-rank of the incidence matrix of a balanced of partially
balanced incomplete block design and its applications to error correcting codes,
Hiroshima Math J. 3, 153-226 (1973).
[4] Hamada N., Ohmori H., On the BIB design having the minimum p-rank,
J.Combin Theory Ser. A Vol 18 (1975) 131 - 140.
[5] Harada M., Lam C., Tonchev V.D., Symmetric (4,4)-nets and generalized
Hadamard matrices over groups of order 4. Des. Codes Cryptogr. 34, 71-87
(2005).
[6] Teirlinck T., On the projective and affine hyperplanes, J. Combin. Theory
Ser. A, Vol. 28 (1980) 290 - 306.
______________________________________________________
96
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Compact and Matrix Mappings on the Space |𝑨𝒇𝛉|𝒌
Fadime Gokce, G.Canan Hazar Gulec
Department of Mathematics, Pamukkale University,
Denizli, Turkey
[email protected], [email protected]
Abstract: In this study, we characterize compact and matrix operator in the
class (|𝐴𝑓θ|𝑘, |𝐵𝑓| ) for k≥1, and give some topological and algebraic properties
of the space |𝐴𝑓θ|𝑘, where A and B are factorable matrices, θ = (θ𝑛) is
nonnegative sequence. Also we determine norms and Hausdorff measure of
noncompactness of matrix operators in these classes. Thus we extend some
recent results of Sarıgöl [8,9] and some well known results.
Keywords: Matrix Transformations; Factorable Matrices; Sequence Spaces;
Measure Hausdorff Noncompactness; Norms; Compact Operators.
References:
[1] Bor, Hüseyin. "On two summability methods." Math. Proc. Cambridge
Philos. Soc. 97 (1985), 147-149.
[2] Maddox, I.J., Elements of functinal analysis, Cambridge University Press,
London, New York, 1970.
[3] Malkowsky E., Rakocevic, V., On matrix domains of triangles, Appl. Math.
Comp. 189 (2007), 1146-1163.
[4] Malkowsky E., Rakocevic, V. An introduction into the theory of sequence
space and measures of noncompactness, Zb. Rad.(Beogr) 9 (2000), 143-234.
[5] Orhan, C. and Sarıgöl, M.A., On absolute weighted mean summability ,
Rocky Moun. J. Math. 23 (3) (1993), 1091-1097.
[6] Rakocevic, V., Measures of noncompactness and some applications, Filomat
12 (1998), 87-120.
[7] Sarıgöl, M.A., Extension of Mazhar's theorem on summability factors,
Kuwait J. Sci. 42 (2015), 1-8.
[8] Sarıgöl, M., A., Characterization of general summability factors and
applications, Comp. Math. Appl. 62 (2011), 2665-2670.
[9] Sarıgöl, M.A., Matrix transformations on fields of absolute weighted mean
summability, Studia Sci. Math. Hungar. 48 (3) (2011), 331-341
______________________________________________________
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
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On Some Classes of Fractional Differential Equations of
Parabolic Type
Dilovar Guljonov
A.Juraev Insitute of Mathematics, Academy of Sciences of the Republic of
Tajikistan
Dushanbe, Tajikistan
Abstract: The present paper is devoted to studying the equations of parabolic
type in which instead of Laplaсe operator considered the differential operator
with fractional orders of derivatives by spatial variables. Instead of classical
equation of normal diffusion of form 𝝏𝒖
𝝏𝒕= ∆𝒖 (𝟏)
is consider a fractional equation of isotropic anomaly diffusion 𝝏𝒖
𝝏𝒕= ∆𝜶/𝟐𝒖, 𝟏 ≤ 𝜶 ≤ 𝟐 (𝟐)
or an equation of anisotropic anomaly diffusion 𝝏𝒖
𝝏𝒕= 𝛁 ∙ (𝓙𝑴
𝟏−𝜷𝛁𝐮), (𝟑)
where 𝛁 − gradient operator and operator 𝓙𝑴𝟏−𝜷[𝒗] is defined for vector-valued
function 𝒗 and has form
𝓙𝑴𝟏−𝜷[𝒗] = 𝑭−𝟏 [ ∫ 𝒎(𝒊𝒎 ∙ 𝝃)𝜷−𝟏𝒎 ∙ (𝝃)𝑴(𝒅𝒎)
|𝒎|=𝟏
].
Here 𝑴 − probability measure in unit sphere ℝ𝒏 described an anisotropic
diffusion, 𝑭−𝟏[𝒗] − an inverse Fourier transform of function 𝒗 ∈ 𝑳𝟐 ⊂ ℝ𝒏.
Equation (1) is correspond to the random walk model and equations (2) and (3)
are correspond to the continuous in time random walk and Levi flights models
(see, e.g., [1]).
Initial-boundary problem for the equations (2) and (3) are invistiges by method
of Fourier fractional analysis.
References:
[1] V.V. Uchaykin, “Self-similar anomaly diffusion and stable laws”, Uspekhi
Physic.Nauk, 173.8(2003), 847-876.
______________________________________________________
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Some Results about ΔI-Statistically Pre-Cauchy Sequences with
an Orlicz Function
Hafize Gumus, Omer Kisi and Ekrem Savas
Abstract: In this study, we define the concept of I-statistically convergence for
difference sequences and we use an Orlicz function to obtain more general
results. We also show that an ΔI-statistically convergent sequence with an Orlicz
function is ΔI -statistically pre-cauchy.
References:
[1] Das, P. and Sava¸s, E., On I-statistically pre-cauchy.sequences, Taiwanese
Journal of Mathematics, Vol.18, No.1, 115-126, (2014).
[2] Khan, V.A., Ebadullah, K., Ahmad, A., I-Pre-Cauchy sequences and Orlicz
functions, Journal of Mathematical Analysis, 3(1), 21-26, (2012).
[3] Dutta, A. J. and Tripathy, B.C., Statistically pre-cauchy fuzzy real-valued
sequences deÖned by an Orlicz function, Proyecciones Jour. of Mathematics,
33(3), 235-243, (2014).
______________________________________________________
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A Numerical Analysis of FLMM for Semilinear Time
Fractional Schrödinger Equations
Betul Hicdurmaz
Department of Mathematics, Istanbul Medeniyet University,
Uskudar, Istanbul, Turkey
Abstract: In this study, semi linear time fractional Schrödinger differential
equations are solved approximately with three types of difference schemes.
Semi-discretization in time variable is provided by an iterated Lubich
approximation and two different iterated Fractional linear multi step method
(FLMM) methods. Numerical analysis of the obtained theoretical results are
presented with a discussion on some particular problems.
Keywords: Semi linear time fractional Schrödinger equation, Fractional linear
multi step method, Lubich approximation.
References:
[1] R. Garrappa, I. Moret, M. Popolizio, “On the time-fractional Schrödinger
equation: Theoretical analysis and numerical solution by matrix Mittag-Leffler
functions", Computers & Mathematics with Applications, 2016, In press.
[2] M. Naber, "Time fractional Schrodinger equation", J. Math. Phys. Vol 45,
No. 8 pages 3339-3352, Aug. 2004.
[3] A. H. Bhrawy, M. A. Zaky, "An improved collocation method for multi-
dimensional space–time variable-order fractional Schrödinger equations",
Applied Numerical Mathematics, 111, 2017, 197–218.
______________________________________________________
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On Modified FLMM Methods for Fractional Population
Equations
Betül Hicdurmaz and Emine Can*
Department of Mathematics, Istanbul Medeniyet University
*Department of Physics Engineering, Istanbul Medeniyet University
Uskudar, Istanbul, Turkey
Abstract: In the present paper, a new modified Fractional Linear Multistep
Method (FLMM) is presented for the numerical solution of linear and semi linear
differential equations. Constructed methods are implemented on the generalized
time fractional-order biological population model (GTFBPM) with one or two
dimensions which arise in population dynamics. Selected problems are equations
which are applied to population growth in species in biology.
Keywords: Population dynamics, Fractional Linear Multistep Method.
References:
[1] V. K. Srivastava, S. Kumar, M. K. Awasthi, B. K. Singh, “Two-dimensional
time fractional-order biological population model and its analytical solution”,
Egyptian Journal of Basic and Applied Sciences, 1 (2014), 71-76.
[2] N. V. Mantzaris, P. Daoutidis, F. Srienc, “Numerical solution of multi-
variable cell population balance models. II. Spectral methods”, Computers and
Chemical Engineering 25 (2001) 1441–1462.
[3] S. Allaart-Bruin, J. ter Maten, S. Verduyn Lunel, Modified Extended BDF
time-integration methods, applied to circuit equations, RANA Report 02-25,
Eindhoven University of Technology, Presented at SCEE-2002, Eindhoven, June
2002.
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Coincidence Best Proximity Points for Geraghty Type
Proximal Cyclic Contractions
Azhar Hussain
Department of Mathematics, University of Sargodha
Sargodha, Pakistan
Abstract: In this talk we introduce the notions of generalized Geraghty proximal
cyclic contractions for non-self mapping and obtain coincidence best proximity
point theorems in the setting of complete metric space. Some examples are given
to show the validity of our results. Our results extended and unify many existing
results in the literature.
Keywords: α-Geraghty proximal contraction of first and second kind, α-
proximal cyclic contraction, α-proximal admissible maps.
References:
[1] Abbas, M, Hussain, A, Kummam, P: A Coincidence Best Proximity Point
Problem in G-Metric Spaces. Abst. and Appl. Anal. 2015, Article ID 243753, 12
pages (2015).
[2] Akbar, A, Gabeleh, M: Global optimal solutions of noncyclic mappings in
metric spaces. J. Optim. Theory Appl. 153, 298-305 (2012).
[3] Basha, S.S. (2011). Best proximity point theorems generalizing the
contraction principle. Nonlinear Anal., 74:5844-5850, (2011).
[4] Basha, SS, Shahzad, N, Jeyaraj, R: Best proximity points: approximation and
optimization. Optim. Lett. (2011).
[5] Shahzad, N, Basha, SS, Jeyaraj, R: Common best proximity points: global
optimal solutions. J. Optim. Theory Appl. 148, 69-78 (2011).
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Estimation of a Loss Function for Spherically Symmetric
Distribution with Constraints on the Norm
Ouassou Idir
Cadi Ayyad University, National School of Applied Sciences
Marrakesh, Morocco
Abstract: In this paper we consider the problem of estimating the quadratic loss
of point estimators of a location parameter θ for family of symmetric distribution
with known scale parameter, when its norm satisfies different constraints and
when a residual vector U is available. We compare the robust and non robust
estimators and condition on the distribution for the domination of competing
estimators are given. In particular we show that it occurs for t-distributions when
the dimension of the residual vector is sufficiently large. The main tools in the
development are upper and lower bounds on the risk are exact at θ = 0.
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An overview on Fuzzy AHP and Its Priority Derivation
1Iftikhar, 2Musheer Ahmad
1,2Department of Applied Sciences and Humanities
Faculty of Engineering and Technology
Jamia Millia Islamia, New Delhi-110025, India
[email protected], [email protected]
Abstract: Fuzzy AHP is a mathematical technique for multicriteria decision
making (MCDM) in fuzzy environments. Priority derivation is one of the pivotal
steps in Fuzzy AHP methods. In this work, we are introducing various methods
for determining the priority vectors, 𝑤 = (𝑤1 , 𝑤2 … , 𝑤𝑛 ) 𝑇 . Each method is
defined by a function, 𝜏: 𝑅 𝑛×𝑛 → , which synthesize pairwise comparisons
into a rating. Several examples are solved for illustrating the working of each
method.
Keywords: Fuzzy AHP; priority vectors; pairwise comparison matrices;
multicriteria decision making.
References:
[1] Saaty T.L., Scaling method for priorities in hierarchical structures, J. Math.
Psychol. 1977, 15, 3, 234-28.
[2] Basak I., Comparison of statistical procedures in analytic hierarchy process
using a ranking test, Math. Comp. Model. 1998, 28, 105-118.
[3] Budescu D.V., Zwick R., Rapoport A., Comparison of the analytic hierarchy
process and the geometric mean procedure for ratio scaling, Appl. Psychol.
Meas. 1986, 10, 69-78.
4] Saaty T.L., Vargas L.G. Comparison of eigenvalue, logarithmic least square
and least square methods in estimating ratio, J. Math. Model. 1984, 5, 309-324.
[5] Koczkodaj W.W., A new definition of consistency of pairwise comparisons,
Mathematical and Computer Modeling 1993, 18(7), 79-84.
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Solutions of (n) (n 1)od od When n 1 Has Three Distinct
Odd Primes
Nazli Yildiz Ikikardes, Daeyeoul Kim and Lianrong Ma
Balikesir University, Turkey, National Institute for Mathematical Sciences, South
Korea, Tsinghua University, China
[email protected], [email protected], [email protected]
Abstract: In this study, we define |n,2 |
(n)od dd
d. We investigate solutions of
the equation (n) (n 1)od od . We find all solutions of the equation
(n) (n 1)od od up to 402n . Also, we obtain the equation
(n) (n 1) (n 2) 1(mod2)od od od has no solution.
Keywords: Congruence, Divisor Functions, Odd Divisor Functions
First author was supported by The Research Fund of Balikesir University,
Project No: 2016/44.
References:
[1] V. Annapurna, “Inequalities for (n) and (n) ”, Math. Mag. 45(1972),
187-190.
[2] B. Cho, D. Kim and H. Park, “The multinomial convolution sums of certain
divisor functions”, J. Math. Anal. Appl, 448(2017), 1163-1174.
[3] P. Erdös, “Some remarks on Eulers function and some related problems”,
Bull. Amer. Math. Soc., 51(1945), 540-544.
[4] J. W. L. Glaisher, “On certain sums of products of quantities depending upon
the divisors of a number”, Mess. Math., 15(1885), 1-20.
[5] R. K. Guy, “Unsolved problems in number theory”, Springer, 2004.
[6] D. Kim and A. Bayad, “Convolution identities for twisted Eisenstein Series
and twisted divisor functions”, Fixed Point Theory and App., (2013), 2013:81.
[7] Y. Li, L. Ma and J. Zhang “Odd solutions of (n) 2 2n have at least six
distinct prime factors”, Publicationes Mathematicae Debrecen, 82(2012), 1-12.
[8] K. S. Williams, “Number theory in the spirit of Liouville”, Cambridge
University Press, 2011
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Hypersurfaces of a Kenmotsu Space Form
Mohammad Ilmakchi
Department of Mathematics, Azarbaijan Shahid Madani University,
Tabriz, Iran
Abstract: The purpose of this paper to introduce of hypersurfaces in Kenmotsu
space form and study with some special conditions. In general, we have some
relations about locally symmetric condition, recurrent and D -recurrent structure
Jacobi operator, weakly constant holomorphic curvature and another inequality
condition.
Keywords: Kenmotsu space form, locally symmetric, recurrent, Jacobi operator.
References:
[1] A. Bejancu, CR-submanifolds of Kaeher Manifold $I$, Proc. Amer.Math.
Soc. 69, no.1, (1978) , 135-142.
[2] A. Bejancu, Geometry of CR-submanifolds, D. Reidel Publishing Company,
Dordrecht, Boston, Lancaster, Tokyo, (1986).
[3] D. E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in
Mathematics, Vol. 509, Springer-Verlag, Berlin, (1976).
[4] M. Djoric, M. Okumura, Certain CR submanifolds of maximal CR dimension
of complex space forms, Differential Geometry and its Applications, 26(2), 208-
217, (2008).
[5] K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku
Math. J.24, (1972) , 93-103.
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On Some Classes of Fractional Integrodifferential Equations in
Hilbert Space
Mamadsho Ilolov
Center of Innovative Development of Science and New Technologies, Academy
of Science of Republic of Tajikistan
Dushanbe, Tajikistan
Abstract: Let 𝑓 ∈ 𝐿1(𝑅+, 𝐻), 𝐻 − separable Hillbert space and 0 ≤ 𝛼 < 1. The
expression
(𝒥𝑡𝛼𝑓)(𝑡) =
1
Γ(𝛼)∫(𝑡 − 1)𝛼−1𝑓(𝑠)𝑑𝑠, 𝑡 > 0, 𝛼 > 0
𝑡
0
with 𝒥𝑡0𝑓(𝑡) = 𝑓(𝑡) is called Riemann-Liouville integral of order 𝛼 of 𝑓. For
𝑓(𝑡) ∈ 𝐶𝑚−1(𝑅+𝐻) the Caputo fractional derivalive of order 𝛼 of 𝑓 defined by
( 𝐷𝑡𝛼
𝐶 )(𝑡) = 𝐷𝑡𝑚𝒥𝑡
𝑚−𝛼 [𝑓(𝑡) − ∑𝑡𝑖
𝑖!
𝑑𝑖𝑓(0)
𝑑𝑡𝑘
𝑚−1
𝑖=0
] (𝑡), 𝐷𝑡𝑚 =
𝑑𝑚
𝑑𝑡𝑚.
We are interested in studying the Cauchy problem for fractional
integrodifferential equation in 𝐻 of the type
( 𝐷𝑡𝛼𝑢𝐶 )(𝑡) + 𝐴𝑢(𝑡) + ∑ ∫ 𝑒−𝛾𝑘(𝑡−𝑠)𝐴𝑘𝑢(𝑠)𝑑𝑠
𝑡
0
𝑛
𝑘=0
= 𝑓(𝑡),
𝑢(0) = 𝑢0, (1)
where 𝐴0, 𝐴1, … , 𝐴𝑛 –unbounded linear self-adjoint operators with 𝐷(𝐴𝑘) ⊃
𝐷(𝐴0), 0 < 𝐴𝑘−1 ∈ ℒ(𝐻), 𝛾𝑘 –positive constants, 0 < 𝛾1 < ⋯ < 𝛾𝑛 < ∞, 𝑓 =
𝑓(𝑡): 𝑅+ → 𝐻 given function, 𝑢0 ∈ 𝐻.
Let 𝑢(𝑡) – strong solution of (1). We introduce new desired functions 𝑢𝑘(𝑡), 𝑘 =
0, … , 𝑛 with accordance with formulas
𝑢0(𝑡) = 𝑢(𝑡), 𝑢𝑘(𝑡) = ∫ 𝑒−𝛾𝑘(𝑡−𝑠)𝐴𝑘
12⁄
𝑢0(𝑠)𝑡
0
𝑑𝑠, 𝑘 = 1,2, … , 𝑛
and then we come to fractional differential equations
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( 𝐷𝛼𝑐 )(𝑡) + 0 = 𝑓(𝑡), (0) = 𝐻0, (2)
in Hilbert space
𝐻 = 𝐻0 + 𝐻1, 𝐻0 = 𝐻, 𝐻1 = ⨁𝑘=1𝑛 𝐻𝑘 , 𝐻𝑘 = 𝐻,
𝑘 = 1,2, … , 𝑛, (3)
where
(𝑡) = (𝑢0(𝑡), 𝑢1(𝑡))𝑇 , 𝑢1(𝑡) = (𝑢1(𝑡), … , 𝑢𝑛(𝑡))𝑇 , 𝑓(𝑡) = (𝑓(𝑡), 0),
(0) = (𝑢0, 0)𝑇
and operator 0 have a following matrix presentation
0 = (𝐴𝑖𝑗)1𝑖𝑗
1= 0, 𝐴00 = 𝐴0, 𝐴01 = (𝐴1
1/2, … , 𝐴𝑛
1/2)
𝑇,
𝐴10 = − (𝐴1
12, … , 𝐴𝑛
12 )
𝑇
, 𝐴11 = 𝑑𝑖𝑎𝑔(𝛾𝑘𝐼)𝑘=1𝑛 .
Integer order of equation (1) was studied in [1].
References:
[1] M. Ilolov, Kh. Kuchakshoev. “The classification of abstract
integrodifferential equation of higher order”, 7th European Congress of
Mathematics, (2016), 483.
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The Generators of Regular, Quasi-regular Representations and
Casimir Operator
Yasemin Isik 1, Mehmet Sezgin 2
Department of Mathematics, Trakya University,
Edirne, Turkey 1 [email protected]
Abstract: Special pseudo-orthogonal group is
𝑆𝑂(𝑝, 𝑞) = 𝐴 ∈ 𝑂(𝑝, 𝑞) | det 𝐴 = 1 .
Dealing with regular and quasi-regular representstion of the group, infinitesimal
operators 𝐽0, 𝐽1, 𝐽2 can be found and Casimir operator of the group can be
obtained using these operators. In this paper we shall obtain generators of
regular, quasi-regular representations and the Casimir operator 𝐶 of 𝑆𝑂(1,2)
group. We also shall analyzed the solutions of
𝐶 𝑓(𝑥) = 𝜎(𝜎 + 1) 𝑓(𝑥),
where 𝜎(𝜎 + 1) is eigenvalue, 𝑓(𝑥) is eigenfunction.
Keywords: Lie group, Casimir operator, regular and quasi-regular
representation.
References:
[1] Y. A. Verdiyev, “Harmonic Analysis on Homogeneous Spaces of SO(1,2)”,
Hadronic Press. (1988)
[2] A. Kirillov, Jr, “Introduction to Lie Groups and Lie Algebras”, Suny at Stony
Brook.
[3] A. M. Perelomov, V. S. Popov, “Casimir Operator for Semisimple Lie
Groups”, Math USSR-Izvestija, 2(1968).
[4] R. da Rocha, E. Capelas de Oliveria “The casimir Operator of SO(1,2) and
the Pöschl-Teller Potential: an AdS Approach”, Analysis, 5(1985), 301-313.
[5] S.A. Mohiuddine and Q.M. Danish Lohani, “On generalized statistical
convergence in intuitionistic fuzzy normed space”, Rev. Mex. Fis., 51 (1) (2005),
1-4.
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Some Properties of Cartan Null Curves in Semi-Euclidean
4-space with index 2
Esen Iyigün
Department of Mathematics, Uludag University,
Görükle, Bursa, Turkey
Abstract: In this paper, we give some properties by using Frenet equations
which are given in [2] of Cartan null curves in Semi-Euclidean 4-space with
index 2. Also, we discuss the conditions for Cartan null curves lying on some
subspaces of these space. Finally, we obtain that the image of the curve lying on
the pseudohyperbolic space H31 in the same space.
Keywords: Semi-Euclidean 4-space with index 2, Frenet frame, Cartan null
curve.
References:
[1]
B. O'Neill, "Semi-Riemannian geometry with applications to relativity",
Academic Press, New York,1983.
[2] A. Uçum, O. Keçilioğlu and K. İlarslan, "Generalized pseudo null Bertrand
curves in Semi-Euclidean 4-space with index 2", Rend. Circ. Mat. Palermo, DOI
10.1007/s12215-016-0246-x, (2016), 1-14,
[3] M.A. Akgün and A.I. Sivridağ, "On the null Cartan curves of R41", Global
Journal of Mathematics, 1. January 26(2015), 41-50.
[4] M.A. Akgün and A.I. Sivridağ, "On the characterizations of null Cartan
curves in R41", International Journal of Mathematics, 1.June1(2015), 1-13.
[5] K.L. Duggal and D.H. Jin, "Null curves and hypersurfaces of Semi-
Riemannian manifolds" World Scientific, London, 2007.
[6] M. Petrovic-Torgasev and E. Sucurovic, "Some characterizations of the
spacelike, the timelike and the null curves on the pseudohyperbolic space H²0 in
E30”, Kragujevac J. Math., 22(2000), 71-82.
[7]
Z. Şanlı and Y. Yaylı, "On indicatrices of null Cartan curves in R41",
International Journal of Engineering Research & Technology (IJERT),
10.2(2013), 2567-2570.
[8] M. Sakaki, "Null Cartan curves in R4
2 ", Toyama Math., 32 (2009), 31-39.
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Proximal Point Algorithms Involving Cesaro Type Mean of
Total Asymptotically Nonexpansive Mappings in CAT(0)
Spaces
Amna Kalsoom and Hafiz Futhar ud Din
Department of Mathematics& Statistics, International Islamic University,
Islamabad, Paksitan
Abstract: Fixed point theory in a CAT(0) space was first studied by Kirk [1].
Since then, fixed point theory for various types of mappings in CAT(0) spaces
has been investigated rapidly. In 2008, Dhompongsa-Panyanak[2] studied the
strong and ∆-convergence for the Mann Iteration process and Ishikawa iteration
process for nonexpansive mappings in CAT(0) spaces.
Alber et al. [3] introduced a unified and generalized notion of a class of nonlinear
mappings in Banach spaces which can be introduced in CAT(0) spaces. A
modified proximal point algorithm involving fixed point of Cesaro type mean
of total asymptotically nonexpansive mappings in CAT(0) spaces is proposed.
Under suitable conditions, the ∆-convergence and the strong convergence to
a common element of the set of minimizers of a convex function and the
set of fixed points of the Cesaro type mean of total asymptotically
nonexpansive mapping in CAT(0) space are proved.
Keywords: CAT (0) space, Cesaro type mean, Proximal point algorithm, Total
asymptotically nonexpansive mapping.
References:
[1] W. A. Kirk, “Geodesic geometry and fixed point theory, Seminar
of Mathematical Analysis (Malaga/Seville, 2002/2003)”, Univ. Sevilla Secr.
Publ., Seville, (2003), 195–225.
[2] S. Dhompongsa, B. Panyanak, “On ∆-convergence theorems in CAT (0)
spaces”, Comput. Math. Appl., 56 (2008), 2572–2579.
[3] C.E. Chidume, E.U. Ofoedu, “Approximation of common fixed points for
finite families of total asymptotically nonexpansive mappings” J. Math. Anal.
Appl., 333(2007), 128-141
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Semi–Empirical Systematic Development for Photon Induced
Nuclear Reaction Cross–Section Calculations
Abdullah Kaplan2, Hasan Ozdogan1,2, Mert Sekerci2, Veli Capali2
1Department of Biophysics, Akdeniz University, Antalya, Turkey
2Department of Physics, Süleyman Demirel University, Isparta, Turkey
Abstract: In this study, photon-neutron cross-section calculations have been
performed using pre-equilibrium nuclear reaction models. For pre-equilibrium
model calculation comparisons, some computation codes have been employed
that include theoretical nuclear reaction models. In addition, by obtaining giant
dipole resonance parameters in standard Lorentzian mode, semi-empirical cross
sections have been calculated. Obtained results have been compared with the
experimental values exist in the literature and nuclear reaction models’
computation results.
Keywords: Semi–Empirical Formula, Nuclear Cross–Section, Asymmetry
Parameter.
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Positive Solutions for Fractional-Order Boundary Value
Problems
Ilkay Yaslan Karaca
Department of Mathematics, Ege University,
35100 Bornova, Izmir, Turkey
[email protected] [email protected]
Abstract: In this study, six functionals fixed point theorem is used to research
the existence of positive solutions for fractional-order nonlinear boundary value
problems. As an applications, examples are presented to illustrate the main
results.
Keywords: Four functionals fixed point theorems, impulsive dynamic
equations, positive solutions, boundary value problems, time scale.
References:
[1] Avery, R. Henderson, J. and O’Regan, D., 2008, Six functional fixed point
theorem, Communications in Applied Mathematics, 12(1):69-81p.
[2] Dalir, M. and Bashour, M., 2010, Applications of fractional calculus,
Mathematical Sciences, Vol. 4, 1021-1032.
[3] Guo D., Lakshmikkantham V., Ames W. F., Nonlinear Problems in Abstract
Cones, Academic Press, New York, 1988.
[4] Kilbas, A.A. Srivastava, H.M., Trujillo, J.J., Theory and Applications of
Fractional Differential Equations, North-Holland Mathematics Studies 204, 69-
79p.
[5] Liu, X., Jia,M., Ge, W., 2013, Multiple Solutions of a p- Laplacian Model
Involving a Fractional Derivatives, Advances in Difference Equations.
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The Existence of Positive Solutions of Boundary Value
Problems with P-Laplacian on the Half-Line
Ilkay Yaslan Karaca and Aycan Sinanoglu
Department of Mathematics, Ege University,
35100 Bornova, Izmir, Turkey
[email protected] [email protected]
Abstract: In this study, four functionals fixed point theorem is used to
investigate the existence of positive solutions for second-order time-scale
boundary value problem of dynamic equations on the half-line.
Keywords: Four functionals fixed point theorems, impulsive dynamic equation,
positive solutions, boundary value problems, time scale. References:
[1] G. Chai, Existence of positive solutions of boundary value problem for
second-order functional differential equations on infinite intervals, Fixed Point
Theory, 13 (2012), 423-437.
[2] X. Chen, X. Zhang, Existence of positive solutions for nonlinear systems of
second-order differential equations with inregral boundary conditions on an
infinite interval in Banach Space, Electron. J. Differential Equations, 2011
(2011), no. 154 19 pp.
[3] X. Chen, X. Zhang, Existence of positive solutions for singular impulsive
differential equations with integral boundary conditions on an infinite interval in
Banach Space, Electron. J. Qual.Differ. Equ., 2011 (2011), no. 28 18 pp.
[4] Y. Guo, C. Yu, J. Wang, Existence of three positive solutions for m-point
boundary value problem in infinite intervals , Nonlinear Anal., 71 (2009),717-
722.
[5] Z. Hao, L. Ma, Existence of positive solutions for multi-point boundary value
problem on infinite intervals in Banach Space, Abstr. Appl. Anal., 2012 (2012),
Art. ID 107276, 18pp.
[6] I. Y. Karaca, F. Tokmak, Existence of three positive solutions for m-point
time scale boundary value problem on infinite intervals, Dynam. Systems Appl.,
20 (2011), 355-367.
[7] X. Zhao, W. Ge, Multiple positive solutions for time scale boundary value
problem on infinite interval, Acta Appl. Math., 106 (2009), 265-273.
[8] X. Zhao, W. Ge, Unbounded positive solutions for m-point time-scale
boundary value problem on infinite intervals, J. Appl. Math. Comput., 33 (2010),
103-123.
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The Dimension of Digital Khalimsky Manifolds
Ismet Karaca1, Gokhan Temizel2
1Ege University
Faculty of Science, Department of Mathematics, Izmir,Turkey
[email protected] 2Ege University
Graduate School of Natural and Applied Sciences, Izmir, Turkey
Abstract: The digital counterpart of Euclidean topology which is defined on the
real line, has been studied by Efim Khalimsky. Khalimsky has defined this
topology on the integers and it is called Khalimsky’s topology. Digital
Khalimsky manifolds, digital manifolds with respect to Khalimsky topology, is a
digital response of real manifolds. These manifolds are used in order to
identifying to digital counterpart of the images on the Euclidean geometry and
they play an important role in image processing and computer graphics. In this
poster, we will explain the dimension of digital Khalimsky manifolds.
Keywords: Khalimsky Topology, Digital Manifold, Join Operator, Topological
Embedding
References:
[1] L. Boxer, “A classical construction for the digital fundamental group”,
Journal of Mathematical Imaging and Vision, 10:51-62, 1999.
[2] E. Melin, “How the find a Khalimsky-continuous approximation of a real-
valued function”, IWCIA 2004, LNSC 3322:351-365, 2004.
[3] E. Melin, “Extension of continuous function in digital spaces with the
Khalimsky topology”, Topology and Its Applications, 153:52-65, 2005.
[4] E. Melin, “Continuous Extension in topological digital spaces”, Applied
General Topology, 9:51-61, 2008.
[5] E. Melin, “Digital Khalimsky Manifolds”, Journal of Mathematical Imaging
and Vision, 33:267-280
[6]L.W. Tu, “An introduction to manifolds”, Springer Science+ Business Media,
LLC, 2008.
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Some Properties of Persistent Homology Groups
Ismet Karaca and Hatice Sevde Denizalti
Department of Mathematics, Ege University,
Bornova, Izmir, Turkey
[email protected]; [email protected]
Abstract: Simplicial homology is a corner stone of algebraic topology in terms
of extracting topological features of spaces and persistent homology is occured
as an extension to simplicial homology. Persistence is investigated in [6] and
then generalized in [4]. Persistent homology is generally used for solving the
problem of unveiling global topological informations obtained from a sample of
a high-dimensional data sets of the space. To find the persistent homology of a
space, the space must be represented as a simplicial complex filtrations. In this
poster, we give some information about history of persistent homology and offer
its fundamental notions.
Keywords: Simplicial homology, simplicial complex filtration, persistent
homology.
References:
[1] A. Hatcher, “Algebraic Topology”, cambridge University Press, (2002).
[2] G. Carlsson, T. Ishkhanov, V. de Silva and A. Zomorodian “On the local
behaviour of spaces of natural images”, International Journal of Computer
Vision, 76.1(2008), 1-12.
[3] H. Edelsbrunner and E. P. Mcke, “Three-dimensional alpha shapes”, ACM
Transactions on Graphics, 13.1(1994), 43-72.
[4] H. Edelsbrunner, D. Letscher and A. Zomorodian “Topological persistence
and simplification”, Discrete Computational Geometry, 33(2005), 249-274.
[5] R. Ghrist, “Barcodes: the persistent topology of data”, Bulletin of the
American Mathematical Society, 45.1(2008), 61-75.
[6] A. Zomorodian and G. Carlsson, “Computing persistent homology”, Discrete
Computational Geometry, 28.4(2002), 511-533
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On Digital Cohomology Groups
Ismet Karaca1, Ozgur Ege2
1Department of Mathematics, Ege University, Bornova, Izmir, Turkey
[email protected] 2Department of Mathematics, Manisa Celal Bayar University, Yunusemre,
Manisa, Turkey
Abstract: Digital topology, introduced by Rosenfeld [8], is an area of great
theoretical interest having the additional bonus of significant applications in
imaging science and related areas. It continues to rise in many fields of science
and engineering such as mathematics, image processing, biology, information
system and computer science with a great number of applications. Important
developments have been made in this area after the works of Boxer[1,2]. Some
results on digital simplicial homology groups were introduced in [4] and [5]. In
[6], simplicial cohomology theory is given for digital images. Digital
cohomology operations were introduced in [7]. In this paper, we compute
simplicial cohomology groups of connected sum of certain minimal simple
surfaces by using the Universal Coefficient Theorem for digital cohomology
groups. We also prove some theorems related to degree properties of a map on
digital spheres.
Keywords: Digital image, Universal Coefficient Theorem, digital cohomology
group.
References:
[1] L. Boxer, “Digital continuous functions”, Pattern Recognition Letters,
15(1994), 833-839.
[2] L. Boxer, “A classical construction for the digital fundamental group”,
Journal of Mathematical Imaging and Vision, 10(1999), 51-62.
[3] L. Boxer, I. Karaca and A. Oztel, “Topological invariants in digital images”,
Journal of Mathematical Sciences: Advances and Applications, 11.2(2011), 109-
140.
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[4] O. Ege and I. Karaca, “Some results on simplicial homology groups of 2D
digital images”, International Journal of Information and Computer Science,
1.8(2012), 198-203.
[5] O. Ege and I. Karaca, “Fundamental properties of simplicial homology
groups for digital images”, American Journal of Computer Technology and
Application, 1.2(2013), 25-42.
[6] O. Ege and I. Karaca, “Cohomology theory for digital images”, Romanian
Journal of Information Science and Technology, 16.1(2013), 10-28.
[7] O. Ege and I. Karaca, “Digital cohomology operations”, Applied
Mathematics and Information Sciences, 9.4(2015), 1953-1960.
[8] A. Rosenfeld, “Digital topology”, American Mathematical Monthly,
86(1979), 76-87.
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Some Common Fixed Point Theorems on Complex Valued
Gb-Metric Spaces
Ismet Karaca1, Ozgur Ege2
1Department of Mathematics, Ege University, Bornova, Izmir, Turkey
[email protected] 2Department of Mathematics, Manisa Celal Bayar University, Yunusemre,
Manisa, Turkey
Abstract: Fixed point theory is very active area with various applications in
mathematics, biology, image processing [2] and computer science. In this theory,
the Banach contraction principle plays a key role to solve many problems. After
the Banach’s work [1], researchers have obtained important results in various
metric spaces. The notion of complex valued Gb-metric space was introduced in
[3]. Then some new fixed point results have been given by several authors [4,5]
in this space. The concept of the common fixed point of mappings satisfying
contractive type condition has generally been used to prove existence problems.
In this study, we prove some common fixed point theorems in complex valued
Gb-metric spaces.
Keywords: Fixed point, common fixed point theorem.
References:
[1] S. Banach, “Sur les operations dans les ensembles abstraits et leurs
applications aux equations integrales”, Fundamenta Mathematicae, 3(1922), 133-
181.
[2] O. Ege and I. Karaca, “Banach fixed point theorem for digital images”,
Journal of Nonlinear Science and Applications, 8.6(2015), 1014-1021.
[3] O. Ege, “Complex valued Gb--metric spaces”, Journal of Computational
Analysis and Applications, 21.2(2016), 363-368.[4] O. Ege, “Some fixed point
theorems in complex valued Gb--metric spaces”, to appear in Journal of
Nonlinear and Convex Analysis, (2017).
[5] A.H. Ansari, O. Ege and S. Radenovic, “Some fixed point results on complex
valued Gb-metric spaces”, to appear in Revista de la Real Academia de Ciencias
Exactas, Fisicas y Naturales, Seria A. Matematicas, Doi: 10.1007/s13398-017-
0391-x, (2017), 1-10
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On Some Deddens Subspaces of Banach Algebras
Mubariz Karaev 1, Mehmet Gurdal2, Havva Tilki2
1Department of Mathematics, King Saud University, Riyadh, Saudi Arabia
2Department of Mathematics, Süleyman Demirel University, Isparta, Turkey
[email protected]; [email protected]; [email protected]
Abstract: Let A be a Banach algebra with a unit e , and let Aa be an
invertible element. We define the following algebra:
.0 and 0 somefor :: x
xx
nnloca cxncxaax
AB
In this article we study some properties of this algebra; in particular, we prove
that 0: pepxxlocpe AB , where p is an idempotent in A . We also
investigate the following Deddens subspace. Let Aba, be two elements. Fix
any number , 10 , and consider the following subspace of :A
. as ::, nnOxbaxD nnba
A
Here we study some properties of the subspaces baD , and .,
abD
Keywords: Banach algebra, Deddens subspace, Deddens algebra, Idempotent
element, Nilpotent element
Acknowledgement. This work is supported by Suleyman Demirel University
with Project 4799-YL1-16.
References:
[1] W.Arveson, Interpolation problems in nest algebras, J.Funct. Anal.,
20(1975), 208-233.
[2] J.A.Deddens, Another description of nest algebras, Lecture Notes in Math.,
693(1978), 77-86.
[3] D.Drissi and M.Mbekhta, Operators with bounded conjugation orbits, Proc.
Amer. Math. Soc., 128(2000), 2687-2691.
[4] J.A.Erdos, Unitary invariants for nests, Pacific J. Math., 23(1967), 229-256.
[5] M.Gürdal, Description of extended eigenvalues and extended eigenvectors of
integration operators on the Wiener algebra, Expo. Math., 27(2009), 153-160.
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Duhamel Operator and Existence of Invariant Subspace
Mubariz Karaev 1, Mehmet Gurdal2, Mualla Birgul Huban2
1Department of Mathematics, King Saud University, Riyadh, Saudi Arabia 2Department of Mathematics, Süleyman Demirel University, Isparta, Turkey
[email protected]; [email protected]; [email protected]
Abstract: In this work, we gives some sufficient conditions in terms of
reproducing kernels and Duhamel operators for the existence of nontrivial
invariant subspace in Hardy-Hilbert Space.
Keywords: Reproducing kernel, Berezin symbol, Invariant subspace, Duhamel
operator, Hardy space
Acknowledgement This work is supported by the Scientific and Technological
Research Council of Turkey (TÜBİTAK) with Project 115F265.
References:
[1] P. Ahern, M. Flores and W. Rudin, “An invariant volume-mean-value
property”, J. Funct. Anal., 111 (2) (1993), 380-397.
[2] M. Engliš, “Functions invariant under the Berezin transform”, J. Funct.
Anal., 121 (1) (1994), 233-254.
[3] M. Lacruz, “Invariant subspaces and Deddens algebras”, Expo. Math., (33)
(1) (2015), 116-120.
[4] A. Lambert, “Hyperinvariant subspaces and extended eigenvalues”, New
York J. Math., 10 (2004), 83-88.
[5] M.M. Malamud, “Invariant and hyperinvariant subspaces of direct sums of
simple Volterra operators”, Oper. Theory Adv. Appl., 102 (1998), 143-167.
[6] N. M. Wigley, “The Duhamel product of analytic functions”, Duke Math. J.,
41 (1974), 211-217.
[7] N.M. Wigley, “A Banach algebra structure for pH ”, Canad. Math. Bull., 18
(4) (1975), 597-603.
[8] K. Zhu, “Operator Theory in Function Spaces”, Marcel Dekker, New York,
1990.
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On Extended Eigenvalues and Extended Eigenvectors of
Toeplitz Operators
Mubariz Karaev 1, Mehmet Gurdal2, Mualla Birgul Huban2
1Department of Mathematics, King Saud University, Riyadh, Saudi Arabia
2Department of Mathematics, Süleyman Demirel University, Isparta, Turkey
[email protected]; [email protected]; [email protected]
Abstract: In this paper, we consider the operators from Englis algebras, in
particular, the Toeplitz operators on the Hardy space, and give some results on
the commutant, extended eigenvalues and extended eigenvectors of operators.
Keywords: English algebra, Hardy space, Toeplitz operator, extended
eigenvalue
Acknowledgement: This work is supported by TUBA through Young Scientist
Award Program (TUBA-GEBIP/2015).
References:
[1] H. Alkanjo, “On extended eigenvalues and extended eigenvectors of
truncated shift”, Concrete Operators, 1 (2013), 19-27.
[2] A. Biswas, A. Lambert and S. Petrovic, “Extended eigenvalues and the
Volterra operator”, Glasgow Math. J., 44 (2002), 521-534.
[3] M. Gürdal, “On the extended eigenvalues and extended eigenvectors of shift
operator on the Wiener algebra”, Appl. Math. Lett., 22 (2009), 1727-1729.
[4] M. T. Karaev, “On extended eigenvalues and extended eigenvectors of some
operator classes”, Proc. Amer. Math. Soc., 134 (2006), 2383-2392.
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A Generalization on the Incidence Energy and Laplacian-
Energy-Like Invariant
Ezgi Kaya and A. Dilek Maden
Department of Mathematics-Computer, Igdir University,
Igdir, Turkey
Department of Mathematics, Selcuk University,
Konya, Turkey
Abstract: For a graph G and a real number α, the graph invariant 𝑠𝛼(𝐺) is the
sum of the powers of signless Laplacian eigenvalues and 𝜎𝛼(𝐺) is equal to the
sum of powers of Laplacian eigenvalues of G. In this study, considering these
sum for some special cases of α, we give some bounds for incidence energy and
Laplacian-energy-like invariant of graphs.
Keywords: Laplacian matrix, signless Laplacian matrix, Incidence energy,
Laplacian-Energy-Like invariant
References:
[1] S. Akbari, E. Ghorbani, J. H. Koolen and M. R. Oboudi, “On sum of powers
of the Laplacian and signless Laplacian eigenvalues of graphs”, Electron. J.
Combin. 17 (2010), R115.
[2] S. Furuichi, “On refined Young inequalities and reverse inequalities”, J.
Math. Inequal., 5(2011), 21-31.
[3] I. Gutman, The energy of a graph, Ber. Math. Statist. Sekt. Forschungsz.
Graz 103 (1978), 1-22.
[4] I. Gutman, D. Kiani, M. Mirzakhah, On incidence energy of graphs, MATCH
Commun. Math. Comput. Chem. 62 (2009), 573-580.
[5] M. Jooyandeh, D. Kiani, M. Mirzakhah, “Incidence energy of a graph”,
MATCH Commun. Math. Comput. Chem. 62 (2009), 561-572.
[6] H. Kober, “On the arithmetic and geometric means and the Hölder
inequality”, Proc. Amer. Math. Soc., 59(1958), 452-459.
[7] J. Liu, B. Liu, A Laplacian-energy like invariant of a graph, MATCH
Commun. Math. Comput. Chem. 59 (2008), 355-372.
[8] B. Liu, Y. Huang, Z. You, A survey on the Laplacian–energy like invariant,
MATCH Commun. Math. Comput. Chem. 66 (2011), 713–730.
[9] B. Zhou, “On sum of powers of the Laplacian eigenvalues of graphs”, Linear
Algebra Appl. 429(2008), 2239–2246.
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A Data Mining Approach: Application to the Extraction of the
Characteristics of IARD Products in the Insurance Sector
Sadi Khadidja1,2, Lounici Mosbah Nora1,2
1. Higher National School of Statistics and Applied Economics
2. Laboratory of Applied Statistics
ENSSEA, University of Kolea, Algeriers, Algeria
[email protected] , [email protected]
Abstract: In this study, we are interested in IARD property and Multi-risk
insurance products, which covers fire, accidents and various risks [1] of an
Algerian insurance company. We want to know the variables that best
characterize each of the two products. To solve this problem, we have combined
three methods borrowed from Data Mining and decisional statistics [2][3]. The
use of data mining tools to realize a classification and to bring out the most
informative variables is usual tasks of this discipline. The aim of this work is to
extract knowledge from an actuarial database by adopting an approach to data
mining [4] and to compare the results obtained by querying tools and techniques,
implemented in data mining software.
Keywords: Insurance IARD, data mining approach, classification, machine
Learning
References :
[1] F. Noël. La gestion des sinistres IARD incendies et risques divers,
édition séfi, Canada 2014.
[2] S. Tuffery. Data mining et statistique décisionnelle 4ième ed, Broché – 21
août 2012.
[3] C. Wesphal & T. Blaxton. "Data Mining Solutions ", John Wiley, New
York, 1998.
[4] M. Boullé. Recherche d’une représentation des données efficace pour la
fouille des grandes bases de données. Ph. D. thesis, ENST. 2007.
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The Le Corbusier Approach in the Relationship between
Architecture and Mathematics
Murat Kilic and Melih Kurnali
Faculty of Fine Arts, Deparment of Interior Architechure & Environment
Design,
Kırıkkale University, Kırıkkale, Turkey
Abstract: In defining the relationship between architecture and mathematics,
dealing with and evaluating different points of view is important and necessary
in terms of both creating new horizons and a new perception for these two
disciplines. In general, architecture and mathematics are dealt with according to
their technical characteristics. Architecture makes use of mathematics as a
technique and a tool. However, these two disciplines should be used together to
create art and allow art reach top level aesthetic values as well. In the period of
Modernism, Le Corbusier who has been in search of this purpose and
mathematical systems which could meet all conditions for architecture is in fact
an important architect who has internalized mathematics to reach artistic
aesthetics. In Le Corbusier’s and contemporary mathematicians’ point of view
on mathematics, it can be seen that there is a deep opposition. This is caused by
the contradictive comparisons made between scientistd and artists. Although
architecture is regarded as an art, it is actually a discipline which is formed by
the perfect synthesis of science and art [1]. Le Corbusier can be considered as
being closer to the artistic side of this synthesis. Although his modular system
seems mathematical, or scientific, we can say that his artistic side gains more
importance due to the fact that he has not been educated on building construction
techniques and the technical complaints he has received about his structures from
his clients. In particular, the Ronchamp Chapel embodies a sculptural artistry and
he is firstly a painter. Although Le Corbusier’s architectural and mathematical
approach has been criticized, it is apparent that he had an intellectual foundation
which gave inspiration. So much so that, the proportional system called modulor
which he developed for architecture has inspired the composition of a piece
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called “Metastassis” [2]. Le Corbusier is at a critical point in the art, mathematics
and architecture triangle and this study is in search of knowledge about Le
Corbusier and his mathematical understanding to allow these disciplines to be
evaluated with new approaches.
Keywords: Architecture, Mathematics, Le Corbusier, Modulor.
References:
[1] J. Loach, “Le Corbusier and the Creative Use of Mathematics”, The British
Society for the History of Science, (1998), 185-215.
[2] Le Corbusier. “Modulor 2”, Yem Press (2011), 328-329.
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The Absolute Möbius Divisor Function and Euler function
Daeyeoul Kim1, Umit Sarp2 and Sebahattin Ikikardes2
1National Institute for Mathematical Sciences, Yuseong-daero 1689-gil,
Yuseong-gu, Daejeon 305-811, South Korea
[email protected] 2Department of Mathematics, Balikesir University, 10100 Balikesir, Turkey
Abstract: In this study,we introduce the absolute Mobius divisor function ( )U n .
Also we investigate the sequences m mU n , which concerns the iteration of
the absolute Mobius divisor function ( )U n . According to some numerical
computational evidence, we consider integer pairs ; 1n n satisfying;
1 1 .n n U n U n
Furthermore, we give some examples and proofs for our results.
Keywords: Mobius divisor function, Fermat pirmes, Euler function, n-gonal
number.
References:
[1] A. Bayad and D. Kim, Polygon Numbers Associated with the Sum of Odd
Divisors Function, to appear of Exp. Math.
http://dx.doi.org/10.1080/10586458.2016.1162231.
[2] V. Annapurna, Inequalities for (n) and '(n), Math. Mag. 45 (1972), 187-190.
[3] L. E. Dickson, History of the theory of numbers. Vol I: Divisibility and
Primality. Chelsea Publishing Co., New York 1966.
[4] P. Erdös, Some remarks on Eulers function and some related problems,
Bull. Amer. Math. Soc. 51 (1945), 540-544.
[5] R. K. Guy, Unsolved Problems in Number Theory, Springer, 2004.
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S-Generalized Lauricella’s Hypergeometric Functions
I. Onur Kiymaz, M. Baki Yagbasan, Aysegul Cetinkaya
Department of Mathematics, Ahi Evran University,
Kırşehir, Turkey
Abstract: In this study, we introduced new generalizations of Lauricella’s
hypergeometric functions by using S- generalized beta function. Furthermore, we
investigated some of their properties such as integral representations and
transformation formulas.
Keywords: S-Generalized Beta function, Lauricella’s hypergeometric functions.
Acknowledgement: This work was supported by Ahi Evran University
Scientific Research Projects Coordination Unit. Project Number: FEF.D1.16.001
References:
[1]Bailey W.N., “Generalized Hypergeometric Series”, Cambridge Tracts in
Mathematics and Mathematical Physics, vol. 32, Cambridge University Press,
Cambridge, (1935).
[2]Chaudhry M. A., Qadir A., Rafique M., Zubair S. M., “Extension of Euler's
beta function”, J. Comput.Appl. Math., 78, (1997): 19-32.
[3]Hasanov, A., Srivastava, H. M., “Some decomposition formulas associated
with the Lauricella function and other multiple hypergeometric functions”, Appl.
Math. Lett., 19.2, (2006): 113-121.
[4]Luo, Min-Jie, Milovanovic, G. V., Agarwal, P., “Some results on the
extended beta and extended hypergeometric functions”, Applied Mathematics
and Computation, 248, (2014): 631-651.
[5]Padmanabham, P. A., Srivastava, H. M., “Summation formulas associated
with the Lauricella function Appl. Math. Lett., 13.1, (2000): 65-70.
[6] Srivastava H. M., Karlsson P. W., “Multiple Gaussian Hypergeometric
Series”, Ellis Horwood Limited, (1985).
[7] Srivastava, H. M., Agarwal, P., Jain, S., “Generating functions for the
generalized Gauss hypergeometric functions”, Applied Mathematics and
Computation, 247, (2014): 348-352.
[8]Srivastava, H. M., Jain, R., Bansal, M. K., “A Study of the S-Generalized
Gauss Hypergeometric Function and Its Associated Integral Transforms”,Turkish
Journal of Analysis and Number Theory, 3.5, (2015): 116-119.
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Some Remarks on Fuzzy Anti-Normed Spaces
Ljubiša D.R. Kočinac
Faculty of Sciences and Mathematics, University of Niš, Serbia
Abstract: Let E be a real linear space with a fuzzy anti-norm with respect to a
t-conorm. We discuss some (statistical) convergence and covering properties of
such spaces. We also consider norms on E generated by .
Keywords: Statistical convergence, fuzzy anti-normed space, boundedness.
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On Asymptotically f-Statistical Equivalent Sequences
Sukran Konca and Mehmet Kucukaslan
Department of Mathematics, Bitlis Eren University, 13000, Bitlis, Turkey
Department of Mathematics, Mersin University, 33343, Mersin, Turkey
[email protected]; [email protected]
Abstract: By using modulus functions, we have obtained a generalization of
statistical convergence of asymptotically equivalent sequences, a new non-matrix
convergence method, which is intermediate between the ordinary convergence
and the statistical convergence. Further, we have examined some inclusion
relations related to asymptotically f-statistical equivalence of real sequences in
the light of a partial order.
Keywords: Statistical Convergence, strong Cesaro summability; f-
asymptotically equivalent sequences.
References:
[1] M. Marouf, “Asymptotic equivalence and summability”, Internat. J. Math.
Math. Sci. 16 (4) (1993), 755-762.
[2] R. F. Patterson, “On asymptotically statistically equivalent sequences”,
Demonstratio Math, 36 (1) (2003), 149-153.
[3] A. Aizpuru, M. C. Listan-Garcia and F. Rambla-Barreno, “Density by moduli
and statistical convergence”, Quaestiones Mathematicae., 37 (4) (2014), 525–-
530.
[4] V. K. Bhardwaj, S. Dhawan, and S. Gupta, “Density by moduli and statistical
boundedness”, Abst. Appl. Analysis, 2016(2016), 6 pages.
[5] H. Nakano, “Concave modulars”, J. Math. Soc. Japan, 5(1953), 29–-49.
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Some Permanents of Hessenberg Matrices
Sibel Koparal, Nese Omur and Cemile Duygu Sener
Department of Mathematics, Kocaeli University,
Kocaeli, Turkey
[email protected] ,[email protected],
Abstract: In this study, we define a sequence 𝑅𝑛(𝑎, 𝑏, 𝑐) and represent
relationships between this sequence and permanents of certain matrices. Some
special cases for permanents are given.
Keywords: Hessenberg matrix, Relation recurrence, Permanent.
References:
[1]R.A. Brualdi and P.M. Gibson, “Convex Polyhedra of Doubly Stochastic
Matrices: Applications of the permanents Function”, J.Combin Theory A,
22(1977), 194-230.
[2]E. Kılıç and D.Taşcı, “On the permanents of some tridiagonal matrices with
applications to the Fibonacci and Lucas numbers”, Rocky Mountain Journal of
Mathematics, 37.6(2007), 203-219.
[3]E. Kılıç, Tribonacci sequences with certain indices and their sums”, Ars
Combinatoria, 86(2008), 31-40.
[4]E.Kılıç and D. Taşcı, “Negatively subscripted Fibonacci and Lucas numbers
and their complex factorizations”, Ars Combinatoria, 96(2010), 275-288.
[5] H. Mine, “Permanents of (0,1)-circulants”, Canad. Math. Bull., 7(1964), 253-
263.
[6]J.L. Ramnrez, “Hessenberh matrices and the generalized Fibonacci-Narayana
sequence”, Filomat, 29.7(2015), 1557-1563.
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
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Best Proximity Points for Generalized Geraghty
Proximal Contraction Mapping in Elliptic Valued Metric Space
Isil Arda Kosal1, Hidayet Huda Kosal2, Mahpeyker Ozturk3
1,2,3 Department of Mathematics,
Sakarya Universitesi, Sakarya, TURKEY
[email protected], [email protected], [email protected]
Abstract: In this study, we introduce the concept of best proximity points for the
generalized Geraghty proximal contraction mappings between two
subsets of elliptic valued metric space. Elliptic numbers are generalized form of
complex and so real numbers. Thus, the obtained results extend, generalize and
complement some known fixed and best proximity point results from the
literature.
Keywords: Contraction mapping, Best proximity, Ellipitc valued metric spaces.
References:
[1] A. Harkin and J. Harkin, “Geometry of generalized complex numbers”,
Mathematics Magazine, 77.2(2004), 118–129.
[2] A. Azam, B. Fisher and M Khan, “Common fixed point theorems in complex
valued metrik spaces”, Numerical Functional Analysis and Optimization. An
International Journal, 32.3(2011), 243–253.
[3] M. Ozturk and N. Kaplan,” Common fixed points of f-contraction mappings
in complex valued metric spaces”, Mathematical Sciences, 8.129(2014).
[4] M. Ozturk, “Common fixed points theorems satisfying contractive type
conditions in complex valued metrik spaces”, Abstract and Applied Analysis,
7(2014).
[5] J. Hamzehnejadi and R. Lashkaripour, “Best proximity points for generalized
Geraghty proximal contraction mapping and its applications”, Fixed
Point Theory and Applications, 72.1(2016), 1-13.
[6] E. Karapinar, “A Discussion on Geraghty contraction type mapping”,
Filomat, 28.4(2014), 761-766.
[7] N. Bilgili, E. Karapinar and K. Sadarangani, “A generalization for the best
proximity point of Geraghty contraction”, Journal of Inequalities and
Applications, 286(2013), 1-9
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Characterizations of , ,p q - Convex Sequences
Xhevat Z. Krasniqi
Faculty of Education, University of Prishtina “Hasan Prishtina”,
10000 Prishtina, Republic of Kosovo
Abstract: The class of convex sequences has important applications in several
branches of mathematics as well as their generalizations. In this paper, we have
introduced a new class of convex sequences, the so-called , ,p q -convex
sequences. Moreover, the characterizations of such sequences belonging to this
class has been shown.
Keywords: Sequence, Convexity,$(p;r)-$monotonicity, $(p,q;r)-$convexity,
$p$-starshaped sequence, $(p,q;\alpha )$-convexity.
References:
[1] H. Bor, A new application of convex sequences. J. Class. Anal. 1 (2012), no.
1, 31--34.
[2] H. Bor, Xh. Z. Krasniqi, A note on absolute Cesàro summability factors.
Adv. Pure Appl. Math. 3 (2012), no. 3, 259--264.
[3] Xh. Z. Krasniqi, Some properties of $(p,q;r)$-convex sequences. Appl. Math.
E-Notes 15 (2015), 38--45.
[4] Xh. Z. Krasniqi, Characterizations of $(p,\alpha )$-convex sequences. Appl.
Math. E-Notes, accepted.
[5] L. M. Koci\'c, I. Z. Milovanovi\'c, A property of $(p,q)$-convex sequences,
Period. Math. Hungar. Vol. 17 (1) (1986), pp. 25--26.
[6] I. B. Lackovi\'c, M. R. Jovanovi\'c, On a class of real sequences which satisfy
a difference inequality, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. No. 678
(1980), 99--104.
[7] B. Makarov, A. Podkorytov, Real Analysis: Measures, Integrals and
Applications, Springer--Verlag London, 2013.
[8] J. E. Pe\ucari\'c, On some inequalities for convex sequences. Publ. Inst.
Math. (Beograd) (N.S.) 33(47) (1983), 173--178.
[9] F. Qi, B.-N. Guo, Monotonicity of sequences involving convex function and
sequence. Math. Inequal. Appl. 9 (2006), no. 2, 247--254.
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A Note on the Numbers Yn(Λ) and the Polynomials Yn(X;Λ)
and Their Generating Functions
Irem Kucukoglu1,a and Yilmaz Simsek2,b
1Department of Software Engineering, Faculty of Engineering and Architecture,
Antalya AKEV University Antalya, Turkey. 2Department of Mathematics, Faculty of Science University of Akdeniz TR-
07058, Antalya, Turkey.
[email protected], [email protected]
Abstract: In this talk, we study on the numbers Yn(λ) and the polynomials
Yn(x;λ) which have been recently introduced by Simsek in [7]. We give partial
derivative formulas including the generating functions of these numbers and
polynomials. By using these formulas and functional equations for the generating
functions, we give some recurrrence relations and identities for these numbers
and polynomials related to some special numbers such as the Apostol-Bernoulli
numbers, the Apostol-Euler numbers, the Stirling numbers of the first kind, the
Cauchy numbers.
Keywords: Generating functions, Functional equations, Partial differential
equations, Daehee numbers, Changhee numbers, Stirling numbers.
References:
[1] T. M. Apostol, On the Lerch zeta function, Pacific J. Math. 1 (1951), pp. 161-
167.
[2] N. P. Cakic and G. V. Milovanovic, On generalized Stirling numbers and
polynomials, Mathematica Balkanica 2004; 18: 241-248.
[3] G. B. Djordjevic and G. V. Milovanovic, Special classes of polynomials,
University of Nis, Faculty of Technology Leskovac, 2014.
[4] D. S. Kim, T. Kim and J. Seo, A note on Changhee numbers and
polynomials, Adv. Stud. Theor. Phys. 7 (2013), 993-1003.
[5] D. S. Kim and T. Kim, Daehee numbers and polynomials, Appl. Math. Sci.
(Ruse) 7 (120) (2013), 5969-5976.
[6] T. Kim, D. V. Dolgy, D. S. Kim and J. J. Seo, Differential equations for
Changhee polynomials and their applications, J. Nonlinear Sci. Appl. 9 (2016),
2857-2864.
[7] Y. Simsek, Generating Functions for family of (q-) generalized Apostol-type
Numbers And Polynomials: Analysis of the p-adic q-integrals, (preprint).
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Modelling Worldwide CO2 Emissions and Oil Consumption
based on the 𝑳𝟏, 𝑳𝟐 𝐚𝐧𝐝 𝑳∞-norm Regressions
1Pranesh Kumar and 2Mohamadtaghi Rahimi
1Department of Mathematics and Statistics,
University Northern British Columbia, Prince George, BC V2N 4Z9, Canada
[email protected] 2Department of Mathematics,
Iran University of Science and Technology, Narmak, Tehran, Iran.
Abstract. Regression models are commonly used to model the relationship
among random variables in statistical data analysis with an aim to use them to
make future predictions. The regression model estimated by the method of least
squares is known to be optimal and perform relatively well under certain
assumptions such as when the errors: follow normal distributions, are free of
large size outliers and satisfy the Gauss-Markov assumptions. However, in
practice, the least squares error linear regression models may fail to provide best
results in non-Gaussian situations especially when the errors follow distributions
with fat tails and error terms possess a finite variance. Historically, in the
eighteenth century, mathematicians, notably, Mayer, Boscovich, Laplace,
Legendre, Simpson, Gauss, and Euler did pioneering work to develop procedures
for fitting functions. The most significant research was the development of
methods of least absolute deviations, least squares deviations and minimax
absolute deviations. The theory of function fitting methods of least squares is
credited to the published works of Legendre (1805) and Gauss (1809).
Alternatively, we may use 𝐿𝑝-norm to estimate the linear regression model
parameters to search for an appropriate regression model. In this paper, we
provide a perspective on the 𝐿1, 𝐿2 and 𝐿∞-norm based regression models.
Worldwide oil consumption and CO2 emissions are an on-going environmental
worldwide concern and often result in both immediate and long-term
environmental damage. We discuss the results on modeling of worldwide CO2
emissions and oil production from these models. We conclude the paper with
relevant concerns in the applications of regression-model methodology and
further research of interest.
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Some Symmerty Identities for Modified Degenerate Apostol-
Bernoulli and Modified Degenerate Apostol-Euler Polynomials
Related to Multiplier Sums
Burak Kurt
Department of Mathematics, Faculty of Educations
University of Akdeniz
TR-07058 Antalya, Turkey
Abstract: Dogly et. al. in [2] defined and investigated modified degenerate
Bernoulli polynomials and numbers. They proved some identities and recurrence
relations for these polynomials. H.-In Known et. al. in [3] defined the modified
degenerate Euler polynomials and numbers. They investigated some properties
for these polynomials. Also, they gave some identities arising from the fermonic
p-adic integral on ℤ _p.
In this article, we define the modified degenerate Apostol-Bernoulli polynomials
and numbers. Also, we give modified degenerate Euler-polynomials and
numbers. We give some symmetric relations between for these polynomials.
Also, we generalize to Srivastava-Pintér summation formulea for the modified
degenerate Apostol-Bernoulli polynomials and the modified degenerate Apostol-
Euler polynomials
Keywords: Bernoulli polynomials and numbers, Euler polynomials and
numbers, Apostol-Bernoulli polynomials and numbers, Apostol-Euler
polynomials and numbers, Degenerate Bernoulli polynomials and numbers,
Degenerate Euler polynomials and numbers, Modified Degenerate Apostol-
Bernoulli polynomials, Modified Degenerate Apostol-Euler polynomials.
References:
[1] L. Carlitz, “Degenerate Stirling Bernoulli and Eulerian numbers”, Utilitas
Math., 15 (1979), 51-88.
[2] D. V. Dolgy, T. Kim, Known H.-In and J. J. Seo, “On the modified
degenerate Bernoulli polynomials”, Adv. Stu. In Comtep. Math., 26(2016), 203-
209.
[3] Q.-M. Luo, “Multiplication formulas for the Apostol-Bernoulli and Apostol-
Euler polynomials of higher order”, Integral Transforms, Spec. Func., 20(2009),
377-391.
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
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Univalency Conditions of a General Nonlinear Integral
Operator of Analytic Functions with Different Domains
Shuhai Li, Huo Tang
School of Mathematics and Statistics, Chifeng University,
Chifeng 024000, Inner Mongolia, China
[email protected]; [email protected]
Abstract: In this paper, we give some new univalence conditions of a general
nonlinear integral operator of analytic functions defined by subordination with
different domains. The results present here improve and generalize some known
results.
Keywords: Analytic function, Univalent functions, Nonlinear integral operator,
Subordination.
References:
[1] P. L. Duren. Univalent functions. Grundlehren der Mathematischen
Wissenschaften, Band 259, Springer-Verlag, New York, Berlin, Heidelberg and
Tokyo, 1983.
[2] W. Janowski. Some extremal problems for certain families of analytic
functions,I, Ann. Polon. Math. 28(1973), 297-326.
[3] J. Stankiewicz and J. Waniurski. Some classes of functions subordinate to
linear transformation and their applications, Ann. Univ, Mariae Curie-
Sklodowska, Section A. 28(1974), 85-94.
[4] B. A. Frasin. Univalency of a nonlinear integral operator of analytic
functions, Journal of Mathematical Inequalities. 9(2015), 763-771.
[5] Adriana Oprea, Daniel Breaz and H. M. Srivastava, Univalence conditions
for a new family of integral operators, Filomat. 30(2016), 1243-1251.
[6] Liangpeng Xiong, Properties of certain nonlinear integral operator associated
with Janowski Starlike and convex functions, Journal of Mathematical Research
with Applications. 36(2016), 432-440.
[7] Sh. Najafzadeh, A. Ebadian and H. Rahmatan, Univalency conditions for a
new integral operator, Journal of Computer Science and Applied Mathematics.
1(2015), 35-37.
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Certain Subclasses of Harmonic Univalent Functions Defined
By Convolution and Subordination
Shuhai Li, Huo Tang
School of Mathematics and Statistics, Chifeng University,
Chifeng , Inner Mongolia, China
[email protected]; [email protected]
Abstract: Let HS be the class of functions ghf that are harmonic
univalent and sense-preserving in the open unit disk 1: zzU for which
01)0()0( ' ff . In the present paper, we introduce some new subclasses of
HS consisting of univalent and sense-preserving functions defined by
convolution and subordination. Sufficient coefficient conditions, distortion
bounds, extreme points and convolution properties for functions of these classes
are obtained. Also, we discuss the radius of starlikeness and convexity.
Keywords: Harmonic univalent functions, subordination, convolution, sufficient
coefficient condition, radius.
References:
[1] J. Clunie and T. Sheil Small, Harmonic univalent functions, Ann. Acad. Sci.
Fenn. Ser. A I Math. 39(1) (1984), 3–25.
[2] J. M. Jahangiri, Coefficient bounds and univalent criteria for harmonic
functions with negative coefficients,Ann. Univ. Marie-Curie Sklodowska Sect.
A. 52 (1998), 57–66.
[3] J. M. Jahangiri, Harmonic functions starlike in the unit disc, J. Math. Anal.
Appl. 235 (1999), 470–477.
[4] H. Silverman and E. M. Silvia, Subclasses of harmonic univalent functions,
New Zealand J. Math. 28(1999), 275–284.
[5] S. Nagpal and V. Ravichandran, A comprehensive class of harmonic
functions defined by convolution and its connection with integral transforms and
hypergeometric functions, Stud. Univ. Babes Bolyai-Math. 59(1) (2014), 41–55.
[6] S. Nagpal and V. Ravichandran, Fully starlike and fully convex harmonic
mappings of order α, Ann. Polon.Math. 108 (2013), 85–107.
[7] R. M. El-Ashwah and B. A. Frasin, Hadamard product of certain harmonic
univalent meromorphic functions, Theory and Applications of Mathematics
Computer Science. 5 (2) (2015), 126–131.
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Refinement of Some Inequalities Concerning to Bn-Operator of
Polynomials with Restricted Zeros
A. Liman
Department of Mathematics, National Institute of Technology Srinagar
Jammu and Kashmir, India
Abstract: Let Pn be the class of polynomials of degree at most n. Rahman
introduced the class Bn of operators B that map Pn into itself. We present the
correct proof of the result of Rather and Gulzar (Adv Inequal Appl 2:16–30,
2013). Moreover our result improves many prior results involving Bn operators
and a number of polynomial inequalities can also be deduced by a uniform
procedure.
Keywords: Polynomials, B-operator, inequalities.
References:
[1] Abdul Aziz, A refinement of an inequality of S. Bernstein, J. Math. Anal.
Appl., 142(1989), 1-10.
[2] N. A. Rather, S. Gulzar, On an operator preserving inequalities between
polynomials. Adv. Inequal. Appl. 2, 16–30 (2013)
[3] S. Bernstein, Sur la limitation des derivees des polynomes, C. R. Acad. Sci.
Paris., 190(1930), 338-340.
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139
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Gaussian Approximation to the Estimator of the Mean of a
Heavy-Tailed Distribution under Random Censoring
Djamel Mearghni
Department of Mathematics, Mohamed Khider University,
Biskra, Algeria
Abstract: In many real life applications, the observations may not be available
in their entirety: they are usually randomly censored. This happens quite often
with, for instance, lifetime, reliability or insurance data. We model this situation
by introducing a non-negative random variable (rv), called censoring rv,
independent of the rv of interest. Then, we focus on minimum of the two rv's and
an indicator rv which determines whether or not there has been censorship. In
this work, we first apply the extreme value theory results to define an estimator
for the mean of a heavy-tailed distribution under random censoring. Then, we
make use of the empirical process theory to provide a Gaussian approximation to
the proposed estimator, which would lead to its asymptotic normality.
Keywords: Empirical process; Gaussian approximation; Heavy-tailed
distribution; Mean estimator; Order statistics; Random censoring.
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140
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Industrial Application of Fuzzy Logic Control for
Torque-ripple Minimization in Electricals Machines
Zineb Mekrini, Seddik Bri
Materials and Instrumentation (MIM), Electrical Engineering Department, High
School of Technology, Moulay Ismail University Meknes-Morocco
Abstract: This paper deals with fuzzy system application in the industry. Fuzzy
logic use linguistic descriptions of variable and linguistic for the input and output
behavior.Numerical input quantities are mapped to numerical output quatities by
using, fuzzification,inference ,and defuzzification procedures.As a
consequence,fuzzy systems can be based as nonlinear systems .The
asynchronous machine constitute a theoretically interesting and practically
important class of nonlinear systems. They are described by nonlinear
differential equation.The major problem that is usually associated with control of
this machine is the high torque ripple as it is not directly controlled. The high
torque ripple causes vibrations to the motor which may lead to component lose,
bearing failure or resonance. The fuzzy logic controller is applied to reduce
electromagnetic torque ripple.
Keywords: Fuzzy logic, Asynchronous machine ,Torque –Electromagnetic flux .
References:
[1] F.Korkmaz, I.Topaloğlu, H.Mamur,“Fuzzy Logic Based Direct Torque
Control Of Induction Motor With Space Vector Modulation ”, International
Journal on Soft Computing, Artificial Intelligence and Applications
(IJSCAI),Vol.2, No. 5/6, pp.32–40, December 2013.
[2]Rajendra .S. Soni, S. Dhamal, “ Direct Torque Control Of Three Phase
Induction Motor Using Fuzzy Logic”, International Conference on Electrical,
Electronics and Computer Engineering , pp.34–38, 25th August 2013,
[3] F.Korkmaz, I.Topaloğlu, H.Mamur,“ Direct Torque Control of Induction
Motor With Fuzzy Logic for Minimization of Torque Ripples”, International
Journal of Engineering Research and General Science , Vol 3, Issue 1, pp.361–
367, January-February, 2015.
[4] D. SUN, HE ,Yikang, I.Topaloğlu, H.Mamur. Fuzzy Logic Direct Torque
Control for Permanent Magnet Synchronous Motors”, IEEE Transactions, the
5Ih World Congress on Intelligent Control and Automation, pp.4401-4405, June
15-19,2004,Hangzhou.
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On Optimal Control of Stochastic Mean Field Systems
Brahim Mezerdi
Laboratory of Applied Mathematics, Mohamed Khider University,
Biskra, Algeria
Abstract: In this talk, we deal with optimal control of systems driven by mean-
field stochastic differential equations. These equations are obtained as limits of
interacting particle systems, as the number of particle tends to infinity. This kind
of approximation result is called "propagation of chaos", which says that when
the number of particles (players) tends to infinity, the equations defining the
evolution of the particles could be replaced by a single equation, called the
McKean-Vlasov equation. This mean-field equation, represents in some sense
the average behavior of the infinite number of particles. Since the earlier papers
by Lasry-Lions and Huang-Malhamé-Caines, mean-field control theory and
mean-field game theory has raised a lot of interest, motivated by applications to
various fields such as game theory, mathematical finance, communications
networks, management of oil ressources. Mean-field control problems occur in
many applications, such as in a continuous-time Markowitz's mean--variance
portfolio selection model where the variance term involves a quadratic function
of the expectation. We are interested in relaxed controls which are measure
valued processes. We prove that the strict and relaxed control problems have the
same value function and that an optimal relaxed control exists. In a second step,
we establish necessary conditions for optimality in the form of a relaxed
stochastic maximum principle, obtained via the first and second order adjoint
processes, see [1,2].
Keywords: Mean-field stochastic differential equation; relaxed control;
martingale measure; adjoint process; stochastic maximum principle; variational
principle.
References:
[1] K. Bahlali, M. Mezerdi, B. Mezerdi, Existence of optimal controls for
systems governed by mean-field stochastic differential equations, Afrika
Statistika, Vol. 9 (2014), No 1, 627-645.
[2] K. Bahlali, M. Mezerdi, B. Mezerdi, Existence and optimality conditions for
relaxed mean-field stochastic control problems, Systems and Control Letters,
Issue in progress 2017 http://dx.doi.org/10.1016/j.sysconle.2016.12.009.
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Ring Theory Approaches to Solve Cauchy-Euler Differential
Equations of Several Variables
Assal Miloud
Department of Mathematics, university of Jeddah,
Jeddah, KSA
Department of Mathematics, Carthage University,
Tunisia
Abstract: In this paper we introduce a new ring R of ponderation functions and
we study a class of modules over R and prove that Laplace transform and
Fourier transform generate some free modules over the ring R. Moreover we
characterize the projective modules and simple modules and we prove that the
socle of this ring is not an injective module. As an application we use the ring
properies to give a new methode to solve equations of the form
Div(Xf)= g
in several variables. Furthermore, we give a general solution of the Cauchy-Euler
Equations in high dimensions.
Keywords: Ring, Cauchy-Euler differential Equations.
References:
[1] Assal M., Zeyada N, “New ring of a class of Bessel integral operators.
Integral Transforms Spec Funct. 2016;27(8):611-619..
[2] Atiyah, MF, Macdonald, IG. “Introduction to Commutative Algebra”.
Westview Press: New York; 1969.
[3] T. Pierce RS. “Associative Algebras”. Graduate Texts in Mathematics
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Subgradient Method of Solving the Problem of Linear
Stochastic Programming with Bifurcation Effect
Fakhriddin Mirzoahmedov
Center of Innovative Development of Science and New Technologies,
Academy of Science of Republic of Tajikistan
Dushanbe, Tajikistan
Abstract: In modern conditions from innovation point of view necessarily of the
mathematical modeling is the presence of uncertainty, nonlinearity, ambiguities,
critical points, branching processes, etc.
Hereinafter, the bifurcation theory has become a source and a part of the
mathematical theory of catastrophes and description of the various systems
associated with the presence of nonlinearity or piecewise linearity.
Examples of bifurcation may be a split in the experiments and processes, when
after the critical point, can be observed in case either one way or the other.
One of the sections developed by mathematical modeling is a linear
programming problem, which is widely used in technological processes of
production systems, where the main objective is to optimize the costs.
However, products manufactured with such a criterion in this period cannot be
implemented (in the case of proficiently) or insufficient to meet the demand
(deficiency case), which by nature is random and creates the effect of
bifurcation.
This report will explore the stochastic analogue of the general problem of linear
programming considering bifurcation effect and subgradient algorithm to solve
it. We give also the results for numerical experiments.
References:
1. Mirzoahmedov F. Conflicting models of linear programming in production
and economic systems. -Dushanbe: Tajik State National University, 2002.
2. Ermoliev YM Methods of stochastic programming. - M .: Nauka, 1976.
3. Mirzoahmedov F. Mathematical models and methods of production
management, taking into account the random faktorov. Kiev, "Naukova Dumka,"
1991.
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Modelling Asymmetric Magnetic Recording Heads with an
Underlayer Using Superposition
Ammar Edress Mohamed
Duhok Polytechnic University, Zakho Technical Institute, Kurdistan Region -
Iraq
Abstract: This paper analyses and calculates the head fields of asymmetrical 2D
magnetic recording heads when the soft-underlayer is present using the
appropriate Green's function to derive the surface potential/field by utilising the
surface potential for asymmetrical head without underlayer. The results follow
closely the corners, while the gap region shows a linear behaviour for d/g < 0.5
compared with the calculated fields from finite-element.
Keywords: Magnetic recording heads, Laplace’s equation, Karlqvis head,
Finite-element.
References:
[1] G. Fan, “A study of the playback process of a magnetic ring head,” IBM
J. Res. Dev., vol. 5, pp. 321–325, 1961.
[2] 0. Karlqvist, “Calculation of the magnetic field in the ferromagnetic
layer of a magnetic drum,” Trans. Roy. Inst. Technol. Stock. Sweden, vol.
86, no. 1, pp. 1–27, 1954.
[3] N. Curland and J. Judy, “Calculation of exact ring head fields using
conformal mapping,” Magnetics, IEEE Transactions on, vol. 22, no. 6.
pp. 1901–1903, 1986.
[4] J. S. Yang and H. L. Huang, “Calculation of exact head and image fields
of recording heads by conformal mapping,” IEEE Trans. Magn., vol. 25,
no. 3, pp. 2761–2768, 1989.
[5] T. J. Szczech, D. M. Perry, and K. E. Palmquist, “Improved Field
Equations For Ring Heads,” IEEE Trans. Magn., vol. M, no. 5, pp. 5–9,
1983.
[6] S. Iwasaki, “Perpendicular Magnetic Recording,” IEEE Trans. Magn.,
vol. 16, no. 1, pp. 71–76, 1980.
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G-compactness for Topological Groups with Operations
1Osman Mucuk and 2Huseyin Cakalli
1Department of Mathematics, Erciyes University, Kayseri, Turkey
[email protected] 2Maltepe University, Graduate School of Science and Engineering, Maltepe,
Istanbul-Turkey
It is well known that for a Hausdorff topological group X, the limits of
convergent sequences in X define a function denoted by lim from the set of all
convergent sequences in X to X. This notion has been modified by Connor and
Grosse-Erdmann in [7] for real functions by replacing lim with an arbitrary
linear functional G defined on a linear subspace of the vector space of all real
sequences. Some authors have recently extended the concept to the topological
group setting and introduced the concepts of G-sequential continuity [2], [10],
G-sequential connectedness [3], [5] and G-sequential compactness [4].
On the other hand in [12] Orzech introduced a certain algebraic category C
called category of groups with operations including groups, rings without
identity, R-modules, Lie algebras, Jordan algebras, and many others. Mucuk and
Çakallı in [6] extended the connectedness of topological groups to more general
topological groups with operations. In this paper we prove some results on the
different types of G- compactness for topological group with operations.
Keywords: Sequences, G-continuity, G-conpactness, topological group with
operations
References:
[1] H. F. Akız, N. Alemdar, O. Mucuk, T. Şahan, Coverings of internal
groupoids and crossed modules in the category of groups with operations,
Georgian Math. J., 20-2 (2013) 223-238.
[2] H. Çakallı, On G-continuity, Comput. Math. Appl. , Vol. 61, No.2, (2011)
313-318.
[3] H. Çakallı, Sequential definitions of connectedness, Appl. Math. Lett., Vol.
25, No.3, , (2012) 461-465.
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[4] H. Çakallı Sequential definitions of compactness, Appl. Math. Lett., 21 , 6,
(2008) 594-598.
[5] H. Çakallı, O. Mucuk, On connectedness via a sequential method, Revista
de la Uniòn Matemática Argentina, Vol.54, No.2, (2013) 101-109.
[6] O. Mucuk, H. Cakalli, G-connectedness for topological groups with
operations, Filomat (ICAAM 2016).
[7] J.Connor, K.-G. Grosse-Erdmann,Sequential definitions of continuity for real
functions, Rocky Mountain J. Math. , Vol. 33, No.1, (2003)93-121.
[8] S. Lin and L. Liu, G-methods, G-sequential spaces and G-continuity in
topological spaces, Top. App.212 (2016) 29-48.
[9] G. D. Maio, L.D.R. Kocinac, Statistical convergence in topology, Topology
Appl. 156 (2008) 28-45.
[10] O. Mucuk, T. Şahan, On G-sequential Continuity, Filomat Vol.28, No.6,
(2014) 1181-1189.
[11] O. Mucuk, T. Şahan, N. Alemdar, Normality and quotients in crossed
modules and group-groupoids, Appl. Categ. Structures, 23-3 (2015) 415-428.
[12] G. Orzech, Obstruction theory in algebraic categories I and II, J. Pure.
Appl. Algebra, Vol.2, (1972) 287-314 and 315-340.
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Topological Aspects of Monodromy Groupoids for Group-
Groupoids
1Osman Mucuk and 2Serap Demir
1Department of Mathematics, Erciyes University, Kayseri, Turkey
[email protected] 2Department of Mathematics, Erciyes University, Kayseri, Turkey
Abstract: One form of the monodromy principle was enunciated by Chevalley
in [4]. The general idea is that of extending a local morphism f on a topological
structure G, or extending a restriction of f, not to G itself but to some simply
connected cover of G. A different approach was indicated by J. Pradines in [8] to
generalise the standard construction of a simply connected Lie group from a Lie
algebra to a corresponding construction of a Lie groupoid from a Lie algebroid.
Let G be a topological groupoid such that the stars G_x the fibres of initial
point map of the groupoid are path connected and have universal covers. Let
Mon(G) be the disjoint union of the universal covers of the stars G_x's at the
base points identities of the groupoid G. Then there is a groupoid structure on
Mon(G) defined by the concatenation composition of the paths in the stars G_x.
We call Mon(G) as the monodromy groupoid of G. In [3] Brown and Mucuk in
the smooth groupoid case including topological groupoids, the star topological
groupoid and topological groupoid structures of Mon(G) were studied under
some suitable local conditions. Then the group-groupoid structure of Mon(G)
was recently developed in [7] and internal groupoid structure of Mon(G) was
given in [1] . In this paper we will develop the topological aspect of Mon(G) and
prove that if G is a topological group-groupoid, then Mon(G) becomes a
topological group-groupoid; and give a monodromy principle for topological
group-groupoids.
Keywords: Group-groupoid, monodromy groupoid, topological group-
grouppoid
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References:
[1] H. F. Akız, N. Alemdar, O. Mucuk, T. Şahan, Coverings of internal
groupoids and crossed modules in the category of groups with operations,
Georgian Math. J., 20-2 (2013) 223-238.
[2] M.E.-S.A.-F., R. Brown, The holonomy groupoid of a locally topological
groupoid, Top. Appl., 47 (1992)7-113.
[3] R. Brown, O. Mucuk, The monodromy groupoid of a Lie groupoid, Cah.
Top. Géom.Diff. Cat. 36 (1995) 345-370.
[4] C. Chevalley, Theory of Lie groups, Princeton University Press, 1946.
[5] L. Douady, M. Lazard, Espaces fibrés en algébres de Lie et en groupes,
Invent. Math. 1 (1966) 133-151.
[6] K.C.H Mackenzie, Lie groupoids and Lie algebroids in differential
geometry, London Math. Soc.Lecture Note Series 124, Cambridge University
Press, 1987.
[7] O. Mucuk, B. Kılıçarslan, T. Şahan, N. Alemdar, Group-groupoid and
monodromy groupoid, Topology Appl. 158 (2011) 2034-2042.
[8] J. Pradines, J., Théorie de Lie pour les groupoïdes différentiables, relation
entre propriétés locales et globales, Comptes Rendus Acad. Sci. Paris, Sér A,
263 (1966), 907-910.
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A Characterization of the Two-Weight Inequality for Riesz
Potentials on Cones of Radially Decreasing Functions
Ghulam Murtaza
Department of Mathematics, GC University, Faisalabad, Pakistan.
Abstract: We establish necessary and sufficient conditions on a weight pair
(v,w) governing the boundedness of the Riesz potential operator Iα defined on a
homogeneous group G from Lpdec,r(w,G) to Lq(v,G), where Lp
dec,r(w,G) is the
Lebesgue space defined for non-negative radially decreasing functions on G. The
same problem is also studied for the potential operator with product kernels Iα1,α2
defined on a product of two homogeneous groups G1 × G2. In the latter case
weights, in general, are not of product type. The derived results are new even for
Euclidean spaces. To get the main results we use Sawyer-type duality theorems
(which are also discussed in this paper) and two-weight Hardy-type inequalities
on G and G1 × G2, respectively.
Keywords: Riesz potential; multiple Riesz potential; homogeneous group; cone
of decreasing functions; two-weight inequality; Sawyer’s duality theorem
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On The Fourth Geometric-Arithmetic Index of Graphs
Y. Nacaroglu and A. Dilek Maden
Department of Mathematics, Selcuk University,
Konya, Istanbul, Turkey
[email protected] and [email protected]
Abstract: Topological indices are the numerical value associated with chemical
constitution professes for correlation of chemical structure with various physical
properties, chemical and biological activity [1]. In 2010, M. Ghorbani and A.
Khaki defined the eccentricity based geometric arithmetic index named as
eccentric version of Geometric arithmetic index [2]. In this paper, we present
some upper and lower bounds on the fourth geometric arithmetic index.
. Keywords: Topological index, Eccentricity, Geometric-arithmetic index, Fourth
geometric arithmetic index
References:
[1] M.K. Jamil, M.R. Farahani, M.R.R. Kanna, “Fourth Geometric Arithmetic
Index of Polycyclic Aromatic Hydrocarbons (PAHk)”, Pharm. and Chem. J.
3(2016), 94-99.
[2] M. Ghorbani and A. Khaki, “A note on the fourth version of Geometric –
Arithmetic index”, Optoelectron. Adv. Mater-Rapid Commun., 4(2010), 2212-
2215.
[3] K. Ch. Das, I. Gutman, B. Furtula, “Survey on Geometric – Arithmetic
indices of graphs”, Match. Commun. Math. Comput. Chem., 65(2011), 595-644.
[4] J. M. Rodríguez, J. M. Sigarreta, “On the Geometric- Arithmetic Index”,
Match. Commun. Math. Comput. Chem., 74(2015), 103-120.
[5] I. Gutman, N. Trinajstić, “Graph theory and molecular orbitals. Total φ-
electron energy of alternant hydrocarbons”, Chemical Physics Letters, 17(4)
(1972), 535-538.
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Laplace Transform of Fractional Differential Equations
Khaled I. Nawafleh
Physics Department, Mu,tah University,
Al-Karak, Jordan;
Abstract: The aim of this work is to study the possible extension of applying the
Laplace transform for solving fractional differential equations. The Laplace
transform allow us to transform fractional differential equations into algebraic
equations and then by solving this algebraic equations, we can obtain the unknown
function by using the inverse Laplace transform. Two illustrative examples are
included to demonstrate the validity and applicability of the presented technique, the
first one is the LC circuit as a conservative system, and the second one is the RC
circuit as a non-conservative system.
Keywords: Fractional Differential Equations, Laplace Transform, LC Circuit,
RC Circuit.
References:
[1] Om P. Agrawal (2001), Formulation of Euler-Lagrange Equations for
Fractional Variational Problems, J. Math. Anal. Appl. 272(2002) 386-379.
[2] Eltayeb. A. M. Yousif and Fatima. A. Alawad. Laplace Transform Method
Solution of Fractional Ordinary Differential Equations, University of Africa
Journal of Sciences. (2012) 2, 139-160.
[3] Saeed Kazem. Exact Solution of Some Linear Fractional Differential
Equations by Laplace Transform, International Journal of.Nonlinear Science,
(2013) 16 (1) 3-11.
[4] Shy-Der Lin and Chia-Hunglu. Laplace transform for solving some families
of fractional differential equations and its applications, a springer open journal,
(2013) 137.
[5] Joseph M. Kimeu (2009), Fractional Calculus: Definitions and Applications,
Masters Theses & Specialist Projects.
[6] Arfken, G., & Weber, H. J. Mathematical Method for Physicists Academic.
New York, (1985) 309.
[7] Saxena R. K., and Nishimoto, K. On a fractional integral formula of .Saigo
operator, J. Fract. Calc., (2002) 22, 57-58.
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Gaussian Approximation of a New Tail Index Estimator for
Right-Censored Pareto-Type Distributions
Abdelhakim Necir
Laboratory of Applied Mathematics, Mohamed Khider University,
Biskra, Algeria [email protected]
Abstract: A new consistent and an asymptotically normal estimator for the
positive tail index of right-censored data is proposed. In this context, a tail
empirical process is introduced and its Gaussian approximation is established. A
simulation study is carried out to compare the proposed estimator with the
existing ones in terms of bias and mean squared error. An application to survival
time of Australian male Aids patients are provided.
Keywords: Extreme value index; Gaussian approximation; Random censoring,
Tail empirical process.
References:
[1] Einmahl, J.H.J., Fils-Villetard, A. and Guillou, A., 2008. Statistics of
extremes under random censoring. Bernoulli 14, 207-227.
[2] de Haan, L. and Ferreira, A., 2006. Extreme Value Theory: An Introduction.
Springer.
[3] Hill, B.M., 1975. A simple general approach to inference about the tail of a
distribution. Ann. Statist. 3, 1163-1174.
[4] Stupfler, G., 2016. Estimating the conditional extreme-value index under
random right-censoring. J. Multivariate Anal. 144, 1-24.
[5] Worms, J. and Worms, R., 2014. New estimators of the extreme value index
under random right censoring, for heavy-tailed distributions. Extremes 17, 337-
358.
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On Residual Algebraic Free Extensions of Valuations
Figen Oke
Trakya University Department of Mathematics
Edirne,Turkey
Abstract: If v is a valuaton on a field K with rankv=2 then there exist three kind
residual algebraic free extensions of v to the rational function field K(x) with
one variable over K. In this study the first kind residual algebraic free extension
of v to K(x) is studied.
Keywords: extensions of valuations, residual algebraic free extensions, valued
fields
References:
[1] V. Alexandru - N. Popescu - A. Zaharescu, A theorem of characterization of
residual transcendental extension of a valuation, J. Math. Kyoto Univ., 28
(1988), 579-592.
[2] V. Alexandru - N. Popescu - A. Zaharescu, Minimal pair of definition of a
residual transcendental extension of a valuation, J. Math. Kyoto Univ. 30 (1990),
no. 2, 207-225
[3] V. Alexandru - N. Popescu - A. Zaharescu, All valuations on K(X), J. Math.
Kyoto
Univ. 30 (1990), no. 2, 281-296.
[4] N. Bourbaki, Algebre Commutative, Ch. V: Entiers, Ch. VI: Valuations,
Hermann, Paris (1964).
[5] O. Endler, Valuation Theory, Springer, Berlin -Heidelberg-New York (1972).
[6] N. Popescu, C. Vraciu, On the extension of valuations on a field K to K(x)-I,
Ren. Sem. Mat. Univ. Padova, 87 (1992), 151-168
[7] N. Popescu, C. Vraciu, On the extension of valuations on a field K to K(x)-II,
Ren. Sem. Mat. Univ. Padova, 96(1996), 1-14
[8] O.F.G. Schilling, The Theory of Valuations, A.M.S. Surveys, no. 4,
Providence, Rhode Island (1950).
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Statistically (C,1,1) Summable Double Sequences of Fuzzy
Numbers and a Tauberian Theorem
Zerrin Onder, Ibrahim Canak, Umit Totur
Department of Mathematics, Ege University, İzmir, Turkey
Department of Mathematics, Ege University, İzmir, Turkey
Department of Mathematics, Adnan Menderes University, Aydın, Turkey
[email protected], [email protected], [email protected]
Abstract: Developed based on the concept of fuzzy sets which was discovered
and introduced by Zadeh, fuzzy set theory have received more and more
attention from researchers who have intended to apply the concept of fuzziness
to individual works with different aspects from theoretical to practical in almost
all scientific areas. One of the areas which the concept of fuzziness was practised
is the summability theory, as well. In this talk, we recall some notations, basic
definitions and theorems with respect to fuzzy numbers and its double sequences
and define the concepts of slow oscillation for the double sequences of fuzzy
numbers in certain senses. In the sequel, we prove that a bounded double
sequence of fuzzy numbers which is statistically convergent is also statistically
(C, 1, 1) summable to the same number. We construct an example that the
converse of this statement is not true in general. Finally, we indicate that the
statistically (C, 1, 1) summable double sequence of fuzzy numbers is convergent
and statistically convergent to the same fuzzy number in Pringsheim's sense
under the slowly oscillating and statistically slowly oscillating conditions in
certain senses, respectively.
Keywords: Double sequences of fuzzy numbers, ,Slowly oscillating sequences,
(C,1,1) summability, Statistical convergence, Tauberian theorems.
References:
[1] H. Fast, “Sur la convergence statistique”, Colloq. Math. 2(1951), 241-244.
[2] I. J. Schoenberg, “The integrability of certain functions and related
summability methods”, Am. Math. Mon. 66(1959), 361-375.
[3] B. C. Tripathy and A. J. Dutta, “On fuzzy real-valued double sequence
spaces”, Soochow J. Math. 32(2006), 509-520.
[4] B. C. Tripathy and A. J. Dutta, “Statistically convergent and Cesaro
summable double sequences of fuzzy real numbers ”, Soochow J. Math.
33(2007), 835-848.
[5] L. A. Zadeh, “ Fuzzy sets”, Inform. Control 8(1965), 338-353.
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The Sheffer Stroke Basic Algebras on the Intervals
Tahsin Oner1, Tugce Katican2
Department of Mathematics, Ege University1,2,
Bornova, Izmir, Turkey
[email protected], [email protected]
Abstract: The axiom system of Sheffer Stroke operation was introduced by
Henry Sheffer in 1913 [6], and the improvements of this operation have beeen
given in [2] and [7]. The notions about basic algebras were mentioned in [1], [3]
and [4]. Afterwards, Oner and Senturk introduce some definitions and notions
about the Sheffer Stroke basic algebras in [5]. In this work, giving basic concepts
about the Sheffer Stroke operation and Sheffer stroke basic algebras 𝒜 = (𝐴; ∣),
we define the operations ∣𝑎, ∣𝑏 and ∣𝑎𝑏 for any elements 𝑎, 𝑏 ∈ 𝐴 such that
([𝑎, 1]; ∣𝑎), ([0, 𝑏]; ∣𝑏) and ([𝑎, 𝑏]; ∣𝑎𝑏) are Sheffer Stroke basic algebras,
respectively. We also show that these interval Sheffer Stroke basic algebras on a
given Sheffer Stroke basic algebra 𝒜 = (𝐴; ∣) verify the patchwork condition.
Keywords: Sheffer Stroke basic algebra, interval sheffer stroke basic algebra,
patchwork condition.
References:
[1] Chajda, Ivan. "Basic algebras, logics, trends and applications." Asian-
European Journal of Mathematics, Vol.8, No 31550040, (2015).
[2] Chajda, Ivan. "Sheffer operation in ortholattices." Acta Universitatis
Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica Vol. 44,
no.1, pp. 19-23, (2005).
[3] Chajda I, Kolařík M. “Independence of the axiomatic system of basic
algebras.” Soft Computing, Vol. 13, pp. 41-43, (2009).
[4] Chajda I, Kolařík M. "Interval Basic Algebras." NOVI SAD J. MATH., Vol.
39, 2, (2009).
[5] Oner, T., Senturk I. "The Sheffer Stroke Operation Reducts of Basic
Algebras", submitted, (2017).
[6] Sheffer, H. M.. “A set of five independent postulates for Boolean algebras,
with application to logical constants.” Transactions of the American
Mathematical Society, 14(4), 481-488, (1913).
[7] Whitehead, A. N., Russell, B. Principia Mathematica. New York, Cambridge
University Press, (1927).
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A Reduction of Basic Algebras: Sheffer Stroke Basic Algebras
Tahsin Oner1, Ibrahım Senturk2
Department of Mathematics, Ege University1,2,
Bornova, Izmir, Turkey
[email protected] [email protected]
Abstract: The concept of basic algebras was introduced in Chajda and
Emanovský [1], see also Chajda [2] and Chajda et al.[3] for the further
information. Basic algebras are an important notions of algebras used in diff erent
non-classical logics since they not only contain orthomodular lattices 𝐿 = (L; ∨,
∧, ⊥, 0, 1), where x ⊕ y = (x ∧ 𝑦⊥) ∨ y and ¬ x = 𝑦⊥, but they also constitute
an axiomatization of the logic of quantum mechanics along with MV-algebras
[4], which get an axiomatization of many-valued Łukasiewicz logics; see Chajda
[5] and Chajda et al. [6]. In this study, we present a term operation Sheffer stroke
in a given basic algebra A and examine properties of the Sheffer stroke reduct of
A. In addition, we qualify such Sheffer stroke basic algebras. Finally, we
construct a bridge between basic algebras and Boolean algebras.
Keywords: Basic algebras, Sheffer Sroke operation, Reduction
References:
[1] I. Chajda and P. Emanovský, “Bounded lattices with antitone involutions
and properties of MV-algebras”, Discussiones Mathematicae, General Algebra
and Applications, 24.1 (2004), 32-42.
[2] I. Chajda, “Lattices and semilattices having an antitone involution in every
upper interval”, Comment. Math. Univ. Carolin, 44.4 (2003), 577-585.
[3] I. Chajda, “Basic algebras”, Clone Theory and Discrete MathematicsAlgebra
and Logic Related to Computer Science, (2013).
[4] R. L. Cignoli, I. M. d’Ottaviano and D. Munduci, Algebraic foundations of
many valued reasoning (Vol. 7), Springer Science & Business Media.
[5] I. Chajda, “Basic algebras and their applications”, an overview. Contr Gen
Algebra, 20, (2011).
[6] I. Chajda, R. Halaš and J. Kühr, “Many-valued quantum algebras”,
AlgebraUniversalis,60.1(2009),63-90.
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Applications on Weak and Strong Forms of Fuzzy α-Open
(Closed) Sets
Hakeem A. Othman*
*Department of Mathematics, AL-Qunfudhah University college, Umm
Al-Qura University, KSA.
*Department of Mathematics, Rada'a College of Education and Science,
Albaydaa University, Albaydaa, Yemen.
[email protected] and [email protected]
Abstract: The present paper tries to introduce some applications on fuzzy
(supra-) infra- α -open (closed) sets, likely, fuzzy (supra-) infra- α –continuous
mappings, fuzzy (supra-) infra- α -open (closed) mappings, fuzzy supra- α -
irresolute mapping and fuzzy supra- α -connected space. Moreover, The relations
and converse relations between these mappings are highlighted. Important results
about these mappings and fuzzy supra- α –connected space are investigated and
presented.
Keywords: fuzzy infra- α -open set; fuzzy infra- α -closed set; fuzzy supra- α -
continuous mapping; fuzzy infra- α -continuous mapping; Fuzzy supra- α -
irresolute mapping; Fuzzy infra- α - irresolute mapping; Fuzzy infra- α -
connected space.
References
[1] K. K. Azad, "On fuzzy semi continuity, fuzzy almost continuity and weakly
continuity", J. Math. Anal. Appl., 82 (1981), pp.14-32.
[2] A. S. Bin Shahna, "On fuzzy strongly semi continuity and fuzzy
precontinuity", Fuzzy Sets and Systems, 44 (1991), pp.330-308.
[3] M. H. Ghanim, E. E. Kerre and A. S. Mashhour, "Separation Axioms,
Subspace and Sums in Fuzzy Topology ", J. Math. Anal Appl, 102(1984), pp.
189-202.
[4] Hakeem A. Othman, "On fuzzy sp-open sets", Hindawi Publishing
Corporation, Advances in Fuzzy Systems Volume 2011, Article ID 768028, 5
pages,doi:10.1155/2011/768028.
[5] Hakeem A. Othman and Md.Hanif.Page, "ON An Infra-_-Open Sets ",
Global Journal of Mathematical Analysis, 4(3) (2016) pp. 12-16.
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Code Verification Using Method of Manufactured Solutions for
CFD Problems
Hatice Ozcan
Department of Mathematics, Ahi Evran University,
Kırsehir, Turkey
Abstract: To find numerical solutions of non-linear hyperbolic, parabolic
systems of partial differential equations (PDEs), which predominantly appear in
computational fluid dynamics (CFD) field, are fundamental parts of discovering
the physical properties of flows [1]. The essential aim of CFD is to utilize
numerical methods and algorithms to solve and analyze fluid dynamic problems.
To this end, the motivation of this work is to ensure that the computer code
designed to solve a set of PDEs is accurate; in another words, it is bug free.
Therefore, Method of Manufactured Solutions (MMS) is used to check the
accuracy of existing code and to estimate order of accuracy of the developed
numerical method [2,3,4]. An example for Euler equations of gas dynamics is
provided to demonstrate the effective use of this method.
Keywords: manufactured solution, code verification, order of accuracy, Euler
equations of gas dynamics.
Acknowledgement : This work is supported by Ahi Evran University Scientific
Research Projects Coordination Unit (Project Number : FEF.E2.17.029).
References:
[1] C. B. Laney, “Computational gas dynamics”, Cambridge University Press
(1998).
[2] B. W. Boehm, “Verifying and validating software requirements and design
specifications”, IEEE Software 1.1(1984), 75-88.
[3] P. J. Roache, “Fundamentals of computational fluid dynamics”, Albuquerque,
NM, Hermosa Publishers (1999). [4] P. J. Roache, “Verification and validation
in computational science and engineering”, Albuquerque, NM, Hermosa
Publishers (1998).
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
On the Existence of Einstein Weyl Manifold with a Special
Metric Connection
F. Ozdemir, M. D. Turkoglu
Faculty of Science and Letters, Department of Mathematics, İstanbul Technical
University
Maslak-Istanbul,Turkey
[email protected] , [email protected]
Abstract: On a Weyl manifold, the existence of a semi-symmetric recurrent
metric connection is proved and curvature invariants and their characteristics of
manifolds having this connection are studied. Also it is introduced and examined
the necessary and sufficient condition for an Einstein Weyl (E𝑊𝑛) manifold to be
an Einstein Weyl manifold with semi-symmetric special metric connection
(EW𝑆𝑛).
Keywords: Einstein Weyl manifold, metric connection, semi-symmetric
recurrent metric connection.
References:
[1] L. P. Eisenhart, “Non-Riemannian Geometry” , New York: The American
Mathematical Society Publishing (1927).
[2] V. Hlavaty, “Theorie d'immersion d'une W_m dans W_n“, Ann. Soc. Polon.
Math., 21 (1949), 196-206.
[3] K. Yano, “On semi-symmetric metric connection”, Rev. Roumaine Math.
Pures Appl., 15(1970), 1579-1586.
[4] Y. X. Liang, “On semi-symmetric recurrent-metric connection”, Tensor
(N.S.), 55 (1994), 107-112.
[5] N. Rosen, “Weyl's geometry and physics”, Foundations Of Physics, 12/3
(1982), 213-248.
[6] E. Scholz, “Weyl geometric gravity and breaking of electroweak symmetry”,
Annalen De Physik, 523(2011), 507-530.
[7] J. T. Wheeler, “Weyl gravity as general relativity”, Phys. Rev. D 90 (2014),
025027.
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160
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Repeat Codes, Even Codes, Odd Codes and Their Equivalence
Mustafa Ozkan and Figen Oke
Department of Mathematics, Trakya University,
Edirne, Turkey
Abstract: Codes over the chain ring are obtained by writting special matrices.
Gray images of these codes are binary codes. It is shown that first repeat code,
second repeat code, even code and odd code are either equivalent or equal to
these codes. The definitions of direct sum and direct product of these codes were
given. Moreover dual codes were classed. Self dual codes and self orthogonal
codes were established.
Keywords: Codes over rings, Lee distance, Even codes, Odd codes, Dual codes.
References:
[1] M. Ozkan and F. Oke, “A relation between Hadamard codes and some
special codes over 2 2u ”, App.Mathematics and Inf. Sci, 10.2 (2016), 701-
704.
[2] M. Ozkan and F. Oke, “ Results On Hadamard Codes and Codes Over
Rings”, 3rd International Conference On Recent Advances In Pure and Applied
Mathematics (2016)
[3] S. Zhu, Y. Wang, M. Shi, Some Result On Cylic Codes Over 2 2v ,
IEEE Trans. Inf. Theory, 56. 4 (2010),1680-1684.
[4] A. Bonnecaze and P. Udaya, Cyclic codes and self dual codes 2 2u ,
IEEE Trans. Inf. Theory, 45, (1999),1250-1255.
[5] Krotov, D. S. Z4-linear perfect codes ,Diskretn. Anal. Issled. Oper.7.4
(2000), 78–90.
[6] J.Wolfmann, Negacyclic and cyclic codes over 𝑍4, IEEE Trans. Inf. Theory,
45, (1999),2527-2532.
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161
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
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Tauberian Theorems for the Weighted Mean Summability
Methods of Integrals
Firat Ozsarac, Ibrahim Canak
Department of Mathematics, Ege University, Bornova, Izmir, Turkey
[email protected]; [email protected]
Abstract: Let 0p x be a nondecreasing real-valued differentiable function
on 0, such that 0 0p
and p x
as x . Given a real-
valued function f x which is continuous on 0,
and
0
x
s x f t dt
We define the weighted mean of s x as
0
1x
p x p t s t dtp x
,
where p t is the derivative of p t .
We give some classical type Tauberian theorems to retrieve convergence of
s x out of the weighted mean integrability of p x
under some Tauberian
conditions.
Key words: Tauberian theorem, Tauberian condition, Weighted mean method of
integrals, slow decrease, slow oscillation.
References:
[1]F. Moricz, ‘‘Ordinary convergence follows from statistical summability (C,1)
in the case of slowly decreasing or oscillating sequences’’, Colloq. Math. , 99(2),
(2004), 207-219.
[2] İ. Çanak and Ü.Totur, ‘‘A Tauberian theorem for Cesaro summability of
integrals’’, Appl. Math. Lett. , 24(3), (2011), 391-395.
[3] İ. Çanak and Ü.Totur, ‘‘Tauberian conditions for Cesaro summability of
integrals’’, Appl. Math. Lett. , 24(6), (2011), 891-896.
[4] İ. Çanak and Ü.Totur, ‘‘Altenative proofs of some classical type Tauberian
theorems for Cesaro summability of integrals’’, Math. Comput. Modell. , 55(3),
(2012), 1558-1561.
[5] A. Fekete and F. Moricz, ‘‘ Necessary and sufficient Tauberian conditions in
the case of weighted mean summable integrals over R+’’ , II. Publ. Math. , 67(1-
2), (2005) , 65-78.
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162
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On Lifting Polynomials and Distinguished Pairs
Burcu Ozturk, Figen Oke
Department of Mathematics,TrakyaUniversity,
Edirne, Turkey
[email protected] , [email protected]
Abstract: Let𝑣 be a valuation of a field 𝐾 and 𝑢 be a residual algebraic free
extension of 𝑣 to the rational function field 𝐾(𝑥). So𝑢 can be defined by using a
residual transcendental extension of 𝑣 to 𝐾(𝑥) and a lifting polynomial. In this
study relations between lifting polynomials and distinguihed pairs are given
bykeeping in view of valuation 𝑢.
Keywords:Valuations, Lifting Polynomials, Distinguished Pairs, Transcendental
Extensions
References:
[1] N. Popescu, A. Zaharescu, “ On the Structure of Irreducible Polynomials over
Local Fields”, J. Number Theory, 52, (1995), 98-118.
[2] V. Alexandru, N. Popescu, A. Zaharescu, “ A Theorem of Characterization of
Residual Transcendental extensions of a Valuation”, J. Math. Kyoto Univ., 28,
(1988), 579-592
[3] S. Bhatia, S.K. Khanduja, “On Extensions Generated by Roots of Lifting
Polynomials”, Mathematika, 49 (1-2), (2002), 107-118
[4] A. Zaharescu, “Lifting Polynomials over a Local Field”, Bol. Soc. Mat.
Mexicana (3) vol.10 (2004), 15-27
[5] S.K. Khanduja, U. Grag, “Rank 2 Valuations of K(x)”, Mathematika, 37,
(1990), 97-105
[6] K. Aghigh, S.K. Khanduja, “ On Chains Associated wirh Elements Algebraic
over a Henselian Valued Field”, Algebra Colloquium 12:4 (2005), 607-616
[7] K. Aghigh, S.K. Khanduja, “ On The Main Invariant of Elements Algebraic
over a Henselian Valued Field”, Proceedings of the Edinburgh Mathematical
Society, 45, (2002), 219-227
[8] P. J. McCarthy, “Algebraic Extensions of Fields” (Blaisdell Publishing
Company, Waltham, Massachusetts, Toronto, London), (1966)
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On Some Fixed Point and Common Fixed Theorems in b-
Metric-Like Spaces
Mahpeyker Ozturk
Department of Mathematics,
Sakarya University, Sakarya, TURKEY
Abstract: In this study, we establish some existence and uniqueness theorems
for mappings via the concept of admissibility in the settings of b-metric-like and
generalized b-metric-like spaces.
Keywords: b-metric-like spaces, fixed point, admissible mappings.
References:
[1] H. Aydi, E. Karapınar, B.Samet, Fixed points for generalized alpha, psi-
contractions on generalized metric spaces., J. Inequal. Appl., (2014), 16 pages.
[2] E. Karapınar, P.Kumam, P. Salimi, On alpha-psi-Meir-Keeler contractive
mappings, Fixed Point Theory and Appl., 2013, (2013), 12 pages.
[3] A. Amini-Harandi, Metric-like spaces, partial metric spaces and fixed points,
Fixed Point Theory and Appl., 2012, (2012), 10 pages.
[4] H. Aydi, A. Felhi, S. Sahmim, Common fixed points via implicit
contractions on b-metric-like spaces, J. Nonlinear Sci. Appl., 10,1524--1537,
(2017).
[5] M.A.Alghamdi, N. Hussain, P. Salimi, Fixed point and coupled fixed point
theorems on b-metric-like spaces, J. Inequal. Appl., 2013, (2013), 25 pages.
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164
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Experimental Evidence of Landau Damping in a Fluid at a
Macroscopic Scale
Eric Padilla, William Cody Wilson, Andrei Ludu
Department of Mathematics, Embry-Riddle Aeronautical University,
Daytona Beach, Florida, USA
[email protected] , [email protected] , [email protected]
Abstract: The Landau damping effect occurs mainly in collisionless plasmas [1-
3] as a microscopic resonant mechanism of the excitation of collective modes of
oscillations. In our paper, we demonstrate the occurrence of this effect at the
macroscopic scale in a fluid populated by a system of freely moving repelling
probes (magnetic buoys) which simulate the free electrons in a plasma. The
electrons’ Coulombian interaction is replaced by magnetic dipole repulsion, and
instead of the electromagnetic wave we use a free, nonlinear, liquid surface wave
traveling through the fluid. We couple the Green-Naghdi Hamiltonian for the
incompressible fluid with the kinetic and magnetic potential of the buoys. The
dynamical resulting equation is a Vlasov-Poisson type equation which includes
at the same time the Benjamin-Feir instability and the Landau damping
phenomenon. We derive analytically and numerically the values of the Phillips’
constant and of the enhancement factor, and we compare the results with
experimental analysis of the dynamics of buoys and waves. We find that the
effect of Landau damping is present in our system, and manifests by suppressing
the formation of coherent structures. In addition, we will study the phase
transitions of the buoy network under nonlinear wave perturbations.
Keywords: Landau Damping, resonance, damping, Benjamin-Feir instability,
Green-Naghdi Hamiltonian, Vlasov-Poisson equation, nonlinear waves, fluid
dynamics, magnetic dipole, collective modes.
References:
[1] L. D. Landau, J. Physics USSR, 10 (1946) 26.
[2] I. Langmuir and L. Tonks, Phys. Rev., 33 (1929) 195.
[3] D. D. Ryutov, “Landau damping: half a century with the great discovery”,
Plasma Phys. Control Fusion, 41 (1999) A1-A12.
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165
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A Boundary Value Problem for an Irrational Order Partial
Equation
A.A. Pashavand, N.A. Aliyev, A.Y. Delshad Gharegheshlaghi
Institute of Mathematics and Mechanics of NAS of Azerbaijan
9, B.Vahabzade str., AZ 1141, Baku, Azerbaijan
Abstract: It is known that as the investigation of the solutions of problems stated
for partial equations is difficult than the investigation of problems stated for
ordinary equations, the solution of problems stated for fractional order equations
is more difficult than the investigation of the solutions of problems stated for
irrational order equations. Here we will be engaged in finding the solution of a
boundary value problem for a partial equation whose order is an irrational
number
Keywords irrational order partial discrete equation, a boundary value problem
for such an equation, finding of the solution in the form of unknown coefficient
series corresponding to Mittag-Loffler functions.
References:
[1] Tricomi F.G. Differential Equations. Blackie & Son Limited 1961, pp. 349.
[2]Petrovsky L.G. Lectures on theory of ordinary differented equations.
Gostichizdat. M.-L, 1952, 232 p. (Russian).
[3]Petrovsky I.G., Lectures on partial equations, “Nauka” Moscow, 1974
(Russian)
[4]Aliyev N. Jahanshahi M. Investiqation of BVP and IVP including Differential
Equations with real orders. Second Joint Seminar On Applied Mathematics.
Zanjan University and Baku State University, 2000, p. 92.
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166
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Generalized Close to Convex Functions with q-Properties
Yasar Polatoglu 1, Oya Mert 2, 3 and Asena Cetinkaya 1
1Department of Mathematics and Computer Sciences, Istanbul Kultur University,
Turkey 2Department of Mathematics Duzce University, Turkey
3Department of Mechanical Engineering, Istanbul Kemerburgaz University,
Turkey 1 [email protected],
2, 3 [email protected] 1 [email protected]
Abstract: q-property of analytic functions can be described as a property of any
class of these functions which use methods of quantum calculus.The main idea
of the present work is inspired on the R.J.Libera [3]. This study uniquely aims to
obtain a generalized close to convex functions that include q-properties.
Keywords: Growth theorem, distortion theorem.
References:
[1] G.E.Andrews, Application of basic Hypergeometric Functions, SIAM
Rew,(16) 1974, 441-484.
[2] M.K. Aouf and M.A.Nasr, On convex functions of complex order,
Bull.Fac.Sci.Univ.Mansoura, (9), 1982, 566-581
[3] V. Paatero, Uber Gebiete von beschrankter randdrehung Ann. Acad. Sci.
Fenn. Ser. A, 37(1933), 1-20.
[4] K. Padmanabhan and R. Parvatham, Properties of a class of functions with
bounded boundary rotation, Ann. Polon. Math., 31(1975), 311-323.
[5] B. Pinchuk, Functions with bounded boundary rotation, Isr. J. Math.,
10(1971), 7-16.
[6] M. S. Roberston, On the theory of univalent functions, Ann. Math., 37(1936),
374-408. 02010 Mathematics Subject Classification: 30C45 Key words and
phrases: Growth theorem, distortion theorem.
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Steady-State Modeling of the Biological Network via
Long-tailed Symetric Distribution
Vilda Purutcuoglu1 and Melih Agraz2
1, 2Department of Statistics, Middle East Technical University,
Ankara, Turkey [email protected] ; [email protected]
Abstract: The steady-state modeling of the biological systems presents the
acivation of the systems’ elements without the randomness. This model is the
most common modeling approach of the complex systems since the majority of
the available data is more suitable in this type of description. In the mathematical
representation of the underlying activation, the Gaussian graphical model (GGM)
is the most well-known probabilistic model which is depedent on the conditional
independence of the nodes (i.e., proteins, genes or other species of the system in
this context), under the multivariate normality assumption of the measurements
[1]. Althougt GGM is successful in the description of the small and moderately
large systems, its inference is computationally demanding particularly for large
networks and it is powerful under the strick normality assumption [2]. Hereby, in
this study, we extend this model by denoting the measurements via the long-
tailed symmetric distribution family which covers a wide range of densities from
Cauchy, student-t to normal. By this way, we can obtain a new graphical
explaination of the system having more realistic assumption abou the data and
we call it the long-tailed graphical model (LTGM). Then, we derive the explicit
form of the model parameteres via the modified maximum likelihood estimators
(MMLE) [3] which is obtained from the order statistics and is the asymptotic
equivalence of the maximum likelihood estimator. From our simulation studies,
we show that LTGM with MMLE is computationally more efficient and accurate
than GGM with its inference algorithms. Hence, we believe that our suggested
approach can be a promising alternative of the steady-state description of the
biological systems.
Keywords: Gaussian graphical model, modified maximum likelihood
estimators, biological networks.
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Acknowledgement: The authors thank the BAP project (no: BAP-01-09-2017-
002) at Middle East Technical University for its support.
References:
[1] J. Whittaker, “Graphical models in applied multivariate statistics”, John
Wiley and Sons, (1990).
[2]E. Ayyıldız, M. Ağraz and V. Purutçuoğlu, “MARS as an alternative approach
of Gaussian graphical model for biochemical networks”, Journal of Applied
Statistics, (2016), 1-19.
[3] M.L. Tiku, “Estimating the mean and standard deviation from a censored
normal sample”, Biometrika, 54 (1967), 155-165.
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169
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Quadrature Formula with High Degree of Exactness
Abedallah Rababah
Department of Mathematics and Statistics, Jordan University of Science andTechnology,
22110 Irbid, Jordan
Abstract: In this article, a quadrature formula of degree 2 is given that has
degree of accuracy 3 and order 5. The formula is valid for any planar curve given
in parametric form unlike existing Gaussian quadrature formulas that are valid
only for functions.
Key words: quadrature formula; quadratic formula; parametric curves; degree of
accuracy three; fifth order.
References:
1. G. Farin, Curves and Surfaces for Computer Aided Geometric Design,
Academic Press, Boston (1988).
2. K. Hollig, J. Horner, Approximation and Modeling with B-Splines, SIAM,
Titles in Applied Mathematics 132, (2013).
3. A. Rababah, Taylor theorem for planar curves, Proc. Amer. Math. Soc. Vol
119 No. 3, (1993), 803-810.
4. A. Rababah, Approximation von Kurven mit Polynomen und Splines, Ph.
Dissertation, Stuttgart Universitat, (1992).
5. A. Rababah, High accuracy Hermite approximation for space curves in <d, J.
Math. Anal. Appl. 325, Iss. 2, (2007), 920-93
6. A. Rababah, The Best Uniform Quadratic Approximation of Circular Arcs
with High Accuracy, Open Mathematics 14, (2016), 118-127.
7. A. Rababah, Quartic approximation of circular arcs using equioscillating error
function, International Journal of Advanced Computer Science and Applications,
7(7), (2016), 590-595.
8. A. Rababah, The best uniform cubic approximation of circular arcs with high
accuracy, Communications in Mathematics and Applications 7(1), (2016), 37-46.
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170
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Best Cubic Spline Interpolation Based on Minimizing the Error
Abedallah Rababah, Mohammed Bani Khalid
Department of Mathematics and Statistics
Jordan University of Science and Technology
Irbid, Jordan
[email protected] ; [email protected]
Abstract: In this talk, a modified cubic spline is introduced. The proposed spline
can be obtained by considering some flexible boundary conditions that involve
some additional parameters. These parameters are incorporated to improve the
accuracy of the classical cubic spline. Moreover, these parameters are estimated
by minimizing the error function in L1 - norm. The boundary conditions are
adjusted to get new parameters that are used to get better approximation. Some
numerical examples are given to demonstrate the advantages in accuracy and
efficiency of the proposed method over traditional cubic methods.
Keywords: cubic spline; minimizing the error; best cubic approximation
References:
K. Hӧllig, J. Hӧrner: Approximation and Modeling with B-Splines, SIAM, Titles
in Applied Mathematics 132, 2013.
I. J. Schoenberg, On equidistant cubic spline interpolation. Bull. Amer. Math.
Soc. 77 (1971), no. 6, 1039-1044.
Rababah, High accuracy Hermite approximation for space curves in Rd, J. Math.
Anal. Appl. 325, Iss. 2 (2007), 920-931.
J. Rice, The approximation of functions, Vol. 1: linear theory. Addison-Wesley,
(1964).
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171
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On Chebyshev Collocation Method and Applications to
Nonlinear Integral Equations
Abdalah Rababah1, Benferhat Leila2, Hichem Ramoul3, Nora Mahloul4
1Department of Mathematics and Statistics, Jordan University of Science and
Technology
Irbid, Jordantage
[email protected] 2Department of Algebra and Numbers Theory, University of Science and
Technology Houari Boumediene, Algiers, Algeria
[email protected] 3ICOSI laboratory, Abbes Laghrour University-Khenchela,
Khenchela, Algérie
[email protected] 4Department of Algebra and Numbers Theory, University of Science and
Technology Houari Boumediene,
Algiers, Algeria
Abstract: This paper is devoted to solve some classes of one-dimensional non-
linear Volterra-Hammerstein integral equations with singular kernels. The key
ingredient is to transform integral equation to algebraic equation with unknown
Chebyshev coefficients. We use here a suitable weighted Chebyshev polynomial
to approximate the solution of the non-linear integral equation.
Keywords: Chebyshev polynomials, integral equations, collocation method.
References:
[1] Dardery, S. M., & Allan, M. M. “Chebyshev polynomials for solving a class
of singular integral equations”, Applied Mathematics, 5.04 (2014), 753.
[2] Mason, John C., and David C. Handscomb. “Chebyshev polynomials”. CRC
Press, 2002.
[3] Danaei, R., Molaei, H., & Khazili, M. “Solving Fredholm integral equations
using with Chebyshev polynomials”, International Journal of Innovative Science,
Engineering & Technology, 2.5(2015), 297-300.
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The Treatment of Fractional Singular Lagrangian
Eqab Rabei
Al al-Bayt University
Abstract: The singular Lagrangian with fractional derivative will be
investigated. The Euler-Lagrangian will be derived and some example will be
given.
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MHD Convective Flow due to a Curved Surface with Thermal
Radiation and Chemical Reaction
Madiha Rashid
Quaid-i-azam University, Islamabad
Abstract: Present work is devoted to the convection flow of viscous fluid by a
curved stretching sheet. Fluid is electrically conducting with the presence of
uniform magnetic field. Heat and mass transfer characteristics are studied by
using heat and mass convective conditions. Thermal radiation and chemical
reaction are also taken into consideration. With the help of allocated
transformations the presented nonlinear partial differential systems are reduced
into the nonlinear ordinary differential system. Impact of pertinent parameters on
physical quantities like fluid velocity, temperature and concentrations fields are
observed. Computations for surface shear stress and heat and mass transfer rates
are carried out. It is observed that pressure inside the boundary layer flow due to
curved stretching plate cannot be neglected
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On The Isolated Points of the Spectrum of M-Paranormal
Operators
Mohammad Rashid
Department of Mathematics, Alkarak, Mutah University
Alkarak, Jordan
Abstract: For 𝑀 −paranormal operator 𝑇 on a separable complex Hilbert space
𝐻 we show that (1) If 𝜎𝑤 = 0, then 𝑇 is compact and normal and (2) every
Riesz idempotent 𝐸 with respect to a non-zero isolated point 𝜆 of 𝜎(𝑇) is self-
adjoint (i.e., it is an orthogonal projection) and satisfies that 𝑅(𝑇) =
ker(𝑇 − 𝜆) = ker(𝑇∗ − 𝜆).
Keywords: paranormal operators, M-paranormal operators, Riesz idempotent.
References:
[1] P. Aiena, Fredholm and local spectral theory with applications to multipliers,
Kluwer, 2004.
[2] S.C. Arora, Ramesh Kumar, M-Paranormal operators, Publ. Inst. Math.,
Nouvelle serie 29 (43) (1981), 5-13.
[3] M. Ch_o and S. ^ Ota, On n-paranormal operators, J. Math. Research 5
(2013), no. 2, 107-114.
[4] R.E. Harte, Invertibility and singularity for bounded linear operators, Dekker,
New York, 1988.
[5] P.R. Halmos, A Hilbert Space Problem Book, Van Nostrand, Princeton,1967.
[6] J.K. Han, H.Y Lee, W.Y Lee, Invertible completions of 2 _ 2 upper triangular
operator matrices, Proc. Am. Math. Soc. 128(2000),no.1, 119-123.
[7] H. Heuser, Functional Analysis, Dekker, New York, 1982.
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Existence of Homoclinic Orbit in Generalized Planar System of
Lienard Type
Vahid Roomi
Department of Mathematics, Azarbaijan Shahid Madani University,
Tabriz, Iran
Abstract: The object of this paper is to study the orbit structure of a generalized
Li_enard type system in a neighborhood of a trajectory which is doubly
asymptotic to an equilibrium solution, i.e., an orbit which lies in the intersection
of the stable and unstable manifolds of a critical point. Such an orbit is called a
homoclinic orbit.
Keywords: Lienard System, Homoclinic orbit.
Consider the planar system
x = P(Q(y) − F(x)
y = −g(x) (1)
which is a generalized Lienard type system, where P, Q, F and g are continuous
functions which ensure the existence of a unique solution to the initial value
problem.
System (1.1) includes the classical Lienard system as a special case, which is of
great importance in various applications (see [1-15] and the references cited
therein). In system (1), a trajectory is said to be a homoclinic orbit if its α − and
ω −limit sets are the origin. The purpose of this paper is to give an implicit
necessary and sufficient condition and some explicit sufficient conditions on
F(x), g(x), P(u) and Q(y) under which system (1) has homoclinic orbits.
References:
[1] R. P. Agarwal, A. Aghajani, V. Roomi, Existence of homoclinic orbits for
generalized planar Dynamical System of Lienard Type”, Dynamic of
Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis
81 (2012), 271-284.
[2] A. Aghajani, A. Moradifam, “”Some sufficient Conditions for the
Intersection with the Vertical Isocline”, Appl. Math. Lett, 19(2006), 491-497.
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Some Results of the Picard-Krasnoselskii Hybrid Iterative
Process
Aynur Sahin and Metin Basarir
Department of Mathematics, Sakarya University,
Sakarya, 54050, Turkey
[email protected], [email protected]
Abstract: In this study, we establish the strong convergence and stability results
of Picard-Krasnoselskii hybrid iterative process for a general class of
contractive-like operators in hyperbolic spaces. Furthermore, we give an
example to support our results. Finally, we apply this iterative process to obtain
the solution of a functional equation in a Banach space.
Keywords: Fixed point, Picard-Krasnoselskii hybrid iterative process, Stability,
Functional equations, Contractive-like operators.
References:
[1] V. Berinde, Iterative Approximation of Fixed Points, Springer, Berlin, 2007.
[2] V. Berinde and A. R. Khan, “On a functional equation arising in
mathematical biology and theory of learning”, Creath. Math. Inform. 24.1(2015),
9-16.
[3] A. O. Bosede and B. E. Rhoades, “Stability of Picard and Mann iteration for
a general class of functions”, J. Adv. Math. Stud. 3.2(2010), 23-25.
[4] C. O. Imoru and M. O. Olatinwo, “On the stability of Picard and Mann
iteration processes”, Carpath. J. Math. 19(2003), 155-160.
[5] G. A. Okeke and M. Abbas, “A solution of delay differential equations via
Picard-Krasnoselskii hybrid iterative process”, Arab. J. Math. 6(2017), 21-29.
[6] M. O. Osilike, “Stability results for Ishikawa fixed point iteration procedure”,
Indian J. Pure Appl. Math. 26.10(1995), 937-941.
[7] I. Timiş, “On the weak stability of Picard iteration for some contractive type
mapping”, Annal. Uni. Craiova, Math. Comput. Sci. Series, 37.2(2010), 106-
114.
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Optimal Coincidence Best Proximity Point Results in Fuzzy
Metric Spaces
Naeem Saleem
Department of Mathematics, University of Management and Technology,
C-II Johar Town, Lahore,Pakistan
Abstract: In this paper, we disscused some sufficient conditions for existence
and uniqueness of the best proximity points and optimal coincidence point
results for non-self mapping in fuzzy metric space. We also mentioned some
interesting aspects of best proximity point theory in the setup of fuzzy metric
spaces. We provided some examples to explain the obtained results, which also
shows that obtained results are generalization of already existing results in
literature. This article could be viewed as a discussion on extension of recent
development on proximal contraction mappings in such spaces.
Keywords: Fuzzy metric Space, Best Proximity point, Optimal Coincidence best
proximity point
References:
[1] K. Fan, “Extensions of two fixed point theorems of F. E. Browder”. Math. Z.
112, 234-240 (1969).
[2] S. Sadiq Basha, N. Shahzad, R. Jeyaraj.“Optimal approximate solutions of
fixed point equations”. Abstr. Appl. Anal. 2011, 174560 (2011).
[3] N. Saleem, B. Ali,M. Abbas, Z. Raza.“Fixed points of Suzuki type
generalized multivalued mappings in fuzzy metric spaces with applications”.
Fixed Point Theory Appl. 2015, 36 (2015).
[4] LA. Zadeh. “Fuzzy sets”. Inf. Control 8, 103-112 (1965).
[5] M. Abbas, N. Saleem and M. De la Sen, “Optimal coincidence point results
in partially ordered non-Archimedean fuzzy metric spaces”, Fixed Point Theory
and Applications, 2016 (1), 1-18.
[6] N. Saleem, M. Abbas and Z. Raza, “Optimal coincidence best approximation
solution in non-Archimedean Fuzzy Metric Spaces”, Iranian Journal of Fuzzy
Systems, 13(3), 113-124, 2016.
[7] Z. Raza, N. Saleem and M. Abbas, “Optimal coincidence points of proximal
quasi-contraction mappings in non-Archimedean fuzzy metric spaces”, Journal
of nonlinear science and application, 9 (2016), 3787- 3801
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New Concept of Determinants with Three Indexes (3D
Determinants) and Possibilities of Use
Armend Salihu
Department of Computer Science, University for Business and Technology
Prishtine, Kosovo
Abstract: In this paper will will present a new concept of determinants with
three indexes (3D Determinants), we will present how we will try to solve the 3D
determinants and what are possibilities of usage of those determinants.
Keywords: Determinants, 3D, Determinants Calculation.
References:
[1] Cramer, Gabriel (1750). "Introduction à l'Analyse des lignes Courbes
algébriques" (in French). Geneva: Europeana. pp. 656–659. Retrieved 2012-05-
18
[2] Thomas S. Shores (2007). Applied Linear Algebra and Matrix Analysis.
Springer Science & Business Media. p. 132. ISBN 978-0-387-48947-6.
[3] Leon, Steven J. (2006), Linear Algebra with Applications (7th ed.), Pearson
Prentice Hall
[4] Hedman, Bruce A. (1999). "An Earlier Date for "Cramer's Rule"". Historia
Mathematica 26 (1999), 365–368
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Boundedness Properties of Some Operators on dM P,Q
Ayse Sandikci
Department of Mathematics, Ondokuz Mayis University,
Samsun, Turkey
Abstract: The Lorentz mixed normed modulation space dM P,Q is the
set of all tempered distributions df S such that the short-time Fourier
transform gV f of f is in the Lorentz mixed norm space 2dL P,Q , where
dg S is a non-zero window function, 1 21 P p ,p and
1 21 Q q ,q . In this work we investigate the boundedness properties
of Wigner distribution and time-frequency localization operator on
dM P,Q . Some key references are given below.
Keywords: Lorentz mixed normed modulation space, Wigner distribution, time-
frequency localization operator.
References:
[1] P. Boggiatto, Localization operators with L^p symbols on the modulation
spaces, In Advances in Pseudo-Differential Operators, vol. 155 of Oper. Theory
Adv. Appl., 149--163, Birkhäuser, Basel, 2004.
[2] E. Cordero, K. Gröchenig, Time-frequency analysis of localization operators,
J. Funct. Anal., 205(1) (2003), 107-131.
[3] D.L. Fernandez, Lorentz spaces, with mixed norms, J. Funct. Anal., 25
(1977), 128-146.
[4] K. Gröchenig, Foundation of Time-Frequency Analysis. Birkhäuser, Boston
2001, ISBN 0-8176-4022-3.
[5] R.A. Hunt, On L(p,q) spaces, Extrait de L'Enseignement Mathematique,
T.XII, fasc.4 (1966), 249-276.
[6] A. Sandıkçı, On Lorentz mixed normed modulation spaces, J. Pseudo-Differ.
Oper. Appl., 3 (2012), 263-281.
[7] A. Sandıkçı, Continuity of Wigner-type operators on Lorentz spaces and
Lorentz mixed normed modulation spaces, Turk J. Math., 38 (2014), 728-745.
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On Approximate Biprojectivity of Banach Algebras
M. H. Sattari
Department of Mathematics Azarbaijan Shahid Madani University,
Tabriz, Iran
Abstract: The notion of approximate biprojectivity of Banach algebras was
introduced by Pourmahmood-Aghababa [4], O. Yu. Aristov [1] and Y. Zhang
[5] in different ways. Here some hereditary properties of this concept is
investigated, according to definaion of Pourmahmood-Aghababa. Among other
things is shown that approximate biprojectivity of the second dual of A implies
approximate biprojectivity of A , where **A is equipped with the first Arens
product [2].
Keywords: Approximate biprojective, Banach Algebra, Second dual.
References:
[1] O. Yu. Aristov, “On approximation of flat Banach modules by free modules”,
Sbornik. Math. 196(11) (2005), 1553–1583.
[2] H. G. DALES. Banach Algebras and Automatic Continuity (Oxford, 2000).
[3] F. Ghahramani and Y. Zhang, “Pseudo-amenable and pseudo-contractible
Banach algebras”, Math. Proc. Cambridge Philos. Soc. 142 (2007), 111–123.
[4] H. Pourmahmood-Aghababa, “Approximately biprojective Banach algebras
and nilpotent ideals”, Bull. Aust. Math. Soc. 87 (2013) 158-173.
[5] Y. Zhang, “Nilpotent ideals in a class of Banach algebras”, Proc. Amer.
Math. Soc. 127(11) (1999), 3237–3242.
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On Some New Sequence Spaces Defined By Almost Lacunary
Bounded Variation
Ekrem Savas
Department of Mathematics, Istanbul Ticaret University,
Sütlüce, Istanbul, Turkey
Abstract: In this paper we introduce and examine a new sequence space by
using Orlicz function and almost lacunary bounded variation. We also study
some basic topological and algebraic properties for these spaces. Furthermore we
shall established inclusion theorems between these sequence spaces.
Keywords: almost convergence, almost lacunary convergence, lacunary
sequence; bounded variation ; Orlicz function .
References:
[1] S. Banach, Theorie des Operations linearies, Warszawa, 1932.
[2] G. Das and S. K. Mishra, Banach limits and lacunary
strong almost convergence, J. Orissa Math. Soc. 2(2) (1983),
[3] V. Karakaya and E. Savas, On almost p-bounded variation of lacunary
sequences , Computer and Math. with Appl., 61(2011), 1502-1506
[4] S. D. Parashar, and B. Choudhury, Sequence space defined by Orlicz
functions, Indian J. Pure Appl. Math., 25(14) (1994)419-428.
[5] E. Savas, and V. Karakaya, Some new sequence spaces defined by lacunary
sequences ,Math. Slovaca, 57(2007), 393-399.
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On Filter Convergence of Nets in Uniform Spaces
Ekrem Savas1 and Ulas Yamanci2
1Department of Mathematics, Istanbul Ticaret University, İstanbul, Turkey 2Department of Statistics, Süleyman Demirel University, Isparta, Turkey
[email protected]; [email protected];
Abstract: In this paper, we introduce F -convergence and stF -fundamental of
nets in uniform space and study some of its consequences
Keywords: Ideal, filter, net, filter-convergence.
References:
[1] B.T. Bilalov, T.Y. Nazarova, “On statistical type convergence in uniform
spaces”, Bull. Iranian Math. Soc., 42(2016), 975-986.
[2] J.A. Fridy, On statistical convergence, Analysis, 5 (1985) 301-313.
[3] P. Das, E. Savaş, “On I -convergence of nets in locally solid Riesz spaces”,
Filomat, 27(2013), 89-94.
[4] B.K. Lahiri, P. Das, “I and I -convergence of nets”, Real Anal. Exchange,
33 (2007-2008), 431-442.
[5] E. Savaş, P. Das, “A generalized statistical convergence via ideals”, Appl.
Math. Lett., 24 (2011), 826-830.
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On E-J Hausdorff Transformations for Double Sequences
Rabia Savas and Hamdullah Sevli
Sakarya University, Sakarya, Turkey
Istanbul Commerce University, Istanbul, Turkey
Abstract: In 1933, Adams [1] developed Hausdorff transformations for double
sequences. Şevli and Savaş [2] proved some result for double Endl- Jakimovski
(E-J) generalization. In this study, we consider some further results for E-J
Hausdorff transformations for double sequences.
Keywords: Hausdorff matrices, double series, absolute summability.
References:
[1] Adams, C. R., Hausdorff transformations for double sequences, Bull. Amer.
Math. Soc. 39, 303-312, 1933.
[2] Şevli, H. and Savaş, R., On double Hausdorff summability method, Journal
of Inequalities and Applications, 240, 1-10, 2014.
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Double Lacunary Statistical Boundedness of Order α
Rabia Savas and Mahpeyker Ozturk
Department of Mathematics, Sakarya University, Sakarya, Turkey
[email protected] and [email protected]
Abstract: In this paper we introduce and the study the concept of the double
lacunary statistical boundedness of order α and also give a general descriptions
of inclusion between double statistical boundedness and double lacunary
boundedness of order α.
Keywords: Double lacunary sequences, double statistical boundedness, double
lacunary statistical boundedness
References:
[1] V. K. Bhardwaj, S. Gupta, S. A. Mohiuddine and A. Kılıçman, On Lacunary
Statistical Boundedness, J.Ineq. Applications, 2014, 2014:311.
[2] M. Et, S.A. Mohiuddine and H. Şengul, On Lacunary Statistical
Boundedness of order α, Facta Universitatis, Ser. Math. Inform. Vol. 31, No 3,
2016, 707-716.
[3] R. F. Patterson and E. Savas, Lacunary Statistical Convergence of Double
Sequences, Mathematical Com. 10, 2005, 55-61.
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Statistıcal Convergent Functions Via Ideals With Respect To
The Intuitionistic Fuzzy 2-Normed Spaces
Rahmet Savas
Department of Mathematics, Istanbul Medeniyet University, Istanbul, Turkey
Abstract: The main objective of this paper is to introduce and study the notion
of ideal -statistical convergence of a non-negative real-valued Lebesque-
measurable function in the interval (1, ) with respect to the intuitionistic fuzzy
2-normed ( , ) . Investigate their relationship, and make some observations
about these classes. Further, we prove some inclusion theorems.
Keywords: Ideal, filter, I-Statistical convergence of function, I - statistical
convergence of functions, intuitionistic fuzzy normed space, intuitionistic fuzzy
2− normed space.
References:
[1] K.T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20(1986)
87–96.
[2] K. Atanassov, G. Pasi, R. Yager, Intuitionistic fuzzy interpretations of multi-
person multicriteria decision making, in: Proceedings of 2002 First International
IEEE Symposium Intelligent Systems, 1(200) ,115–119.
[3] R. Colak, Statistical convergence of order α, Modern methods in Analysis
and its Applications, New Delhi, India, Anamaya Pub., (2010), 121-129.
[4] R. Colak, C. A. Bektas, λ-statistical convergence of order α, Acta Math.
Scientia, 31B (3) (2011), 953-959. [5] J. Connor, The statistical and strong p -
Cesaro convergence of sequences, Analysis, 8(1988), 47-63.
[6] H. Fast, Sur la convergence statistique, Colloq. Math. 2, 1951, 241-244.
[7] J.A. Fridy, On statistical convergence, Analysis 5 (1985) 301-313.
[8] S. G¨ahler, Linear 2-normietre Raume, Math. Nachr. 28(1965).
[9] P. Kostyrko, T. ˇSal´at, W. Wilczynki, I-convergence, Real Anal. Exchange
26 (2) (2000-2001) 669-685.
[10] Mohiuddine, S. A., Lohani, Q. M. D. On generalized statistical convergence
in intuitionistic fuzzy normed space, Chaos, Solitons and Fractals, 42, 3, 2009
[11] M. Mursaleen, λ-statistical convergence, Math. Slovaca 50 (2000) 111–115.
[12] M. Mursaleen and Q. M. Danish Lohani, Intuitionistic fuzzy 2- normed
space and some relates concepts Chaos, Solitons and Fractals, 42,(2009), 224-
234.
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Submanifolds in 1
2H ( 1)m with Finite Type Pseudo-
Hyperbolic Gauss Map
Ruya Yegin Sen* and Ugur Dursun**
* Department of Mathematics, Istanbul Medeniyet University,
Uskudar, Istanbul, Turkey
** Department of Mathematics, Isik University,
Sile, Istanbul, Turkey
Abstract: The notion of finite type submanifold of a Euclidean space has been
introduced in late seventies. Since then the finite type submanifolds of Euclidean
or pseudo-Euclidean spaces have been studied extensively. In this work, we
mention the pseudo-hyperbolic Gauss map in the Obata’s sense. We study
pseudo-Riemannian submanifolds of 1
2H ( 1)m with finite pseudo-hyperbolic
Gauss map. We classify the pseudo-Riemmanian submanifolds of 1
2H ( 1)m
with 1-type pseudo-hyperbolic Gauss map. Then, we investigate the maximal
surface fully lying in 4 1
2 2H ( 1) H ( 1)m with 2-type pseudo-hyperbolic
Gauss map.
Keywords: Finite type map, pseudo-hyperbolic Gauss map, pseudo-hyperbolic
space.
References:
[1] Chen, B.-Y., Finite type submanifolds in pseudo-Euclidean spaces and
applications, Kodai Math. J., 8 (1985), 358-374.
[2] Chen, B.-Y., Finite-type pseudo-Riemannian submanifolds, Tamkang Journal
[3] Dursun, U. and Yeğin, R., Hyperbolic submanifolds with finite type
Hyperbolic Gauss map, Int. J. Math., 26(2015).
[4] Ishihara, T., Maximal spacelike submanifolds of a pseudo-Riemannian space
of constant curvature, Michigan Math. J., 35 (1988), 345-352.
[5] Sakaki, M., Spacelike maximal surfaces in 4-dimensional space form of
index 2, Tokyo J. Math , 25(2002), 295-306.
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On the Determination of Validity of Categorical Syllogisms by
Using a Mathematical Model
Ibrahım Senturk1, Tahsin Oner2
Department of Mathematics, Ege University1,2,
Bornova, Izmir, Turkey
[email protected] [email protected]
Abstract: The earliest systematic approachment for determination of validity of
syllogisms was introduced by Aristotle [1] . In the 19th. and 20th. centuries,
Lewis Caroll [2] and Jan Łukasiewicz [3] made a significant contribution to
convert categorical syllogisms into modern logical structures. In this work, we
examine the validity of categorical syllogisms with the help of Caroll
Diagrammatic Method (SLCD) by constructing a logical calculus system [4] . In
the sequel, we indicate that any categorical syllogism is valid if and only if it is
provable in this system. In addition to these, we tackle with sorites validity
problems in categorical syllogisms. This enables us to construct a more general
solution technique for determination of their conclusions and validity.
Keywords: Categorical Syllogisms, Syllogistic systems, Carrolls' Diagrammatic
Method
References:
[1] Aristotle, “Prior Analytics” translation and commentary by Robin Smith,
Hackett Publishing, (1989).
[2] L. Carroll, “Symbolic Logic”, Clarkson N. Potter, (1896).
[3] J. Łukasiewicz, “Aristotle's Syllogistic From the Standpoint of Modern
Formal Logic”, Oxford University Press (1957).
[4] I. Senturk and T. Oner, “A Construction of Heyting Algebra on Categorical
Syllogisms”, Matematichki Bilten, 40.4 (2016), 5-12.
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Converse Theorems for Statistical Convergence
Sefa Anil Sezer 1, Rahmet Savas 1, Ibrahim Canak 2
1 Department of Mathematics, Istanbul Medeniyet University, Istanbul, Turkey 2 Department of Mathematics, Ege University, Izmir, Turkey
[email protected]; [email protected];
Abstract: A real or complex sequence ( )ns is said to be statistically convergent
to a finite if for all 0 ,
1
lim : 0,1
nn
n N sN
where the vertical bars indicate the cardinality of the enclosed set. It is known
that the statistical convergence can be studied as a regular summability method,
and also it is not included by any matrix method. In this study we investigate
relations between statistical convergence and a certain class of matrix
summability methods. Besides, we establish conditions needed for a statistically
convergent sequence to be ordinary convergent.
Keywords: Statistical convergence, converse theorems, Tauberian theorems,
matrix summability methods.
References:
[1] H. Fast, “Sur la convergence statistique”, Colloq. Math. 2(1951), 241-244.
[2] I. J. Schoenberg, “The integrability of certain functions and related
summability methods”, Amer. Math. Monthly, 66(1959), 361-375.
[3] J. A. Fridy, “On statistical convergence”, Analysis, 5(1985), 301-313.
[4] J. A. Fridy, H. I. Miller, “A matrix characterization of statistical
convergence”, Analysis, 11(1991), 59-66.
[5] F. Mòricz, “Theorems relating to statistical harmonic summability and
ordinary convergence of slowly decreasing or oscillating sequences”, Analysis,
24(2004), 127–145.
[6] S. A. Sezer, İ. Çanak, “Tauberian theorems for the summability methods of
logarithmic type”, Bull. Malays. Math. Sci. Soc. (2016), doi:10.1007/s40840-
016-0437-9
[7] S. A. Sezer, İ. Çanak, “Power series methods of summability for series of
fuzzy numbers and related Tauberian Theorems”, Soft Comput. 21(2017), 1057–
1064
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Cesàro Summability of Sequences in 2-Normed Spaces
Sefa Anil Sezer, Rahmet Savas
Department of Mathematics, Istanbul Medeniyet University,
Istanbul, Turkey
[email protected]; [email protected]
Abstract. The concept of 2-normed spaces was introduced by Gähler [7] in
1964. This notion recieved the attention of a wider audience after the study of
White [1] in 1969. He defined convergent sequences and Cauchy sequences in 2-
normed spaces which lead the birth of theory of 2-Banach spaces. In the last
decade, 2-normed spaces has attained noticeable importance and popularity from
the researchers working on summability theory. Firstly, Gürdal and Pehlivan
[4,5] presented the statistical convergence of sequences in 2-normed spaces.
Meanwhile, Şahiner et al. [2] defined the ideal convergence of sequences in such
spaces. Later, Savaş [3] and Das et al. [6] determined certain new sequence
spaces using ideal convergence and Orlicz functions in 2-normed spaces and
examined some of their properties.
In this study we have introduced the concept of Cesàro summability for
sequences in 2-normed spaces and obtained necessary and sufficient conditions
under which convergence follows from Cesàro summability.
Keywords: Tauberian conditions, 2-normed spaces, Cesàro summability.
References:
[1] A. G. White Jr., “2-Banach spaces”, Math. Nachr. 42(1969), 43–60.
[2] A. Şahiner, M. Gürdal, S. Saltan, H. Gunawan, “Ideal convergence in 2-
normed spaces”, Taiwanese J. Math., 11(2007), 1477-1484.
[3] E. Savaş, “Δm-strongly summable sequences spaces in 2-normed spaces
defined by ideal convergence and an Orlicz function”, Appl. Math. Comput.,
217(2010), 271-276.
[4] M. Gürdal, S. Pehlivan, “The statistical convergence in 2-Banach spaces”,
Thai J. Math., 2(2004), 107-113.
[5] M. Gürdal, S. Pehlivan, “Statistical convergence in 2-normed spaces”,
Southeast Asian Bull. Math., 33(2009), 257-264.
[6] P. Das, E. Savaş, S. Bhunia, “Two valued measure and some new double
sequence spaces in 2-normed spaces”, Czechoslovak Math. J., 61(2011), 809-
825.
[7] S. Gähler, “Lineare 2-normierte Räume”, Math. Nachr., 28(1964), 1–43.
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Applications of the Schwarz Lemma to Inequalities for
Polynomials with Restricted Zeros
Lubna Wali Shah
Department of Mathematics, National Institute of Technology,
Srinagar, Jammu and Kashmir India
Abstract: By using a boundary refinement of the classical Schwarz Lemma
some results for the polynomial inequalities with restricted zeros have been
proved.The estimates obtained strengthen some known results earlier proved by
Lax, Turan, Aziz and others.
Keywords: Schwarz Lemma, Inequalities in the complex domain, s-fold zeros
References:
[1] Abdul Aziz, A refinement of an inequality of S. Bernstein, J. Math. Anal.
Appl., 142(1989), 1-10.
[2] A. Aziz and W. M. Shah, Inequalities for a polynomial and its derivative,
Math. Inequal. Appl., 7(3) (2004), 379-391.
[3] S. Bernstein, Sur la limitation des derivees des polynomes, C. R. Acad.
Sci.Paris., 190(1930), 338-340.
[4] V. N. Dubinin, Applications of the Schwarz Lemma to inequalities for entire
functions with constraints on zeros. J. Math. Sci.,(N.Y) 143(3)(2007), 3069-
3076.
[5] S. G. Krantz, The Schwarz Lemma at the Boundary, Complex Var.
EllipticEqu., 56(5)(2011), 455-468.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Growth of Maximum Modulus of Polynomials and Rational
Functions in the Complex Domain
Wali Mohammad Shah
Department of Higher Education
University of Kashmir, Srinagar, India.
Abstract: In this talk we discuss the latest developments concerning the
extremal properties and growth of maximum modulus of polynomials and
rational functions. Our main objective will be to discuss Bernstein [4] type of
inequalities for rational functions with prescribed poles and the use of a
boundary refinement of Schwarz lemma [2,3] and a lemma due to Dubinin [1].
We [5] also show how the inequalities for the derivative and polar derivative
besides the growth of polynomials can be deduced as special cases from these
inequalities concerning the rational functions.
Key words : Polynomials, Rational functions, Inequalities , zeros
References:
[1] V.N. Dubinin, Distortion theorems for polynomials on the circle, Sb. Math.,
191(12) (2000) 1797-1807.
[2] S. G. Krantz, The Schwarz lemma at the boundary, Complex Var. Elliptic
Equ., 56 (5) (2011), 455-468.
[3] R. Osserman, A sharp Schwarz inequality on the boundary for functions
regular in the disk, Proc. Amer . Math. Soc., 12(2000), 3513-3517 .
[4] Q. I. Rahman and G Schmeisser, Analytic Theory of Polynomials, Oxford
University Press, New York, 2002.
[5] S. L. Wali and W. M. Shah, Some applications of Dubinin's lemma to
rational functions with prescribed poles., J. Math. Anal. Appl., 450(2017), 769-
779.
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192
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Trace Formula for Witt Vector Rings
Mokhfi Siham
Department of Mathematics, Saad DahlabUniversity,
Blida, Algérie
Abstract: We commence by giving a generalisation of Pulita exponential series.
We thenuse series to establish an analog of the trace formula for Witt vector
rings.
Keywords: Trace formula, Pulita series, Witt vector rings.
References:
[1] E. Artin, “Algebraic Numbers and Algebraic Functions”, Gordon and Breach,
New York. Math (1967).
[2] D. Barsky, “On Morita's p-adic gamma Functions”, Math. Proc.Camb.phil.
Soc, 89, Fasc 1(1981), 23-27.
[3] B. Benzaghou, “Algèbres de Hadamard ”, Soc. Math. France Slovaca,
98(1970), 209-252.
[4] R. Blache, “Stickelberger Theorem for p-adic Gauss sums”, Acta
Arithmetica, vol 18 n°1(2005), 11-26.
[5] B. Dwork , “The Rationality of the zeta Function of an Algebraic Variety ”,
Amer. Math 82 (1960) 631-648.
[6] M. Hazewinkel, “Witt vectors ”, Part 1 . Handbook of Algebra , Vol 6
section 4H, 319-472. Elsiever , North Holland. (1960) 631-648
[7] J. Lubin and J.Tate , “Formal Complex Multiplication in Local Fields ”, Ann
of Math (2) 81 (1965) 380-387.
[8]B. Benzaghou and S. Mokhfi , “Trace formula for Witt Vector Rings”,
Comptes Rendus Mthématiques (2016)
[9] A. Pulita , “Rank one solvable p-adic Differential Equations and Finite
Abelian Characters via Lubin-Tate groups ”, Math. Ann. 337 (2007) n°03 489-
555.
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193
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
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On Parametrization of the q-Bernstein Basis Functions
Yilmaz Simsek
Department of Mathematics, Faculty of Science University of Akdeniz TR-07058,
Antalya, Turkey
Abstract: In this talk, we study main properties of the q-Bernstein basis
functions with their generating functions. We show that these q-Bernstein basis
functions are parametrizations of the standard Bernstein basis functions. We
define q-Bezier type curves. Moreover, we plot graphs of these basis functions,
their generating funtions and q-Bezier type curves. Finally, we give remarks and
observations on the q-Bezier type curves related to parametrizations of the q-
Bernstein basis functions.
Keywords: q-Bernstein basis functions, Bezier curves, Generating function.
References:
[1] S. N. Bernstein, “Démonstration du théorème de Weierstrass fondée sur la
calcul des probabilités”, Comm. Soc. Math. Charkow Sér. 2 t. 13, 1-2 (1912-
1913).
[2] R. Goldman, “Identities for the Univariate and Bivariate Bernstein Basis
Functions”, Graphics Gems V, edited by Alan Paeth, Academic Press, (1995),
149-162.
[3] T. Kim, L.-C. Jang, and H. Yi, “A note on the modified q-Bernstein
polynomials”, Discrete Dyn. Nat. Soc. 2010, Article ID 706483, 12 pages, 2010.
[4] T. Kim, “Some identities on the q-integral representation of product of
several q-Bernstein-type polynomials”, Abst. Appl. Anal., 2011, Article ID:
634675, 1-11.
[5] M.-S. Kim, D. Kim, T. Kim, “On q-Euler numbers related to the modified q-
Bernstein polynomials”, Abst. Appl. Anal. 2010, Article ID 952384, 15 pages.
[6] G. M.Phillips, “Bernstein polynomials based on the q-integers”, The heritage
of P. L. Chebyshev: a Festschrift in honor of the 70th birthday of T. J. Rivlin,
Annals of Numerical Math. 1-4 (1997), 511-518.
[7] Y. Simsek, “Interpolation function of generalized q-Bernstein type
polynomials and their application, Curve and Surface”, Springer Verlag Berlin
Heidelberg 2011, LNCS 6920, (2011), 647-662.
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194
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Control of the Performance of the Panel of Judge in Sensory
Analysis by a Functinal Principal Component Analysis of
Probability Densities Function
Yousfi Smail
Mouloud Mammeri University
Abstract: In this work, the Functional Principal Component Analysis (FPCA) of
a set of probability density functions is used to study the performance of a panel
of 14 judges in sensory analysis context. For this, we integrate the FPCA of
densities in the context of Multiblock data analysis where, each block contain the
scores assigned by judges for 10 rosebushes according two sensory variables at
three different occasions. The planes of representations of densities gives a firt
global appreciation of variations contained in the data, one part of these
variations summarizes the repetability of the scores assigned by the judges and
another part, the discrimination of products tested.
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195
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Optimization of an Execution Time for Parallel Matrix
Multiplication by adding a New Set of Processors on the Array
1Halil Snopce, 2Sadri Alija, 3Azir Aliu and 4Artan Luma
1,3,4 Faculty of Contemporary Sciences and Technologies, SEE-University Tetovo,
Macedonia 2Faculty of Business and Economics, SEEU, Ilindenska n.335, Tetovo,
Macedonia [email protected], , [email protected], [email protected],
Abstract: In this paper we investigate the possible methods of optimization of
the execution time of some parallel algorithms for matrix-matrix multiplication.
Actually, there is known that the time complexity of execution the algorithm of
matrix multiplication by using just one processor element is O(n3). If one uses
the hexagonal array of n2 processor the optimized execution time is proved to be
3n-2. In this research, among others we show that if the array of processors is
increased by n new processors (putting new column of processors), the execution
time will be shortened for one unit of time. If we continue adding new columns
of processors, the execution time of the algorithm is shortened consecutively per
one unit of time after each new step.
Assuming that there are put k columns of n processors, then we show that the
time complexity of an algorithm is optimized to the order of O(N). Actually, we
show that this value at the worst case is equal to 2n-k where n is the number of
processors per column and k is the number of new added columns of processors
to the hexagonal array of processors.
For confirmation of obtained results, there are used some methods of linear
algebra.
.
Keywords: Matrix multiplication, optimization, execution time of algorithm,
time complexity, hexagonal array of processors, linear methods.
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196
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
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From Dido to Morrey: Variational Problems and
Regularity Theory!
Lubomira G. Softova
Second University of Naples
Department of Civil Engineering, Design, Construction and Environment, Italy
Abstract: Although ancient Greek and Roman sources report that Dido, the
founder and first queen of Carthage was the first person who formulated a
problem in Calculus of Variations (CV), the classical existence theory is
connected mainly with the names of Euler, Lagrange and Ostrogradskij. The
notorious Euler-Lagrange equation is a second order Partial Differential
Equation (PDE), the solvability of which ensures the existence of a minimizer of
a given functional. The question of regularity for the solutions of this PDE was
firstly posed by David Hilbert in his 19th and 20th problem, presented during a
celebrated lecture at the International Congress of Mathematics (ICM) 1900 in
Paris. During the last century, these two problems gave a strong impulse to the
development of the regularity theory for problems from CV and PDE. Our goal
is to present some classical and new results concerning regularity properties of
the solutions to the Dirichlet problem for elliptic equations and systems. We
obtain essential boundedness of the solution to a class of nonlinear elliptic
systems. In addition, we establish estimates in
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197
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
A Publicly Verifiable Authenticated Encryption Scheme Based
on Chaotic Maps and Factoring Problems
Nedal Tahat
Department of Mathematics, Faculty of Sciences
The Hashemite University, Zarqa 13133, Jordan
Abstract: In this study, an authenticated encryption scheme with public
verifiability based on chaotic maps and factoring problems is proposed. The
main aim of deploying a chaos-based cryptosystem is to provide encryption with
several advantages over traditional encryption algorithms such as high security,
speed, and reasonable computational overheads and computational power
requirements. Therefore, to enhance system security, we explore the
implementation of a cryptosystem algorithm based on both cryptographic and
chaotic system characteristics. We also provide security against known
cryptographic attacks and discuss the performance analysis of the developed
system.
Keywords: Authenticated encryption scheme, chaotic maps, factoring problem.
References: [1] C. Tsai, C. Liu, S. Tsaur and M. Hwang, A publicly verifiable authenticated
encryption scheme based on factoring and discrete logarithms. International
Journal of Network Security, 2017, 19(3): 443-4480
[2] P. Horster, M. Michel and H. Peterson, “Authenticated encryption schemes
with low communication costs,” Electronics letters, 1994, 30(15): 1212-1213.
[3] W.-B. Lee and C.-C. Chang, “Authenticated Encryption without Using a
One Way Function,” Electronics Letters,1995,31(19):1656-1657.
[4] Y. Zheng, “Digital Signcryption or How to Achieve Cost (Signature &
Encryption) << Cost (Signature) + Cost (Encryption),” Proc. CRYPTO’97,
LNCS 1294, Springer Verlag,1997: 165-179.
[5] Y. Zheng, “Signcryption and Its Application in Efficient Public Key
Solution,” Proc. Information Security Workshop (ISW’97), LNCS 1397,
1998.Springer-Verlad: 291-312.
[6] C. Ma and K. Chen, “Publicly Verifiable Authenticated Encryption,”
Electronics Letters, 2003. 39(3): 281-282.
[7] S. F. Tzeng, Y. L. Tang, and M. S. Hwang, \A new convertible authenticated
encryption scheme with message linkages," Computers and Electrical
Engineering, vol. 33, no. 2, pp. 133-138, 2007.
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198
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Third-Order Differential Sandwich-type Results Involving the
Liu-Owa Operator
Huo Tang1
, M. K. Aouf2
, Shigeyoshi Owa3
and Shu-Hai Li1
1. School of Mathematics and Statistics, Chifeng University, Chifeng 024000,
Inner Mongolia, People's Republic of China
[email protected]; [email protected]
2. Department of Mathematics, Faculty of Science, Mansoura University,
Mansoura 35516, Egypt
3. Department of Mathematics, Faculty of Education, Yamato University,
Abstract: In this paper, we derive some third-order differential subordination
and superordination results for multivalent analytic functions in the open unit
disk, which are defined by using the Liu-Owa operator. The results are obtained
by investigating appropriate classes of admissible functions. New third-order
differential sandwich-type results for the Liu-Owa operator are also obtained.
Keywords: Differential subordination; Differential superordination; Multivalent
analytic functions; Sandwich-type results; Liu-Owa operator.
References:
[1] R. M. Ali, V. Ravichandran and N. Seenivasagan, Differential subordination
and superordination of analytic functions defined by the Dziok-Srivastava
operator, J. Franklin Inst. 347 (2010), 1762-1781.
[2] R. M. Ali, V. Ravichandran and N. Seenivasagan, On subordination and
superordination of the multiplier transformation for meromorphic functions,
Bull. Malaysian Math. Sci. Soc. 33 (2010), 311-324.
[3] J. A. Antonino and S. S. Miller, Third-order differential inequalities and
subordinations in the complex plane, Complex Var. Elliptic Equ. 56 (2011),
439-454.
[4] I. B. Jung, Y. C. Kim and H. M. Srivastava, The Hardy space of analytic
functions associated with certain one-parameter families of integral operators, J.
Math. Anal. Appl. 176 (1993), 138-147.
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199
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Second-Order Differential Superordination for Analytic
Functions in the Upper Half-Plane
Huo Tang1
, H. M. Srivastava2,3
, Guan-Tie Deng4
and Shu-Hai Li1
1. School of Mathematics and Statistics, Chifeng University, Chifeng 024000,
Inner Mongolia, People's Republic of China
[email protected]; [email protected]
2. Department of Mathematics and Statistics, University of Victoria,
Victoria, British Columbia V8W 3R4, Canada
3. Department of Medical Research, China Medical University Hospital,
China Medical University, Taichung 40402, Taiwan, Republic of China
4. School of Mathematical Sciences, Beijing Normal University, Beijing 100875,
People's Republic of China
Abstract: There are many articles in the literature dealing with the second-order
differential subordination and differential superordination problems for analytic
functions in the unit disk : 1U z z C and z , but there are only a few
articles dealing with the above problems in the upper half-plane
: Im( ) 0z z C and z . The concept of second-order differential
subordination in the upper half-plane was introduced by Raducanu and Pascu in
[1], and studied recently by Tang et al. in [2]. Let be a set in the complex
plane C . Also let ( )p z be analytic in the upper half-plane and suppose that
3:C C . In this paper, we investigete the problem of determining
properties of functions ( )p z that satisfy the following second-order differential
superordination:
( ( ), ( ), ( ); ) :p z p z p z z z C .
Applications of these results to second-order differential superordination for
analytic functions in are also presented.
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200
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Keywords: Differential subordination; Differential superordination; Analytic
functions; Admissible functions; Upper half-plane.
References:
[1] D. Raducanu and N. N. Pascu, Differential subordinations for holomorphic
functions in the upper half-plane, Mathematica (Cluj). 36(1994), 215-217.
[2] H. Tang, M. K. Aouf, G.-T. Deng and S.-H. Li, Differential subordination
results for analytic functions in the upper half-plane, Abstr. Appl. Anal. 2014
(2014), Article ID 565727, 1-6.
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201
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PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Capacity Sizing and Pricing with Heterogeneous Products and
Flexible Resources
Salih Tekin
Industrial Engineering Department, TOBB University of Economics and
Technology,
Ankara, Turkey
Abstract: We consider the capacity and pricing decisions made by a
monopolistic firm producing three heterogeneous products under demand
uncertainty. The objective is to maximize profit. Our model includes dedicated
and flexible resources, product substitutability, and processing rates that may
depend on the product and on the resource type. We provide the optimum prices
and production quantities as functions of resource capacities and demand
intercepts. We also show that investment in flexible capacity is only desirable
when it is optimal to invest in dedicated capacities for both products, and obtain
upper bounds for the costs of the dedicated capacities that need to be satisfied for
investment in the flexible resource. We conclude with numerical examples that
illustrate the points discussed and provide insights into how the optimal
capacities and expected production quantities, prices, and profit depend on
various model parameters.
Keywords: Revenue Management, Stochastic Programming, Pricing.
______________________________________________________
202
INTERNATIONAL CONFERENCE on RECENT ADVANCES in
PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)
May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
A New Class of the r-Stirling Numbers and the Generalized
Bernoulli Polynomials
Meriem Tiachachat
Faculty of Mathematics, RECITS's laboratory, USTHB
Algiers, Algeria.
Abstract: The r-Stirling number of the second kind, counts the number of
partitions of an n-set into k non-empty subsets such that the r-first elements are
in different subsets [3]. In [11], the authors expressed the n-th high order
polynomial [7, 14] in terms of the r-Stirling numbers of both kinds by some
formulas. In 2010, Kurt [6] introduced an extension of the generalized Bernoulli
polynomials. The main object of this paper is to express the values at non
negative integers of the generalized Bernoulli polynomials on using a new class
of the Stirling numbers of the second kind.
Keywords: The r-stirling numbers, the quasi associated r-Stirling numbers, the
generalized Bernoulli polynomials
References:
[1] E. T. Bell, Exponential polynomials, Ann. Math., 35 (1934) 258-277.
[2] G. Bretti, P. Natalini, P. E. Ricci, Generalizations of the Bernoulli and Appell
polynomials, Abst. Appl. Anal., 7 (2004) 613–623.
[3] A. Z. Broder, The r-Stirling numbers, Discrete Math., 49 (1984) 241-259.
[4] L. Comtet, Advanced Combinatorics, D. Reidel Publishing Company,
Dordrecht-Holland / Boston-U.S.A, (1974).
[5] H. W. Gould, Higher order extensions of Melzaks formula, Util. Math., 72
(2007) 23-32.
[6] B. Kurt, A further generalization of the Bernoulli polynomials and on the 2D-
Bernoulli polynomials B 2
n (x; y); Appl. Math. Sci., 4 (2010) 2315-2322.
[7] Y. L. Luke, The special functions and their approximations, vol. I, Academic
Press, New York, London, 1969.
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203
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
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Degree Sequences and Inverse Problem on Graphs
Muge Togan, Aysun Yurttas, Ismail Naci Cangul
Department of Mathematics, Uludag University,
Bursa, Turkey
[email protected], [email protected], [email protected]
Abstract: Degree sequence of a graph is the set of all vertex degrees of the given
graph in non-decreasing order. There are algorithms to determine which sets of
positive integers can be the degree sequence of a graph, but yet no complete
solution is given. Topological graph indices are getting more and more interest
every day due to their applications in Chemistry and Pharmacology and most of
them are calculated for many graph types. Molecular graphs are the graphs with
vertex degree at most 4. A recent problem in graph theory is called inverse
problem. This problem deals with what integer values can be taken by these
topological graph indices. In this talk, by means of degree sequences, we give the
answer for several topological indices.
Keywords: Degree sequence, inverse problem, topological graph index
References:
[1] H. Wang, G. Yu, All but 49 numbers are Wiener indices of trees, Acta Appl
Math 92 (2006) 15-20
[2] I. Gutman, Y.-N. Yeh, The sum of all distances in bipartite graphs, Math.
Slovaca 45 (4) (1995) 327-334
[3] S. M. Cioaba, Sums of powers of the degrees of a graph, Discrete
Mathematics 306 (2006) 1959-1964
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204
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
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Notes on Permuting tri-derivations on Prime and Semi-prime
Rings
Seda Oguz Unal, Hasret Durna
Cumhuriyet University,
Sivas, Turkey
[email protected], [email protected]
Abstract: Derivations in prime rings firstly initiated by Posner [1] and it
is considered a fundamental construction in the theory of centralizing maps on
prime rings.. A great deal of work in this context are available in the literature
(see, for example [2] and [3]). In this sense, in [4], Ozturk presented permuting
tri-derivations in prime and semi-prime rings.The aim of this talk is to show that
a ring is a prime and semiprime ring admitting the trace satisfying several
conditions of permuting tri-derivation.
Keywords: Permuting tri-derivations, traces, prime rings, semi-prime rings, Lie
ideals.
References:
[1] E. C. Posner,"Derivations in prime rings", Proc. Amer. Math. Soc., 8(1957),
1093–1100.
[2] N. Argac and M. S. Yenigul,"Lie ideals and symmetric bi-derivation on
prime and semi-prime rings", Pure and Applied Mat. Sci., 44(1996), 17–21.
[3]M. A. Ozturk, D. Ozden and Y. B. Jun,"Permuting tri-derivations in prime
and semi-prime gamma rings",Kyungpook Math. J., 46(2011), 153–167.
[4] M. A. Ozturk, " Permuting tri-derivations in prime and semi-prime rings",
East Asian Math. J., 15(1999), 177–190.
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205
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Weakly Invariant Subspaces for Multivalued Linear Operators
on Banach Spaces
Gerald Wanjala
Department of Mathematics and Statistics, Sultan Qaboos University,
Muscat, Oman
Abstract: Losomonov [1] showed that if a bounded linear operator T on a
Banach space X commutes with a non-zero compact operator, then T has a
nontrivial invariant subspace. This result was generalized by Peter Saveliev [2]
to the case of multivalued linear operators by applying fixed point techniques. In
particular, he proved that if S and K are multilivalued linear operators defined on
a Banach space X and having finite dimensional multivalued parts, and if K is
compact and right commutes with S, that is SK ⊂ KS, then S has a nontrivial
weakly invariant subspace. However, the case of left commutativity remained
open. In this talk, we address the case of left commutativity. We apply the
operator representation techniques developed in [3] to acheive the desired result.
Keywords: Multivalued linear operator, Weakly invariant subspace.
References:
[1] V. I. Lomonosov, “Invariant subspaces for the family of operators which
commute with a completely continuous operator”, Func. Anal. Appl., 7(1973),
213-214.
[2] P. Savelieve, “Lomonosov’s invariant subspace theorem for multivalued
linear operators”, Proc. AMS, 131(2002), 825-8344.
[3] G. Wanjala, “Operator representation of sectorial linear relations and
applications”, J. Ineq. Appl., (2015), 2015:60.
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206
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
Speech Quality Analysis with Respect to Noise Corruption by a
Kalman Filter to Estimation the Parameters of the SWLP
Method
Ervenila Xhaferraj (Musta)
Department of Mathematics, Faculty of Mathematics and Physics
Engineering, Polytechnic University of Tirana
Tirane, Albania
Abstract: Revolutions Applications such as telecommunications, hands-free
communications, recording, etc. which need at least one microphone, the signal
is usually infected by noise and echo. The important application is the speech
enhancement, which is done to remove suppressed noises and echoes taken by a
microphone, beside preferred speech. Accordingly, the microphone signal has to
be cleaned using digital signal processing DSP tools before it is played out,
transmitted, or stored. Engineers have so far tried different approaches to
improving the speech by get back the desired speech signal from the noisy
observations. Especially Mobile communication, so in this paper will do
reconstruction of the speech signal, observed in additive background noise, using
the Kalman filter technique to estimate the parameters of the Autoregressive
Process (AR) in the state space model and the output speech signal obtained by
the MATLAB. The accurate estimation by Kalman filter on speech would
enhance and reduce the noise then compare and discuss the results between
actual values and estimated values which produce the reconstructed signals.
References:
[1]. J. R. Deller, J. H. L. Hanson and J. G.Proakis. Diccrere-The Processing of
Speech Signal, EEE PRESS, NewYork 2000.
[2]. K. K. Paliwal and A.Basu, “A speech enhancement method based on Kahan
filtering, Proceedings of ICASSP’87,pp.177-180. Dallas, TX, USA, 1987.
[3]. T.K.Mmn, “The Expectation-Maxlmizaion Algorithm”,IEEE Signof
Processing Magazine, pp. 47-60, Nov. 1996.
[4] Shumway, Robert H., Stoffer, David S., Time Series Analysis and Its
Applications with R Examples, second edtition, Springer Texts in Statistics
Series, 2006.
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207
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
Kusadasi - Aydin, TURKEY www.icrapam.org
S-Generalized Srivastava’s Triple Hypergeometric Functions
M. Baki Yagbasan, Aysegul Cetinkaya, I. Onur Kiymaz
Department of Mathematics, Ahi Evran University,
Kırşehir, Turkey
Abstract: In this study, we introduced new generalizations of Srivastava's triple
hypergeometric functions by using S-generalized beta function. Furthermore, we
investigated some properties of these new functions.
Keywords: S-Generalized Beta function, Srivastava's triple hypergeometric
functions.
Acknowledgement: This work was supported by Ahi Evran University
Scientific Research Projects Coordination Unit. Project Number: FEF.A4.17.002
References:
[1] Çetinkaya, A., Yagbasan, M. B., Kıymaz İ. O., “The extended Srivastava’s
triple hypergeometric functions and their integral representations”, Journal of
Nonlinear Sciences and Applications, 9.6, (2016): 4860-4866.
[2] Bailey W.N., “Generalized Hypergeometric Series”, Cambridge Tracts in
Mathematics and Mathematical Physics, vol. 32, Cambridge University Press,
Cambridge, (1935).
[3]Chaudhry M. A., Qadir A., Rafique M., Zubair S. M., “Extension of Euler's
beta function”, J. Comput.
Appl. Math., 78, (1997): 19-32.
[4] Luo, Min-Jie, Milovanovic, G. V., Agarwal, P. “Some results on the extended
beta and extended hypergeometric functions”, Applied Mathematics and
Computation, 248, (2014): 631-651.
[5] Srivastava H. M., Karlsson P. W., “Multiple Gaussian Hypergeometric
Series”, Ellis Horwood Limited, (1985).
[6] Srivastava, H. M., Agarwal, P., Jain, S. “Generating functions for the
generalized Gauss hypergeometric functions”, Applied Mathematics and
Computation, 247, (2014): 348-352.
[7] Srivastava, H. M., Jain, R., Bansal, M. K., “A Study of the S-Generalized
Gauss Hypergeometric Function and Its Associated Integral Transforms”,
Turkish Journal of Analysis and Number Theory, 3.5, (2015): 116-119.
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208
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Berezin Number Inequality for Convex Function in
Reproducing Kernel Hilbert Space
Ulas Yamanci1, Mehmet Gurdal2, Mubariz T. Garayev3
1Department of Statistics, Süleyman Demirel University, Isparta, Turkey
2Department of Mathematics, Süleyman Demirel University, Isparta, Turkey 3Department of Mathematics, King Saud University, Riyadh, Saudi Arabia
[email protected]; [email protected]; [email protected]
Abstract: By using Hardy-Hilbert's inequality, some power inequalities for the
Berezin number of a self-adjoint operators in Reproducing Kernel Hilbert Spaces
(RKHSs) with applications for convex functions are given.
Acknowledgement: The second author is supported by TUBA through Young
Scientist Award Program (TUBA-GEBIP/2015).
Keywords: Berezin number, Hardy-Hilbert’s inequality, convex function, self-
adjoint operator.
References:
[1] G. Hardy, J.E. Littlewood, G., Polya, “Inequalities”, 2 nd ed. Cambridge
University Press, Cambridge, 1967.
[2] F.A. Berezin, “Covariant and contravariant symbols for operators”, Math.
USSR-Izv., 6 (1972), 1117-1151.
[3] M. Kian, “Hardy-Hilbert type inequalities for Hilbert space operators”, Ann.
Funct. Anal., 3(2)(2012), 128-134.
[4] M.T. Garayev, M. Gürdal, M., A. Okudan, “Hardy-Hilbert's inequality and a
power inequality for Berezin numbers for operators”, Math. Inequal. Appl.,
(3)(19)(2016), 883-891.
[5] B. Yang, “Discrete Hilbert-type inequalities”, Bentham Science Publishers
Ltd., 2011.
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209
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May 11-15, 2017, Palm Wings Ephesus Resort Hotel,
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On Power Inequalities for Berezin Number of Operators and
Convex Functions
Ulas Yamanci1, Mehmet Gurdal2, Ceren Celik2
1Department of Statistics, Süleyman Demirel University,
2Department of Mathematics, Süleyman Demirel University,
Isparta, Turkey
[email protected]; [email protected]; [email protected]
Abstract: In this paper, some power inequalities are given for Berezin numbers,
defined by reproducing kernel, on reproducing kernel Hilbert spaces.
Acknowledgement. This work is supported by Suleyman Demirel University
with Project 4903-YL1-17.
Keywords: Berezin number, Hardy-Hilbert’s inequality, convex function,
reproducing kernel Hilbert space.
References:
[1] G. Hardy, J.E. Littlewood, G., Polya, “Inequalities”, 2 nd ed. Cambridge
University Press, Cambridge, 1967.
[2] F.A. Berezin, “Covariant and contravariant symbols for operators”, Math.
USSR-Izv., 6 (1972), 1117-1151.
[3] M. Kian, “Hardy-Hilbert type inequalities for Hilbert space operators”, Ann.
Funct. Anal., 3(2)(2012), 128-134.
[4 M.T. Karaev, “Berezin symbol and invertibility of operators on the functional
Hilbert spaces”, J. Funct. Anal., 238(2006), 181-192.
[5] S. Saitoh, Y. Sawano, “Theory of reproducing kernels and applications”,
Springer, 2016.
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210
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Spectral Properties of Discrete Klein-Gordon Equations
Nihal Yokus, Nimet Coskun
Department of Mathematics, Karamanoglu Mehmetbey University,
Karaman, Turkey
[email protected] ; [email protected]
Abstract: Spectral analysis of Sturm-Liouville boundary value problem was
investigated by Naimark[1]. Bairamov and Celebi[2] studied the Klein-Gordon s-
wave equation which includes the Sturm-Liouville equation as a special case in
their paper. As a result of developments in discrete calculus, discrete analogues
of the Sturm-Liouville and Klein-Gordon equation have gained a prominent
attention. Spectral theory of discrete Klein-Gordon equation has been treated by
Adivar[3]. In this study, we shall present Jost solution, discrete spectrum and
spectral singularities of the discrete Klein-Gordon equation under certain
conditions.
Keywords: Discrete equations, spectral analysis, Klein-Gordon equation.
References:
[1] M.A. Naimark, ‘‘Investigation of the spectrum and the expansion in
eigenfunctions of a non-selfadjoint operator of second order on a semi-axis’’,
AMS Transl. 2(1960), 103-193.
[2] E. Bairamov and A.O. Celebi, ‘‘Spectral properties of the Klein-Gordon s-
wave equation with complex potential’’, Indian J. Pure Appl. Math. 28(1997),
813-824.
[3] M.
Adivar, ‘‘Quadratic pencil of difference equations: Jost solutions,
spectrum, and principal vectors’’, Quaestiones Mathematicae, 33(2010), 305-
323.
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211
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On the Inverse Problem on Graphs
Aysun Yurttas, Muge Togan, Ismail Naci Cangul
Department of Mathematics, Uludag University,
Bursa, Turkey
[email protected], [email protected], [email protected]
Abstract: Topological graph indices are getting more and more interest every
day due to their applications in Chemistry and Pharmacology. Their values are
calculated for many graph types and relations with molecular graphs are
established. Molecular graphs are the graphs with vertex degree at most 4. A
recent problem in graph theory is called inverse problem. This problem deals
with what integer values can be taken by these topological graph indices. In this
talk, we give the answer for several topological indices.
Keywords: Molecular graph, inverse problem, topological graph index
References:
[1] H. Wang, G. Yu, All but 49 numbers are Wiener indices of trees, Acta Appl
Math 92 (2006) 15-20
[2] I. Gutman, Y.-N. Yeh, The sum of all distances in bipartite graphs, Math.
Slovaca 45 (4) (1995) 327-334
[3] S. M. Cioaba, Sums of powers of the degrees of a graph, Discrete
Mathematics 306 (2006) 1959-1964
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Summability of Subsequences of Divergent Sequences
Maria Zeltser with Johann Boss
School of Digital Technologies, Mathematics and Didactics of Mathematics,
Tallinn University,
Tallinn, Estonia
Abstract: C. Stuart proved in [1] that the Cesàro matrix 𝐶1 cannot sum almost
every subsequence of a bounded divergent sequence 𝑥. At the end of the paper
he stated the problem whether this proposition could be generalized for any
regular matrix. We confirm Stuart's conjecture, and even we extend it to the
more general case of divergent sequences x. Moreover we determine a class 𝑄 of
subsequences (𝑥𝑛𝑖) of 𝑥 such that a given regular matrix does not sum sum all
elements of Q.
Keywords: Regular matrices, summability of subsequences.
References:
[1] C. Stuart. Summability of subsequences of a divergent sequence. Rocky
Mountain J. Math., 44(1): 289-295, 2014.
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Many to one Embedding Crossed Cube into Pancake
Mohamed Faouzi Zerarka
Abstract: Among Cayley graphs on the symmetric group, the pancake graph is
one as a viable interconnection scheme for parallel computers, which has been
examined by a number of researchers. The pancake was proposed as alternatives
to the hypercube for interconnecting processors in parallel computers. Some
good and attractive properties of this interconnection network include: Small
degree, a sub-logarithmic diameter, extendability, and high connectivity
(robustness), easy routing, and regularity of topology, fault tolerance,
extensibility and embeddability of other topologies. A graph embedding has been
known as a powerful tool for implementation of parallel algorithms and
simulation of interconnection networks. In this paper, we present the many-to-
one model of mapping nodes and edges of crossed cubes into nodes and paths of
pancake respectively and to minimize the dilation and the expansion costs.
Keywords: Embedding; dilation, expansion, crossed cubes, pancake.
References:
1. X. Yang, Q. Dong and Y.Y. Tan, Embedding meshes/tori in faulty crossed
cubes, Information Processing Letters, Vol. 110, no. 14-15, 559 - 564, 2010.
2. P.-L. Lai and C.-H. Tsai, Embedding of tori and grids into twisted cubes,
Theoretical Computer Science, Vol. 411, no. 40-42, 3763 - 3773, 2010. 11.
3. Y. Han, J. Fan, S. Zhang, J. Yang and P. Qian, Embedding meshes into locally
twisted cubes, Information Sciences, Vol. 180, no. 19, 3794 - 3805, 2010. 12.
4. J. Fan and X. Jia, Embedding meshes into crossed cubes, Information
Sciences, Vol. 177, no. 15, 3151 - 3160, 2007.
5. Y. Saad and M.H. Schultz, Topological properties of hypercubes, IEEE
Transactions on Computers,Vol. 37, no. 7, 867 - 872, 1988.
6. K. Efe, The crossed cube architecture for parallel computing,IEEE
Transactions Parallel and Distruibuted Systems, Vol. 3, no. 5, 513 -524, 1992
8. Akers S. and Krishnamurthy B., “A Group Theoretic Model for Symmetric
Interconnection Networks,” IEEE Transactions on Computers, vol. 38, no. 4, pp.
555-566, 1989.
9. Asai S., Kounoike Y., Shinano Y., and Kaneko K., “Computing the Diameter
of 17-Pancake Graph Using a PC Cluster,” Euro-Par 2006 Parallel Processing,
Dresden, Germany, pp. 1114-1124, 2006
10. Christian Lavault. Embeddings into the Pancake Interconnection Network.
Parallel Processing Letters, World Scientific Publishing, 2002, 12 (3-4), pp.297-
310