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International Conference on Mathematical Advances and Applications, May 11-13, 2018,

Istanbul / TURKEY

http://icomaa2018.com/

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INTERNATIONAL CONFERENCE ON MATHEMATICAL

ADVANCES AND ITS APPLICATIONS

MAY, 11-13, 2018, ISTANBUL / TURKEY

Abstract Book

Editors:

Assoc.Prof. Dr. Yusuf ZEREN Prof. Dr. Necip ŞİMŞEK Yıldız Technical University İstanbul Commerce University

İstanbul, TURKEY İstanbul, TURKEY

Prof. Dr. Farman MAMEDOV Prof. Dr. Bilal BILALOV Azerbaijan National Academy of Sciences Azerbaijan National Academy of Sciences

Baku, AZERBAIJAN Baku, AZERBAIJAN

ISBN: 978-605-245-207-3 Yıldız Technical University, İstanbul, TURKEY – 2018


http://websiteyonetimi.ahievran.edu.tr/_Dosyalar/Genel/8bf368fe-87d8-49f6-af18-4aa29d3ad5b4-9f763441-54c9-4597-a1bb-3f5477ba3df9.pdf

http://www.amu.ac.in/dshowfacultydata.jsp?did=6&eid=605




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FOREWORDS

Dear Conference Participant, Welcome to the International Conference on Mathematical Advances and Applications (ICOMAA-2018). The aim of the International Conference on Mathematical Advances and Applications (ICOMAA-2018), to bring together experts and young analysts from all over the world to present their research in analysis and work, to exchange ideas, to collaborate and interact with each other, to discuss challenging issues, and to encourage the future. The main objective of the workshop is to discuss recent results in functional analysis, approximation theory, applications in differential equations and partial differential equations and Mathematics Education. We expect the participation of many prominent experts from different countries who will present the state-of-the-art in real analysis, complex analysis, harmonic and non-harmonic analysis, operator theory and spectral analysis, applied analysis.

The conference brings together about 200 participants from 13 countries (Algeria, Azerbaijan, Bishkek, Czech Republic, Egypt, India, Iran, Jordan, Pakistan, Qatar, Russia, Saudi Arabia, Turkey), out of which 174 are contributing to the meeting with oral and 42 with poster presentations, including six invited talks.

It is also an aim of the conference to encourage opportunities for collaboration and networking between senior

academics and graduate students to advance their new perspective. Additional emphasis on ICOMAA-2018 applies

to other areas of science, such as natural sciences, economics, computer science, and various engineering

sciences, as well as applications in related fields. The articles submitted to this conference will be addressed on the

conference web sites and in the journals listed below:

Azerbaijan Journal of Mathematics,

Sigma Journal of Engineering and Natural Sciences,

Istanbul Commerce University Journal of Sciences,

Transactions Issue Mathematics.

This booklet contains the titles and abstracts of almost all invited and contributed talks at the International Conference on Mathematical Advances and Applications. Only some abstracts were not available at the time of printing the booklet. They will be made available on the conference website http://icomaa2018.com/ when the organizers receive them.

We wish everyone a fruitful conference and pleasant memories in Istanbul, Turkey.

Assoc. Prof. Yusuf ZEREN

On Behalf of Organizing Committee Chairman


http://www.advancesindifferenceequations.com/

http://carpathian.ubm.ro/

http://www.ybook.co.jp/jnca.html

http://www.journalofinequalitiesandapplications.com/



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It was a big excitement moment when Assoc. Prof. Yusuf ZEREN discussed with me on the issue of

"International Mathematical Developments and Applications Conference" (ICOMAA-2018) in Yıldız Technical

University, Istanbul. It is a great pleasure that this conference is going to take place now. As one of the organizers

of the conference, I am delighted with all the delegates, distinguished mathematicians, speakers and young

researchers in this international event. It is expected that delegates and participants will benefit from this conference

experience and the legacy of information dissemination will continue.

I wish all of you to have a nice and enjoyable participation in the conference.

Prof. Necip SIMSEK



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SCIENTIFIC COMMITTEE

Abdel-Aty, M., Egypt

Abdullayev, F., Turkey

Ahlatcioglu, M., Turkey

Akarsu, M., U.S.A.

Akbas, M., Turkey

Alexandrovich, A. Y., Russia

Aliyev, I., Turkey

Altun, Y., Turkey

Aydin, B., Turkey

Baldemir, H., U.K.

Basarir, M., Turkey

Bilalov, B., Azerbaijan

Bouhamidi, A., France

Burenkov, V. I., U.K.

Celik, E., Turkey

Chalabi, A., France

Colak, R., Turkey

Cruz-Uribe, D., U.S.A.

Diening, L., Germany

Dogan, M., Turkey

Duman, O., Turkey

Duru, A., Turkey

Ekincioglu, I., Turkey

Ersoy, B. A., Turkey

Gogatishvili, A., Czech

Gok, O., Turkey

Gul, E. Turkey

Guliyev, V. S., Azerbaijan

Guzel, N., Turkey

Huseynli, A., Azerbaijan

Isgenderoglu, M., Turkey

Izgi, A., Turkey

Jbilou, K., France

Kara, E. E., Turkey

Karakaya, V., Turkey

Kaya, D., Turkey

Kokilashvili, V., Georgia

Kucuk, I., Turkey

Mamedov, F., Azerbaijan

Manafli, M., Turkey

Manapovich, S. A., Kazakhstan

Mardanow, M. J., Azerbaijan

Monsurro, S., Italy

Mursaleen, M., India

Nuray, F., Turkey

Oleg, R., Russia

Ozdemir, A. S., Turkey

Ozdemir, M. E., Turkey

Pascu, M., Romania

Polat, H., Turkey

Samko, S., Portugal

Sari, M., Turkey

Savas, E., Turkey

Secer, A., Turkey

Serbetci, A., Turkey

Sevli, H., Turkey

Simsek, N., Turkey

Tok, I., Turkey

Transirico, M., Italy

Ugur, T., Turkey

Vladimirovich, K. L., Russia

Zeren, Y., Turkey



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ORGANIZING

COMMITTEE

Yusuf ZEREN (Chairman)(Turkey)

Misir J. MARDANOV (Azerbaijan)

Necip SIMSEK (Turkey)

Lutfi AKIN (Turkey)

Fatih SIRIN (Turkey)

LOCAL ORGANIZING

COMMITTEE

Erdoğan Mehmet Ozkan, Yildiz Technical University,

Turkey

Faik Gursoy, Adiyaman University, Turkey

Faruk Dusunceli, Mardin Artuklu University, Turkey

Hulya Burhanzade, Yildiz Technical University, Turkey

Kadri Dogan, Artvin Coruh University, Turkey

Muzeyyen Erturk, Adiyaman University, Turkey

Nilgun Aygor, Yildiz Technical University, Turkey

Ozgur Yildirim, Yildiz Technical University, Turkey

Ozlem Baksi, Yildiz Technical University, Turkey

Selmahan Selim, Yildiz Technical University, Turkey

Suayip Toprakseven, Artvin Coruh University, Turkey

Yunus Atalan, Aksaray University, Turkey

Adem Cengiz Cevikel, Yildiz Technical University,

Turkey

Ibrahim Demir, Yildiz Technical University, Turkey

Ihsan Kaya, Yildiz Technical University, Turkey

Murat Kirisci, Istanbul University, Turkey

Emirhan Hacioglu, Yildiz Technical University, Turkey

Halil Ibrahim Uzun, Yildiz Technical University, Turkey

Hande Uslu, Yildiz Technical University, Turkey

Mustafa Gezek, Namik Kemal University, Turkey

Serkan Onar, Yildiz Technical University, Turkey

Arshed Adham Ahmad, Yildiz Technical University,

Turkey

Cemil Karacam, Yildiz Technical University, Turkey

Kader Simsir, Yildiz Technical University, Turkey

Ruken Celik, Istanbul Commence University, Turkey

Reyhan Tellioglu, Istanbul Commence University, Turkey

Seyma Cetin, Yildiz Technical University, Turkey

Caner Kazar, Yildiz Technical University, Turkey

Elif Deniz, Yildiz Technical University, Turkey

Salih Yazar, Yildiz Technical University, Turkey

Selim Yavuz, Yildiz Technical University, Turkey

Zhamile Askerova, Istanbul Commence University, Turkey


http://avesis.yildiz.edu.tr/mozkan/

http://avesis.yildiz.edu.tr/mozkan/

http://abys.adiyaman.edu.tr/faik-gursoy-500/

http://www.artuklu.edu.tr/tr/mimarlik-fakultesi/akademik/yrddocdr-faruk-dusuncel

http://avesis.yildiz.edu.tr/hulyab/

https://www.artvin.edu.tr/kadri-dogan

http://abys.adiyaman.edu.tr/muzeyyen-erturk-534/

http://avesis.yildiz.edu.tr/aygor/

http://avesis.yildiz.edu.tr/ozgury/

http://avesis.yildiz.edu.tr/baksi/

http://avesis.yildiz.edu.tr/sselim/

https://www.artvin.edu.tr/suayip-toprakseven

http://obs.aksaray.edu.tr/oibs/akademik/per_akademik_cv.aspx?id=101432

http://avesis.yildiz.edu.tr/acevikel/

http://avesis.yildiz.edu.tr/acevikel/

http://avesis.yildiz.edu.tr/idemir/

http://avesis.yildiz.edu.tr/ihkaya/

http://aves.istanbul.edu.tr/murat.kirisci/kimlik

http://avesis.yildiz.edu.tr/hacioglu/

http://avesis.yildiz.edu.tr/hiuzun/kimlik

http://avesis.yildiz.edu.tr/usluh/

http://avesis.yildiz.edu.tr/sonar/


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FOREWORDS........................................................................................................................................................................ 2

SCIENTIFIC COMMITTEE ....................................................................................................................................................... 4

ORGANIZING COMMITTEE ................................................................................................................................................... 5

LOCAL ORGANIZING COMMITTEE ........................................................................................................................................ 5

INVITED TALKS

INCLUSIONS AND NONINCLUSIONS OF SPACES OF MULTIPLIERS OF SOME WIENER AMALGAM SPACES ........................... 17

A. TURAN GURKANLI

CONSTRUCTION OF VARIABLE EXPONENT LEBESGUE SPACE 𝑳𝒑 ⋅ (𝑻) CLOSE TO 𝑳∞(𝑻) WITH ASSOCIATE SPACE CLOSE TO 𝑳𝟏(𝑻) ........................................................................................................................................................................... 18

DAVID EDMUNDS 1 , AMIRAN GOGATISHVILI 2 AND TENGIZ KOPALIANI 3

BASIS PROPERTIES OF TRIGONOMETRIC SYSTEMS IN WEIGHTED MORREY SPACES ........................................................... 19

BILAL BILALOV,1 YUSUF ZEREN2 AND SEYMA CETIN2

LACUNARY ALMOST CONVERGENCE AND SOME NEW SEQUENCE SPACES ........................................................................ 20

EKREM SAVAS

ON SOLVABILITY OF SOME NONLINEAR EIGENVALUE PROBLEM IN VARIABLE EXPONENT LEBESGUE SPACES ................. 21

FARMAN MAMEDOV1,3 YUSUF ZEREN2 AND SAYALI MAMMADLI1

PROCESSING OF QUADRATURE DOPPLER ULTRASOUND SIGNALS – AN ENGINEERING PERSPECTIVE OF COMPLEX ANALYSIS ........................................................................................................................................................................... 22

NIZAMETTIN AYDIN

MAXIMAL OPERATOR AND ITS COMMUTATORS ON GENERALIZED WEIGHTED MORREY SPACES WITH VARIABLE EXPONENT ......................................................................................................................................................................... 23

VAGIF S. GULIYEV1

CONTRIBUTED TALKS

A HYPERBOLIC PENALTY METHOD TO SOLVE STRUCTURED CONVEX MINIMIZATION PROBLEMS ..................................... 24

H. ALSAOUD1, T.S. AL-MAADEED AND A. HAMDI2

LYAPUNOV-TYPE INEQUALITIES FOR FOURTH-ORDER BOUNDARY VALUE PROBLEMS....................................................... 25

MUSTAFA FAHRI AKTAŞ1, DEVRIM ÇAKMAK2 AND ABDULLAH AHMETOĞLU2

THE ESTIMATES OF FUNCTIONS TYPE OF WEIERSTRASS KERNEL IN SPECIAL DOMAINS ..................................................... 26

ABDURRAHIM GULIYEV AND MUSHFIQ ALIYEV



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EXACT SOLUTIONS OF SOME NONLINEAR EQUATIONS ...................................................................................................... 27

ADEM C. CEVIKEL1 AND ÖZGÜR YILDIRIM2

BRIGHT AND DARK SOLITON SOLUTIONS OF THE GVCKP EQUATION ................................................................................. 28

ADEM C. CEVIKEL1 AND ÖZGÜR YILDIRIM2

ON SUFFICIENT CONDITION FOR STARLIKENESS OF CONFLUENT HYPERGEOMETRIC FUNCTIONS ...................................... 29

İSMET YILDIZ1, ALAATTIN AKYAR1, OYA MERT2 AND NESLIHAN UYANIK3

A NEW ITERATIVE ALGORITHM FOR THE TIME-FRACTIONAL FISHER EQUATION INCLUDING SMALL DELAY ...................... 30

ALI DEMIR1 , MINE AYLIN BAYRAK2 AND METIN BAYRAK2

EXPLİCİT COMPUTATİON OF THE UNİPOTENT TERMS İN THE TRACE FORMULA FOR GL(2) OVER A NUMBER FİELD ........... 31

ALI AYDOĞDU1, ENGIN ÖZKAN2 AND RUKIYE ÖZTÜRK3

ON 2-FİBONACCİ POLYNOMİALS ........................................................................................................................................ 32

ENGIN ÖZKAN1, MERVE TAŞTAN1 AND ALI AYDOĞDU2

ON KOROVKIN TYPE THEOREMS IN NON-STANDARD SPACES AND THEIR STATISTICAL VARIANTS................................... 33

ALI HUSEYNLI,1 FATIH SIRIN2 AND FIDAN SEYIDOVA3

BOUNDEDNESS OF SOME SUBLİNEAR OPERATORS AND THEİR COMMUTATORS ON GENERALİZED LOCAL MORREY SPACES .......................................................................................................................................................................................... 34

AYHAN ŞERBETÇI

CONFIGURATIONAL MEAN-FIELD TRANSFER MATRIX METHOD FOR ISING SYSTEMS......................................................... 35

TUNCER KAYA1 AND BAŞER TAMBAŞ2

SOLUTION OF THE MAXIMUM DIFFERENCE EQUATION 1 1

1 1 1 1

max , ; max ,n n

n n

n n n n

y xA Ax y

x x y y

.......................... 36

BURAK OĞUL1, DAĞISTAN ŞIMŞEK2,3, NURTILEK JAMSHITOV4

ON THE RECURSIVE SEQUENCE 19

1

3 7 11 151

n

n

n n n n

xx

x x x x

................................................................................................ 37

BURAK OĞUL1, DAĞISTAN ŞIMŞEK2,3, PEIL ESENGUL KYZY4

INTEGRAL OPERATORS OF HARMONIC ANALYSIS IN LOCAL MORREY-LORENTZ SPACES .................................................... 38

CANAY AYKOL1 AND AYHAN SERBETCI1

ON PROPERTIES OF THE PELL AND PELL-LUCAS SEDENIONS ............................................................................................... 39

CENNET ÇIMEN1

FAN-GOTTESMAN COMPACTIFICATION AND STONE SPACE ............................................................................................... 40

CEREN SULTAN ELMALI1 AND TAMER UĞUR2

RELATIVELY C3 AND D3-MODULES ..................................................................................................................................... 41

DENIZ GÖKALP1 AND TÜLAY YILDIRIM2

SOME SPECTRAL ASPECTS OF FRACTIONAL SINGULAR STURM-LIOUVILLE EQUATION ....................................................... 42

AHU ERCAN1



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AN INCREASE THEOREM FOR POSITIVE SOLUTIONS OF THE PARABOLIC EQUATION SECOND ORDER............................ 43

ELIF DENIZ1, YUSUF ZEREN2, ABDURRAHIM GULIYEV3 AND SELIM YAVUZ4

A NOTE ON Q-BI-PERIODIC FIBONACCI AND LUCAS SEQUENCES ........................................................................................ 44

ELIF TAN1, SEMIH YILMAZ2, AND MURAT ŞAHIN3

SOLUTION OF MATHEMATICAL MODEL FOR SUPERCRITICAL FLUID EXTRACTION OF LAVENDER FLOWER ESSENTIAL OIL WITH FINITE DIFFERENCE METHOD ................................................................................................................................... 45

ELVEDA GAMZE MEMIŞ, ELIF TEKIN TARIM

SOME RESULTS FOR MAX-PRODUCT OPERATORS VIA POWER SERIES METHOD ................................................................ 46

EMRE TAŞ1 AND TUĞBA YURDAKADIM2

UPPER AND LOWER SOLUTİONS FOR FOURTH ORDER THREE POİNT BVPS WİTH İNTEGRAL BOUNDARY CONDİTİONS ON A HALF LİNE .......................................................................................................................................................................... 47

ERBIL ÇETIN1AND ŞERIFE MÜGE EGE2

ON ABEL CONVERGENCE .................................................................................................................................................... 48

ERDAL GÜL1 AND MEHMET ALBAYRAK2

ON CHAOTIC SOLUTIONS OF GROSS-PITAEVSKII EQUATION .............................................................................................. 49

EREN TOSYALI1 AND FATMA AYDOGMUS2

MATHEMATİCAL BEHAVİOR OF SOLUTİONS OF SEMİLİNEAR KLEİN-GORDON EQUATİONS ................................................ 50

ERHAN PIŞKIN

DESIGNING A MODEL FOR MOVING BLOCK SIGNALLING SYSTEM WITH STATE-SPACE MODELLING .................................. 51

ERTUGRUL ATES 1 AND ILKER USTOGLU 2

HIGH ORDER METHODS FOR ADVECTION DIFFUSION EQUATION ...................................................................................... 52

EVREN TOPCU1 , MELDA TURHAN1 AND DURSUN IRK1

NUMERICAL SOLUTIONS BY LEGENDRE POLYNOMIALS FOR HANTAVIRUS INFECTION MODEL .......................................... 53

FARUK DUSUNCELI

NEW SOLUTIONS FOR LINEER COMPLEX DIFFERENTIAL EQUATIONS ................................................................................. 54

FARUK DUSUNCELI1 AND LUTFI AKIN2

SOLVING THE ARTIFICIAL ANT ON THE SANTA FE TRAIL PROBLEM USING ARTIFICIAL BEE COLONY PROGRAMMING ........ 55

FATEH BOUDARDARA1 AND BEYZA GORKEMLI 2

SOME PARSEVAL TYPE RELATIONS ON THE PV,4N-INTEGRAL TRANSFORM .......................................................................... 56

A. NESE DERNEK1 AND FATIH AYLIKCI2

MODULES HAVE S2 PROPERTY ........................................................................................................................................... 57

FATIH KARABACAK1

SOME CLASSICAL SOLUTIONS OF DIRAC-GURSEY FIELD EQUATION ................................................................................... 58

FATMA AYDOGMUS1 AND EREN TOSYALI2



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BASES OF THE PERTURBED SYSTEM OF EXPONENTS IN GENERALIZED WEIGHTED LEBESGUE SPACE WITH A GENERAL WEIGHT ............................................................................................................................................................................. 59

FATIMA GULIYEVA,1 AND SABINA SADIGOVA1

ON THE BIFURCATION DIAGRAMS OF FRACTIONAL LOGISTIC MAP ................................................................................... 60

FATMA YAVCIN AND NURAN GUZEL

MULTIPLE SCALES METHOD FOR HIGHER ORDER KDV EQUATION ..................................................................................... 61

FEDAKAR ÇAKIR1, MURAT KOPARAN2 AND ÖMER ÜNSAL1

STABILIZATION OF OPTIMAL CONTROL OF NAVIER-STOKES EQUATIONS ........................................................................... 62

FIKRIYE NURAY YILMAZ

QUADRATURE FORMULA UTILIZING SPARSE GRID QUASI-INTERPOLATION WITH GAUSSIAN ............................................ 63

FUAT USTA1

SOME PROPERTİES OF A SECOND ORDER MİXED TYPE İMPULSİVE DİFFERENTİAL EQUATİON WİTH PİECEWİSE CONSTANT ARGUMENTS ..................................................................................................................................................................... 64

GIZEM S. ÖZTEPE

VALUE OF GAME FOR INFINITE MATRIX GAMES WITH INTERVAL PAYOFFS ....................................................................... 65

AYKUT OR1 AND G. SELIN SAVAŞKAN2

LEXICOGRAPHIC METHOD IN INTERVAL POSITIONAL GAMES ............................................................................................ 66

G. SELIN SAVAŞKAN1 AND AYKUT OR2

FUZZY MIXED POISSON REGRESSION MODEL ON A SMOKING CESSATION STUDY ............................................................. 67

GODRICK OKETCH1 AND FILIZ KARAMAN1

SOME PROPERTIES OF HYPERBOLIC SPLIT QUATERNION MATRICES .................................................................................. 68

GÖZDE ÖZYURT1 AND YASEMIN ALAGÖZ2

CLOSED-FORM SOLUTIONS OF OPTIMAL GROWTH MODEL WITH ENVIRONMENTAL ASSET .............................................. 69

GÜLDEN GÜN POLAT1, AHU COŞKUN ÖZER2 AND TEOMAN ÖZER 3

ESTEMATIONS FOR THE ROOT FUNCTIONS OF A DIRAC TYPE OPERATOR .......................................................................... 70

HAJIYEVA GUNEL RAZIM

APPROXIMATION PROPERTIES OF FOURIER SERIES BY NONLINEAR BASIS IN GENERALIZED HÖLDER SPACES ................... 71

HATICE ASLAN1 AND ALI GÜVEN2

SOME IDENTITIES ON FRACTIONAL INTEGRALS AND INTEGRAL TRANSFORMS .................................................................. 72

AYSE NESE DERNEK1 AND GULCIN BOZKURT2

SOLUTIONS FOR SOME FAMILIES OF FRACTIONAL DIFFERENTIAL EQUATIONS .................................................................. 73

NEŞE DERNEK1 AND GÜLÇIN BOZKURT2

LIE GROUP ANALYSIS AND GALILEAN GROUP ANALYSIS FOR PARTIAL DIFFERENTIAL EQUATIOS ....................................... 74

DOGAN KAYA1 AND GULISTAN ISKANDAROVA2



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ON THE PARALLEL SURFACES TO TRANSLATION SURFACE WITH Q-FRAME IN EUCLIDEAN 3-SPACE ................................... 75

HATICE TOZAK1, GÜLŞAH AYDIN ŞEKERCI2 AND CUMALI EKICI3

GENERALIZATION OF REFLEXIVE RINGS AND THEIR APPLICATIONS ................................................................................... 76

HANDAN KOSE1 AND BURCU UNGOR2

A SUBCLASS OF CONCAVE UNIVALENT FUNCTIONS DEFINED BY A LINEAR OPERATOR ...................................................... 77

HASAN BAYRAM1 AND SIBEL YALCIN2

ACCELERATION CENTRES OF ORDER (R-1) OF HOMOTHETIC MOTIONS.............................................................................. 78

HASAN ES

NUMERICAL SCHEME FOR THE SOLUTION OF MULTI ORDER FRACTIONAL DIFFERENTIAL EQUATION .............................. 79

HATICE YALMAN KOSUNALP1, YALÇIN ÖZTÜRK2, MUSTAFA GÜLSU3

ON NUMERICAL APPROXIMATION OF GENERALIZED DIFFERENTIAL DIFFERENCE EQUATIONS WITH LINEAR FUNCTIONAL ARGUMENT ....................................................................................................................................................................... 80

HATICE YALMAN KOSUNALP1, YALÇIN ÖZTÜRK2, MUSTAFA GÜLSU3

COMPARISON OF ARTIFICIAL NEURAL NETWORK AND LOGISTIC REGRESSION MODEL FOR A MEDICINE APPLICATION .... 81

MURAT KIRIŞCI1 AND NECIP ŞIMŞEK2

A DIFFERENCE SCHEME FOR THE BURGERS EQUATION ...................................................................................................... 83

MURAT SARI1, SUFII HAMAD MUSSA1 AND HUSEYIN TUNC1

COMMON FIXED POINT OF NONCOMMUTING ALMOST CONTRACTION MAPPING IN CONE METRIC SPACE OVER BANACH ALGEBRA ........................................................................................................................................................................... 84

MUTTALIP ÖZAVŞAR1 AND HATICE ÇAY2

COMMON FIXED POINT OF NONCOMMUTING ALMOST CONTRACTION MAPPING IN CONE B-METRIC SPACE OVER BANACH ALGEBRA ............................................................................................................................................................. 85

MUTTALIP ÖZAVŞAR1 AND HATICE ÇAY2

TIMELIKE TRANSLATION SURFACE ACCORDING TO Q-FRAME IN MINKOWSKI 3-SPACE ..................................................... 86

CUMALI EKICI1, HATICE TOZAK2 AND MUSTAFA DEDE3

COMPLETENESS OF CATEGORY OF RACK CROSSED MODULES ........................................................................................... 87

HATICE GÜLSÜN AKAY AND İ.İLKER AKÇA

PULLBACK DIAGRAMS FOR RACK CROSSED MODULES ....................................................................................................... 88

HATICE GÜLSÜN AKAY AND KADIR EMIR

ON ROUGH GENERALIZED PARAMETRIC MARCINKIEWICZ INTEGRAL ................................................................................ 89

HUSSAIN AL-QASSEM 1, LESLIE CHENG2 AND YIBIAO PAN3

ON THE EVALUATİON OF THE DİFFİCULTİES THAT 12TH GRADE STUDENTS FACE AT FACTORİZATİON PROCESS İN THE QUESTİONS ........................................................................................................................................................................ 90

HÜLYA BURHANZADE

ON THE SOLUTIONS OF A NEW SEMI-ANALYTICAL ITERATIVE METHOD FOR SOLVING NONLINEAR PDES .......................... 91

ZEHRA PINAR1 AND HÜSEYIN KOCAK2



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SOME PROBLEMS ABOUT ALGEBRAIC PROPERTIES OF ARISTOTELIAN LOGIC .................................................................... 92

IBRAHIM SENTURK1 AND TAHSIN ONER2

COVARIANT DIFFERENTIAL CALCULI ON ℱ(ℝ𝒒(1|1)) ......................................................................................................... 93

SALIH CELIK1 AND ILKNUR TEMLI2

LP-APPROXIMATION VIA ABEL CONVERGENCE .................................................................................................................. 94

İLKNUR ÖZGÜÇ

SOME CLASSES OF ALMOST Α-PARA-KENMOTSU MANIFOLDS .......................................................................................... 95

İREM KÜPELI ERKEN

CONSUMER AND PRODUCER SURPLUS OF THE LİNEAR DEMAND AND SUPPLY FUNCTİONS BY USİNG POLYGONAL FUZZY NUMBERS .......................................................................................................................................................................... 96

İSMAIL ÖZCAN AND SALIH AYTAR

THE STRUCTURE OF ALL GENERATING SETS OF CERTAIN MONOTONE PARTIAL TRANSFORMATION SUBSEMIGROUPS .... 97

LEYLA BUGAY1

ON THE BOUNDEDNESS OF FRACTIONAL MAXIMAL OPERATOR WITH VARIABLE KERNEL ON HERZ-MORREY SPACES ...... 98

LÜTFI AKIN1 , YUSUF ZEREN2 AND FARUK DÜŞÜNCELI3

APPROXIMATION ON VARIABLE EXPONENT SPACES BY FRACTIONAL MAXIMAL OPERATORS ........................................... 99

LÜTFI AKIN

NUMERICAL INVESTIGATION OF FREE CONVECTION STABILITY IN CYLINDRICAL ANNULUS WITH HEATER INNER CYLINDER ........................................................................................................................................................................................ 100

FATEH MEBAREK OUDINA1

BOREL'S FIXED POINT THEOREM FOR FINITE DIMENSIONAL COMPACT ABELIAN GROUPS .............................................. 101

MEHMET ONAT

EXAMINING OF THE EFFECT OF REACT STRATEGY ON CONCEPTUAL KNOWLEDGE OF SECONDARY SCHOOL 7TH GRADE STUDENTS ........................................................................................................................................................................ 102

MEHMET ERCOBAN1 AND CUNEYT YAZİCİ2

MAXIMUM LIKELIHOOD TYPE ESTIMATIONS OF PARAMETERS IN DISTRIBUTIONS .......................................................... 103

MEHMET NIYAZI ÇANKAYA1

M-ESTIMATION OF PARAMETERS FOR DISTRIBUTED LAG MODELS IN REGRESSION ........................................................ 104

MEHMET NIYAZI ÇANKAYA1

SEMI-ANALYTICAL SOLUTION FOR THE HIEMENZ FLOW OF A MICROPOLAR FLUID ......................................................... 105

MEHMET ŞIRIN DEMIR

EXACT SOLUTION FOR THE FLOW OF A MICROSTRETCH FLUID BETWEEN TWO CONCENTRIC CYLINDERS ........................ 106

MEHMET ŞIRIN DEMIR

SEPTIC B-SPLINE GALERKIN METHOD FOR THE ADVECTION DIFFUSION EQUATION ......................................................... 107

MELDA TURHAN1, EVREN TOPÇU1 AND DURSUN IRK1



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A HIGH ACCURACY NUMERICAL METHOD FOR SOLUTION OF THE RLW EQUATION ......................................................... 108

MELIS ZORSAHIN GORGULU1 AND DURSUN IRK1

NORMS AND LOWER BOUNDS FOR SOME MATRIX OPERATORS ..................................................................................... 109

MERVE İLKHAN1 AND EMRAH EVREN KARA2

APPLICATIONS OF MEASURE OF NONCOMPACTNESS TO THE INFINITE SYSTEM OF DIFFERENTIAL EQUATIONS IN SOME BANACH SPACES .............................................................................................................................................................. 110

MERVE İLKHAN1 NECIP ŞIMŞEK2 AND EMRAH EVREN KARA3

A NOVEL ITERATIVE ALGORITHM ON THE TIME-FRACTIONAL FISHER EQUATION WITH SMALL DELAY ............................ 111

MINE AYLIN BAYRAK1 , ALI DEMIR2 AND METIN BAYRAK2

ON A STRONGER OPTIMALITY CONDITION FOR SINGULAR CONTROLS IN DISCRETE SYSTEMS. ........................................ 112

MARDANOV M.J., MELIKOV T.K.

AN EXTENTION OF A CLASSICAL MAXIMUM PRINCIPLE OF AN ELLIPTIC SYSTEM OF DIFFERENTIAL EQUATIONS TO A MORE GENERAL FORM .................................................................................................................................................... 113

MOHAMMAD ALMAHAMEED

HARDY-HILBERT INEQUALITY AND BEREZIN NUMBER ..................................................................................................... 114

MEHMET GÜRDAL1 , MÜBARIZ T. GARAYEV2 AND MUALLA BIRGÜL HUBAN1

DEGENERATE HARDY-BERNDT SUMS ............................................................................................................................... 115

MUHAMMET CIHAT DAĞLI AND MÜMÜN CAN

ON THE GEOMETRY OF TANGENT BUNDLE WITH BERGER TYPE DEFORMED SASAKI METRIC .......................................... 116

MURAT ALTUNBAS1 AND AYDIN GEZER2

ON HK-TYPE DISCRETIZATION OF A HEAVY RIGID BODY .................................................................................................. 117

SERPIL USLU1 AND MURAT TURHAN1

DIOPHANTINE EQUATIONS INVOLVING ODD PRIME POWERS ......................................................................................... 118

MURAT ALAN1 AND MURAT YOĞURTÇU2

PARTIAL GEOMETRIES PG(12,12,9) AND STRONGLY REGULAR GRAPHS ARISING FROM MAXIMAL (52,4)-ARCS .............. 119

MUSTAFA GEZEK

STRICT STABILITY OF UNPERTURBED FUZZY DIFFERENTIAL EQUATIONS ......................................................................... 120

MUSTAFA BAYRAM GÜCEN1 AND COŞKUN YAKAR2

ON THE FIXED POINT SYSTEM FOR DETERMINING THE EVOLUTION OF THE SOURCE TERM OF A THIRD ORDER NONLINEAR PARTIAL DIFFERENTIAL EQUATION .............................................................................................................. 121

MÜJDAT KAYA

THE EVALUATION OF THE PROBLEM SOLVING SKILLS OF 10TH GRADE STUDENTS’ON QUADRATIC EQUATION WITH ONE UNKNOWN ...................................................................................................................................................................... 122

NILGÜN AYGÖR

ON THE APPROXIMATION OF FIXED POINTS OF MULTIVALUED NONEXPANSIVE MAPPINGS .......................................... 123

BIROL GÜNDÜZ1 FATMA SOLMAZ2 OSMAN ALAGÖZ3 SEZGIN AKBULUT4



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COMPARING CONVERGENCE RATE OF 𝑴-ITERATION WITH SOME FASTER İTERATION PROCESSES ................................. 124

OSMAN ALAGÖZ1 BIROL GÜNDÜZ2 AND SEZGIN AKBULUT3

ON LAPLACE TRANSFORM TECHNIQUE FOR THE SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS ....................... 125

OZGUR YILDIRIM1 , ADEM CENGIZ CEVIKEL2

INCLUSION RELATIONS BETWEEN HARMONIC BERGMAN-BESOV SPACES ON THE UNIT BALL OF ℝ𝒏 ............................. 126

ÖMER FARUK DOĞAN1

HARMONIC BERGMAN-BESOV SPACES WITH SMALL EXPONENTS IN THE UNIT BALL ...................................................... 127

ÖMER FARUK DOĞAN1

RADIATION FLUID STARS IN A NON-MINIMAL GRAVITY MODEL ...................................................................................... 128

ÖZCAN SERT1

FIRST ORDER MAXIMALLY ACCRETIVE QUASI-DIFFERENTIAL OPERATORS ....................................................................... 129

PEMBE IPEK AL1 AND ZAMEDDIN I. ISMAILOV2

SPECTRAL ANALYSIS OF CANONICAL TYPE FIRST ORDER SELFADJOINT QUASI-DIFFERENTIAL OPERATORS ...................... 130

ZAMEDDIN I. ISMAILOV1, PEMBE IPEK AL2 AND RUKIYE ÖZTÜRK MERT3

QUARTIC TRIGONOMETRIC B-SPLINE GALERKIN METHOD FOR THE EQUAL WIDTH WAVE EQUATION ............................ 131

PINAR KESKIN YILDIZ1 AND DURSUN IRK1

OPERATOR IDEALS DEFINED BY USING BLOCK SEQUENCE SPACES ................................................................................... 132

PINAR ZENGIN ALP1 AND EMRAH EVREN KARA2

A NOTE ON EQUIVALENT QUASINORMS .......................................................................................................................... 133

PINAR ZENGIN ALP1 AND EMRAH EVREN KARA2

SMOOTHNESS MODULI FOR SOME BANACH FUNCTION SPACES ..................................................................................... 134

RAMAZAN AKGÜN

MUSIELAK ORLICZ SPACES AND APPROXIMATION PROBLEMS ........................................................................................ 135

RAMAZAN AKGÜN

ON A SPACE OF -STATISTICAL CONTINUOUS FUNCTIONS ............................................................................................. 136

RAZIYYA HASANLI1 AND CEMIL KARACAM2

LIE GROUP ANALYSIS OF SOME EVOLUTION EQUATIONS ................................................................................................ 137

SAADET S. ÖZER

A NEW CUBIC PICTURE FUZZY INFORMATION AGGREGATION AND ITS APPLICATION TO MULTI-ATRIBUTE DECISION MAKING PROBLEM .......................................................................................................................................................... 138

SALEEM ABDULLAH1 AND SHAHZAIB ASHRAF 1

INVENTORY WITHOUT BACKORDER USING THE POLYGONAL FUZZY NUMBERS............................................................... 139

İSMAIL ÖZCAN AND SALIH AYTAR

NEW TYPE INTEGRAL INEQUALITIES FOR FOURTH TIMES DIFFERENTIABLE PREQUASIINVEX FUNCTIONS ........................ 140

İMDAT İŞCAN1, SELAHATTIN MADEN2 AND HURIYE KADAKAL3



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NEW TYPE INTEGRAL INEQUALITIES FOR N-TIMES DIFFERENTIABLE PREINVEX FUNCTIONS ............................................ 141

İMDAT İŞCAN1, MAHIR KADAKAL1 AND SELAHATTIN MADEN2

SOME RESULTS ON GENERALIZED FIBONACCI AND LUCAS QUATERNIONS ...................................................................... 142

SEMIH YILMAZ1, ELIF TAN2, AND MURAT ŞAHIN3

INVESTIGATION OF MATHEMATICAL PROBLEM SOLVING AND POSING PROCESSES OF PRIMARY SCHOOL STUDENTS .... 143

MUSTAFA DOĞAN1 AND SEVGI AKTEN2

ON WEIGHTED WEAK STATISTICAL CONVERGENCE ......................................................................................................... 144

SINAN ERCAN1

NONCOMMUTATIVE GEOMETRY AND APPLICATION TO DIFFERENEIEL SCHRÖDINGRE EQUATION ................................. 145

ZAIEM SLIMANE

A NOTE ON DUAL CODES OF PSEUDO-CYCLIC CODES ....................................................................................................... 146

SUMEYRA BEDIR1 AND FATMANUR GURSOY2

MATRIX REPRESENTATIONS OF COMPRESSIBLE FLUID EQUATIONS ................................................................................. 147

SÜLEYMAN DEMIR1 AND MURAT TANIŞLI1

ESTIMATES OF FABER POLYNOMIAL COEFFICIENTS FOR BI-UNIVALENT FUNCTIONS EQUIPPED WITH THE JACKSON (P,Q)-DERIVATIVE OPERATOR ................................................................................................................................................... 148

ŞAHSENE ALTINKAYA1 AND SIBEL YALÇIN2

ANALYTICAL SOLUTIONS OF THE BISWAS-MILOVIC AND GERDJIKOV-IVANOV EQUATIONS ............................................. 149

ŞERIFE MÜGE EGE

GENERALİZED SYLVESTER POLYNOMİALS OF THREE VARİABLES ...................................................................................... 150

NEJLA ÖZMEN1 AND SULE SOYTÜRK2

STATISTICAL HYPO-CONVERGENCE IN SEQUENCE OF FUNCTIONS ................................................................................... 151

ŞÜKRÜ TORTOP1

ON THE SPECIAL CASE OF THE RIEMANN BOUNDARY VALUE PROBLEM .......................................................................... 152

TATSIANA URBANOVICH1,2 AND ZAHIR MURADOGLU1

EIGENPARAMETER DEPENDENT DISCONTINUITY CONDITION IN WEIGHTED LEBESQUE SPACES ...................................... 153

TELMAN GASYMOV,1 SELIM YAVUZ2 AND NIGAR AHMEDZADE 1

VARIATIONAL APPROXIMATION FOR MODIFIED MEYER-KÖNIG AND ZELLER OPERATORS .............................................. 154

TUĞBA YURDAKADIM1 AND EMRE TAŞ2

HARDY-TYPE INEQUALITIES AND SOME RELATED RESULTS .............................................................................................. 155

TUGCE UNVER1

A SPATİAL CURVE ADJOİNİNG ANOTHER SPATİAL CURVE BASED ON BİSHOP FRAME ...................................................... 156

VAHIDE BULUT

THEOREM ON LOCAL EQUICONVERGENCE FOR DIRAC OPERATOR .................................................................................. 157

VALI KURBANOV1AND AFSANA ABDULLAYEVA2



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DETERMİNATİON YOUNG’S MODULUS BY USİNG ADDİTİONAL DATA İN THE SYSTEM COMPOSED OF THE PLATES WİTH DİFFERENT PROPERTİES ................................................................................................................................................... 158

VİLDAN YAZICI AND ZAHİR MURADOĞLU

A SOLUTION OF AIRY DIFFERENTIAL EQUATION VIA NATURAL TRANSFORM ................................................................... 159

YASIN UCAKAN1, KEVSER KOKLU2 AND SEDA GULEN3

COMPONENTWISE UNIFORM EQUICONVERGENCE THEOREM FOR A THIRD ORDER DIFFERENTIAL OPERATOR ............... 160

YULIYA G.ABBASOVA

ON THE SOLUTIONS OF REACTION-DIFFUSION EQUATIONS ............................................................................................. 161

ZEHRA PINAR1 AND HÜSEYIN KOCAK2

ON WEIGHTED ZORKO SUBSPACES AND RIESZ TYPE THEOREMS FOR ANALYTIC FUNCTIONS .......................................... 162

YUSUF ZEREN1 AND SELIM YAVUZ1

ON A SOLVABILITY FOR SOME VARIABLE EXPONENT EIGENVALUE PROBLEM ................................................................. 163

YUSUF ZEREN1 LUTFI AKIN2 KADER SIMSIR3 AND CANER KAZAR4

POSTER SESSION

RECONSTRUCTION OF TOMOGRAPHIC IMAGES FROM LIMITED PROJECTIONS USING TVCIM-P ALGORITHM .................. 164

ABDESSALEM BENAMMAR1 AICHA ALLAG1,2, REDOUANE DRAI1

ON THE MISCONCEPTIONS OF 10TH GRADE STUDENTS ABOUT ANALYTICAL GEOMETRY ................................................ 165

AYTEN ÖZKAN1, ERDOĞAN MEHMET ÖZKAN1

PRIVATE INFORMATION RETRIEVAL ................................................................................................................................ 166

FATIH DEMIRKALE AND EDANUR TAŞTAN

SOME CLASSICAL SOLUTIONS OF DIRAC-GURSEY FIELD EQUATION ................................................................................. 167

FATMA AYDOGMUS1 AND EREN TOSYALI2

A NEW TOPP-LEONE EXTENDED WEIBULL DISTRIBUTION AS A SAMPLING DISTRIBUTION ............................................... 168

GAMZE ÖZEL KADILAR1 AND CEM KADILAR2

A FUZZY APPROACH TO THE ESTİMATİON OF PM LEVELS ................................................................................................ 169

KARDELEN KILIÇ1 AND FILIZ KANBAY2

ON DISCRETE MORSE THEORY ......................................................................................................................................... 170

MUSTAFA AKKAYA AND İSMET KARACA

STABILITY ANALYSIS OF CONFORMABLE FRACTIONAL-ORDER NONLINEAR SYSTEMS .................................................... 171

GHANIA REBIAI, ABDELLATIF BEN MAKHLOUF

ANALYSIS OF JUDD–OFELT THEORY TO THE RARE EARTH ION PR3+ DOPED KY3F10 SINGLE CRYSTAL ........................... 172

S. KHIARI1,2 AND M. DIAF2

NOTE ON A-POLYNOMIAL OF KNOTS ...................................................................................................................... 173

SELINHATIPOĞLU*,İSMETKARACA,



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A FUZZY APPROACH TO THE ESTIMATION OF 𝑪𝑶𝟐 EMISSION EMITTED FROM THE LAND AND SEA TRANSPORT ............ 174

YASEMIN ERGIN1 AND FILIZ KANBAY2

INDEX .............................................................................................................................................................................. 175



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17

INVITED TALKS

Inclusions and Noninclusions of Spaces of Multipliers of some Wiener Amalgam Spaces

A. Turan Gurkanli Istanbul Arel University , Faculty of Science and Letters,

Department of Mathematics and Computer Science, 34537,

Tepekent-Buyukcekmece, Istanbul, TURKEY

Abstract

The main purpose of this paper to work on inclusions and noninclusions among the spaces of multipliers of the Wiener

amalgam spaces. M. G. Cowling and J. J. F Fournier in [1], L. Hrmander in [5] and G. I. Gaudry in [4]; have worked on the

space MG (Lp;Lq); the space of convolution multipliers from Lp into Lq; and worked inclusions and noninclusions among

these spaces. In this paper we consider a much larger classes of spaces than Lp and Lq spaces, we consider the Wiener

amalgam spaces W (Lp;Lq) and weighted Wiener amalgam spaces W (Lp;Lq !). Firstly, we work on inclusions between the

spaces of multipliers of Wiener amalgam spaces. Later by using the Rudin-Shapiro measures, we investigate noninclusions

among the spaces of multipliers of Wiener amalgam spaces.

References

1. M. G. Cowling and J. J. F. Fournier, Inclusions and noninclusion of spaces of convolution operators, Trans. Amer. Math. Soc.

221-1, (1976), 59-95. 2. H. G. Feichtinger, Banach convolution algebras of Wiener type. In Proc. Conf. Functions, Series, Operators, Budapest,

Colloquia Math. Soc. J. Bolyai, Amsterdam- Oxford- New York (1980), 509-524; North Holland.

3. H. G. Feichtinger, Banach spaces of distributions of Wieners type and interpolation, Proc. Conf. Oberwolfach, 1980: Functional

Analysis and Approximation. Ed. P. Butzer, B. Sz. Nagy and E. Grlich. Int. Ser. Num. Math. Vol. 69, Birkhauser- Verlag.

Basel- Boston- Stuttgart (1981), 153-165.

4. G. I. Gaudry, Bad behavier and inclusion results for multipliers of type (p,q), Pasic j. Math. 35, (1970), 83-94.

5. L. Hrmander, Estimates for translation invariant operators in Lp spaces. Acta Math., 104, (1960), 93-140.



Istanbul / TURKEY


18

Construction of variable exponent Lebesgue space 𝑳𝒑(⋅)(𝑻) close to 𝑳∞(𝑻) with associate space

close to 𝑳𝟏(𝑻)

David Edmunds 1 , Amiran Gogatishvili 2 and Tengiz Kopaliani 3

1Department of Mathematics,University of Sussex

[email protected]

\addressAmiran Gogatishvili \\

2Institute of Mathematics of the Czech Academy of Sciences

[email protected]

3Faculty of Exact and Natural Sciences, I. Javakhi\-shvili Tbilisi State University

[email protected]

Abstract

We introduces a variable exponent Lebesgue space 𝑳𝒑(⋅)( 𝑻 ) with 1 < 𝑝(⋅) < ∞ a.e. which has in common with 𝑳∞(𝑻))

the property that the space C(T) of continuous functions on T is a closed linear subspace in it. The associate space 𝑳𝒒(⋅)(𝑻),

where 1/𝑞(𝑥) = 1 − 1/𝑝(𝑥) for all x. contains both the Kolmogorov and the Marcinkiewicz examples of functions 𝑳𝟏(𝑻)

with a.e. divergent Fourier series.

Keywords: Banach function space, variable Lebesgue spaces, a.e. divergent Fourier series, Hardy-Littlewood maximal

function

References

1. Edmunds, D., Gogatishvili, A., Kopaliani, T Construction of variable exponent Lebesgue space 𝐿𝑝(.)(𝑇) close to 𝐿∞(𝑇) with

associate space close to𝐿1(𝑇)

(2017) Journal of Fourier Analysis and Applications, pp. 1-15. Article in Press.

https://link.springer.com/article/10.1007/s00041-017-9574-2


mailto:[email protected]



https://link.springer.com/article/10.1007/s00041-017-9574-2


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19

Basis Properties of Trigonometric Systems in Weighted Morrey Spaces

Bilal Bilalov,1 Yusuf Zeren2 and Seyma Cetin2

1Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan 2 Department of Mathematics, Yildiz Technical University, Istanbul, Turkey

[email protected], [email protected], [email protected]

Abstract

In this work the basis properties (completeness, minimality and basicity) of the system of exponents are investigated

in weighted Morrey spaces, where the weight function is defined as a product of power functions. Although the same

properties of the system of exponents, as well as their perturbations, are well studied in weighted Lebesgue spaces, the

situation changes cardinally in Morrey spaces. For instance, since Morrey spaces are not separable, the first difficulty arises

concerning with the formulation of the problem: to find the ``suitable'' subspace, in which the above mentioned properties

have a ``chance'' to be true in. Another difficulty, that frustrates the ``usual'' attempts is that, the infinite differentiable

functions(even continuous functions) are not dense in Morrey spaces. Nevertheless, there are works, that study these problems.

For example, in the paper [1], there were studied the basis properties of the system of exponents in Morrey space. Also, in

[2;3] the basis properties of the perturbed systems of exponentials in Morrey space have been investigated. On the other hand,

some approximation problems have been investigated in Morrey-Smirnov classes in [4].

Keywords: Morrey space, minimality, completeness, basis.

References

1. B.T. Bilalov, T.B. Gasymov, A.A. Guliyeva, On solvability of Riemann boundary value problem in Morrey-Hardy classes,

Turkish Journal of Mathematics, 40(5) (2016), 1085-1101

2. B.T. Bilalov, A.A. Guliyeva, On basicity of the perturbed systems of exponents in Morrey-Lebesgue space, International Journal

of Mathematics, 25, 1450054 (2014), 10 pages.

3. B.T. Bilalov, T.B. Gasymov, On basicity of eigenfunctions of second order discontinuous differential operator, Ufimsk. Mat.

Zh., 9(1) (2017), 109-122.

4. D.M. Israfilov, N.P. Tozman, Approximation in Morrey-Smirnov classes, Azerb. J. Math.,

1 (1) (2011), 99-113.






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20

Lacunary Almost Convergence And Some New Sequence Spaces

Ekrem SAVAS

Usak University, Usak, Turkey

[email protected]

Abstract

A new type of convergence called lacunary statistical convergence was introduced as follows :

A lacunary sequence is an increasing integer sequence ( )kr

such that

0 0k and 1r r rh k k as r . Let 1( , ]r r rI k k .

Ekrem Savas and Vatan Karakaya, [1] studied some new sequence spaces defined by lacunary sequences.

In this paper we introcude the spaces of strongly almost summable sequences, which will fill up a gap in the existing

literature.

Keywords: lacunary sequence, new sequence spaces, almost convergence

References

1. G. G. Lorentz (1948), 'A contribution to the theory of divergent

sequences, Acta Math. 80, 167-190.

2. I. J. Maddox (1967), 'Spaces of strongly summable sequences',

Quart. J. Math. Oxford Ser. (2) 18, 345-55.

3. S. Nanda, Some sequence spaces and almost convergence, J. Austral. Math. Soc. 22(Series A), (1976), 446-455.

4. E. Savas and V. Karakaya, Some new sequence spaces defined by lacunary sequences, Mathematica Slovaca 57(4)(2007):393-

399.




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21

On solvability of some nonlinear eigenvalue problem in variable exponent Lebesgue spaces

Farman Mamedov1,3 Yusuf Zeren2 and Sayali Mammadli1

1Mathematics and Mechanics Institute of National Academy of Science, Azerbaijan

[email protected] 2Department of Mathematics, Yildiz Technical University,

[email protected] 2Oil Gas scientific reaserch project institute, Socar, Azerbaijan

[email protected]

Abstract

In this notice, we study eigenvalue problem:

lxxylyy

xlxyyy xp

xqxqxp

0,0)(,0)()0(

'''1

)('

)(21)(2)(

𝛿 ∈ (0,1) is a fixed number. The proof based on mountain pass theorem and the new results

‖(𝑙𝑥 − 𝑥2)−

1

𝑝′ −1

𝑞(.) 𝑦(𝑥)‖𝐿𝑞(.)(0,𝑙)

≤ ‖𝑦′‖𝐿𝑝(.)(0,𝑙)

, 𝑦(0) = 𝑦(𝑙) = 0

on boundedness and compactness in variable exponent Lebesgue spaces- from 𝑊𝑝(𝑥)1

(0, 𝑙) into 𝐿𝑞(𝑥), −

1

𝑝′ (𝑥)−

1−𝛿

𝑞(𝑥)(0, 𝑙) .

Following main result is stated in this note.

Theorem. Let 1 < 𝑝− < 𝑝(𝑥) ≤ 𝑝+ < 𝑞− ≤ 𝑞(𝑥) ≤ 𝑞+ < ∞ be measurable functions on (0, 𝑙) such that 𝑝(𝑥) be

increasing and the function 𝑥−

1

𝑝′ +휀 is almost decreasing on (0, 𝑙): 𝑡2

−1

𝑝′ (𝑡2)+휀

≤ 𝐶𝑡1

−1

𝑝′ (𝑡1)+휀

, 0 < 𝑡1 < 𝑡2<l . Then for

any fixed 𝜆 > 0 the problem (1), (2) has a nontrivial positive solution.

Keywords: Montain Pass Theorem, variable exponent Lebesgue spaces, bounded and compact embedding, Hardy;s operator.

References

1. F.I. Mamedov and Y. Zeren, A necessary and sufficient condition for Hardy's operator in the variable Lebesgue space, Abst.

Appl. Anal., 5/6, 2014, 7 pages.

2. F.I. Mamedov and S. Mammadli, Compactness for the weighted Hardy operator in variable exponent spaces, Compt. Rend. Math.,

355(3), 325-335, 2017.






Istanbul / TURKEY


22

Processing of Quadrature Doppler Ultrasound Signals – An Engineering Perspective of Complex

Analysis

Nizamettin AYDIN

Yildiz Technical University, Istanbul, Turkey

[email protected]

Abstract

Quadrature signals are based on the notion of complex numbers used in many digital signal processing applications

such as Communication, Radar, Sonar, Ultrasound, MR imaging, Direction finding schemes, Antenna beamforming

applications, and Single sideband modulators. A quadrature signal is a twodimensional signal whose value at any given time

can be specified by a single complex number such as a(t)+jb(t). Quadrature signal processing is used in many fields of science

and engineering. Processing of complex quadrature signal provides additional processing power by enabling to measure

amplitude and phase of a signal simultaneously.

The Doppler principle, which was first described in the nineteenth century, has many applications in astronomy,

physics, communication and medicine. In medicine, it is mainly used for the study of blood flow. Doppler ultrasound is based

on the fact that any moving object in the path of a sound beam will shift the frequency of the transmitted signal. It can be shown

that the difference between the transmitted frequency ft and received frequency fr is given by fd = ft – fr = (2vftcos)/c where v

is the velocity of the target, the angle between the ultrasound beam and the direction of the target's motion, and c the velocity

of sound in the medium.

In this talk, various processing methods including Fourier and wavelet transforms for processing quadrature Doppler

ultrasound signals within blood flow research context will be presented.




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23

Maximal operator and its commutators on generalized weighted Morrey spaces with variable

exponent

Vagif S. Guliyev1

1 Institute of Mathematics and Mechanics of NAS of Azerbaijan

[email protected]

Abstract

It is well known that maximal operator and its commutator play an important role in harmonic analysis. In this work we

give sufficient conditions for the boundedness of maximal operator and its commutators in the generalized weighted Morrey

spaces with variable exponent.

Keywords: maximal function, generalized weighted Morrey spaces with variable exponent, commutator, BMO



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24

CONTRIBUTED TALKS

A Hyperbolic Penalty Method to Solve Structured Convex Minimization Problems

H. Alsaoud1, T.S. Al-Maadeed and A. Hamdi2

1Department of Mathematics, King Saud University,

[email protected] 2Qatar University- College of Arts and Sciences- Dept. of Mathematics-Statistics and Physics.

[email protected] and [email protected]

Abstract

Our objective in this paper is to present a decomposition algorithm based on smooth hyperbolic penalty, which leads

to a scheme suitable for decentralized and parallelized computations. The algorithm can be seen as a separable version of the

hyperbolic penalty method

built up by Xavier ([1]-2001) and its main idea is closely related to the

separable augmented lagrangian algorithm SALA developed by Hamdi and Hamdi et al. [3, 4].

In other words, we present a penalty-type scheme mixed with a kind of resources allocation approach to decompose

large-scale separable constrained minimization programs.

Keywords: Hyperbolic Penalty methods, Decomposition, Convex functions, Large scale optimization.

References

5. A. E. Xavier, "Hyperbolic penalty: a new method for noninear programming with inequalities," International Transactions in

Operational Research 8(2001), pp. 659-671.

6. R. Polyak, "Modified Barrier Function. (Theory and Methods)". Mathematical Programming, 54, (1992), pp.177-222.

7. A. Hamdi, "Decomposition for Structured Convex Programs with Smooth Multiplier Methods ". Applied Mathematics and

Computation. Vol. 169/1 pp 218-241, 2006.

8. A. Hamdi and S.K. Mishra, "Decomposition Methods Based on Augmented Lagrangians: A Survey", Topics in Nonconvex

Optimization: Theory and Applications- pp 175-204-Springer, (2011).



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25

Lyapunov-type inequalities for fourth-order boundary value problems

Mustafa Fahri Aktaş1, Devrim Çakmak2 and Abdullah Ahmetoğlu2

1Department of Mathematics, Gazi University

[email protected]

[email protected] 2Department of Mathematics Education, Gazi University

[email protected]

Abstract

This paper is concerned with some two-point boundary vakue problems for fourth-order linear differential equations.

Our study is Bsed on the absolute maximum of Green’s functions corresponding to two-point boundary value problems.

Keywords: Lyapunov-type inequalities, Green’s functions, Two point boundary value problems.

References

1. A. M. Liapunov, Probleme general de la stabilite du mouvement, Ann. Fac. Sci. Univ. Toulouse 2 (1907), 203-407.

2. A. Cabada, J. A. Cid, B. Maquez-Villamarin, Computation of Green's functions for boundary value problems with Mathematica,

Appl. Math. Comput. 219 (2012), 1919-1936. 3.

D. Çakmak, M. F. Aktaş, A. Tiryaki, Lyapunov-type inequalities for nonlinear systems involving the (p₁,p₂,...,p_n)-Laplacian,

Electron. J. Differ. Eq. 128 (2013), 1-10.






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26

The Estimates of Functions Type of Weierstrass Kernel in Special Domains

Abdurrahim Guliyev and Mushfiq Aliyev Institute of Mathematics and Mechanics of NAS of Azerbaijan

[email protected]

Abstract

In order to obtain theorems on the growth of positive solutions for the parabolic equations, it is necessary to

estimate of functions type Weirstrass’s kernel ( [1], [2]) in special domains, i.e. in cylinders, trapezoids and lateral surfaces

of the cylinders. For the kernal of Weierstrass type

𝐾𝑠,𝛽(𝑡, 𝑥) = 𝑡−𝑠𝑒𝑥𝑝 −

|𝑥|2

4𝛽𝑡 , 𝑡 > 0

0 , 𝑡 ≤ 0

in special domains,i.e. in trapezoids 𝑇𝑚,𝑘(𝑗)

,𝑗 = 1,2, … , 𝑛0 ,or the minimal finite partition 𝑇𝑚,𝑘 = 𝐶𝑚,𝑘\𝑃𝑚 of the compliment

of paraboloids 𝑃𝑚(𝑡, 𝑥): |𝑥|2 < −𝜆𝑚𝑡, 𝑡 < 0 with respect to cylinders 𝐶𝑚,𝑘 = (𝑡, 𝑥): −𝑡𝑘 < 𝑡 < 0, |𝑥| < 𝑎𝜌𝑚,𝑘, where

𝑡𝑘+1 =𝑡𝑘

4, 𝑡1 > 0, 𝑎 > 0, 𝜌𝑚,𝑘

2 = 𝑎𝜆𝑚𝑡𝑘 ,for which the following

|𝑥 − 𝜉| ≤ |𝜉|

is fulfilled at (𝑡, 𝑥) ∈ 𝑇𝑚,𝑘+1(𝑗)

and (𝜉, 𝜏) ∈ 𝑇𝑚,𝑘(𝑗)

for every fixed j and in lateral surface 𝑆𝑚,𝑘 of cylinders 𝐶𝑚,𝑘 we are obtained

the main result

Theorem. There exist the following absolute constants 𝐶1 > 0 and 𝐶2 > 0 depending only on fixed numbers

𝛌,𝑎, 𝑛, 𝑠, 𝛽 such that holds sup

(𝑡,𝑥)∈𝑆𝑚,𝑘

𝐾𝑠,𝛽 (𝑡 − 𝜏, 𝑥 − 𝜉) ≤ 𝐶1𝐾𝑠,𝛽(−𝜏, −𝜉) and inf(𝑡,𝑥)∈𝑇𝑚,𝑘+1

(𝑗)𝐾𝑠,𝛽 (𝑡 − 𝜏, 𝑥 − 𝜉) ≥ 𝐶2𝐾𝑠,𝛽(−𝜏, 𝜉) ,

where 𝐶1 < 𝐶2 and for fixed (𝜏, 𝜉) ∈ 𝐻𝑚,𝑘 = (𝑃𝑚+1\𝑃𝑚) ∩ [−𝑡𝑘; −𝑡𝑘

4] ∩ 𝑇𝑚,𝑘

(𝑗) and fixed 𝑗 ∈ 1, … , 𝑛0 .

References

1. Landis E.M. Second order equations of elliptic and parabolic types. M. Nauka, 1971, 228p. (Russian). 2. Guliyev A.F. Capacity regularity conditions of boundary points for parabolic equations of second order. Izv. AN Azerb. SSR, ser.

FTMN, 1988. N.3, pp. 23-29 (Russian)




Istanbul / TURKEY


27

Exact Solutions of Some Nonlinear Equations

Adem C. Cevikel1 and Özgür Yıldırım2

1Department of MathematicsEducation, Yildiz Technical University,


[email protected]

Abstract

In this work, we have investigated the exact soliton solutions of some nonlinear equations. We obtained the soliton

solutions by using a solitary wave ansatz in the form of sech^p and tanh^p functions.

Keywords: Exact solutions, Bright soliton, dark soliton, solitons.

References

1. H., Triki and A.M.,Wazwaz, Bright and dark soliton solutions for a K(m,n) equation with t-dependent coefficients. Phys. Lett. A

373, (2009) 2162-2165.

2. H., Triki and M.S., Ismail, Soliton solutions of a BBM(m, n) equation with generalized evolution, Applied Mathematics and

Computation, 217, 1 (2010) 48-54.

3. Biswas, A., Triki, H. and Labidi, M., Bright and Dark Solitons of the Rosenau-Kawahara Equation with Power Law Nonlinearity,

Physics of Wave Phenomena,19, 1 (2011) 24—29.

4. H., Triki and A.M.,Wazwaz, Dark solitons for a combined potential KdV and Schwarzian KdV equations with t-dependent

coefficients and forcing term, Applied Mathematics and Computation, 217 (2011) 8846--8851





Istanbul / TURKEY


28

Bright and Dark Soliton Solutions of the GVCKP Equation

Adem C. Cevikel1 and Özgür Yıldırım2

1Department of MathematicsEducation, Yildiz Technical University,


[email protected]

Abstract

In this work, we have derived the exact bright and dark soliton solutions of the variable-coefficient equations. We

showed that all the physical parameters of the obtained solutions are expressed in terms of the t-dependent model coefficients.

Keywords: Bright soliton, dark soliton, solitons.

References

1. Z., Lü and F., Xie, Explicit bi-soliton-like solutions for a generalized KP equation with variable coefficients, Mathematical and

Computer Modelling 52 (2010) 1423 1427.

2. H., Triki and A.M.,Wazwaz, Bright and dark soliton solutions for a K(m,n) equation with t-dependent coefficients. Phys. Lett. A

373, (2009) 2162-2165.

3. H., Triki and M.S., Ismail, Soliton solutions of a BBM(m, n) equation with generalized evolution, Applied Mathematics and

Computation, 217, 1 (2010) 48-54.

4. Biswas, A., Triki, H. and Labidi, M., Bright and Dark Solitons of the Rosenau-Kawahara Equation with Power Law Nonlinearity,

Physics of Wave Phenomena,19, 1 (2011) 24—29.

5. H., Triki and A.M.,Wazwaz, Dark solitons for a combined potential KdV and Schwarzian KdV equations with t-dependent

coefficients and forcing term, Applied Mathematics and Computation, 217 (2011) 8846--8851





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29

On Sufficient Condition for Starlikeness of Confluent Hypergeometric Functions

İsmet Yıldız1, Alaattin Akyar1, Oya Mert2 and Neslihan Uyanık3

1Department of Mathematics, Düzce University, Turkey.

[email protected]

[email protected] 2Department of Mechanical Engineering, İstanbul Altınbaş University, Turkey

[email protected], 3Kazım Karabekir Education Faculty, Atatürk University

[email protected]

Abstract

In the present paper, firstly some univalent functions are obtained as special case of hypergeometric functions and then,

discussed the starlikeness of confluent hypergeometric functions.

Keywords: Analytic function, Univalent function, Starlike function, Hypergometric series, Hypergeometric function.

References

1. S.S. Miller, P.T. Mocanu, Differential subordinations and inequalities in the complex plane, J. Differential Equations, 67

(1987), 199-211

2. S.S. Miller, P.T. Mocanu, Univalence of Gaussian and confluent hypergeometric functions, Proc. Amer. Math. Soc. 110 (1990),

333-342.

3. S. Owa, H.M. Srivastava, Univalent and starlike generalized hypergeometric functions, Canad. J. Math., 39 (1987), 1057-1077.

4. H. Srivastava, S. Owa, Some characterization and distortion theorems involving fractional calculus, generalized hypergeometric

functions, Hadamard products, linear operators, and certain subclasses of analytic functions, Nagoya Math. J. 106 (1987), 1-28.

5. K. Kuroki, S. Owa, I. Yildiz, On starlikeness of confluent hypergeometric functions, International Journal of Applied

Mathematics, Volume 25 No.4 2012, 538-589.







Istanbul / TURKEY


30

A new iterative algorithm for the time-fractional Fisher equation including small delay

Ali Demir1 , Mine Aylin Bayrak2 and Metin Bayrak2

1,2,3Department of Mathematics, Kocaeli University,

[email protected]

[email protected] , [email protected]

Abstract

The aim of this study is to implement the residual power series method (RPSM) for time-fractional Fisher equation

including small delay. The fractional derivative is described in the Caputo sense. By taking the advantage of the small delay

𝜺, the time fractional Fisher equation is expanded in powers of 𝜺.The coefficients of the 𝜺 series is obtained by using RPSM

. The solution of the time-fractional Fisher equation is established in the form of rapidly convergent series whose components

are computed by Matlab Software Package. As a result, it is verified that the proposed method in this study is very efficient,

effective and reliable.

Keywords: Fractional delay differential equation, Fisher equation, Caputoderivative , Residual power series method.

References

1. I. Podlubny , Fractional Differential equations, Academic Press, San Diego (1999).

2. A. A. Kilbas, H.M. Srivastava and H.M. Trujillo, Theory and Applications of Fractional Differential Equations: North-Holland

Mathematics Studies, vol.24, Elsevier, Amsterdam, (2006).

3. A. El-Ajou, o. Abu-Arqub,Z. Al Zhour, et al., New results on fractional power series: theories and applications, Entropy, (2013).

4. M. Mohamed Al Qurashi, Z. Korpinar, D. Baleanu and M. Inc., A new iterative algorithm on the time-fractional Fisher equation:

Residual power series methos, Advances in Mechanical Engineering, 9(9) (2017) 1-8.






Istanbul / TURKEY


31

Explicit Computation of the Unipotent Terms in The Trace Formula for GL(2) Over a Number

Field

Ali Aydoğdu1, Engin Özkan2 and Rukiye Öztürk3

1Department of Mathematics, Beykent University,

[email protected] 2Department of Mathematics, Erzincan University,

[email protected] 3Department of Finance, Avrasya University,

[email protected]

Abstract

In this work, we give a detailed proof of the unipotent terms which appear in the trace formula for GL(2) over a

number field.

Keywords: Trace formula, Number field, GL(2).

References

1. Arthur J. The local behavior of weighted orbital integrals. Duke Math. J. 56 (1988) 223-293.

2. Aydoğdu A., Flicker Y.Z., Özkan E. & Öztürk R. Explicit forms of the trace formula for GL(2). Journal d’Analyse Mathématique.

131(1) (2017) 1-71.

3. Deligne P., Flicker Y.Z. Counting local systems with principal unipotent local monodromy. Ann. Of Math. 178(2) (2013) 921-

982.

4. Lang S. Algebraic Number Theory, Second edition. Springer-Verlag, New York, 1994.




mailto:mailto

mailto:mailto


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32

On 2-Fibonacci Polynomials

Engin Özkan1, Merve Taştan1 and Ali Aydoğdu2

1Department of Mathematics, Erzincan University,

[email protected]

[email protected] 2Department of Mathematics, Beykent University

[email protected]

Abstract

We define a 2-Fibonacci Polynomials by using terms of a new family of Fibonacci numbers given in [3]. We give

some important properties of the polynomial. Then, we compare the polynomials with known Fibonacci polynomial. We

expressed these polynomials using the Fibonacci polynomials. Furthermore, we prove some theorems related to the

polynomial.

Keywords: Fibonacci numbers, Fibonacci polynomials, Generalized fibonacci polynomials.

References

1. Özkan E. On Truncated Fibonacci Sequences. Indian J. Pure of and Appl. Mathematics. 38(4) (2007) 241-251.

2. Özkan E., Altun İ., & Göçer A. On Relationship Among A New Family Of k-Fibonacci, k-Lucas Numbers, Fibonacci And Lucas

Numbers. Chiang Mai Journal Of Science. 44 (2017) 1744-1750.

3. Mikkawy M., Sogabe T. A new family of k-Fibonacci numbers. Applied Mathematics and Computation. 215 (2010) 4456–4461.

4. Hoggatt V. E. Jr., Bicknell M. Generalized Fiboncci polynomials. Fİbonacci Quarterly 11(5) (1973) 457-465.

5. Ramirez J. On convelved generalized Fibonacci and Lucas polynomials. Apllied Mathematics and Computation. 229 (2014) 208-

213.

6. Stanimirovic P.S., Nikolov J., & Stainimirovic I. A generalizations of Fibonacci and Lucas matrices. Discrete Appl. Math. 156

(2008) 2606-2619.

7. T. Koshy, Fibonacci and Lucas Numbers with Applications. New York, NY, USA: Wiley, 2001






Istanbul / TURKEY


33

On Korovkin type Theorems in Non-standard Spaces and Their Statistical Variants

Ali Huseynli,1 Fatih Sirin2 and Fidan Seyidova3

1Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan

[email protected] 2 Istanbul Aydin University, Istanbul, Turkey

[email protected] 3Ganja State University, Ganja, Azerbaijan

[email protected]

Abstract

In this work nonstandard function spaces rL ; and grand Lebesgue spaces are considered. Theorems on the approximation by

Kantorovich polynomials are proved in these spaces. Their statistical analogues are obtained. A new concept of statistical fundamentality,

which is a direct generalization of a similar classical concept is introduced.

It should be noted that, earlier, Y. Katznelson [20] paid attention to the rp lL type space in connection with the existence of

the set of uniqueness of the positive measure with respect to the Fourier-Stieltjes coefficients.

Keywords: non-standard grand Lebesgue spaces, Kantorovich polynomials, statistical convergence.

References

1. Y. Katznelson, Sets of uniqueness for some classes of trigonometrical series, Bull. Amer. Math. Soc., 70 (5) (1964),

722-723.






Istanbul / TURKEY


34

Boundedness of some sublinear operators and their commutators on generalized local Morrey

spaces

Ayhan Şerbetçi Department of Mathematics, Faculty of Sciences, Ankara University,

[email protected]

Abstract

In this talk we prove the boundedness of certain sublinear operators , , (0, ),T n generated by fractional integral

operators with rough kernels 1( ), 1,n

sL S s from one generalized local Morrey space 0

1

,

x

pLM to another 0

2

,

x

qLM ,

1 11 ,p q

p q n

, and

from the space 0

1

1,

xLM to the weak space 0

2

,

x

qWLM , 1

1 , 1qq n

. In the case b belongs to the local Campanato space

0

2

,

x

pLC and the commutator operators , ,bT

is a linear operator, we find the suffcient conditions on the pair 1 2( , ) which

ensures the boundedness of , ,bT

from 0

1 1

,

x

pLM to 0

2

, ,x

qLM

1 2

1 1 11 , ,q

p p p

1 1

1 1 1 1, ,

q p n q p n

. In all cases

the conditions for the boundedness of ,T

are given in terms of Zygmund-type integral inequalities on 1 2( , ) , which do

not assume any assumption on monotonicity of 1 2, in .r

Keywords: Sublinear operator, fractional integral operator, generalized local Morrey spaces.

References

1. A.S. Balakishiyev, V.S. Guliyev, F. Gurbuz and A. Serbetci, Sublinear operators with rough kernel generated by

Calderon-Zygmund operators and their commutators on generalized local Morrey spaces, Journal of Inequalities

and Applications 2015, 2015:61. doi:10.1186/s13660-015-0582-y.

2. F. Soria, G. Weiss, A remark on singular integrals and power weights, Indiana Univ. Math. J., 43 (1994), 187-

204.

3. Y. Ding, D. Yang, Z. Zhou, Boundedness of sublinear operators and commutators on , ( )p nL R , Yokohama Math.

J., 46 (1998), 15-27.

4. Y. Ding and S.Z. Lu, Higher order commutators for a class of rough operators, Ark. Mat., 37 (1999), 33-44.




Istanbul / TURKEY


35

Configurational Mean-Field Transfer Matrix Method for Ising Systems

Tuncer Kaya1 and Başer Tambaş2

1Department of Physics, Yildiz Technical University,

[email protected] 2 Department of Physics, Yildiz Technical University

[email protected]

Abstract

A mean-field theory for hypercubic nearest-neighbor Ising system1 is presented by substantially combining

Kadanoff’s2 mean-field approach with the model previously introduced by T.Kaya3,4. Also, applications to the method are

demonstrated.

The mean-field approximation is defined as replacement of the central spin in Ising Hamiltonian with the average

value of particular spin configuration, i.e, the approximation is considered within each configuration. This approximation is

used in two different mean-field-type approaches. First one is a pure mean-field-type treatment in which all the neighboring

spins are replaced with the assumed configurational average. The second one is introduced by reducing transfer matrix

method. Estimations of critical coupling strengths are evaluated both numerically and analytically by using of saddle-point

approximation.

In this work, we think that the method introduced here is more relevant physical picture than self-consistent mean-

field-type models since the method introduced here does not assume the existence of the phase transition from the outset.

Therefore, introduced method possibly makes our work very useful mean-field-type picture for the treatment of phase

transition.

Keywords: Ising model, block-spin transformation, critical phenomena.

References

1. E. Ising, Z. Phys. 31, (1925) 253.

2. L. P. Kadanoff, Statistical Physics: Statics, Dynamics and Renormalization, (2000) World Scientific Pub. Co. Inc.

3. T. Kaya and M. Arık, IJMPB 25, (2011) 2895.

4. T. Kaya, IJMPB 26, (2012) 1250085





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36

Solution of the Maximum Difference Equation 1 1

1 1 1 1

max , ; max ,n n

n n

n n n n

y xA Ax y

x x y y

Burak Oğul1, Dağıstan Şimşek2,3, Nurtilek Jamshitov4

I Institute of Science Kyrgyz Turkish Manas University,

[email protected] 2Department of Applied Mathematics and Informatics, Kyrgyz Turkish Manas University,

[email protected] 3Department of Industrial Engineering, Selcuk University,

[email protected]; 4Faculty of Science Kyrgyz Turkish Manas University,

[email protected]

Abstract

Recently, there has been a great interest in studying the periodic nature of nonlinear difference equations. Although

difference equations are relatively simple in form, it is, unfortunately, extremely difficult to understand thoroughly the

periodic behavior of their solutions. The periodic nature of nonlinear difference equations of the max type has been

investigated by many authors. See for example [1-4].

In this paper we consider positive solutions of the following difference equations,

1 1

1 1 1 1

max , ; max ,n n

n n

n n n n

y xA Ax y

x x y y

(1)

0 1 0 1, , , , 1A x x y y for 0 1 1 0 1x x y y A according to these initial condition we obtain that result;

2 321 1 1

0 02 2 3

1 0 1 0 1 1 0 0 1 0 1 0

43 41

0 03 4

1 1 0 0

1 1 1, , , , , , , , , , , , , ,

,1

, , , , , , ...

n

y x yA A A A A AAy A x

x x y y A y x y Ax x x yA A y Ax

xA AA y A x

y x y A x A

2 321 1

0 02 2

1 1 0 0 1 0 1 0 1 1 0 0

43 41 1

0 03 3 4

1 0 1 0

1 1 1, , , , , , , , , , , , ,

1, , , , , , , ...

n

x yA A A A A AAx A y

y x y x A x x y Ay y x yA A xy

x yA AA x A y

x x yA A y A

.

Keywords: Difference Equations, Maximum Operatiors, Periodicity

References

1. Cinar, C., On the positive solutions of the difference equation system 1 1

1 1

1; n

n n

n n n

yx y

y x y

, Journal of Applied

Mathematics and Computation. 158 (2004) 303–305.

2. Elsayed, E.M., Stevic, S., On the max type equation 1 2,n n

n

Ax x

x

, J. Nonlinear Analysis. 71 (2009) 910–922.

3. Simsek, D., Dogan, A., Solution of the System of Maximum Difference Equations Manas Journal of Engineering, 2(2) (2014)

9-22.

4. Simsek, D., Ogul, B., Solutions of the maximum difference equations 1 1

1 3 1 3

1 1max , ; max ,n n

n n

n n n n

y xx y

x x y y

,

Manas Journal of Engineering, 5(1) (2017) 14-28.






Istanbul / TURKEY


37

On The Recursive Sequence 19

1

3 7 11 151

n

n

n n n n

xx

x x x x

Burak Oğul1, Dağıstan Şimşek2,3, Peil Esengul kyzy4

I Institute of Science Kyrgyz Turkish Manas University,

[email protected] 2Department of Applied Mathematics and Informatics, Kyrgyz Turkish Manas University,

3Department of Industrial Engineering, Selcuk University,

[email protected]; 4Faculty of Science Kyrgyz Turkish Manas University,

[email protected]

Abstract

Recently, a high attention to studying the periodic nature of nonlinear difference equations has been attracted. For some

recent results concerning the periodic nature of scalar nonlinear difference equations, among other problems, see, for example,

1,3 .

In this paper we study the behavior of the positive solutions of the following non-linear difference equation,

19

1

3 7 11 15

, 0,1,2,...1

n

n

n n n n

xx n

x x x x

(1)

where the initial conditions are positive real numbers.

Keywords: Difference equations, recursive sequence, rational difference equations.

References

1. Cinar, C., On the positive solutions of the difference equations 1

1

11

n

n

n n

xx

x x

. Applied Mathematics and Computation.

1880(1), 040003. . 158(3) (2004) 809–812.

2. Elsayed, E. M., New method to obtain periodic solutions of period two and three of a rational difference equations, Nonlinear

Dynamics. 79(1) (2015) 241–250.

3. Simsek, D., Ogul, B., Solutions of the rational difference equations 2 1

11

n k

n

n k

xx

x

, Manas Journal of Engineering. 5(3) (2017)

57–68.




Istanbul / TURKEY


38

Integral Operators of Harmonic Analysis in Local Morrey-Lorentz Spaces

Canay Aykol1 and Ayhan Serbetci1

1Department of Mathematics, Ankara University

[email protected]

[email protected]

Abstract

In a series of papers by the authors jointly with their co-authors V.S. Guliyev and A. Kucukaslan the local Morrey-Lorentz spaces have been introduced and the basic properties of these spaces have been given, and the boundedness of the Hilbert transform, the Hardy-Littlewood maximal operator and the Calderon-Zygmund operators, and Riesz potential on the spaces has been extensively studied. In this talk the basic properties of the local Morrey-Lorentz spaces will be given. The boundedness of classical operators of

harmonic analysis, such as Hilbert transform, the Hardy-Littlewood maximal operator, the Calderon-Zygmund operators, and

Riesz potential will be proved on the local Morrey-Lorentz spaces

Keywords: Local Morrey-Lorentz spaces, Hilbert transform, Hardy-Littlewood maximal operator, Calderon-Zygmund

operator, Riesz potential.

References

1. C. Aykol, V.S. Guliyev and A. Serbetci, Boundedness of the maximal operator in the local Morrey-Lorentz spaces, Jour. Inequal.

Appl., 2013, 2013:346.

2. C. Aykol, V.S. Guliyev, A. Kucukaslan and A. Serbetci, The boundedness of Hilbert transform in the local Morrey-Lorentz

spaces, Integral Transforms Spec. Funct. 27, (2016), no. 4, 318–330.

3. C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, Boston, 1988.

4. V.S. Guliyev, C. Aykol, A. Kucukaslan and A. Serbetci, Maximal operator and Calderon-Zygmund operators in local Morrey-

Lorentz spaces, Integral Transforms Spec. Funct. 27 (2016), no. 11, 866--877.

5. N. Samko, Weight Hardy and singular operators in Morrey spaces, J. Math. Anal. Appl. 35(1) (2009) 183–188.





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39

On Properties of the Pell and Pell-Lucas Sedenions

Cennet Çimen1 1Hacettepe Ankara Chamber of Industry 1st Organized Industrial Zone Vocational School

[email protected]

Abstract

The purpose of this paper is to give new classes of sedenion numbers associated with the familiar Pell and Pell-Lucas

numbers. Also, we obtain the various results here for these classes of sedenion numbers include recurrence relations,

summation formulas, Binet's formulas and generating functions.

Keywords: Pell numbers; Pell-Lucas numbers; Sedenion algebra; Generating Function.

References

1. Akyigit M., Kösal H. H. and Tosun M., “Split Fibonacci quaternions.”, Adv. Appl. Clifford Algebras, 23(2013):535-545.

2. Cariow A. and Cariowa G., “An algorithm for fast multiplication of sedenions”, Inform. Process. Lett.,113(2013), 324-331.

3. Cerin Z., Gianella G. M., “On sums of Pell numbers”, Acc. Sc. Torino-Atti Sc. Fis., 140, 2006.

4. Cerin Z., Gianella G. M., “On sums of squares of Pell-Lucas numbers”, Integers: Electronic Journal of Combinatorial Number

Theory, 6, 2006.

5. Szynal-Liana A. and Wloch I., “The Pell Quaternions and the Pell Octonions”, Adv. Appl. Clifford Algebras, 26(2016), 435-440.




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40

Fan-Gottesman Compactification and Stone Space

Ceren Sultan ELMALI1 and Tamer UĞUR2

1Department of Mathematics, Erzurum Technical University,

[email protected] 2Department of Mathematics, Atatürk University

[email protected]

Abstract

It is well known that a Stone space is a totally disconnected, compact topological space. Equivalently a Stone space

is a zero dimensional, compact and T0 topological space. Also it is called Boolean space. In this paper, it is shown that Fan-

Gotttesman compactification of a 𝑇3 space is a Stone space.

Keywords: Fan-Gottesman compactification, Stone Space

References

1. P. S. Aleksandrov, P. Urysohn, Memorie sur les espaces topologiques compacts. Koninkl. Nederl. Akad. Wetensch.,

Amsterdam (1929)

2. E. Cech, On bicompact spaces Ann.of Math.(2) 38:4(1937) 823-844

3. C. Elmali and T. Ugur, Fg-morphism and Fg-extension, Hacettepe Journal of Mathematics and Statistics, Vol.43 (6) (2014),

915-922.

4. K. Fan and N. Gottesman, On compacti.cation of freudenthal and Wallman. Indag. Math. 13 (1952) 184-192.

5. M. Al-Hajri, K. Belaid and O. Echi, Stone Spaces and Compacti.cations, Pure Mathematical Sciences, Vol. 2(2)(2013) 75-81

6. M. H. Stone, Applications of the theory of Boolean rings to general topology. Trans. Amer. Math. Soc.4 (1937)375-481

7. H. Wallman, Lattices and Topological Spaces. Annals of Mathematics 39, (1938) 112.126





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41

Relatively C3 and D3-Modules

Deniz Gökalp1 and Tülay Yıldırım2

1,2Department of Mathematics, Gebze Technical University,

[email protected] [email protected]

Abstract

One of the continuity conditions identified by Utumi [1] on self-injective rings is the C3-condition. In addition to

injective modules, the class of C3-modules includes the semisimple, continuous, regular modules and indecomposable.

Dually recall D3-modules. The aim of this paper is to introduce the notion of relatively C3 and D3-modules, i.e., N-C3 and

M-D3-modules for some R-modules M and N. These notions are a non-trivial generalization of C3-modules and D3-

modules, respectively. Several characterizations of these modules are provided and used to describe some well-known

classes of rings and modules. In this talk, after a brief introduction to the subject is discussed, a recent result with a joint

work Deniz Gökalp, Tülay Yıldırım, M.Tamer Koşan [2] among these lines will be presented.

Keywords: C3-modules, D3-modules, injective and quasi-injective modules, projective and quasi-projective modules.

References

1. Y. Utumi, On continuous rings and self-injective rings, Trans. Amer. Math. Soc., 118(1965), 158-173

2. Deniz Gökalp, Tülay Yıldırım, M. Tamer Koşan, Relatively C3 and D3-Modules, preprint.





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42

Some Spectral Aspects of Fractional Singular Sturm-Liouville Equation

Ahu Ercan1 1Department of Mathematics, Fırat University,

[email protected].

Abstract

In this paper, we define Sturm-Liouville problem with generalized Riemann-Liouville and Caputo fractional derivative

and we show the self-adjointness of the operator, orthogonality of distinct eigenfunctions and reality of eigenvalues.

Keywords: Fractional, Sturm-Liouville Operator, Singularity.

References

1. I. Podlubny, Fractional differential equations: an introduction to fractional derivatives fractional differential equations, to methods

of their solution and some of their applications, 198, (1998).

2. Y. Xu, O. P., Agrawal, New fractional operators and application to fractional variational problem. Computers & Mathematics

with Applications, (2016).

3. R. Hilfer, Y. Luchko, Y., & Tomovski, Z., Operational method for the solution of fractional. differential equations with

generalized Riemann-Liouville fractional derivatives, Fract. Calc. Appl. Anal, 12(3), (2009), 299-318.

4. E. Bas, Fundamental spectral theory of fractional singular Sturm-Liouville operator, Journal of Function Spaces and Applications,

(2013).




Istanbul / TURKEY


43

An Increase Theorem for Positive Solutions of The Parabolic Equation second order

Elif Deniz1, Yusuf Zeren2, Abdurrahim Guliyev3 and Selim Yavuz4

1Yildiz Technical University

[email protected] 2 Yildiz Technical University

[email protected] 3Institute of Mathematics and Mechanics of NAS of Azerbaijan

[email protected] 4Yildiz Technical University

[email protected]

Abstract

In this work the increase theorem is proved in special domains for positive solutions of the parabolic equation second order:

∑ 𝑎𝑖𝑘(𝑡, 𝑥)𝑢𝑥𝑖𝑥𝑘

𝑛

𝑖,𝑘=1

(𝑡, 𝑥) − 𝑢𝑡(𝑡, 𝑥) = 0

which more exactly characterizes important local properties.

Keywords: parabolic equations, increase theorem, local properties solutions.

References:

1. Landis E.M. Second order equations of elliptic and parabolic types, M., Nauka,1971, 288 p. (Russian).

2. Guliev A.F. Capacity regularity conditions of boundary points for parabolic equations of second order, Izv. AN Azerb.

SSR. FTMN, 1988, N.3, pp. 23-29 (Russian).


mailto:%[email protected]





Istanbul / TURKEY


44

A note on q-bi-periodic Fibonacci and Lucas sequences

Elif Tan1, Semih Yılmaz2, and Murat Şahin3

1Department of Mathematics, Ankara University

[email protected] 2Department of Actuarial Sciences, Kırıkkale University

[email protected] 3Department of Mathematics, Ankara University

[email protected]

Abstract

In this talk, motivated by the Ramirez’s study in [1], we present a q-analog for the bi-periodic Lucas sequence and

give some identities related to q-bi-periodic Fibonacci and Lucas sequences. By means of matrix representation for the q-bi-

periodic Fibonacci sequences, we obtain several properties of these sequences [2]. Moreover, by using the explicit formulas

for the q-bi-periodic Fibonacci and Lucas sequences, we introduce q-analogs for the bi-periodic incomplete Fibonacci and

Lucas sequences.

Keywords: bi-periodic Fibonacci and Lucas sequences, q-analog, matrix formula.

References:

3. Ramírez, J. L. and Sirvent, V. F., A q-Analoque of the Bi-Periodic Fibonacci Sequence, Journal of Integer Sequences, Vol.

19 (2016).

4. Tan, E. A q-analog of the bi-periodic Lucas sequence, Commun. Fac. Sci. Univ. Ank. Series A1, 67(2), 220-228, 2018.





Istanbul / TURKEY


45

Solution of Mathematical Model for Supercritical Fluid Extraction of Lavender Flower Essential

Oil with Finite Difference Method

Elveda Gamze Memiş, Elif Tekin Tarım

Department of Mathematics, Yildiz Technical University,

[email protected], [email protected]

Abstract

Mathematical modeling of lavender flower essential oil extraction with Supercritical CO2 (SC-CO2) was used in this

study [1] and “Shrinking-Core Mass Transfer” equations was modeled with Finite Difference (FD) Method. The equations

were applied implicit Crank-Nicolson method. Results obtained from numerical solution were compared with experimental

results [1]. FD modeling was solved numerically with MATLAB R2018a software.

This work was supported by Research Fund of the Yildiz Technical University.

Project Number: FYL-2018-3209

Keywords: Finite difference method, implicit Crank-Nicolson, Supercritical fluid extraction, Modeling.

References

1. Akgün M., Akgün N.A. Dinçer S., Extraction and Modeling of Lavender Flower Essential Oil Using Supercritical Carbon

Dioxide , Ind. Eng. Chem. Res. 2000,39,473-477.

2. Goodarznia I., Eikani M.H., Supercritical Carbon Dioxide Extraction of Essential Oils: Modeling and Simulation, Chemical

Engineering Science,53(7),1387-1395, 1998.

3. Nei Nei H.Z., Fatemi S., Mehrnia M.R., Salimi A.,Mathematical Modeling and Study of Mass Transfer Parameters in Supercritical

Fluid Extraction of Fatty Acids from Trout Powder. Biochemical Engineering Journal, 40 (2008) 72-78

4. Lin M.L., Ping T. S., Saptoro A., Freddie P. Mass Transfer Coefficients and Correlation of Supercritical Carbon Dioxide

Extraction of Sarawak Black Pepper. International Journal of Food Engineering ,2013,10.1515-0219.




Istanbul / TURKEY


46

Some Results for Max-Product Operators via Power Series Method

Emre Taş1 and Tuğba Yurdakadim2

1Department of Mathematics, Ahi Evran University,

[email protected] 2Hitit University

[email protected]

Abstract

In this talk, we obtain an approximation theorem by max-product operators with the use of power series method which is

more effective than ordinary convergence and includes both Abel and Borel methods. We also estimate the error in this

approximation. Finally, we provide an example which satisfies our theorem.

Keywords: Power series method, Max-Product operators, approximation theory.

References

1. B. Bede, L. Coroianu & S. G. Gal, Approximation by truncated Favard-Szasz-Mirakjan operator of max-product kind.

Demonstratio Math. 44 (2011) 105-122.

2. B. Bede, L. Coroianu & S. G. Gal, Approximation by Max-Product Type Operators, Springer, New York, 2016.

3. O. Duman, Statistical convergence of max-product approximating operators. Turk. J. Math. 34 (2010) 510-514.

4. U. Stadtmüller & A. Tali, On certain families of generalized Nörlund methods and power series methods. J. Math. Anal. Appl.

238 (1999) 44-66.





Istanbul / TURKEY


47

Upper and lower solutions for fourth order three point BVPs with integral boundary conditions

on a half line

Erbil Çetin1and Şerife Müge Ege2

1,2Department of Mathematics, Ege University,


Abstract

In this study, we consider the existence of solutions of the following fourth-order three-point

boundary value problem with integral boundary conditions on a half-line.

𝒙′′′′ (𝒕) + 𝒒(𝒕)𝒇(𝒕, 𝒙(𝒕), 𝒙′(𝒕) , 𝒙′′(𝒕) , 𝒙′′′(𝒕) ) = 𝟎, 𝒕 ∈ (𝟎, +∞),

𝒙(𝟎) = 𝝀 ∫ 𝒙(𝒔)𝒅𝒔𝜼

𝟎, 𝒙′(𝟎) = 𝑨, 𝒙′′(𝟎) = 𝑩, 𝒙′′′(+∞) = 𝑪,

where 𝜆 > 0, 0 < 𝜆𝜂 < 1 and 𝑓: [0, +∞) × ℝ4 → ℝ satifies Nagumo's condition. For this purpose, we apply Schauder's

fixed point theorem, the upper and lower solution method. We show easily confirrmable sufficient conditions for the existence

of at least one solution of this problem. An additional feature of our results is that the obtained solutions may be unbounded.

An illustrative example is given to demonstrate of our result.

Acknowledgement: This research is supported by Ege University, Scientific Research Project (BAP), Project Number: 2015

FEN 070.

Keywords: fourth order, three point, integral boundary condition Schauder fixed point theorem, Naguma condition

References

1. J. Ehme, P.W. Eloe, J. Henderson, Upper and lower solution methods for fully nonlinear boundary value problems, J. Differential

Equations, 180 (2002), 51-64.

2. E. Ç etin, R.P. Agarwal, Existence of solutions for fourth order three-point boundary value problems on a half-line, Electron. J. Qual. Theory Differ. Equ, 62 (2015), 1-23.

3. J. R. Graef, C. Qian, B. Yang, A three point boundary value problem for nonlinear fourth order differential equations, J. Math.

Anal. Appl., 287 (2003), 217-233. 4. R.P. Agarwal, On fourth-order boundary value problems arising in beam analysis, Differential Integral Equations, 2 (1989), 91-110. 5. M. Briki, T. Moussaoui, D. O'Regan, Existence of solutions for a fourth-order boundary value problem on the half-line via critical point theory,

Electron. J. Qual. Theory Differ. Equ., 24 (2016), 1-11.





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48

On Abel Convergence

Erdal Gül1 and Mehmet Albayrak2

1Department of Mathematics, Yildiz Technical University,

[email protected] 2Department of Mathematics, Yildiz Technical University

[email protected]

Abstract

In this paper, we introduce and investigate the concepts of Abel uniform convergence and Abel pointwise convergence

of sequences of real functions. It turned out that Abel uniform limit of continuous functions is continuous and that Abel

uniform convergence inherits the basic properties of uniform convergence..

Keywords: Abel continuity, Abel convergence, point-wise convergence, uniform convergence.

References

1. Duman O. , Orhan C. (2004), u-statitically convergent function sequences, 84 (129), 413-422.

2. Hardy G. H., (1991), Divergent Series, 2nd ed. New York, NY: Chelsea.

3. Gül E. and Albayrak M. (2017), Tauberian Theorems For Statistical Convergence. Tamkang Journal of Mathematics, 48 (4), 321-

330.

4. Kolk, E., (1999), Convergence-preserving function sequences and uniform convergence. J. Math. Anal. Appl, 238, 599-603.

5. K. Knopp., (1990), Theory and application of infinite series, Dover Publications.





Istanbul / TURKEY


49

On Chaotic Solutions of Gross-Pitaevskii Equation

Eren Tosyali1 and Fatma Aydogmus2

1 Vocational School of Health Services, Istanbul Bilgi University,

[email protected]

2Department of Physics, Istanbul University


Abstract

Various experimental and theoretical studies have been performed on nonlinear properties in Bose-Einstein

Condansate. It is well known that Bose Einstein condensation is well described by Gross-Pitaevskii Equation. Because the

integrability of Gross-Pitaevskii equation can be easily broken by external potentials of different forms, it is difficult to obtain

its exact solutions analytically. So in this study, we present some numerical results of the equation with 1D tilted bichromatical

optical lattice potential.

References

1. S.N. Bose, Z. Phys. 26 (1924) 168.

2. A. Einstein, Sitzungsber. K. Preuss. Akad. Wiss. 261 (1925) 3.

3. E.P. Gross, Nuovo Cimento 20 (1961) 454.

4. L.P. Pitaevskii, S. Stringari, Clarendon Press, Oxford, New York, ISBN: 0198507194, (2003).

5. Eren Tosyali and Fatma Aydogmus, Numerical Solutions of GPE under Gaussian Trap, Proceedings of the 16th

International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE),

ISBN 13-978-84-608-6082-2, no.2, pp.1516-1524, (2016).






Istanbul / TURKEY


50

Mathematical Behavior of Solutions of Semilinear Klein-Gordon Equations

Erhan Pişkin

Dicle University, Department of Mathematics, Diyarbakır, Turkey

E-mail: [email protected]

Abstract

In this talk, we consider semilinear Klein-Gordon equations in a bounded domain. The asymptotic behavior of the solution

is established by using Nakao’s inequality. We also prove the blow up of the solution in finite time and lower bounds for the

time of blow up of solutions.

Keywords: Klein-Gordon equation, Asymptotic behavior, Blow up

References

1. M.O. Korpusov, Blow up the solution of a nonlinear system of equations with positive energy, Theoretical and Mathematical

Physics. 171(3) (2012) 725-738. 2. E. Pişkin, Uniform decay and blow-up of solutions for coupled nonlinear Klein-Gordon equations with nonlinear damping

terms, Mathematical Methods in the Applied Sciences, 37(18) (2014) 3036-3047.

3. E. Pişkin, Lower Bounds for Blow-up Time of Coupled Nonlinear Klein-Gordon Equations, Gulf Journal of Mathematics, 5(2)

(2017) 56-61.

4. S.T. Wu, Blow-up results for system of nonlinear Klein-Gordon equations with arbitrary positive initial energ, Electronic

Journal of Differential Equations, 2012 (2012), 1-13.




Istanbul / TURKEY


51

Designing a Model for Moving Block Signalling System with State-Space Modelling

Ertugrul Ates 1 and Ilker Ustoglu 2

1Computer Engineering Department, Nigde Omer Halisdemir University,

[email protected] 2 Control and Automation Engineering Department, Yildiz Technical University

[email protected]

Abstract

This study represents a Moving Block Signalling System model. In this system, differently from traditional railway

systems, there are access points near the railway and trains are moving by communicating via these. In this way, not only

faster railway traffic flow, but also less waiting time for passengers is obtained, especially in metro lines. In this work,

representing a multi-carriage train, multi degree of freedom mass-spring-damper models are used. Then, a tractive force and

braking force are applied to this system as an input and a location is obtained from this output. In addition, a limit movement

authority is defined for control algorithm. So, trains move according to this authority. Finally, for safe stop of trains, brake

distance value is calculated. This calculation is solved depending on speed of the rear train. So, if the rear train accelerates,

distance will increase according to square of speed of the rear train. Besides, depending on speed of the rear train and travel

time, a safety margin distance is obtained. In simulations prepared using Matlab-SimulinkTM, train models, speed profiles,

locations, accelerations etc. are showed.

Keywords: CBTC system, moving-block signaling, limit movement authority

References:

1. Allotta, B., Chisci, L., D’Adamio, P., Papini, S., & Pugi, L. (2013). Design of an Automatic Train Operation (ATO) system based

on CBTC for the management of driverless suburban railways. 12th IMEKO TC10 Workshop on Technical Diagnostics: New

Perspective in Measurements, Tools and Techniques for Industrial Applications, Proceedings, 0, 84–89.

2. Farooq, J., & Soler, J. (2017). Radio Communication for Communications-Based Train Control (CBTC): A Tutorial and Survey.

IEEE Communications Surveys and Tutorials. https://doi.org/10.1109/COMST.2017.2661384

3. Takagi, R. (2012). Synchronisation control of trains on the railway track controlled by the moving block signalling system. IET

Electrical Systems in Transportation, 2(3), 130. https://doi.org/10.1049/iet-est.2011.0053

4. Yin, J., Tang, T., Yang, L., Xun, J., Huang, Y., & Gao, Z. (2017). Research and development of automatic train operation for

railway transportation systems: A survey. Transportation Research Part C: Emerging Technologies.

https://doi.org/10.1016/j.trc.2017.09.009





Istanbul / TURKEY


52

High Order Methods for Advection Diffusion Equation

Evren Topcu1 , Melda Turhan1 and Dursun Irk1

1Department of Mathematics-Computer, Eskişehir Osmangazi University,


[email protected]

Abstract

Advection–diffusion equation is one of the governing equations used for modeling many physical and chemical

phenomena. In the literature, one-dimensional advection-diffusion equation has been solved with various methods

accompanied with spline functions by many researcher [1], [2], [3], [4]. In this study, high order numerical solution of one

dimensional advection-diffusion equation is presented using sextic B-spline collocation finite element method. In the method,

second, three and fourth order single step methods are used for the time integration, and the space variable is discretized by

means of sextic B-spline functions. Two numerical examples are studied to illustrate the accuracy and the efficiency of the

method. The numerical results obtained by each proposed methods are compared with analytical solution by measuring the

error between them.

Keywords: Advection diffusion equation, Collocation finite element method, Sextic B-spline.

References

1. Z. Ahmad, (2000), Numerical solution for advection-diffusion equation with spatially variable coefficients. ISH Journal of

Hydraulic Engineering, 1(6), 46-54.

2. Z. Ahmad, U.C. Kothyari, (2001), Time-line cubic spline interpolation scheme for solution of advection equation, Computer

&Fluids, 30(6), 737-752.

3. D. Irk, İ. Dağ and M. Tombul, (2015) Extended Cubic B-Spline Solution of the Advection-Diffusion Equation, KSCE Journal of

Civil Engineering 19(4), 929-934.

4. A. Korkmaz and İ. Dağ, (2016), Quartic and quintic B-spline methods for advection diffusion equation. Appl. Math. Comput.,

274, 208-219.






Istanbul / TURKEY


53

Numerical Solutions by Legendre Polynomials for Hantavirus Infection Model

Faruk Dusunceli

Mardin Artuklu University,

[email protected]

Abstract

Mathematical models and computer simulations are useful experimental tools for building and testing theories. Many

mathematical models in biology and the others can be formulated by a nonlinear system of ordinary differential equations.

This presentation deals with the numerical solution of the hantavirus infection model[1-3].

In this paper, a new matrix method based on Legendre polynomials[4-6] and collocation points is proposed to obtain

approximate solutions of Hantavirus infection model corresponding to a class of systems of nonlinear ordinary differential

equations.The reliability and efficiency of the proposed scheme is demonstrated by the numerical applications and all

numerical computations have been made by using a computer program written in Matlab.

Keywords: Hantavirus infection model, Legendre Polynomials, Collocation Method.

References

1. S. Yuzbasi, An exponential collocation method for the solutions of the HIV infection model of CD4+T cells, Int. J. Biomath. 9

(2016) 1650036.

2. M. Merdan, A. Gokdogan and A. Yildirim, On the numerical solution of the model for HIV infection of CD4+T cells, Comput.

Math. Appl. 62 (2011) 118–123.

3. K.Parand, H.Yousefi, M.Fotouhifar and M. Delkhosh, Shifted Boubaker Lagrangian approach for solving biological systems,

International Journal of Biomathematics Vol. 11, No. 2 (2018) 1850039.

4. F. Düşünceli and E. Çelik. An Effective Tool: Numerical Solutions by Legendre Polynomials for High-order Linear Complex

Differential Equations. British Journal of Applied Science & Technology.(2015) 8(4): 348-355.

5. F.Düşünceli, E.Çelik, 2017. Numerical Solution for High-Order Linear Complex Differential Equations By Hermite Polynomials.

Iğdır Univ. J. Inst. Sci. & Tech. 7(4): 189-201.

6. F.Düşünceli, E.Çelik, 2017. Numerical Solution for High-Order Linear Complex Differential Equations with variable coefficients.

Numerical Methods for Partial Differential Equations, DOI 10.1002/num.22222.




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54

New Solutions for Lineer Complex Differential Equations

Faruk Dusunceli1 and Lutfi Akin2

1,2 Mardin Artuklu University,

[email protected]

[email protected]

Abstract

In this paper, the matrix relations between the Boubaker polynomials and their derivatives, we develop a method for

solving linear complex differential equation.

∑ Pn(z)f (n)(z) = g(z)mn=0 (1)

with the initial conditions

𝑓(𝑡)(𝛼) = 𝜗𝑡 𝑡 = 0,1, … . , 𝑚 − 1 (2)

We will let f(z) is unknown function, Pn(z) and g(z) are analytical functions in the circular domain which 𝐷 = 𝑧 = 𝑥 +𝑖𝑦, 𝑧 ∈ 𝐶, |𝑧 − 𝑧0| ≤ 𝑟, 𝑟 ∈ 𝑅+, 𝛼, 𝑧0 ∈ 𝐷, is appropriate complex or real constant. We assume that the solution of (1) under

the conditions (2) is approximated in the form

𝑓(𝑧) = ∑ 𝑎𝑛𝐵𝑛(𝑧),𝑁𝑛=0 𝑧 ∈ 𝐷 (3)

which is the Boubaker series of the unknown function, where all of are the Boubaker coefficients to be determined. We also

use the collocation points

𝑧𝑝𝑝 = 𝑧0 +𝑟

𝑁𝑝𝑒

𝑖𝜃

𝑁𝑝 , 0 < 𝜃 ≤ 2𝜋, 𝑟 ∈ 𝑅+, 𝑝 ∈ 0,1, … , 𝑁 (4)

Consequently, we have obtained the numerical solutions of linear complex diferential equations by using the Boubaker

Polynomials and performed it a test problems. When we have compared exact solutions and numerical solutions of tables and

graphs, we realized that our method is reliable, practical and functional.

Keywords: Linear complex differential equations, Boubaker Polynomials, Collocation Method.

References

1. O.D. Oyodum, O.B. Awojoyogbe1,a, M. Dada, K.B. Ben Mahmoud, and J. Magnuson, On the earliest definition of the Boubaker

polynomials, Eur. Phys. J. Appl. Phys. 46, 21201 (2009).

2. F. Düşünceli and E. Çelik. An Effective Tool: Numerical Solutions by Legendre Polynomials for High-order Linear Complex

Differential Equations. British Journal of Applied Science & Technology.(2015) 8(4): 348-355.

3. F.Düşünceli, E.Çelik, 2017. Numerical Solution for High-Order Linear Complex Differential Equations By Hermite Polynomials.

Iğdır Univ. J. Inst. Sci. & Tech. 7(4): 189-201.

4. F.Düşünceli, E.Çelik, 2017. Numerical Solution for High-Order Linear Complex Differential Equations with variable coefficients.

Numerical Methods for Partial Differential Equations, DOI 10.1002/num.22222.





Istanbul / TURKEY


55

Solving the Artificial Ant on the Santa Fe Trail Problem Using Artificial Bee Colony

Programming

Fateh Boudardara1 and Beyza Gorkemli 2

1Department of Computer Engineering, Erciyes University, Kayseri, Turkey

[email protected] 2Department of Computer Engineering, Erciyes University, Kayseri, Turkey

[email protected]

Abstract

Today, automatic path planning of mobile robots is an important topic in many fields such as robotics, aerospace

research, mining industry, virtual environments, games, etc. In automatic path planning problem, a mobile robot tries to find

the optimal path from the starting point to the goal. Artificial ant problem can be seen as a sub-problem of robotic path planning

where the artificial ant has to find the path (trail) which allows it to collect all the food along this trail in a limited amount of

time called “number of steps” [1, 2].

Artificial Bee Colony Programming (ABCP) is a novel evolutionary computation based automatic programming

algorithm and a machine learning method which uses tree structure to find the optimal computer programs [3]. Aritficial Bee

Colony (ABC) is an an artificial intelligence optimization algorithm which simulates the foraging behavior of honey bees [4].

It is one of the most popular metaheuristics used to find optimal solutions for different kinds of numerical optimization problems

[5]. For moving on the search space, ABCP uses the basic structure of ABC algorithm.

In this study, we applied ABCP method to Artificial Ant problem with Santa Fe Trail, and ABCP carries out an

optimization process aims to find optimal computer programs which navigate the artificial ant so that it collects maximum

number of foods. In order to see the performance of this method some experimental studies are done, and simulation results are

presented.

Keywords: Optimization, Robotic path planning, Artificial Ant Problem, Santa Fe Trail, Evolutionary Computation,

Evolutionary Computation based Automatic Programming, Artificial Bee Colony Programming.

References:

1. V. Pshikhopov, Path Planning for Vehicles Operating in Uncertain 2D Environments, 1st ed. Butterworth-Heinemann, 2017.

2. A. C. Nearchou, “Path planning of a mobile robot using genetic heuristics,” Robot. Cambridge Univ. Press, vol. 16, pp. 575–588,

1998.

3. D. Karaboga, C. Ozturk, N. Karaboga, and B. Gorkemli, “Artificial bee colony programming for symbolic regression,” Inf. Sci.,

vol. 209, pp. 1–15, 2012.

4. D. Karaboga and B. Basturk, “A powerful and efficient algorithm for numerical function optimization: artificial bee colony ( ABC

) algorithm,” pp. 459–460, 2007.

5. D. Karaboga, B. Gorkemli, C. Ozturk, and N. Karaboga, “A comprehensive survey: Artificial bee colony (ABC) algorithm and

applications,” Artif. Intell. Rev., vol. 42, no. 1, pp. 21–57, 2014.




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56

Some Parseval Type Relations on the Pv,4n-Integral Transform

A. Nese Dernek1 and Fatih Aylikci2

1Department of Mathematics, Marmara University,

[email protected] 2Department of Mathematical Engineering, Yildiz Technical University

[email protected]

Abstract

In this paper, the authors consider the Pv,4n-transform and the generalized some other integral transforms. Many

identities involving these transforms are given. A number of new Parseval-type identities are obtained for these and many

other well-known integral transforms. Some useful corollaries for evaluating infinite integrals of special functions are

presented. Illustrative examples are given for the results.

Keywords: Laplace transforms, L4n-transforms, Pv,4n-transforms, G2n-transforms, Parseval-type relations.

References

1. Dernek N., Ölçücü E.Ö. and Aylikci F., New identities and Parseval-type relations for the generalized integral transforms L4n,

P4n, Fs,2n, Fc,2n, Applied Mathematics and Computation 269 (2015) 536-547

2. N. Dernek and F. Aylikci, Identities for the Ln-transform, the L2n-transform and the P2n-transform and their applications, J.

Inequal. Spec. Funct. 5 (2014) 1-16.

3. Erdelyi A., Magnus W., Oberhettinger F., Tricomi F.G., Tables of Integral Transforms Vol I, New York NY USA, McGraw-Hill,

(1954).

4. Erdelyi A., Magnus W., Oberhettinger F., Tricomi F.G., Tables of Integral Transforms Vol II, New York NY USA, McGraw-

Hill, (1954).

5. Yurekli O. and Sadek I., A Parseval-Goldstein type theorem on the Widder potential transform and its applications, International

Journal of Mathematics and Mathematical Sciences 14 (1991) 517-524.





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57

Modules have S2 Property

Fatih Karabacak1 1Department of Mathematics, Education Faculty, Anadolu University,

[email protected]

Abstract

An R-module M has the summand intersection property (briefly SIP) if the intersection of any two direct summands

is again a direct summand. It is clear that every direct summand is a supplement and the converse of this statement, in general,

is not true. The SIP-module definition is based on direct summands. Therefore, the definition on supplements may be

transformed to S2. A module M has the supplement intersection property 2 (S2), if the intersection of every two supplements

in M is a supplement in M. In this note, the characterization of S2 property over rings and modules is investigated.

Keywords: Direct summand, SIP, Supplement

References

3. Alkan M, Harmancı A. On summand sum and summand intersection property of modules. Turk J. Math 26 (2002) 131-147.

4. Arnold DM, Hausen JA. Characterization of modules with the summand intersection property. Comm. Algebra 18 (1990) 519-

528.

5. Garcia JL. Properties of direct summands of modules. Comm. Algebra 17(1) (1989) 73-92.

6. Wilson GV. Modules with the summand intersection property. Comm. Algebra 14 (1986) 21-38.




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58

Some Classical Solutions of Dirac-Gursey Field Equation

Fatma Aydogmus1 and Eren Tosyali2

1Department of Physics, Istanbul University,


2Istanbul Bilgi University

[email protected]

Abstract

In this study, we consider the classical equation derived from the conformal invariant 4D pure spinor fermionic system

obtained by the Heisenberg’s ansatz. This classical field equation has particle-like solutions so-called instantons. It is well

known that instantons are classical solutions that originate from topological structure of vacuum in non-Abelian gauge field

theories with zero energy and finite action. We simulate the phase portraits and Poincare sections of the system numerically.

References

1. P. A. M. Dirac, The quantum theory of the electron, Proc. R. Soc. London 23 (1928) 351–361, DOI:10.1098/rspa.1928.00.

2. W. Heisenberg, Zur quantentheorie nichtrenormierbarer wellengleichungen, Z. Nat.

9a (1954) 292.

3. F. Gursey, On a conform-invariant spinor wave equation, Nuovo Cimento 3 (1956) 988.

4. F. Aydogmus, Dynamics of excited instantons in the system of forced Gursey nonlinear

differential equations, J. Exp. Theor. Phys. 120(2) (2015) 210–216.

5. F. Aydogmus, Chaos in a 4D dissipative nonlinear fermionic model, J. Mod. Phys. C

26(7) (2015) 1550083.

6. F. Aydogmus, Unstable Behaviours of Classical Solutions in Spinor-type Conformal

Invariant Fermionic Models, J. Exp. Theor. Phys. 125(5) (2017) 719–727.






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59

Bases of the Perturbed System of Exponents in Generalized Weighted Lebesgue Space with a

General Weight

Fatima Guliyeva,1 and Sabina Sadigova1

1Institute of Mathematics and Mechanics of NAS of Azerbaijan


Abstract

When solving many problems for equations of mixed type by Fourier method (see e.g., [1-5], there appear perturbed

systems of sines and cosines of the following form

Nntnt sin , Nntnt cos , (1)

where R ,0: is some real function. Basis properties of system (1) is closely related to the analogous properties of the

system of exponents of the form

Zn

nsigntntie , (2)

where R ,: is some function.

In this work, the basicity of system (2) is studied in weighted variable Lebesgue space ,,, pp LL with a

general weight . For the basicity of this system the sufficient conditions on the function and weight are obtained

in ,pL For this, firstly, the weighted variable Hardy classes dpH , are defined, the basicity of a part of exponential

system is studied in these classes, and these results are applied to the basicity of the system (2) in ,pL . It should be noted

that previously known results follows as a particular case from the obtained results.

Keywords: the weighted space, system of exponents, basicity, variable exponent

References

1. E.I. Moiseev, Some boundary value problems for mixed-type equations, Diff. Equations, 28(1)(1992) 105-115.

2. E.I. Moiseev, Solution of the Frankl Problem in a Special Domain, Diff. Uravn., 28(4) (1992), 721-723.

3. E.I. Moiseev, On existence and uniqueness of solution a classical problem, Dokl. RAN, 336(4) (1994), 448--450.

4. S.M. Ponomarev, On an eigen value problem, DAN SSSR, 249(5) (1979), 1068--1070.

5. L.V. Kritskov, Necessary Condition for the Uniform Minimality of Kostyuchenko Type Systems, Azerbaijan Journal of

Mathematics, 5(1) (2015), 97-103





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60

On The Bifurcation Diagrams of Fractional Logistic Map

Fatma Yavcin and Nuran Guzel

Department of Mathematics, Yildiz Technical University, Esenler, İstanbul, 34210

[email protected]

Abstract

In this study new chaotic maps are generated from logistic map and behaviour of these chaotic maps is

investigated. Dependence of the control parameter is presented with bifurcation diagrams. Dynamics of the fractional

logistic map for the various degree of fractional integral is investigated. Then we demonstrate that fractional logistic map

has similar bifurcation diagram and when degree of integral increases, value of bifurcation points increases.

Keywords: Bifurcation Diagram, Fractional Order Logistic Equation, Chaos

References

1. Das, S., Gupta, P.K. and Vishal, K. Approximate Approach to the Das Model of Fractional Logistic Population Growth. Appl.

Math. Vol. 05, Issue 2 (2010), pp. 605 611.

2. Martelli, M. Introduction to Discrete Dynamical Systems and Chaos. John Willey and Sons, Inc. New York, Chichester,

Weinheim, Brisbane, Singapore, Toronto, 1999.

3. Miller, K. and Ross, B. An introduction to fractional calculus and fractional differential equations, Wiley, New York, 1993.

4. Munkhammar, J.D. Numerical Chaos in Fractional Order Logistic Equation. arXiv:1011.2389v1 [math.GM], 2010.

5. Munkhammar, J.D. Chaos in a Fractional Order Logistic Map. Fract. Calc. Appl. Anal. Vol. 16, Issue 3 (2013), pp. 411-519.




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61

Multiple Scales Method for Higher Order KdV Equation

Fedakar Çakır1, Murat Koparan2 and Ömer Ünsal1

1Department of Mathematics-Computer Sciences,Arts and Science Faculty,

Eskisehir Osmangazi University, Eskisehir-Turkey

[email protected] , [email protected] 2Department of Mathematics and Science Education,Faculty of Education,

Anadolu University, Eskisehir-Turkey

[email protected]

Abstract

Nonlinear evolution equations are the mathematical models of problems that arise in many field of science such as

engineering, physics, chemistry, applied mathematics. In recent years, multiple scales method has become an important

member of perturbation methods. In this work, multiple scales is presented for (1+1)-dimensional ninth-order Korteweg-de

Vries equation and we derive nonlinear Schrödinger (NLS) type equation.

Keywords: Multiple scales method, ninth-order Korteweg-de Vries equation, nonlinear Schrödinger type equation.

Acknowledgements: This work was supported by Anadolu University Scientific Research Projects (Grant No. 1705E408).

References

1. Zakharov V, Kuznetsov E.A. Multiscale expansions in the theory of systems integrable by the inverse scattering transform.

Physica D 18, 455-63 (1986).

2. S. Calegora F, Degasperis A, Xiaosdo Ji. Nonlinear Schrödinger-type equations from multiscale reduction of PDEs I.

Systematic derivation. J Math Phys 42, 2635-2652 (2001).

3. Degasperis A, Manakov SV, Santini PM. Multiple-scale perturbation beyond nonlinear Schrödinger equation I. Physica D 100,

187-211 (1997).

4. Osborne A. R, Boffetta G. A. Summable multiscale expansion for the KdV equation. In: Degasperis A, Fordy AP, Lakshmanan

M, editors. Nonlinear evolution equations. Integrability and spectral Methods. MUP, Manchester and New York, 559-571

(1991).






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62

Stabilization of optimal control of Navier-Stokes equations

Fikriye Nuray Yılmaz

1Department of Mathematics, Gazi University,

[email protected]

Abstract

Optimal control theory of viscous flows has several applications in physics and engineering science. The viscocity

term causes unstable numerical solutions. So that, a numerical stabilization should be used. Most popular stabilization

techniques for flow problems are Streamline Upwind Galerkin(SUPG) and Pressure Stabilization methods, Large Eddy

Simulation methods and Variational Multiscale Methods(VMS). In this work, stabilization of the optimal control of the

Navier-Stokes equations are studied. Here, optimize-then-discretize approach is used to get the optimality conditions. Then,

numerical solution are presented with varying values of viscocity term.

Keywords: Optimal control, finite element method, Navier-Stokes equations.

References

1. M. Hintermüller and M. Hinze, An SQP semi-smooth Newton-type algorithm applied to the instationary Navier-Stokes system

subject to control constraints, SIAM J. Optim., 16 (4) (2006), 1177-1200.

2. M. Hinze, Optimal and instantaneous control of the instationary Navier-Stokes equations, Uberarbeitete Version der

Habilitationsschrift, Technische Universitat Dresden, 2002.

3. V. John, S. Kaya and W. Layton, A two-level variational multiscale method for convection-diffusion equations, Comput. Meth.

Appl. Mech. Engrg., 195 (2005), 4594-4603.




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63

Quadrature Formula Utilizing Sparse Grid Quasi-Interpolation with Gaussian

Fuat Usta1 1Department of Mathematics, Düzce University, Düzce, Turkey

[email protected]

Abstract

In this talk, a quadrature formula via quasi interpolation by using sparse grid with Gaussian kernel has been presented.

Then in order to overcome convergence problem we define multilevel version of this algorithm. At the end the results of

numerical experimentation for numerical integration for high dimensions have been provided.

Keywords: Gaussian, Quasi interpolation, Numerical integration, High dimension.

References

1. F. Usta and J. Levesley, Multilevel quasi-interpolation on a sparse grid with the Gaussian, Numerical Algorithms, (2018) 77:

793. https://doi.org/10.1007/s11075-017-0340-y

2. E. H. Georgoulis, J. Levesley, and F. Subhan. Multilevel sparse kernel based interpolation. SIAM Journal of Scientific

Computing, 35:815-832, 2013.

3. V. Mazya and G. Schmidt. Approximate Approximations. 2007. Providence.





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64

Some properties of a second order mixed type impulsive differential equation with piecewise

constant arguments

Gizem S. Öztepe

Department of Mathematics, Ankara University,

[email protected]

Abstract

The existence and uniqueness of the solutions of a second order mixed type impulsive differential equation with

piecewise constant arguments is proved in this work. Also some qualitative properties of the solutions are studied.

Keywords: Existence of solutions, Impulsive differential equation, Piecewise constant arguments.

References

1. Wiener, J. and Lakshmikantham, V. Excitability of a second-order delay differential equation, Nonlinear Analysis: Theory,

Methods and Applications 38 (1), 1-11, 1999.

2. Lopez, R. R. Nonlocal boundary value problems for second-order functional differential equations, Nonlinear Analysis: Theory,

Methods and Applications 74 (18), 7226-7239, 2011.

3. Yuan, R. Pseudo-almost periodic solutions of second-order neutral delay differential equations with piecewise constant argument,

Nonlinear Analysis: Theory, Methods and Applications 41 (7), 871-890, 2000.

4. Yuan, R. On the spectrum of almost periodic solution of second-order differential equations with piecewise constant argument,

Nonlinear Analysis: Theory, Methods and Applications 59 (8), 1189-1205, 2004.

5. Bereketoglu, H., Seyhan, G. and Karakoc, F. On a second order differential equation with

piecewise constant mixed arguments, Carpathian Journal of Mathematics 27 (1), 1-12, 2011.




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65

Value of Game for Infinite Matrix Games with Interval Payoffs

Aykut Or1 and G. Selin Savaşkan2

1,2Department of Mathematics, Çanakkale Onsekiz Mart University,

[email protected]

[email protected]

Abstract

This study deals with two person infinite games with interval payoff. We investigate the infinite interval matrix

games. It is assumed that the sequences which are formed by the rows and columns of the considered infinite matrices, are

convergent. Then, some of the properties of the existence of the game value are studied in detailed form.

Keywords: Interval matrix game, infinite interval matrix, interval sequence.

References

1. Tijs S, Semi-infinite and infinite matrix and bimatrix games. University of Nijmegen, PhD Thesis (1977).

2. Moore R.E., Method and Application of Interval Analysis, SIAM, Philadelphia, (1979).

3. Owen G., Game Theory. Academic Press, New York, London, Third Edition (1995).

4. Mendez-Naya L., On the value of some infinite matrix games. Math. of Operations Research, 26, 1 (2001) 82-88.

5. Nayak P. K. and M. Pal, Solution of interval games using graphical method. Tamsui Oxf. Jour. Of Math. Sciences, 22(1), (2006)

95-115.





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66

Lexicographic Method in Interval Positional Games

G. Selin Savaşkan1 and Aykut Or2

1,2Department of Mathematics, Çanakkale Onsekiz Mart University,

[email protected]

[email protected]

Abstract

The mothod is an approach to solve interval-valued matrix games. It converts into from interval linear programming

model to classical system of inequalities. In this work, we consider positional games with interval pay-offs and adapt

Lexicographic method for solving such games. Also, numerical examples are illustrated.

Keywords: Interval matrix games, Interval pay-offs, Positional games, Lexicographic method.

References

1. Moore R.E., Methods and Applications of Interval Analysis, SIAM, Philadelphia, USA, (1979).

2. Li D. F., Nan J. X. ve Zhang M. J., Interval Programming Models for Matrix Games with Interval Payoffs. Optimization Methods

and Software (2010) 1-16.

3. Kolobaşkina, L.V., Osnov Teori gr BNOM, Laboratiriya Znaniy, (2011).

4. Li, D.F., Notes on “Linear Programming Technique to Solve Two-Person Matrix Games with Interval Pay-Offs”, Asia-Pacific

Journal of Operational Research, Vol.28, No.6 (2011) 705-737.





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67

Fuzzy mixed Poisson Regression model on a smoking cessation study

Godrick Oketch1 and Filiz Karaman1

1Department of Statistics, Yildiz Technical University

[email protected]

Abstract

The theory of Poisson models which is based on precise counts as dependent variables is commonly applied in medical

and social science applications. However, there are situations when these counts may fail to be definite and therefore are fuzzy.

This study, relies on the assumption that heaped data points are fuzzy as a way of identifying observations that are imprecise.

The paper then proposes a Poisson likelihood function that subsumes both precise and fuzzy observations on one hand but also

includes alpha cuts of fuzzy numbers on the other hand. Finally, we illustrated the proposed model through a real data on the

number of cigarettes smoked in a month. The model results gave better predictions of the outcome variable when impreciseness

of the fuzzy numbers is increased than the traditional Poisson model.

Keywords: Fuzzy counts, Poisson Regression, α-cuts, Maximum Likelihood function.

References:

1. M. Akbari, R. Mohammadalizadeh, M. Rezaei, Bootstrap statistical inference about the regression coe_cient based on fuzzy data,

International Journal of Fuzzy Systems 14 (2012) 549-556.

2. F. Moradi, A. Arabpour, A. Shadrokh, A bootstrap-based method of statistical inference in fuzzy logistic regression, Journal of

Engineering and Applied Sciences 11 (2016) 2105-2112.

3. R. C. Klesges, M. Debon, J. W. Ray, Are self-reports of smoking rate biased? evidence from the second national health and

nutrition examination survey, Journal of Clinical Epidemiology 48 (1995) 1225-1233.

4. T. H. Cummings, J. W. Hardin, A. C. McLain, J. R. Hussey, K. J. Bennett, G. M. Wingood, Modeling heaped count data, The

Stata Journal 15 (2015) 457-479.




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68

Some Properties of Hyperbolic Split Quaternion Matrices

Gözde Özyurt1 and Yasemin Alagöz2


[email protected] 2 Yildiz Technical University

[email protected]

Abstract

The purpose of this study, to investigate hyperbolic split quaternions as in 2x2 hyperbolic matrix form. To achieve

this, we use 2x2 hyperbolic matrices corresponding to hyperbolic split quaternion basis elements. Hence we search some

properties of hyperbolic split quaternion matrices and we give a method to find the determinant of these matrices.

Keywords: Hyperbolic split quaternion, hyperbolic split quaternion matrices.

References

1. Ebbinghaus, H.-D., Hermes, H., Hirzebruch F., Koecher, M., Mainzer, K., Neukirch, J., Prestel A. and Remmert, R., Numbers.

New York etc.: Springer-Verlag, (1990).

2. Rosenfeld, B., Geometry of Lie groups. Dordrecht: Kluwer Academic Publishers, (1997).

3. Erdoğdu, M. and Özdemir, M., Matrices over hyperbolic split quaternions. Filomat, 30(4):913-920, (2016).

Inoguchi, J., Timelike surfaces of constant mean curvature in Minkowski 3-space. Tokyo J. Math., 21(1):141-152, (1998).





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69

Closed-Form Solutions of Optimal Growth Model with Environmental Asset

Gülden Gün Polat1, Ahu Coşkun Özer2 and Teoman Özer 3

1,3Faculty of Civil Engineering, İstanbul Technical University,

[email protected], [email protected] 2Vocational School of Social Sciences, Marmara University

[email protected]

Abstract

This work focuses on the model which is called an optimal growth model with an environmental assets, is developed

by Le Kama and Schubert [1]. By using the current and present value Hamiltonian systems of this model, based on the different

mathematical approaches that are Jacobi and λ-symmetry, closed-form solutions of the model are presented .

Keywords: Current value Hamiltonian, present value Hamiltonian, Jacobi method, Lie symmetries, λ-symmetries

References:

1. A.A. LeKama and K. Schubert, A note on the consequences of an endogenous discounting depending on the environmental quality,

Macroeconomic Dynamics, 11(02), (2007), 272-289.

2. R. Naz, The applications of the partial Hamiltonian approach to mechanics and other areas, International Journal of Non-Linear

Mechanics, 86(1), (2016) 1-6.

3. R. Naz, F.M. Mahomed, and A. Chaudhry, A partial Hamiltonian approach for current value Hamiltonian systems, Communications

in Nonlinear Science and Numerical Simulation, 19(10), (2014) 3600-3610.

4. C. Muriel and J.L. Romero, First integrals, integrating factors and symmetries of second order differential equations, J. Phys. A:

Math. Theory. 42(36), (2009).

5. M.C. Nucci, Jacobi Last Multiplier and Lie symmetries: A Novel Application of an Old Relationship, J. Nonlinear Math. Phys.,

12(2), (2005), 284-304.

6. P. J Olver, Applications of Lie Groups to Differential Equations, Springer-Verlag, (1993).

7. G. Gün Polat and T. Özer, New conservation laws, Lagrangian forms and exact solutions of modified-Emden equation, Journal of

Computational and Nonlinear Dynamics, (2017), 12(4),041001.





https://www.scopus.com/sourceid/21116?origin=recordpage

https://www.scopus.com/sourceid/21116?origin=recordpage


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70

Estemations for the root functions of a Dirac type operator

Hajiyeva Gunel Razim Azerbaijan State Pedagogical University

[email protected]

Abstract

It is considered of Dirac type operator on a finite interval baG , . Estimates for the root (eigen and

associated) functions of the given operator are established.

Keywords: root functions, Dirac type operator, eigenvalue, assosiated function.

Consider the Dirac type operator TxyxyyyxyBLu 21 ,, , where

xqxpdiagxbbb

bB ,;0,0,

0

021

2

1

, xp and xq a complex-valued functions defined on a

arbitrary finite interval baG , .

The root (eigen and associated) functions 0, lxul

, corresponding to the eigenvalue , are understood in the

sense of papers [1], [2], i.e. 1

lll

uuuL .

Theorem. Let xp and xq belong to GL1. Then for the root functions xu

l

the following estimates

1,Im1,,,2.

211

2.

1

lubbGlCull

,0,1,Im1,,,2.

1

212

2.

1

lrubbGlCur

lr

l

is valid. Where constants 1C and

2C is independed from the .

References

1. V.M.Kurbanov, On Bessel property and a unconditional basicity of the system of root vector-functions of Dirac operator.

Differ. Uravn. 1996. 32 (12), 1608–1617.

2. V.M.Kurbanov and A.I.Ismayilova, Riesz inequality for the system of root vector-functions of Dirac operator. Differ. Uravn.

2012. 48 (3), 334–340.




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71

Approximation Properties of Fourier Series by Nonlinear Basis in Generalized Hölder Spaces

Hatice Aslan1 and Ali Güven2

1Department of Mathematics, Fırat University,

[email protected] 2Balıkesir University

[email protected]

Abstract

In this paper, the value of the deviation of a function 𝑓 from its generalized de la ValleePoussin means respect to the

nonlinear trigonometric system for classes of piecewise smooth 2𝜋-periodic functions is estimated in generalized Hölder

spaces.

Keywords: nonlinear Fourier basis, generalized de la Vallee-Poussin mean, generalized Hölder spaces

Referances:

1. Chen Q. H., Li L. Q., Qian T., ”Stability of frames generated by nonlinear Fourier atoms”, Int J Wavelets Multiresolut Inf

Process, 3, 465-476, (2005).

2. Chen Q. H., Li L. Q. and Qian T., ” Two families of unit analytic signals with nonlinear phase”, Phys D, (221), 1-12,

(2006).

3. Leindler L., ”Generalization of Prössdorf’s Theorems”, Studia Scientiarum Mathematicarum Hungarica (14), 431-

439,(1979).

4. Leindler L., ”On summability of Fourier series”, Acta science math, Szeged 29, 147- 162,(1968).

5. Huang, C., Yang, L H., ”Approximation by the nonlinear Fourier basis”, Sci China Math, 54(6), 12071214, (2011).





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72

Some Identities on Fractional Integrals and Integral Transforms

Ayse Nese Dernek1 and Gulcin Bozkurt2


[email protected] 2Department of Mathematics, Marmara University

[email protected]

Abstract

In this paper, we introduce various theorems that associate the generalized Riemann-Liouville fractional integral operator

and the generalized Weyl fractional integral operator with some well-known integral transforms including generalized Laplace

transform, Widder potential transform, generalized Widder transform, Hankel transform and Bessel transform. As

applications of these theorems and their results, we evaluate certain integrals of some elementary functions and some special

functions.

Keywords: Riemann-Liouville fractional integral, Weyl fractional integral, Fractional derivatives, Laplace transform, Widder

potential transform, Hankel transform, Bessel transform, Error function, Complementary error function, Exponential integral

function.

References

1. Dernek A., Dernek N., Yurekli O. Identities for the Hankel transform and their applications. J. Math. Anal. and Appl. 354 (2009)

165–176.

2. Dernek A. N., Aylikci F. Some Results on the Pν,2n, Kν,n, Hν,n integral transforms. Turkish Journal of Mathematics, 41 (2017)

337–349.

3. Dernek A. N., Kurt V., Simsek Y., Yurekli O. A generalization of the Widder potential transform and applications. Integral

Transforms and Special Functions, 22 (2011) 391-401

4. Erdelyi A., Magnus W., Oberhettinger F., Tricomi F. Tables of Integral Transforms Vol:1. Mc Graw-Hill Book Company, New

York, Toronto and London, (1954).

5. Erdelyi A., Magnus W., Oberhettinger F., Tricomi F. Tables of Integral Transforms Vol:2. Mc Graw-Hill Book Company, New

York, Toronto and London, (1954).





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73

Solutions for Some Families of Fractional Differential Equations

Neşe Dernek1 and Gülçin Bozkurt2


[email protected] 2Department of Mathematics, Marmara University

[email protected]

Abstract

In this paper, we use Laplace transform method to solve certain families of fractional order differential equations.

Fractional derivatives that appears in these equations are defined in the sense of Caputo. We first state and prove our main

results regarding the solutions of some families of fractional order differential equations, and then give examples to illustrate

these results. In particular, the exact solution for a special case of the Bagley-Torvik equation is given as an application.

Keywords: Fractional-order differential equations, Riemann-Liouville fractional integral, Fractional derivatives, Laplace

transform of fractional derivative, Wright function, Bagley-Torvik equation.

References

1. Lin S. D., Lu C. H., Laplace Transform for Solving Some Families of Fractional Differential Equations and Its Applications.

Advances in Difference Equations, 137, (2013).

2. Kazem S., Exact Solution of Some Linear Fractional Differential Equations by Laplace Transform. International Journal of

Nonlinear Science, 16, (2013), 3-11.

3. Li C., Qian D., Chen Y., On Riemann Liouville and Caputo Derivatives. Discrete Dynamics in Nature and Society, 2011, (2011),

(10 pages).

4. Miller K.S., Ross B., An Introduction to the Fractional Calculus and Fractional Differential Equations. A Wiley-Interscience

Publication, (1993).

5. Diethelm K., Ford N. J., Numerical Solution of the Bagley-Torvik Equation. BIT Numerical Mathematics. 42(3), (2002), 490-

507.




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74

Lie Group Analysis and Galilean Group Analysis for Partial Differential Equatios

Dogan Kaya1 and Gulistan Iskandarova2

1Department of Mathematics, Faculty of Art and Science, Istanbul Commerce University,

[email protected]

2Istanbul Commerce University


Abstract

As we know there are many methods to obtaın solutıons for partial differential equations. One of these methods is

symmetry analysis method [1, 2]. In this work, we studied the Lie symmetry group and Galilean symmetry group methods

[3-6]. We explored the common features and differences between these methods.

Keywords: Lie symmetry groups, Galilean symmetry groups, Partial Differential Equations.

References

1. Gazizov, R.K., Kasatkin, A.A., Lukashchuk, S.Y. (2007). Continuous transformation group of fractional differential equations.

Vestn. USATU, 9, 125-135.

2. Bluman, G.W., Anco, S. (2002). Symmetry and integration methods for differential equations. Springer-Verlag, Heidelburg.

3. Iskandarova, G., Kaya, D. (2017). Symmetry solution on fractional equation. IJOCTA. Vol.7, No.3, 255-259.

4. Lévy-Leblond, J.M. (1971). Galilei group and Galilean invariance. Group Theory and Applications. Vol. 2 (New York:

Academic), 221-299.

5. Inönü, E., Wigner, E. (1952). Representations of the Galilei group. Nuov. Cim. 9B, 705-718.

6. Takahashi, Y. (1988). Towards the many-body theory with the Galilei invariance as a guide. I. Fortschr. Phys. 36, 63-81.





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75

On the Parallel Surfaces to Translation Surface with q-Frame in Euclidean 3-Space

Hatice Tozak1, Gülşah Aydın Şekerci2 and Cumali Ekici3 1Department of Mathematics-Computer, Eskişehir Osmangazi University,

[email protected] 2Department of Mathematics, Süleyman Demirel University,

[email protected] 3Department of Mathematics-Computer, Eskişehir Osmangazi University,

[email protected]

Abstract

Translation surfaces are defined as the surfaces that generated by two space curves in 3-dimensional Euclidean space.

In this study, it is aimed to examine the relationship between the q-frames of the curves that are located on the translation

surface itself and a parallel surface to that translation surface. Also, we investigate fundamental forms of parallel surface to

translation surface.

Keywords: q-frame, translation surfaces, parallel surfaces, space curve.

References

1. H. Liu, Translation surfaces with constant mean curvature in 3-dimensional spaces, Journal of Geometry 64 (1999) 141–149.

2. L. Verstraelen, J. Walrave, S. Yaprak, The minimal translation surfaces in Euclidean space, Soochow Journal of Mathematics

20(1) (1994) 77–82.

3. M. Dede, C. Ekici, A. Görgülü, Directional q-frame along a space curve, IJARCSSE 5 (2015) 775–780.

4. M. Dede, C. Ekici, H. Tozak, Directional tubular surfaces, International Journal of Algebra 9(12) (2015) 527–535.

5. M. Munteanu, A. I. Nistor, On the geometry of the second fundamental form of translation surfaces in E3, Houston Journal of

Mathematics 37(4) (2011) 1087–1102.






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76

Generalization Of Reflexive Rings And Their Applications

Handan Kose1 and Burcu Ungor2

1Department of Mathematics, Ahi Evran University,


[email protected]

Abstract

Let 𝑅 be a ring and 𝐼 an ideal of 𝑅. The ring 𝑅 is called left N-reflexive if for any nilpotent element 𝑎 ∈ 𝑅 and 𝑏 ∈ 𝑅,

being 𝑎𝑅𝑏 = 0 implies 𝑏𝑅𝑎 = 0. We investigate properties of this class of rings. We show that some results of reflexive rings

can be extended to the left N-reflexive rings for this general setting. We obtain some characterizations of left N-reflexive

rings. As applications, some subrings of full matrix rings are investigated in terms of left N-reflexivity. Also, many families

of left N-reflexive rings are presented.

Keywords: Reflexive ring, left N-reflexive ring, quasi-Armendariz ring.

This work was supported by the Ahi Evran University Scientific Research Projects Coordination Unit. Project Number:

FEF. A4. 18. 008

References

1. Y. Hirano, On annihilator ideals of a polynomial ring over a noncommutative ring, J. Pure Appl. Algebra 168(1) (2002) 45-52.

40(4).

2. J. Y. Kim, Certain rings whose simple singular modules are GP-injective, Proc. Japan Acad. Ser. A Math. Sci 81(7) (2005) 125-

128.

3. L. Zhao, X. Zhu and Q. Gu, Reflexive rings and their extensions, Math. Slovaca 63(3) (2013) 417-430.





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77

A Subclass of Concave Univalent Functions Defined by a Linear Operator

Hasan Bayram1 and Sibel Yalcin2

1Department of Mathematics, Uludag University,

[email protected] 2Department of Mathematics, Uludag University

[email protected]

Abstract

In the present paper, we investigate some basic properties of a subclass of concave univalent functions defined by a

new derivative operator.And we get new results of this subclass. Such as, coefficient inequalities, distortion bounds and

extreme points.

Keywords: Concave univalent functions, Salagean operator, linear operator, coefficient bounds, and multiplier

transformation.

References

1. F. G. Avkhadiev and K. J. Wirths (2002), Convex holes produce lower bounds for coefficients, Complex Variables, Theory and

Application, 47, 556-563.

2. F. M. Al-Aboudi (2004), On univalent functions defined by a generalized Salagean operator, J. Math. Sci., 27, 1429-1436.

3. A. Catas, G. L. Oros, G. Oros (2008), Differential subordinations associated with multiplier transformations, Abstract Appl.,

Anal. ID: 845724: 1-11.

4. B. Bhowmik, S. Ponnusamy and K. J. Wirths (2010), Characterization and the pre-Schwarzian norm estimate for concave

univalent functions, Monatsh Math., 161, 59-75.

5. M. K. Aouf, A. Shamandy, A. O. Mostafa, S. M. Madia (2010), A subclass M-W starlike functions, Acta Universitatis Apulensis.

21, 135-142.





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Acceleration Centres of Order (r-1) of Homothetic Motions

Hasan Es

Department of Mathematics and Science Education, Gazi University,

[email protected]

Abstract

In this study, firstly acceleration centres of order (r-1) of planar homothetic motions are obtained. These motions are

also generalized to 4-dimensional Euclidean space 𝐸4.

Keywords: Homothetic motion, Acceleration centre.

References

1. Hacisalihoglu, H.H., “On the rolling of curveor surface upon another”. Proceedings of the Royal Irish Academy. Vol. 71,

Section A, No.2 Dublin 1971.




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Numerical Scheme for the Solution of Multi Order Fractional Differential Equation

Hatice Yalman Kosunalp1, Yalçın Öztürk2, Mustafa Gülsu3

1 Bayburt University, Social Sciences Vacational School, Bayburt

[email protected] 2 Muğla Sıtkı Koçman University, Ula Ali Koçman Vacational School, Muğla

[email protected] 3 Muğla Sıtkı Koçman University, Mathematics Department, Muğla

[email protected]

Abstract

In this study, the Hermite operational matrix method is improved to solve the multi order fractional differential

equation. The fractional derivatives are described in the Caputo sense. For the numerical solution of the multi order fractional

differential equation, an equation system is obtained by using the Hermite operational matrix method. By the solution of the

equation system, the Hermite coefficients of the multi order fractional differential equations are found. The example is

included to demonstrate the validity and applicability of the technique and performed on the computer using a program written

in Matlab algebraic system. Numerical solutions are seen to be compatible with the exact solutions.

Keywords: Multi order fractional differential equation, Numerical approximation, Fractional derivative, Caputo derivative,

Hermite polynomials

References 1. I. Podlubny, Fractional differential equations, Academic Press,1999.

2. K.B.Oldham, J.Spanier,The Fractional Calculus,Academic Press,1999.

3. E.H. Doha, H.M. Ahmed, S.I.El-Soubhy, Explicit Formulae for the Coefficients of Integrated Expansions of Laugerre and Hermite

Polynomials and Their Integrals, 491-503, 2009.

4. B.H. Ali, T.M. Taha, An Operational Matrix of Fractional İntegration of the Laugerre Polynomials and its Application on a Semi-

Infinite Interval, 2012.




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On numerical approximation of generalized differential difference equations with linear

functional argument

Hatice Yalman Kosunalp1, Yalçın Öztürk2, Mustafa Gülsu3

1 Bayburt University, Social Sciences Vacational School, Bayburt

[email protected] 2 Muğla Sıtkı Koçman University, Ula Ali Koçman Vacational School, Muğla

[email protected] 3 Muğla Sıtkı Koçman University, Mathematics Department, Muğla

[email protected]

Abstract

In this study, the basic ideas of the collocation method are developed and applied to the generalized differential

difference equations with linear functional argument with initial conditions using Hermite polynomials. We use collocation

method to solve the generalized differential difference equations with linear functional argument. The main characteristic

behind the approach using this technique is that it collocates the solution into a rapidly convergent series thus greatly

simplifying the problem. Numerical examples are used to illustrate the preciseness and effectiveness of the proposed method.

For the all numerical algorithm we used Matlab algebraic system. Numerical examples demonstrate that the accuracy of

lower-order approximations is very satisfactory. The numerical and exact solutions for different orders have been showed in

tables and solutions were supported by the graphics.

Keywords: Differential difference equation, Numerical approximation, Hermite polynomials

References 1. S.B.Damelin,H.S,Jung,K.H.Kwon, Convergence of Hermite and Hermite-Fejer Interpolation of Hıgher Order for Freud Weights,

Journal of Approximation Theory.113(2001)21-58.

2. S.Cabay,G.Labahn,B.Beckerman, On The Theory and Computation of Nonperpect Pade-Hermite Approximations, Journal of

Computational and Applied Mathematics,39(1992)295-313.

3. G.Claessens, The rational Hermite Interpolation Problem and Some Related Recurrence Formulas.Computers&Mathematics with

Applications, 2(1976)117-123.

4. A.La Rocca, A.Hernandez Rosales, H.Power, Radial Basis Function Hermite Collocation approach for the Solution of time

dependent convection-diffusion problems, Engineering Analysis with Boundary Elements,29(2005)359-370.




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Comparison of Artificial Neural Network and Logistic Regression Model for a Medicine

Application

Murat Kirişci1 and Necip Şimşek2

1Department of Mathematical Educaiton, Istanbul University,

[email protected] 2Istanbul Ticaret University

[email protected]

Abstract

Aim— To compare the ANN and logistic regression analyzes to determine the factors affecting birth weight.

Methods— This study included 223 newborn babies. The records of babies born between January 2017 and December 2017

were used. The data were obtained from Beykoz district of Istanbul. ANN and logistic regression analysis of the method

obtained based on these records were evaluated.

Results— Logistic regression revealed the items GB, MA, GA, NH, BMI, MPPW, MWGP, MsAU, MsCU, MsE as significant

factors for BW. The area under the receiver operating characteristic (AuROC) curve 0.941 (sd=0.0012) for ANN and 0.909

(sd=0.019) for Logistic Regression model. The ANNs may be trained with data acquired in various contexts and can consider

local expertise, differences, and other variables with uncertain effects on outcome.

Conclusion— Although the ANN value is greater than the LR value, these results are very close to each other. This shows

us that in terms of their classification ability, these two methods are approximately equal to each other. The results we have

seen in our study show that in the medical diagnosis, neither model can change the other. Both models can be used as a

complement to help with decision-making. Both models have the potential to help physicians with respect to understanding

BW risk factors, risk estimation.

Keywords: neonate, birth weight, logistic regression, artificial neural network.

References:

1. World Health Organization, 2010. International statistical classification of diseases and related health problems, 10th

ed. Geneva.

2. World Health Organization, 2018. Global Database on Body Mass Index. Available online at:

http://apps.who.int/bmi/index.jsp?introPage=intro_3.html. accessed March 12, 2018

3. Austin, P. C., and Merlo, J. (2017) Intermediate and advanced topics in multilevel logistic regression

analysis. Statist. Med., 36: 3257–3277. doi: 10.1002/sim.7336.

4. Hon-Yi Shi, Jinn-Tsong Tsai, Wen-Hsien Ho, Shih-Chin Wang, I-Te Chen and King-Teh Lee, 2012. Comparison of

Artificial Neural Network and Logistic Regression Models for Predicting In-hospital Survival after Hepatocellular

Carcinoma Surgery. SICE Annual Conference 2012 August 20-23, 2012, Akita University, Akita, Japan

5. Iraji, Mohammad S.,,2017, Prediction of post-operative survival expectancy in thoracic lung cancer surgery with soft

computing. Journal of Applied Biomedicine, 15, 151-159.

6. Kanbayashi, Y., Ishikawa, T., Kanazawa, M. et al., 2018, Predictive factors in patients eligible for pegfilgrastim

prophylaxis focusing on RDI using ordered logistic regression analysis, Med Oncol, 35: 55.

7. Torres, A., Nieto, Juan J., 2006. Fuzzy Logic in Medicine and Bioinformatics. Journal of Biomedicine and

Biotechnology Volume 2006, Article ID 91908, Pages 1–7.




http://apps.who.int/bmi/index.jsp?introPage=intro_3.html

https://doi.org/10.1002/sim.7336


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8. Shi H-Y, Lee K-T, Lee H-H, Ho W-H, Sun D-P, et al. (2012) Comparison of Artificial Neural Network and Logistic

Regression Models for Predicting In-Hospital Mortality after Primary Liver Cancer Surgery. PLoS ONE 7(4):

e35781. doi:10.1371/journal.pone.0035781

9. Wiest, M.M., Lee, K.J., and Carlin, J.B., 2015. Statistics for clinicians: An introduction to logistic regression. Journal

of Paediatrics and Child Health 51, 670–673.



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83

A difference scheme for the Burgers equation

Murat Sari1, Sufii Hamad Mussa1 and Huseyin Tunc1 1Department of Mathematics, Yildiz Technical University,

[email protected]

Abstract

This paper investigates the sharp behaviour of the nonlinear advection-diffusion process.To achieve this, compact

finite difference formulations have been produced for corresponding process represented by the unsteady Burgers equation.

After the formulation has been derived, different numerical approaches are considered for both time and spartial derivatives.The

proposed approaches have been shown to be capable of solving the equation. Two examples have been taken to illustrate

physical behaviour in detail. The computed results are seen to be highly accurate and be oscillation free.

Keywords: Nonlinear Advection diffusion process, Compact finite difference method, Nonlinear Modelling.

References

1. G. Gurarslan, Numerical Modelling of Linear and Non Linear of diffusion equations by compact finite difference

method. Applied Mathematics and Computation, 216 (2010) 2472-2478.

2. Z. Pei-Guang, W. Jian-Ping, A predictor-corrector compact finite difference method for Burger’s Equation, Applied

Mathematics and Computaion, 219 (2012) 892–898.

3. M. Vijitha, A. Ashish. Effecient Numerical Techniques for Burgers Equations. Applied Mathematics and

Computation, 262(2015), 282-297.

4. M. Sari, G. Gurarslan. A sixth-order compact finite difference scheme to the numerical solutions of Burger’s Equation.

Applied Mathematics and Computation, 208 (2009) 475–483.

5. M. Sari, H. Tunç. An optimization technique in analyzing of the Burgers equation. Sigma Journal of Engineering and

Natural Sciences, 35 (2017) 369-386.




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84

Common Fixed Point of Noncommuting Almost Contraction Mapping in Cone Metric Space over

Banach Algebra

Muttalip Özavşar1 and Hatice Çay2


[email protected] 2Istanbul Medipol University

[email protected]

Abstract

In this study we aim to extend and generalize the common fixed point theorem of noncommuting almost contraction

in cone metric spaces over Banach algebra.

Keywords: Common fixed point theorem, Cone metric space with Banach algebra, noncommuting almost contraction.

References

1. V. Berinde, Common fixed points of noncommuting almost contractions in cone metric spaces, Math. Commun., Vol. 15, No. 1,

(2010) 229-241.

2. H. Liu and S. Xu, Cone metric spaces with Banach algebras and fixed point theorems of generalized Lipschitz mappings, Fixed

Point Theory and Applications (2013), 2013:320.





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Common Fixed Point of Noncommuting Almost Contraction Mapping in Cone b-Metric Space

over Banach Algebra

Muttalip Özavşar1 and Hatice Çay2


[email protected] 2Istanbul Medipol University

[email protected]

Abstract

In this work our aim is to extend the common fixed point theorem of noncommuting almost contraction in cone b-

metric spaces over Banach algebra.

Keywords: Common fixed point theorem, Cone b-metric space with Banach algebra, noncommuting almost contraction.

References

1. V. Berinde, Common fixed points of noncommuting almost contractions in cone metric spaces, Math. Commun., Vol. 15, No. 1,

(2010), 229-241.

2. H. Huang, S. Radenović, Some fixed point results of generalized Lipschitz mappings on cone b-metric spaces over Banach

algebras, J. Comput. Anal. Appl., 20 (1) (2016), 566-583.





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86

Timelike Translation Surface According to q-Frame in Minkowski 3-Space

Cumali Ekici1, Hatice Tozak2 and Mustafa Dede3 1Department of Mathematics-Computer, Eskişehir Osmangazi University,

[email protected] 2Department of Mathematics-Computer, Eskişehir Osmangazi University,

[email protected] 3Department of Mathematics, Kilis 7 Aralık University,

[email protected]

Abstract

In this paper, we studied the translation surfaces generated by two space curves according to q-frame in 3-dimensional

Minkowski space. The curvatures of the translation surface are obtained in terms of q-frame curvatures. Finally, some special

cases are investigated for these surfaces.

Keywords: q-frame, translation surfaces, space curve.

References

1. H. Liu, Translation surfaces with constant mean curvature in 3-dimensional spaces, Journal of Geometry 64 (1999) 141–149.

2. L. Verstraelen, J. Walrave, S. Yaprak, The minimal translation surfaces in Euclidean space, Soochow Journal of Mathematics

20(1) (1994) 77–82.

3. M. Dede, C. Ekici, A. Görgülü, Directional q-frame along a space curve, IJARCSSE 5 (2015) 775–780.

4. M. Dede, C. Ekici, H. Tozak, Directional tubular surfaces, International Journal of Algebra 9(12) (2015) 527–535.

5. M. Çetin, H. Kocayigit, M. Önder, Translation surfaces according to Frenet frame in Minkowski 3-space, International Journal

of Physical Science 7(47) (2012) 6135-6143.






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87

Completeness of Category of Rack Crossed Modules

Hatice Gülsün Akay and İ.İlker Akça

Department of Mathematics and Computer Science,

Eskisehir Osmangazi University,

[email protected]

[email protected]

Abstract

We say that a category C is (finitely) complete if it has all (finite) limits. On the other hand, all (finite) limits can be

constructed via product and equalizer objects.

A rack is a set equipped with a non-associative binary operation such that satisfying rack axioms [1]. A quandle (which

is a certain case of rack) is related to the Reidemeister moves of knot diagrams that yields a connection between knot theory

and the theory of racks [3].

Crossed modules are introduced by Whitehead in [4] for groups as a model of homotopy 2-types and used to classify

higher dimensional cohomology groups. Rack crossed modules are introduced by Crans and Wagemann in [1] as the

generalization of group crossed modules.

In this work, we prove that the category of rack crossed modules is (finitely) complete [2].

Keywords: Complete category, limit, rack, crossed module.

References

1. A.S. Crans and F. Wagemann. Crossed modules of racks. Homology Homotopy Appl., 2014.

2. H. Gülsün Akay and İ.İlker Akça, Completeness of the Category of Rack Crossed Modules.

3. S. Nelson. What is...a quandle? Notices of AMS, 63, April:378, 2016.

4. J.H.C. Whitehead. On adding relations to homotopy groups. Ann. Math. (2), 1941.





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Pullback Diagrams for Rack Crossed Modules

Hatice Gülsün Akay and Kadir Emir

Department of Mathematics and Computer Science,

Eskisehir Osmangazi University,

[email protected]

[email protected]

Abstract

A rack R is a set equipped with a non-associative binary operation such that satisfying rack axioms [1]. Quandle (a certain

case of rack) axioms are related to the Reidemeister moves of knot diagrams that yields a connection between knot theory and

the theory of racks [4].

Crossed modules of groups are introduced by Whitehead in [5] where they are used for the definition of homotopy systems

of connected CW complexes. Later, crossed modules are used for the classification of algebraic 2-types.

A rack crossed module is given by a rack homomorphism satisfying two Peiffer conditions. Moreover, they generalize

the group crossed module notion in the sense of conjugation [1].

For any category, a pullback is the limit of a diagram consisting of two morphisms with a common codomain. In this

work, we examine various pullback diagrams for rack crossed modules where,

- both of the morphisms are rack crossed modules [3],

- one of the morhisms is just a rack morphism [2].

Keywords: Pullback, limit, rack, crossed module.

References

1. A.S. Crans and F. Wagemann, Crossed modules of racks. Homology Homotopy Appl., 2014.

2. K. Emir and H. Gülsün Akay, Pullback Crossed Modules in the Category of Racks, Hacettepe Journal of Mathematics and

Statistics, 10.15672/HJMS.2017.532.

3. H. Gülsün Akay, The Categorical Properties of Crossed Modules of Racks, PhD Thesis, 2017.

4. S. Nelson. What is...a quandle? Notices of AMS, 63, April:378, 2016.

5. J.H.C. Whitehead, On adding relations to homotopy groups. Ann. Math. (2), 1941.





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89

On Rough Generalized Parametric Marcinkiewicz Integral

Hussain Al-Qassem 1, Leslie Cheng2 and Yibiao Pan3

1Department of Math., Stat & Physics, Qatar University, Doha-Qatar, [email protected]

2Bryn Mawr College, Bryn Mawr, U.S.A.

[email protected] 3University of Pittsburgh, Pittsburgh, U.S.A

[email protected]

Abstract

We obtain certain sharp 𝐿𝑝 bounds for the generalized parametric Marcinkiewicz integrals 𝑀Ω,ℎ,ρ(λ)

. singular kernels

are allowed to be rough on the unit sphere as well as in the radial direction. By the virtue of these estimates along with an

extrapolation argument we obtain some new and improved results on generalized parametric Marcinkiewicz integrals. Our

conditions on Ω and h are known to be the weakest conditions in their respective classes. One of our main results answers a

question posed by Fan and Wu.

Keywords: Marcinkiewicz integrals, Triebel-Lizorkin spaces, rough kernels, Orlicz spaces, Block spaces, extrapolation,

𝒓𝟐𝑳𝒑 boundedness.

References

1. H. Al-Qassem and Y. Pan, On rough maximal operators and Marcinkiewicz integrals along submanifolds, Studia Math. 190, No.

1 (2009), 73--98.

2. D. Fan, H. Wu, On the generalized Marcinkiewicz integral operators with rough kernels. Canad. Math. Bull., 54(1) (2011), 100-

-112.

3. S. Sato, Estimates for singular integrals and extrapolation, Studia Math. 192 (2009), 219--233.

4. E. M. Stein, On the functions of Littlewood-Paley, Lusin and Marcinkiewicz, Trans. Amer. Math. Soc. 88 (1958), 430--466.



mailto:%[email protected]



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90

On the evaluation of the difficulties that 12th grade students face at factorization process in the

questions

Hülya Burhanzade Department of Mathematics, Yildiz Technical University,

[email protected]

Abstract

The purpose of this study is to determinate the information deficiencies in factorization processes and what type of

mistakes make by the students. The study was qualitative in nature. Samples of the research are 25 students from 3 different

schools in 12th grade, in the 2016-2017 education years in Istanbul. To gather the information of the research 7 questions

given to the students that will be answered in classical methods. Results analyzed by the researcher. Findings of the research

will be explained in presentation with details. The problems faced by the students determinated as process error, lack of

information, misconceptions. It's seen that as the students learn by heart without knowing what-why they learn they have

difficulty with the questions based on the former information. Findings of the research will be explained in presentation with

details.

Keywords: Mathematics education, secondary school mathematics, Learning difficulties, factorization.

References:

1. Baki A. & Kutluca T. (2009b). Dokuzuncu sınıf matematik öğretim programında zorluk çekilen konuların belirlenmesi. e-Journal

of New World Sciences Academy, 4(2), 604-619.

2. Kutluca T. & Baki A. (2009a), 10. sınıf matematik dersinde zorlanılan konular hakkında öğrencilerin, öğretmen adaylarının ve

öğretmenlerin görüşlerinin incelenmesi. Kastamonu Eğitim Dergisi, 17(2), 609–624.

3. Tatar E.,Okur M.,Tuna A.(2008). Ortaöğretim matematiğinde öğrenme güçlüklerinin saptanmasına yönelik bir çalışma,

Kastamonu Eğitim Dergisi , 16(2), 507-516.

4. Tatar E., Dikici R. (2008). Matematik eğitiminde öğrenme güçlükleri, Mustafa Kemal Journal of University Social Sciences

Institute, 5 (9).

5. Yenilmez K.,Avcu T.(2009).Altinci sinif öğrencilerinin cebir öğrenme alanindaki başarı Düzeyleri, Ahi Evran Üniversitesi Eğitim

Fakültesi Dergisi, 10(2), 37-45.




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91

On the Solutions of a New Semi-Analytical Iterative Method for Solving Nonlinear PDEs

Zehra Pinar1 and Hüseyin Kocak2

1Department of Mathematics, Namık Kemal University,

[email protected] 2Quantitative Methods Division, Pamukkale University

[email protected]

Abstract

It is well-known that nonlinear partial differential equations (PDEs) are the most important tools describing processes

in engineering and science. Since it is not easy to obtain the analytical or exact solutions, researchers use the semi-analytical

methods for such equations. There are many approximate methods to solve nonlinear PDEs. In this work, we examine a new

semi-analytical method, which is called TAM, for initial value problems and its effectiveness is also discussed.

Keywords: Klein-Gordon equation, Burger’s equation, semi-analytical solutions.

References

1. H. Temimi, A. R. Ansari, A semi – analytical iterative technique for solving nonlinear problems, Comput Math Appl 61 (2011)

203–210.

2. H. Temimi, A. R. Ansari, A new iterative technique for solving nonlinear second order multi – point boundary value problems,

Appl Math Comput 218 (2011) 1457–1466.

3. H. Temimi, A. R. Ansari, A computational iterative method for solving nonlinear ordinary differential equations, LMS J

Comput Math 18 (2015) 730–753.

4. M. A. Al-jawary, A semi-analytical iterative method for solving nonlinear thin film flow problems, Chaos Solitons Fractals 99

(2017) 52–56.





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92

Some Problems About Algebraic Properties of Aristotelian Logic

Ibrahim Senturk1 and Tahsin Oner2

1Department of Mathematics, Ege UniversityUniversity,

[email protected] 2 Department of Mathematics, Ege UniversityUniversity

[email protected]

Abstract

Aristotelian logic, known as categorical logic, is the logic of classes, or equivalently, it is the logic of categories. In

this work, we correspond this logical system to different algebraic structures via some transformations and we examine each

structure in itself. We show that the conditional or unconditional validity of syllogism protects for each algebraic structure.

Afterwards, we bring up some problems in this algebraic structures, and following this, we give answers of these questions

for each one.

Keywords: Aristotelian logic, Syllogism, Validity, Algebraic structures.

References

1. Aristotle, “Prior Analytics” translation and commentary by Robin Smith, Hackett Publishing, (1989).

2. J. Łukasiewicz, “Aristotle's Syllogistic From the Standpoint of Modern Formal Logic”, Oxford University Press (1957).

3. Senturk I., Oner T., An Algebraic Analysis of Categorical Syllogisms by Using Carroll Diagrams, Filomat, (Accepted).

4. Turunen E., An algebraic study of Petersons Intermediate Syllogisms, Soft Computing, vol.18, no.12, (2014), 2431--2444.

5. Cignoli R. L., d'Ottaviano I. M., Mundici D., Algebraic foundations of many-valued reasoning (Vol. 7). Springer Science &

Business Media, (2013).





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93

Covariant Differential Calculi on ℱ(ℝ𝒒(1|1))

Salih Celik1 and Ilknur Temli2


[email protected] 2 Department of Mathematics, Yildiz Technical University.

[email protected]

Abstract

One of the basic structure giving direction to the noncommutative supergeometry [1] is ℤ2-graded differential

calculus on an associative superalgebra [2]. There exist covariant differential calculi [3] on coordinate algebras of ℤ2-graded

quantum spaces (or, quantum superspaces). Differential calculus can be applied to a super-Hopf algebra considered as a left

(right) quantum superspace with respect to the coproduct [4]. The function algebra on the extended quantum superplane is a

super-Hopf algebra [5], denoted by ℱ(ℝ𝑞(1|1)). To obtain bicovariant differential calculi on the super-Hopf algebra

ℱ(ℝ𝑞(1|1)) we also use the left and the right covariance.

Keywords: Quantum superplane; super-Hopf algebra; differential calculus; quantum supergroup.

References

1. F.A. Berezin, F.A (ed. A.A. Kirillov), Introduction to Superanalysis, D. Reidel Publ. Company, 1987.

2. Manin, Y. I., Multiparametric quantum deformation of the general linear supergroups, Commun. Math. Phys. 123, 163–175

(1989).

3. Wess, J. and Zumino, B., Covariant differential calculus on the quantum hyperplane, Nucl. Phys B 18, 302-312 (1990).

4. Woronowicz, S. L., Differential calculus on compact matrix psedogroups (quantum groups), Comn. Math. Phys. 122, 125-170

(1989).

5. Celik, S., Differential geometry of 𝑞-superplane, J. Phys A: Math. Gen. 31, 9695-9701 (1998).





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94

Lp-Approximation via Abel Convergence

İlknur Özgüç

Ankara University

[email protected]

Abstract

In this talk, using the concept of the Abel convergence method, we give a Korovkin type approximation theorem

for a sequence of positive linear operators acting from Lp [a, b] into itself. We also study some quantitative estimates for Lp

approximation via Abel convergence.

Keywords: Abel convergence, sequence of positive linear operators, Korovkin type theorem, modulus of smoothness, rate of

Abel convergence.

References

1. H. Berens, R.A. DeVore, Quantitative Korovkin theorems for positive linear operators on Lp-spaces, Trans. Amer. Math. Soc.

245 (1978) 349-361.

2. J.J. Swetits, B. Wood, Quantitative estimates for Lp approximation with positive linear operators, J. Approx. Theory 38 (1983)

81-89.

3. İ. Sakaoğlu, C. Orhan, Strong summation process in Lp-spaces, Nonlinear Analysis 86 (2013) 89-94.

4. M. Unver, Abel transforms of positive linear operators, AIP Conference Proceedings 1558 (2013) 1148-1151.




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95

Some classes of Almost α-Para-Kenmotsu Manifolds

İrem Küpeli Erken

Department of Mathematics, Bursa Technical University,

[email protected]

Abstract

The object of this study is considering projectively flat, conformally flat and concircularly flat almost α –para-

Kenmotsu manifolds (with the η- parallel tensor field φh) and get some new properties. We conclude this study by giving

an example of almost α –para-Kenmotsu manifold which verifies our results.

Keywords: Almost α-para-Kenmotsu manifold, projectively flat, conformally flat, concircularly flat.

References

1. Boeckx E. and Cho J. T., η-parallel contact metric spaces, Differential Geom. Appl. 22 (2005) 275-285.

2. Küpeli Erken I., Dacko P. and Murathan C., Almost α-paracosymplectic manifolds, J. Geom. Phys., 88 (2015) 30-51.

3. Öztürk H., Aktan N. and Murathan C., Almost α-cosymplectic (κ,μ,ν)-spaces, Submitted. Available in Arxiv:1007.0527 [math.

DG].

4. Zamkovoy S., Canonical connections on paracontact manifolds, Ann. Glob. Anal. Geom. 36 (2009) 37-60.




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96

Consumer and Producer Surplus of the Linear Demand and Supply Functions by Using

Polygonal Fuzzy Numbers

İsmail Özcan and Salih Aytar

Department of Mathematics, Süleyman Demirel University,

[email protected]

[email protected]

Abstract

In the present paper, using the polygonal fuzzy numbers the linear demand and supply functions are fuzzified. Then

consumer surplus of the demand function and the producer surplus of the supply function are estimated. Finally, we prove

with a numerical example that our polygonal fuzzy model gives more optimum results than the triangular fuzzy model.

Keywords: Polygonal Fuzzy Number, Consumer and Producer Surplus, Signed Distance.

References

1. Báez-Sánchez A.D., Moretti A.C., Rojas-Medar M.A., On polygonal fuzzy sets and numbers, Fuzzy Sets and Systems 209 (2012)

54-65.

2. Kaufmann, A., Gupta, M.M., Introduction to Fuzzy Arithmetic: Theory and Application, Van Nostrand Reinhold, New York,

1992.

3. Yao J.-S., Wu K., Ranking fuzzy numbers based on decomposition principle and signed distance, Fuzzy Sets and Systems 116

(2000) 275-288.

4. Yao J.-S., Wu K., Consumer surplus and producer surplus for fuzzy demand and fuzzy supply, Fuzzy Sets and Systems 103

(1999) 421-426.





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97

The Structure of All Generating Sets of Certain Monotone Partial Transformation

Subsemigroups

Leyla Bugay1

1Department of Mathematics, Çukurova University,

[email protected]

Abstract

Let 𝑷𝒏 be the monoid of all partial transformations on a finite chain 𝑿𝒏 = 𝟏, … , 𝒏 under its natural order. For any 𝜶 ∈ 𝑷𝒏, if (∀ 𝒙, 𝒚 ∈ 𝑿𝒏) 𝒙 ≤ 𝒚 ⇒ 𝒙𝜶 ≤ 𝒚𝜶 (𝒙 ≤ 𝒚 ⇒ 𝒙𝜶 ≥ 𝒚𝜶) then 𝜶 is called an isotone (an antitone) partial transformation, and if 𝜶 is isotone or antitone then 𝜶 is called a monotone partial transformation. Moreover, let 𝑷𝑶𝑫𝒏 be the submonoid of 𝑷𝒏 consists of all monotone partial transformations, and let

𝑷𝑶𝑫𝒏,𝒓 = 𝜶 ∈ 𝑷𝑶𝑫𝒏: |𝐢𝐦(𝜶)| ≤ 𝒓 for 𝟎 ≤ 𝒓 ≤ 𝒏 − 𝟏. In this paper, to specify the structure of all generating sets and provide convenience for presentation theory, we develop a useful method, by using graphs, to decide whether an arbitrary non-empty subset 𝑿 of 𝑷𝑶𝑫𝒏,𝒓 is a (minimal) generating set of 𝑷𝑶𝑫𝒏,𝒓, or not. Also, we re-obtain the conclusion

𝐫𝐚𝐧𝐤(𝑷𝑶𝑫𝒏,𝒓) = ∑ (𝒏𝒌

) ( 𝒌 − 𝟏𝒓 − 𝟏

)

𝒏

𝒌=𝒓

for 𝟏 ≤ 𝒓 ≤ 𝒏 − 𝟏. Keywords: Isotone/Antitone/Monotone partial transformation, Generating set, Rank.

References

1. P. Zhao, V. H. Fernandes, The Ranks of Ideals in Various Transformation Monoids, Comm. Algebra 43 (2015) 674-692.

2. I. Dimitrova, J. Koppitz, On the Maximal Subsemigroups of Some Transformation Semigroups, Asian-European Journal of

Mathematics 1-2 (2008) 189-202.

3. F. Al-Kharousi, R. Kehinde, A. Umar, On the Semigroup of Partial Isometries of a Finite Chain, Comm. Algebra 44-2 (2016)

639-647.

4. V. H. Fernandes, G.M.S. Gomes, M.M. Jesus, Congruences on monoids of order-preserving or order-reversing transformations

on a finite chain, Glasgow Math. J. 47 (2005) 413-424.

5. J. M. Howie, Fundamentals of Semigroup Theory,Oxford University Press, New York (1995).




Istanbul / TURKEY


98

On the Boundedness of Fractional Maximal Operator with Variable Kernel on Herz-Morrey

spaces

Lütfi Akın1 , Yusuf Zeren2 and Faruk Düşünceli3

Mardin Artuklu University1,3

[email protected], [email protected] Yıdız Technical University2

[email protected]

Abstract

In last years, many researchers have been interested in the theory of the variable exponent function space and its

applications. Compactness of Hardy spaces with weighted and variable exponent in Lebesgue spaces [1]. Our aim in this

paper, we study on boundedness of the fractional maximal operator with variable kernel on Herz-Morrey spaces.

Theorem. Let 0 < 𝜌 < 𝑚, 0 < 𝜇 ≤ 1, 𝛼 < 𝛽 < 𝑚𝜆1 + 𝜇, 0 < 𝑞1 ≤ 𝑞2 < ∞. Suppose that Θ ∈ 𝐿∞(𝑅𝑚) × 𝐿𝑛(𝑆𝑚−1)(𝑛 >𝑝2

+) , and the integral modulus of continuity 𝑤𝑛(𝜆) satisfies

∫𝑤𝑛(𝜆)

𝜆1+𝜇

1

0

𝑑𝜇 < ∞.

And let 𝑝1(. ) ∈ Π(𝑅𝑚) satisfy 0 < 𝑝 ≤𝑚

(𝑝1)+ and define the variable exponent 𝑝2(𝑥) by

1

𝑝1(𝑥) −

1

𝑝2(𝑥)=

𝜌

𝑚 , then we have

for all ‖𝑓‖𝑀𝐻𝑞1,𝑝1(.)

𝛽,𝛼(𝑅𝑚)

‖𝑀Θ,𝜌𝑓‖𝑀𝐻𝑞2,𝑝2(.)

𝛽,𝛼(𝑅𝑚)

≤ 𝐶‖𝑓‖𝑀𝐻𝑞1,𝑝1(.)

𝛽,𝛼(𝑅𝑚)

Keywords: Variable exponent, Herz space, Operator theory

References 1. Mamedov I. F., Zeren Y., Akin L., (2017), Compacti_cation of Weighted Hardy Operator in Variable Exponent Lebesgue

Spaces. Asian Journal Mathematics and Computer Research,17(1):38-47.

2. Izuki, M. (2010),Fractional Integrals on Herz-Morrey Spaces with Variable Exponent. Hiroshima Mathematical Journal, 40,

343-355.






Istanbul / TURKEY


99

Approximation on Variable Exponent Spaces by Fractional Maximal Operators

Lütfi Akın Mardin Artuklu University

[email protected]

Abstract

Approximation of functions by positive linear operators is a classical topic in approximation theory starting with the

Bernstein operators [1], for approximating functions in the space

C[0; 1] of continuous functions on [0,1], defined by for with the Bernstein basis

. The Bernstein operators have been extended in various forms for the purpose of approximating

discontinuous functions, by replacing the point evaluation functionals by some integrals.

Theorem. Suppose the exponent function satisfies and the log-Hölder continuity

condition. If the kernel satisfies conditions ∫ Θ(𝑥, 𝑡)𝑑𝑡 ≡ 1𝑅𝑠 and |Θ(𝑥, 𝑡)| ≤

𝐶𝑚

(1+|𝑥−𝑡|)𝑚 ,∀𝑥, 𝑡 ∈ 𝑅𝑠 with

, then the operators on are uniformly bounded by a positive constant as , .

Moreover, we have , .

Here and are constants depending on .

Keywords: Variable exponent space, log-Hölder continuity, Maximal operators, Bernstein type operators, K-functional

References 1. S. N. Bernstein, Demonstration du teoreme de Weirerstrass, fondee sur le calcul des

probabilit_es, Commun. Soc. Math. Kharkow 13 (1912-1913), 1-2

2. Bing-Zheng Li, Bo-Lu He and Ding-Xuan Zhou, (2017), Approximation on Variable Exponent Spaces by Linear Integral

Operators Journal of Approximation Theory DOI: 10.1016/j.jat.2017.07.009




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100

Numerical Investigation of Free Convection Stability in Cylindrical Annulus with Heater inner

Cylinder

Fateh Mebarek Oudina1

1Department of Physics, Faculty of Sciences, University 20 août 1955-Skikda,

[email protected]

[email protected]

Abstract

In this work, natural convection stability of molten metal in inclined cylindrical annulus with heater inner cylinder is

numerically investigated. The top and bottom walls are adiabatic, while the outer cylinder is maintained at uniform

temperature and the inner cylinder in heated. The finite volume method is used to solve numerically the governing equations

with the boundary conditions. Solution is obtained by SIMPLER and TDMA algorithms. The numerical results for various

inclination angle at onset oscillatory state are discussed in terms of streamlines, isotherms in the annulus. The inclination of

annulus has a significant effect on the stabilization of the convective flow, and shows that the best stabilization of oscillatory

natural convection is obtained for vertical annulus γ = 0°.

Keywords: Numerical modeling, Inclined cylindrical annulus, Heater inner cylinder, Hydrodynamic Stability, Finite volume

method, SIMPLER algorithm.

References

1. Mebarek-Oudina, F. (2017) Numerical Modeling of the Hydrodynamic Stability in Vertical annulus with Heat Source of different Lengths, Engineering Science and Technology, 20 (4), 1324-1333.

2. Mebarek-Oudina F., Bessaïh R., (2014) Numerical modeling of MHD stability in a cylindrical configuration, Journal of Franklin

Institute. 351( 2) 667–681.

3. Mebarek-Oudina, F., Bessaïh, R. (2007) Magnetohydrodynamic Stability of Natural Convection Flows in Czochralski Crystal

Growth, World Journal of Engineering, 4 (4) 15–22..

4. Mebarek-Oudina, F. and Bessaïh, R. (2007) Stabilité Magnétohydrodynamique des Écoulements de Convection Naturelle dans

une Configuration Cylindrique de type Czochralski. Société Française de Thermique 1, 451-457.

5. Mebarek-Oudina, F., Bessaïh, R. (2016) Oscillatory Magnetohydrodynamic Natural Convection of Liquid Metal between Vertical

Coaxial Cylinders, Journal of Applied Fluid Mechanics 9 (6), 1655-1665.





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101

Borel's fixed point theorem for finite dimensional compact abelian groups

Mehmet Onat Department of Mathematics, Çukurova University,

[email protected]

Abstract

In this study, we extend Borel's fixed point theorem for compact Lie group actions in equivariant cohomology to actions of finite dimensional compact abelian groups which are extensions of a p-group by finite dimensional compact connected abelian groups.

Keywords: Equivariant cohomology, Compact groups, Fixed point.

References

1. A. Borel, Seminar on Transformation Groups, Princeton, NJ, USA: Princeton University Press, (1960).

2. K. H. Hofmann and P.S. Mostert, Cohomology Theories for Compact Abelian Groups, Springer-Verlag, Berlin Heidelberg New-

York, (1973).

3. K. H. Hofmann and S.A. Morris, The Structure of Compact Groups, 3rd ed. Berlin: de Gruyter, (2013).

4. L. S. Pontryagin, Topological Groups, 3rd ed. Gordon and Breach Science Publishers, New York, (1986).

5. S. Jackowski, A fixed-point theorem for p-group actions, Proc Amer Math Soc, 102 (1988), no. 1, 205-208.

6. T. T. Dieck, Existence of fixed points, Proc Second Conf on Compact Transformation Groups, Part I, Lecture Notes in Math., vol

298, Springer-Verlag, Berlin and New York, (1971) pp. 163-169.

7. W. Y. Hsiang, Cohomology Theory of Transformation Groups, Springer-Verlag, Berlin and New York, (1975).




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102

Examining of the Effect of REACT Strategy on Conceptual Knowledge of Secondary School 7th

Grade Students

Mehmet Ercoban1 and Cuneyt Yazici2 1MEB, Mathematics Teacher,

[email protected] 2Faculty of Education, Kocaeli University

[email protected]

Abstract

Mathematics has played an important role in human life from past to today. Therefore, mathematics education is very important for people's mathematics to understand better. Algebra, is a field that is intertwined with everyday life like other learning areas of mathematics. The fact that the field of algebra learning is integrated with everyday life allows the algebra to be taught contextual. In this case, the REACT strategy, which is an approach for contextual learning method, emerges. In this study, pre-test and post-test control groups pattern were used for quasi-experimental research. In the experiment group, the course material was prepared according to the REACT strategy while the control group was learned lesson with the traditional method. The sample group consisted of 44, 7th grade students in total, including 24 students in the experimental group and 20 students in the control group. The conceptual knowledge test was developed as a data collection tool. The conceptual knowledge test consists of closed-ended questions. The validity and reliability study of the developed test was conducted in the 8th grade. As a result of the corrections made, the conceptual knowledge test was applied to the control and experiment group in the form of pre-test and post-test. It is aimed to determine the effect of the REACT strategy, which is the approach of contextual learning method, on the conceptual knowledge of students on algebra learning area with conceptual knowledge test. There was no significant difference in the pre-test results between the students in the experimental group and the students

in the control group. In the post-test results, it was seen that there was a significant difference in favor of the experimental

group. It is suggested to investigate that the lesson plans are prepared and impact in various ways on different topics and

lessons in relation to the REACT strategy.

Keywords: Mathematics Education, Algebra, Contextual Learning, REACT Strategy, Conceptual Knowledge Test.

References

1. Crawford, M. L. (2001). Teaching contextually: research, rationale, and techniques for improving student motivation and

achievement in mathematics and science, CCI Publishing, Waco, Texas.

2. Kirman Bilgin, A., 2015. “Maddenin Yapısı ve Özellikleri” Ünitesi Kapsamında REACT Stratejisine Yönelik Tasarlanan Öğretim

Materyallerinin Etkililiğinin Değerlendirilmesi. Doktora tezi, Karadeniz Teknik Üniversitesi, Trabzon.

3. Parnell, D., 1995. Why Do I Have to Learn This? CORD Communications, Waco, TX.





Istanbul / TURKEY


103

Maximum Likelihood Type Estimations of Parameters in Distributions

Mehmet Niyazi Çankaya1

1Department of Statistics, Uşak University

[email protected]

Abstract

The maximum likelihood estimation (MLE), distorted MLE and maximum q-log-likelihood estimation (MqLE) are used

to estimate robustly the parameters of distributions, such as Weibull, inverse Weibull, Burr III, etc. The definition of Fisher

information is similar to the likelihood type estimation method. Thus, a new form of Fisher information (FI) for distorted

MLE and MqLE is derived. The MSE values obtained from simulation for MLE, distorted MLE and MqLE are compared

with the inverse of FI evaluated with the true values of parameters in distributions. The MSE results of simulation and the

inverse of new FI with the true values of parameters are near to each other, which shows that new FI and the likelihood type

estimation methods accommodate each other well.

Keywords: Generalized MLE, Fisher information, Simulation, Estimation.

References

1. D. Ferrari and Y. Yang, Maximum Lq-likelihood estimation, The Annals of Statistics, 38(2) (2010) 753-783.

2. V. Kumar, Characterization results based on dynamic Tsallis cumulative residual entropy, Communications in Statistics - Theory

and Methods, 46(17) (2017) 8343-8354.

3. J. Bercher, On generalized Cramer-Rao inequalities, generalized Fisher information and characterizations of generalized q-

Gaussian distributions, Journal of Physics A: Mathematical and Theoretical 45(25) (2012) 255-303.




Istanbul / TURKEY


104

M-Estimation of Parameters for Distributed Lag Models in Regression

Mehmet Niyazi Çankaya1

1Department of Statistics, Uşak University

[email protected]

Abstract

M-estimation is used to estimate the parameters robustly if the data include outlier(s). The lag models are proposed to

construct a regression model including the dependent variable y and the explanatory variables x. The regression model has

explanatory variables that are responsible to explain the affects of previous times of event, which is called to be a distributed

lag model. If the observed value for the variable y has (an) outlier(s), the hypothetical model which is used to fit the data set

is not capable for fitting data efficiently. The maximum likelihood estimators (MLEs) of parameters in some hypothetical

models are affected by outlier(s). In this study, M-estimation method is used for the distributed lag models in regression. The

synthetic data set with outliers is generated as an arbitrary manner. For these different designs of data set, the M-estimators

of parameters of the distributed lag models in regression are tested via performing a simulation. Simulation results show that

the MLEs of regression coefficients (location) of normal distribution have high mean squared errors (MSEs) than MSEs of

M-estimators. The computational MSE values of M-estimators of the restricted form of distributed lag model are smaller MSE

than that of non-restricted form as well. It is concluded that M-estimators of the parameters of distributed lag models in

regression are efficient than MLEs of parameters in the the hypothetical model if the data include outlier(s).

Keywords: M-estimation, Regression, Distributed lag model.

References

1. P.J. Huber, Robust estimation of a location parameter. The Annals of Mathematical Statistics. 35(1) (1964) 73-101.

2. G.S. Maddala, Ridge Estimators for distributed lag models, Working Paper No.69 (1974).

3. S.J. Haberman, Concavity and estimation. The Annals of Statistics. JSTOR, 17(4), (1989) 1631-1661.

4. R.A. Maronna, R.D. Martin and V. J. Yohai, Robust statistics: theory and methods, Wiley Series in Probability and Statistics

(2006).




Istanbul / TURKEY


105

Semi-Analytical Solution for the Hiemenz Flow of a Micropolar Fluid

Mehmet Şirin Demir Department of Mechanical Engineering, Istanbul University,

[email protected]

Abstract

Many modern engineering and industrial fluids exhibit certain microscopic effects arising from the local structures and

microdeformation of fluid elements. In these situations, the continuum assumption is not valid and the classical Navier–Stokes

theory is not adequate for the description of such fluids. Eringen [1] introduced the theory of micropolar fluids in which the

local effects arising from the local structure and intrinsic motions of the fluid elements are taken into account.

The purpose of the present study is to investigate the two-dimensional stagnation-point flow of an incompressible

micropolar fluid. The governing partial differential equations are reduced to a set of ordinary differential equations by using

the appropriate similarity transformations. The transformed system is nonlinear and has no analytical solution. Therefore a

semi-analytical method namely, the homotopy analysis method (HAM) is employed to solve these nonlinear ordinary

differential equations.

Mathematica package BVPh 2.0 based on the HAM is successfully applied to the problem under consideration. The

effects of the flow parameters on the velocity components, microrotation components, and wall shear stress are discussed

through the graphs and tables. In order to have a check on the accuracy of the results, they are compared with the results

obtained by the MATLAB routine BVP4c. The comparison shows that the BVPh 2.0 can easily achieve good results in

predicting the solutions to such problems.

Keywords: Convection, Homotopy analysis method (HAM), Magnetohydrodynamics (MHD), Micropolar fluid, Stagnation

point flow.

References

1. Eringen, A.C. (1964). Simple microfluids. International Journal of Engineering Science, 2 (2), 205-217.




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106

Exact Solution for the Flow of a Microstretch Fluid between Two Concentric Cylinders

Mehmet Şirin Demir Department of Mechanical Engineering, Istanbul University,

[email protected]

Abstract

Couette flow of a microstretch fluid is considered. The microstretch fluids are a subclass of the microfluid theory

introduced by Eringen [1]. According to the microstretch continuum theory, the fluid particles are considered to stretch

(expand or contract) in addition to microrotation. Thus, the microstretch fluid particles possess four extra degrees of freedom

over the classical fluid dynamics. The field equations of the microstretch fluids are solved and exact analytical solutions are

obtained for the velocity, microrotation, and microstretch fields for the case of a flow between two rotating concentric

cylinders. It has been shown that the previous solutions corresponding to pure Newtonian fluid and micropolar fluid appear

as the special cases of the present analysis. Results are represented graphically for the velocity, microrotation, and microstretch

for various values of the pertinent parameters.

Keywords: Couette flow, Exact analytical solution, Microstretch fluid.

References

1. Eringen, A.C. (1964). Simple microfluids. International Journal of Engineering Science, 2 (2), 205-217.




Istanbul / TURKEY


107

Septic B-spline Galerkin Method for the Advection Diffusion Equation

Melda Turhan1, Evren Topçu1 and Dursun Irk1



[email protected]

Abstract

The advection-diffusion equation (sometimes called the convection-diffusion equation) is the basis of many physical and

chemical phenomena, and it is a one dimensional parabolic partial differential equation which illustrates advection and

diffusion of quantities such as mass, energy, heat, vorticity etc. Various numerical techniques have been developed and

compared for solving the one dimensional advection-diffusion equation with constant coefficient so far [1], [2], [3], [4]. In

this study, septic B-spline Galerkin finite element method, based on second and fourth order single step methods for time

integration is proposed for numerical solution of the advection diffusion equation.Two numerical examples are studied to

illustrate the accuracy and the efficiency of the method. The numerical results of this study demonstrate that the proposed

fourth order single step method is a remarkably successful numerical technique for solving the advection-diffusion equation.

Keywords: Advection diffusion equation, Galerkin finite element method, Septic B-spline.

References

1. M. Sarı, G. Güraslan and A. Zeytinoglu, (2010) High-Order finite difference schemes for solving the advection-diffusion equation,

Math. Comput. Appl. 15(3), 449-460.

2. A. Mohebbi and M. Dehghan, (2010) High-order compact solution of the one-dimensional heat and advection- diffusion

equations, Appl. Math. Model. 34: 3071-3084.

3. D. Irk, İ. Dağ and M. Tombul, (2015) Extended Cubic B-Spline Solution of the Advection-Diffusion Equation, KSCE Journal of

Civil Engineering 19(4), 929-934.

4. A. Korkmaz and İ. Dağ, (2016), Quartic and quintic B-spline methods for advection diffusion equation. Appl. Math. Comput.,

274, 208-219.






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108

A High Accuracy Numerical Method for Solution of the RLW Equation

Melis Zorsahin Gorgulu1 and Dursun Irk1

1Department of Mathematics-Computer, Eskisehir Osmangazi University,


Abstract

In this study, a comparison is made between the numerical solutions of the regularized long wave (RLW) equation. The

RLW equation describing many physical phenomena was first introduced by Peregrine [1]. Many numerical methods have

been proposed in the literature for this equation [2-5]. The collocation method which is one of the finite elements methods

frequently applied by researchers for the numerical solutions of the partial differential equations has been used in this study.

While the collocation method based on extended cubic B-spline functions is used for space discretization, Crank-Nicolson

and Simpson's methods having different accuracy orders for time discretization are applied to the RLW equation. The obtained

results are compared to see the accuracy of the proposed methods.

Keywords: Collocation method, Crank-Nicolson method, Simpson’s method, extended cubic B-spline function, regularized

long wave equation.

References

1. D. H. Peregrine, Calculations of the development of an undular bore, J. Fluid Mech. 25 (1966) 321–330

2. K. Zheng and J. Hu, High-order conservative Crank-Nicolson scheme for regularized long wave equation, Adv. Differ. Equ. 2013

(2013) 287

3. D. Irk, Solitary wave solutions for the regularized long-wave equation, Phys. Wave Phenom. 20 (2012) 174–183

4. Ö. Oruç, F. Bulut and A. Esen, Numerical Solutions of Regularized Long Wave Equation by Haar Wavelet Method, Med. J. Math.

13 (2016) 3235–3253

5. D. Irk and P. Keskin, Quadratic Trigonometric B-spline Galerkin Methods for the Regularized Long Wave Equation, J. Appl.

Anal. Comput. 7 (2017) 617–631





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109

Norms and Lower Bounds for Some Matrix Operators

Merve İlkhan1 and Emrah Evren Kara2

1Department of Mathematics, Düzce University,

[email protected] 2 Department of Mathematics, Düzce University

[email protected]

Abstract

It is useful to compute the lower bounds for a matrix operator since it has so many applications in functional analysis. In

this presentation, we compute the norm and the lower bounds for certain matrix operators after introducing a new weighted

difference sequence space.

Keywords: Matrix operators, lower bounds, quasi-summable matrices, weighted sequence space.

References

1. R. Lyons, A lower bound for the Cesaro operator, Proc. Amer. Math. Soc. 86 (1982), 694.

2. G. Bennett, Lower bounds for matrices, Linear Algebra Appl. 82 (1986), 81-98.

3. G. Talebi and M. A. Dehghan, Approximation of upper bound for matrix operators on the Fibonacci weighted sequence spaces,

Linear Multilinear Algebra 64(2) (2016), 196-207.

4. M. A. Dehghan and G. Talebi, Lower bound for matrices on the Fibonacci sequence spaces and its applications in frame theory,

Results Math. 72 (2017), 1087-1107.

5. D. Foroutannia and H. Roopaei, The norms and the lower bounds for matrix operators on weighted difference sequence spaces,

U.P.B. Sci. Bull. Series A 79(2) (2019), 151-160.





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110

Applications of measure of noncompactness to the infinite system of differential equations in

some Banach spaces

Merve İlkhan1 Necip Şimşek2 and Emrah Evren Kara3

1Department of Mathematics, Düzce University,

[email protected] 2 Department of Mathematics, İstancul Commerce University

[email protected]

3 Department of Mathematics, Düzce University [email protected]

Abstract

In this presentation, we apply the technique of measures of noncompactness to the theory of infinite system of differential

equations in some Banach spaces derived by generalized Fibonacci matrix. Our aim is to present some existence results for

infinite system of differential equations formulated with the help of measures of noncompactness.

Keywords: Differential equations, Fibonacci numbers, Banach spaces, Hausdorff measure of noncompactness.

References

1. J. Banas, K. Goebel, Measure of noncompactness in Banach spaces, in: Lecture Notes in Pure and Applied Mathematics, Vol. 60,

Marcel Dekker, New York and Basel, 1980.

2. M. Mursaleen, V. Karakaya, H. Polat, N. Şimşek, Measure of noncompactness of matrix operators on some difference sequence

spaces of weighted means, Comput. Math. Appl. 62 (2011) 814-820.

3. M. Mursaleen, Application of measure of noncompactness to infinite systems of differential equations, Canad. Math. Bull. 56(2)

(2013) 388-394.

4. E.E. Kara, M. İlkhan, Some properties of generalized Fibonacci sequence spaces, Linear and

Multilinear Algebra, 65(11) (2016) 2208-2223.

5. J. Banas, M. Jleli, M. Mursaleen, B. Samet, C. Vetro, Advances in Nonlinear Analysis via

the Concept of Measure of Noncompactness, Springer Singapore, 2017.






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111

A novel iterative algorithm on the time-fractional Fisher equation with small delay

Mine Aylin Bayrak1 , Ali Demir2 and Metin Bayrak2

1,2,3Department of Mathematics, Kocaeli University,

[email protected]

[email protected] , [email protected]

Abstract

This paper presents the residual power series method (RPSM) for solving a kind of fractional delay differential equations

which is the time-fractional Fisher equation with small delay. The fractional derivative is described in the Caputo sense. The

time fractional Fisher equation is expanded in powers of 𝜺 which represents the small delay. The coefficients of the 𝜺 series

is determined and RPSM is used to solve on each of the nonlinear time-fractional equation. The solution of the nonlinear

equations are obtained in the form of rapidly convergent series whose components are computed by Matlab Software Package.

Solving these nonlinear equations the desired solution is established. The obtained results and graphical consequences show

that the proposed method in this study is very efficient,effective and reliable for the solution of the time-fractional Fisher

equation with small delay.

Keywords: Fractional delay differential equation, Fisher equation, Caputo derivative , Residual power series method.

References

1. I. Podlubny , Fractional Differential equations, Academic Press, San Diego (1999).

2. A. A. Kilbas, H.M. Srivastava and H.M. Trujillo, Theory and Applications of Fractional Differential Equations: North-Holland

Mathematics Studies, vol.24, Elsevier, Amsterdam, (2006).

3. A. El-Ajou, o. Abu-Arqub,Z. Al Zhour, et al., New results on fractional power series: theories and applications, Entropy, (2013).

4. M. Mohamed Al Qurashi, Z. Korpinar, D. Baleanu and M. Inc., A new iterative algorithm on the time-fractional Fisher equation:

Residual power series methos, Advances in Mechanical Engineering, 9(9) (2017) 1-8.






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112

On a Stronger Optimality Condition for Singular Controls in Discrete Systems.

Mardanov M.J., Melikov T.K. Institute of Mathematics and Mechanics of ANAS

[email protected], [email protected] Assume that it is required to minimize the functional

u

txuS min1, (1)

1,...,1,:,),,(,1 10000 tttItxtxttutxftx , (2)

ItRtUtu r , . (3)

Here 𝑅𝑟 is 𝑟-dimensional Euclidian space, nRx is a state vector, rRu is a control vector, t is time

(discrete), 010 ,, xtt are given points, ,,, f are given functions, IttU , are given sets.

The controls, satisfying the constraint are said to be admissible. The admissible control ,, Ittu affording a

minimum to the functional (1) under constraint (2) is said to be optimal, while the relevant solution 1:, tIIttx

of the system (2) an optimal trajectory. We call the pair xu , an optimal process.

In the paper, we introduce the following new notions (called by the authors convex and convex sets):

Definition. The set mEZ is said to be convex ( convex) with respect to Zz 0 if for any point Zz

there exists 1,0 z such that for all ,0 ( either for all ,0 or for all 0, ) the inclusion

to Zzzz 00 is valid. If the set Z is convex ( convex) with respect to each of its point, we call it

convex ( convex).

Using the technique of the paper [1] and the suggested notions, we prove a stronger necessary condition for optimality

of singular controls for the problem (1)-(3).

References 1. Mardanov M.J., Melikov T.K. A method for studying the optimality of controls in systems // Proceedings of the Institute of

Mathematics and Mechanics, National Academy of Sciences of Azerbaijan. vol 40. 2, 2014. p. 5-13.





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113

An Extention Of A Classical Maximum Principle Of An Elliptic System Of Differential

Equations To A More General Form

Mohammad Almahameed

Department of Mathematics

Irbid National University

Irbid, Jordan

[email protected]

Abstract

In this paper we discuss a classical maximum principle for weakly coupled second order homogeneous elliptic

systems. We find a sufficient condition for the classical maximum principle which extend the result of a semidefinite matrix

to a more general form.

Keywords and phrases: maximum principles , elliptic systems.

AMS classification : 35B50, 58J15.

References 1. S. N. Chow and D. R. Dunninger, “A Maximum Principle for nMetaharmonic Function”, Proc. Amer, Math. Soc, 43

(1974), 79-83.

2. M. A. Dow, “Maximum principles for weakly coupled systems of quasilinear parabolic inequalities”, J. Austral. Math. Soc. 19

(1975), 79-83.

3. M. Franciosi, “Maximum Principles for Second Order Elliptic Equations and Applications” , J.Math.Anal.Appl.(2)138(1989),

343-348.

4. G. N. Hille and M. H. Protter, “Maximum Principles for a Class of First Order Elliptical Systems”, J.Diff. Eqs. 24(1977),136-

151.

5. J. L. Massera, “Contributions to Stability Theory”, Ann. Of Math. (2) 64 (1956), 182-206.

6. M. H. protter and H. F. weinberger, “ Maximum Principles in Differential Equations” Springer – verlag, Berlin, 1984.

7. J. Snyders and M. Zakai, “On Nonnegative Solutions of the Equation AD+DA*= C”, SIAM J. Appl. Math. 18 (1970), 704-714.

8. R. Sperb, “Maximum Principles and Their Applications”. Academic Press, New York, 1981.

9. Struwe, M. , Variational Methods. Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, third

edition, Springer- Verlag, Berlin, 2000.



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114

Hardy-Hilbert Inequality and Berezin Number

Mehmet Gürdal1 , Mübariz T. Garayev2 and Mualla Birgül Huban1

1Department of Mathematics, Süleyman Demirel University,

[email protected], [email protected] 2King Saud University

[email protected]

Abstract

We prove some new inequalities for Berezin number of operators.

Keywords: Reproducing kernel, Berezin symbol, Hardy space, Berezin number.

Acknowledgement: This work is supported by TUBA through Young Scientist Award Program (TUBA-GEBIP/2015)

References

1. Aronzajn, N., Theory of reproducing kernels, Trans. Amer. Math. Soc., 68 (1950); 337-404.

2. Dragomir, S.S., A survey of some recent inequalities for the norm and numerical radius of operators in Hilbert spaces,

Banach J. Math. Anal., 1 (2007); 154-175.

3. Garayev, M.T., Gürdal, M., Huban, M.B., Reproducing kernels, Engli. algebras and some applications, Studia Mathematica,

232 (2) (2016), 113-141.

4. Furuta, T., Micic Hot, J., Peµcari´c, J. and Seo, Y., Mond-Peµcari´c method in operator inequalities, Inequalities for bounded

sef-adjoint operators on a Hilbert space, Element, Zagreb, 2005.

5. Halmos, P.R., A Hilbert Space Problem Book, Springer-Verlag, 1982.

6. Karaev, M.T., Reproducing kernels and Berezin symbols techniques in various questions of operator theory, Complex Anal.

Oper. Theory, 7(4) (2013), 983-1018.

7. Kılıç, S., The Berezin symbol and multipliers of functional Hilbert spaces, Proc. Amer. Math. Soc., 123 (1995), 3687-3691.

8. Nikolski, N.K., Operators, Functions and Systems: An Easy Reading, volume I: Hardy, Hankel and Toeplitz, Amer. Math.

Soc., Mathematical Surveys and Monographs volüme 92; 2002.

9. Zhu, K., Operator Theory in Function spaces, New York etc., Marcel-Dekker. Inc., 258 p., 1990.






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115

Degenerate Hardy-Berndt Sums

Muhammet Cihat Dağlı and Mümün Can

Department of Mathematics, Akdeniz University,

[email protected]

[email protected]

Abstract

In this talk, we define degenerate analogues of Hardy-Berndt sums which are explicit extensions of Hardy-Berndt sums. We express these sums in terms of Dedekind sums 𝒔𝒓(𝒉, 𝒌: 𝒙, 𝒚|𝛌) with 𝒙 = 𝒚 = 𝟎 and obtain corresponding reciprocity formulas. Keywords: Dedekind sum, Hardy-Berndt sum, Bernoulli numbers and polynomials.

References

1. Berndt, B. C., Analytic Eisenstein series, theta functions and series relations in the spirit of Ramanujan. J. Reine Angew. Math.

303/304 (1978) 332-365.

2. Carlitz, L., Degenerate Stirling, Bernoulli and Eulerian numbers. Utilitas Math. 15 (1979) 51-88.

3. Dağlı, M. C. and Can, M., A new generalization of Hardy-Berndt sums. Proc. Indian Acad. Sci. (Math. Sci.) 123(2) (2013) 177-

192.

4. Goldberg, L. A., Transformations of theta-functions and analogues of Dedekind sums. Ph.D. thesis, University of Ulinious,

Urbana (1981).

5. Rademacher, H. and Grosswald, E., Dedekind sums. Math. Assoc. of America, Washington, D.C. (1972).





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116

On the Geometry of Tangent Bundle with Berger Type Deformed Sasaki Metric

Murat Altunbas1 and Aydin Gezer2


[email protected] 2Ataturk University

[email protected]

Abstract

In this work, we investigate the paraholomorphy property of an almost anti-paraHermitian structure and characterize

the geodesics on tangent bundle with Berger type deformed Sasaki metric.

Keywords: Berger type deformed Sasaki metric, paracomplex structure, geodesics, tangent bundle.

References

1. Yampolski, A. (2012). On geodesics of tangent bundle with fiberwise deformed Sasaki metric

over Kahlerian manifolds. Journal of Math. Physics, Analysis, Geometry. 8 (2), 177-189.

2. Hou, H. Z. and Sun, L. (2013). Geometry of tangent bundle with Cheeger-Gromoll type metric.

J. Math. Anal. App. 402, 493-504.

3. Salimov, A., Işcan, M. and Etayo, F. (2007). Paraholomorphic B-manifold and its properties. Topology Appl. 154 (4), 925-933.

4. Yano, K. and Ishihara, S. (1973). Tangent and Cotangent Bundles. Marcel Dekker, Inc., New York.

5. Zagane, A. and Djaa, M. (2017). On geodesics of warped Sasaki metric. Mathematical Sci. and

App. E-Notes 5 (1), 85-92.





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117

On HK-Type Discretization of a Heavy Rigid Body

Serpil Uslu1 and Murat Turhan1

Yıldız Technical University, Faculty of Arts and Sciences, 1Department of Mathematics, Davutpaşa Campus, Esenler-Istanbul-Turkey

[email protected] and [email protected]

Abstract

There are three integrable cases of a heavy rigid body which are Euler, Lagrange and Kowalevski tops. The third one

is a highly nontrivial integrable system because one of its integrals of motion is of a complicated form. The continuous

equations for the motion of a rigid body are given by the following system:

Π = Π × Χ + Mgl Γ × Υ

Γ = Γ × Χ

where Χ corresponds to the angular velocity of the body measured relative to the moving frame and Υ indicates the center of

mass of the body. Π corresponds to the angular momentum of the body, related to the angular velocity by the classic formulas

Πi = IiXi , i = 1,2,3. After applying bilinear method and using the gauge invariance and the time reversibility of the equations, we get gauge-

invariant bilinear difference equations. Finally, we derive the explicit discrete Kowalevski system by considering HK bilinear

transformation method and present sufficient number of the discrete conserved quantities for integrability.

Keywords: Discretization, heavy rigid body, bilinear method, gauge invariance.

References

1. Marsden, J.E. and Ratiu, T.S.: Introduction to Mechanics and Symmetry, Texts in Applied Mathematics, Second Edition, second

printing, 2017, Springer-Verlag.

2. Hirota, R., Kimura, K. and Yahagi, H., [2001], How to find the conserved quantities of nonlinear discrete equations,

J.Phys.A:Math.Gen. 34, 10377–10386

3. Kowalevski, S. [1889], Sur le problème de la rotation d’un corps solide autour d’un point fixe, Acta Math. 12, 177–232.





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118

Diophantine Equations Involving Odd Prime Powers

Murat Alan1 and Murat Yoğurtçu2



[email protected]

Abstract

Let a,b,c be relatively prime fixed positive integers greater than 1. With many special cases the exponential Diophantine

equations 𝑎𝑥 + 𝑏𝑦 = 𝑐𝑧 has a great attention in number theory. Another version of Diophantine equations is the exponential-

polynomial Diophantine equations as 𝑎𝑥 + 𝑏𝑦 = 𝑧2. In this study we consider the special cases of exponential-polynomial

Diophantine equations when a (or b) is a certain odd primes.

Keywords: Diophantine equations, integer solutions.

References

1. R. Scott, R. Styer Number of solutions to 𝑎𝑥 + 𝑏𝑦 = 𝑐𝑧, Publ. Math. Debrecen, 88:131-138, 2016.

2. Y. Bugeaud, T.N. Shorey, On the number of solutions of the generalized Ramanujan–Nagell equation. J. Reine Angew. Math.

539, 55–74 (2001).




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119

Partial Geometries pg(12,12,9) and Strongly Regular Graphs arising from Maximal (52,4)-arcs

Mustafa Gezek

Namik Kemal University [email protected]

Abstract

In this talk, a method for finding new maximal (52,4)-arcs is given and the details of partial geometries pg(12,12,9) and

strongly regular graphs associated with the known maximal 52-arcs (including newly discovered ones in [2] are provided.

We conclude that the number of non-isomorphic partial geometries arising from degree 4 maximal arcs is > 43 (a partial

geometry and its dual are considered to be two different partial geometries if they are not isomorphic).

Keywords: Maximal arcs, Resolvable Designs, Strongly Regular Graphs, Partial Geometries, Projective Planes

References

1. Assmus, E. F. Jr., Key, J. D.: Designs and their codes, Cambridge, 1992.

2. Gezek M.: Combinatorial problems related to codes, designs, and finite geometries, PhD Thesis, Michigan Technological

University, 2017.

3. Gezek M., Tonchev V., Wagner T.: Maximal arcs in projective planes of order 16 and related designs, Advances in Geometry

(2018), https://www.degruyter.com/view/j/advg.ahead-of-print/advgeom-2018-0002/advgeom-2018-0002.xml

4. Hamilton N., Stoichev S.D., Tonchev V.D.: Maximal arcs and disjoint maximal arcs in projective planes of order 16., J. Geometry

67 117-126 (2000).

5. Thas J. A.: Construction of maximal arcs and partial geometries, Geom. Dedicata 3 61 - 64 (1974).

6. Thas J. A.: Construction of maximal arcs and dual ovals in translation planes, European J. Combin. 1 189 - 192 (1980).

7. Tonchev V.D.: On resolvable Steiner 2-designs and maximal arcs in projective planes. Designs, Codes, and Cryptography, 84

165-172 (2017).



https://www.degruyter.com/view/j/advg.ahead-of-print/advgeom-2018-0002/advgeom-2018-0002.xml


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120

Strict Stability of Unperturbed Fuzzy Differential Equations

Mustafa Bayram Gücen1 and Coşkun Yakar2


[email protected] 2Department of Mathematics, Gebze Technical University,

[email protected]

Abstract

In this work, we have studied the strict stability of unperturbed fuzzy differential systems. We have compared the strict

stability criteria of ordinary differential equations and the notion of strict stability of unperturbed fuzzy differential systems.

Strict stability is a stability definition that it can yield us a knowledge about the rate of decay of the solutions.

Lyapunov's second method have an advantage for the study of the qualitative behavior of fuzzy differential systems along

with a comparison result. Using of the comparison result allows the prediction of behavior of the solution of a unperturbed

fuzzy differential system. And also, similarly this method is a usefull for investigating the strict stability of unperturbed fuzzy

systems.

Firstly, we have given some definitions and fundamental knowledge. Secondly, we have discussed and compared the

differences between the classical notion of strict stability and the strict stability of unperturbed fuzzy systems. And then, we

have given some results and a comparison theorem. Consequently, we have used Lyapunov second method and we have

proved a comparison result of fuzzy unperturbed systems with scalar differential equations.

Keywords: Fuzzy differential equations, Strict stability, Unperturbed systems, Lyapunov stability.

References

1. C. Yakar,. Strict stability criteria of perturbed systems with respect to unperturbed systems in terms of initial time difference. In

Complex Analysis and Potential Theory, (2007) 239-248.

2. C. Yakar , M. Çiçek and M. B. Gücen, Practical Stability, Boundedness Criteria and Lagrange Stability of Fuzzy Differential

Systems, Journal of Computers and Mathematics with Applications. 64 (2012) 2118-2127.

3. V. Lakshmikantham and S. Leela, Fuzzy differential systems and the new concept of stability, Nonlinear Dynamics and Systems

Theory, 2, (2001) 111-119.





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121

On the Fixed Point System for Determining the Evolution of the Source Term of a Third Order

Nonlinear Partial Differential Equation

Müjdat Kaya

Department of Mechanical Engineering, Başkent University,

[email protected]

Abstract

Inverse problems for partial differential equations are important concepts of mathematics. They are studied to determine

some terms which are not unknown in the case of direct problems.

In this study, we derive a fixed point system to determine the evolution of the source term of a third order, nonlinear partial

differential equation via a nonlocal final overdetermination condition.

Keywords: Inverse problem, direct problem, source term, fixed point system.

References

1. N. A. Larkin, Korteweg-de Vries and Kuramoto-Sivashinsky Equation in Bounded Domains, Journal of Mathematical Analysis

and Applications. 297 (2004) 169-1855.

2. M. Kaya, On Determination of the Source Term of Modified KdV Equation, Hittite Journal of Science and Engineering, accepted

2018

3. M. Kaya, On Determination of the Unkown Source Term in a Parabolic Problem from the Measured Data at the Final Time,

Applications of Mathematics, 59 (2014) 715-728

4. V. Isakov, Inverse Source Problems, Mathematical Surveys and Monographs, Vol. 34, American Mathematical Society,

Providence, RI, 1990




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122

The evaluation of the problem solving skills of 10th grade students’on quadratic equation with

one Unknown

Nilgün Aygör Department of Mathematics, Yildiz Technical University,

[email protected]

Abstract

The purpose of this study is to examine the students’ performance in solving a quadratic equation with one unknown

and determine their errors. The research had been done in a qualitative form. Sample of the research is 32 students from 2

different schools in 10th grade in Istanbul. To get the information to determine the performance of students for the research,

quadratic equations with one unknown questions gathered from different books. Students are asked to answer 6 questions.

These questions are not the same degree of difficulty. The data was analyzed by researchers jointly. As a result of this research,

it is seen that the students have difficulty in quadratic equations required interpretation, they try to solve the questions by rote-

learned information, and in addition, as they cannot interpret the question correctly they solve it wrongly or leave the question

without completing. The findings and result will be discussed in details.

Keywords: Mathematics education, quadratic equation with one unknown (2nd degree equations with one unknown), the

achievement of solving equation.

References

1. Dede, Y. (2005). I.Dereceden Denklemlerin Yorumlanması: Eğitim Fakültesi 1. Sınıf Öğrencileri Üzerine Bir Çalışma, C.Ü.

Sosyal Bilimler Dergisi, Aralık, 29 (2), 197-205.

2. Dede, Y. & Peker, M. (2007). Öğrencilerin Cebire Yönelik Hata ve Yanlış Anlamaları, İlköğretim Online, 6(1), 35-49.

3. Hallagan, J.E. (2004). A Teacher’s Model of Students’ Algebraic Thinking about Equivalent Expressions, Proceedings of the 28th

Conference of the International Group for the Psychology of Mathematics Education, 3, 1-8.

4. Sleeman, D. (1984). An Attempt to Understand Student’s Understanding of Basic Algebra, Cognitive Science, 8, 367-412.

5. Stacey, K. & McGregor, M. (2000). Learning the Algebraic Method of Solving Problems, Journal of Mathematical Behavior,18

(2), 149-147.




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123

On the Approximation of Fixed Points of Multivalued Nonexpansive Mappings

Birol Gündüz1 Fatma Solmaz2 Osman Alagöz3 Sezgin Akbulut4



[email protected] 3Department of Mathematics, Bilecik Şeyh Edebali University,

[email protected] 4Department of Mathematics, Atatürk University,

[email protected]

Abstract

In this study, we get some fixed point theorems for multivalued nonexpansive mapping by using a faster iteration

process in Banach spaces. We also give an example to show that our theoem is applicable.

Keywords: Multivalued nonexpansive mapping, Faster iteration, Banach spaces.

References

1. N. Shahzad and H. Zegeye, On Mann and Ishikawa iteration schemes for multivalued maps in Banach spaces, Nonlinear

Anal.71 (2009) no. 3-4 838–844.

2. S. B. Nadler, Multivalued contraction mappings, Pacific J. Math. 30 (1969) 475–488.

3. Y. Song and Y.J. Cho, Some notes on Ishikawaiteration for multivalued mappings, Bull. Korean. Math. Soc., 48 (2011) No. 3,

pp. 575-584.

4. B. Panyanak, Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces, Comp. Math. Appl., 54 (2007)

872-877.







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124

Comparing Convergence Rate of 𝑴-Iteration with Some Faster İteration Processes

Osman Alagöz1 Birol Gündüz2 and Sezgin Akbulut3

1Department of Mathematics, Bilecik Şeyh Edebali University,


[email protected] 3Department of Mathematics, Atatürk University,

[email protected]

Abstract

In this paper, we prove that 𝑀-iteration process converges faster than 𝑆-iteration and Picard-𝑆 iteration processes. We

also give show that 𝑀-iteration process converges faster than 𝑆𝑛-iteration process under an appropriate condition for Berinde

mappings defined on a normed lineer space. Furthermore, we give two numerical examples to support our theoretical findings

Keywords: Faster iteration, Berinde mapping, Rate of convergence.

References

1. V. Berinde, Picard iteration converges faster than Mann iteration for a class of quasicontractive operators, Fixed Point Theory

and Applications 2 (2001) 97-105.

2. W. Sintunawarat and A. Pitea, On a new iteration scheme for numerical reckoning fixed points of Berinde mappings with

convergence analysis, J. Nonlinear Sci. Appl., 9 (2016) 2553-2562.

3. R. P. Agarwal, d. O’ Regan and D. R. Sahu, Itarative construction of fixed points of nearly asymptotically nonexpansive mappings.

J. Nonlinear Convex Anal. 8 (1), (2007) 61-79.

4. K. Ullah and M. Arshad, Numerical Reckoning Fixed Points for Suzuki’s Generalized nonexpansive Mappings via Iteration

Process, Filomat, 32:1 (2018) 187-196.

5. F. Gursoy, V. Karakaya, A Picard-S hybrid type iteration method for solving a differential equation with retarded argument,

arXiv: 1403.2546v2 (2014).






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125

On Laplace Transform Technique for the Solution of Partial Differential Equations

Ozgur Yildirim1 , Adem Cengiz Cevikel2

and Sumeyra Caglak1


[email protected], [email protected] 2Department of Elementary Mathematics Education, Yildiz Technical University

[email protected]

Abstract

In this study some applications of Laplace transform method on the analytical solution of partial differential equations with Dirichlet and nonlocal boundary value conditions are considered. Finite difference method is used to obtain numerical solutions of these problems. Some results of numerical experiments are presented.

Keywords: Laplace Transform, Pde, Finite difference method.

References

1. A. J. Hermans, Water Waves and Ship Hydrodynamics Springer-Verlag, 2nd edition, Netherlands,2011.

2. H. O. Fattorini, Second Order Linear Differential Equations in Banach Space, Elsevier Science Publishing Company, North-

Holland, 1985.

3. O. Yildirim and M. Uzun, On the numerical solutions of high order stable difference schemes for the hyperbolic multipoint

nonlocal boundary value problems, Appl. Math. Comput, 254(2015):210–218, 2015.

4. O. Yildirim and M. Uzun (2015). On third order stable difference scheme for hyperbolic multipoint nonlocal boundary value

problem, Discrete Dynamics in Nature and Society, (2015):1–16, 2015.






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126

Inclusion Relations Between Harmonic Bergman-Besov Spaces on the Unit Ball of ℝ𝒏

Ömer Faruk Doğan1 1Department of Mathematics, Tekirdağ Namık Kemal University,

[email protected]

Abstract

We consider harmonic Bergman-Besov spaces 𝑏𝛼𝑝 on the unit ball of ℝ𝑛 for the full ranges of parameters 0 < 𝑝 < 1,

𝛼 ∈ ℝ. We determine the precise inclusion relations among them. To verify these relations we use Carleson measures and

suitable radial differential operators.

Keywords: Harmonic Bergman-Besov space, Radial differential operators, Carleson measure.

References

1. S. Axler, P. Bourdon & W. Ramey, Harmonic function theory, 2nd ed., Grad. Texts in

Math., vol. 137, Springer, New York, 2001.

2. B. R. Choe, H. Koo & Y. Lee, Positive Schatten class Toeplitz operators on the ball, Studia Math. 189 (2008), 65–90.

3. B. R. Choe, Y. J. Lee & K. Na, Positive Toeplitz operators from a harmonic Bergman space into another, Tohoku Math. J. (2) 56

(2004), no.2, 255–270.

4. A. E. Djrbashian & F. A. Shamoian, Topics in the theory of AαP spaces, Teubner Texts in Mathematics, 105, BSB B. G. Teubner

Verlagsgesellschaft, Leipzig, 1988.

5. S. Gergün, H. T. Kaptanoğlu & A. E. Üreyen, Harmonic Besov spaces on the ball, Int. J. Math. 27 (2016), no.9, 1650070, 59 pp.




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127

Harmonic Bergman-Besov Spaces with Small Exponents in the Unit Ball

Ömer Faruk Doğan1 1Department of Mathematics, Tekirdağ Namık Kemal University,

[email protected]

Abstract

We study two-parameter family of harmonic Bergman-Besov spaces 𝑏𝛼𝑝 on the unit ball of ℝ𝑛, where 0 < 𝑝 < 1 and

𝛼 ∈ ℝ. We provide characterizations in terms of partial and radial derivatives and certain radial differential operators that are

more compatible with reproducing kernels of harmonic Bergman-Besov spaces. We show that the dual of harmonic Bergman-

Besov space 𝑏𝛼𝑝, 0 < 𝑝 < 1 is weighted Bloch space 𝑏𝛽

∞ (for any 𝛽 ∈ ℝ) under certain volume integral pairing.

Keywords: Harmonic Bergman-Besov space, Reproducing kernel, Radial fractional derivative, Duality.

References

1. S. Axler, P. Bourdon & W. Ramey, Harmonic function theory, 2nd ed., Grad. Texts in Math., vol. 137, Springer, New York,

2001.

2. R. R. Coifman & R. Rochberg, Representation theorems for holomorphic and harmonic

functions in 𝐿𝑃, Asterisque 77 (1980), 11-66.

3. Ö. F. Doğan & A. E. Üreyen, Weighted harmonic Bloch spaces on the ball, Complex Anal. Oper. Theory, to appear.

4. S. Gergün, H. T. Kaptanoğlu & A. E. Üreyen, Harmonic Besov spaces on the ball, Int. J. Math. 27 (2016), no.9, 1650070, 59 pp.

5. G. Ren, Harmonic Bergman spaces with small exponents in the unit ball, Collect. Math. 53(2003), 83-98.




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128

Radiation Fluid Stars in a Non-minimal Gravity Model

Özcan Sert1

1Department of Mathematics, Pamukkale University,

[email protected]

Abstract

We consider a non-minimally coupled gravity model in Y(R)F2 form to describe the radiation fluid stars which have

the equation of state between the energy density and the pressure as ρ=3P. We obtain the gravitational and electromagnetic

field equations taking the infinitesimal variations of the model in differential form notation. We find the non-minimally

coupled model which admits new exact solutions in the interior and Reissner-Nordstrom solution at the exterior region of

the star. By using vanishing pressure condition and the continuity conditions of the metric functions and the electric charge

at the boundary, we find the charge-radius ratio, mass-radius ratio and gravitational redshift depending on the parameter of

the model for the radiation fluid star. We obtain general restrictions for the ratios and redshift of the charged compact stars.

Keywords: Non-minimal Couplings, Gravity, Electromagnetism, Radiation Fluid Stars.

References

1. Ö. Sert, Radiation Fluid Stars in the Non-minimally Coupled Y(R)F2 Gravity, Eur. Phys. J. C (2017), 77, 97.

2. Ö. Sert, Regular Black Hole Solutions of the Non-minimally Coupled Y(R)F2 Gravity, Journal of Mathematical Physics (2016),

57, 032501.

3. M. K. Mak, and T. Harko, Quark stars admitting a one-parameter group of conformal motions, Int. J. Mod. Phys. D, (2004) 13,

149 , arXiv:gr-qc/0309069.




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129

First Order Maximally Accretive Quasi-Differential Operators

Pembe Ipek Al1 and Zameddin I. Ismailov2

1Institute of Natural Sciences, Karadeniz Technical University,

[email protected] 2Department of Mathematics, Karadeniz Technical University,

[email protected]

Abstract

The general representation of all linear maximally accretive quasi-differential operators for first order in the weighted

Hilbert space in terms of boundary conditions is given. Lastly, the geometry of spectrum sets of this type operators has been

investigated.

Keywords: Accretive operator, quasi-differential operator, spectrum.

References

1. T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag Inc., New York, (1966) .

2. V. I. Gorbachuk , M. L. Gorbachuk, Boundary Value Problems for Operator Differential Equations, Kluwer Academic Publisher,

Dordrecht, (1991).

3. V. V. Levchuk, Smooth maximally dissipative boundary-value problems for a Parabolic Equation in a Hilbert Space, Ukrainian

Mathematic Journal 35(4) (1983) 502–507.

4. L. Hörmander, On the theory of general partial differential operators, Acta Mathematica 94 (1955) 161-248.

5. C. Fischbacher, On the Theory of Dissipative Extensions, PhD Thesis, University of Kent School of Mathematics, Statistic and

Actuarial Science, Canterbury, February 11, (2017).



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130

Spectral Analysis of Canonical Type First Order Selfadjoint Quasi-Differential Operators

Zameddin I. Ismailov1, Pembe Ipek Al2 and Rukiye Öztürk Mert3

1Department of Mathematics, Karadeniz Technical University,

[email protected] 2Institute of Natural Sciences, Karadeniz Technical University,

[email protected] 3Department of Mathematics, Hitit University,

[email protected]

Abstract

In this work, in terms of abstract boundary conditions the complete description of canonical type selfadjoint quasi-

differential operators for first order in the weighted Hilbert space of vector-functions in semi-infinite interval is given. And

also the spectrum set of such extensions has been studied.

Keywords: Selfadjoint operator, quasi-differential operator, spectrum.

References

1. J. von Neumann, Allgemeine eigenwerttheories hermitescher funktionaloperatoren, Math. Ann. 102 (1929-1930) 31-49.

2. A. Zettl, J. Sun, Self-adjoint ordinary differential operators and their spectrum, Rosky Mountain Journal of Mathematics 45(1)

(2015) 763-886.

3. M. A. El-Gebeily, D. O’Regan, R. Agarwal, Characterization of self-adjoint ordinary differential operators, Mathematical and

Computer Modelling 54 (2011) 659-672.

4. W. N. Everitt, A. Poulkou, Some observations and remarks on differential operators generated by first order boundary value

problems, Journal of Computational and Applied Mathematics 153 (2003) 201-211.

5. F. S. Rofe-Beketov, A. M. Kholkin, Spectral Analysis of Differential Operators. World Scientific Monograph Series in

Mathematics 7, USA, (2005).





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131

Quartic Trigonometric B-spline Galerkin Method for the Equal Width Wave Equation

Pınar Keskin Yıldız1 and Dursun Irk1



Abstract

The EW wave equation suggested by Morrison et.al. is used as a model partial differential equation for the simulation of

one-dimensional wave propagation in a nonlinear medium with a dispersion process [1]. Nonlinear dispersive wave equations

exhibit types of solutions such as solitary waves and solitons. Solutions of them are not analytically available for every

boundary and initial conditions in general. Since only a few analytical solutions to the EW equation with some initial and

boundary conditions have been known so far, numerical methods are a useful tool for studying the EW equation [2,3]. The

EW wave equation also represents an alternative to the better known Korteweg–de Vries (KdV) equation and the regularized

long wave (RLW) equation. In this study, the EW equation will be solved numerically using the Galerkin finite-element

method, based on Crank Nicolson method for time integration and quartic trigonometric B-spline for space integration. The

proposed algorithm is tested on the solitary wave motion and interaction of two solitary waves test problems. The three

conserved quantities of motion are calculated to determine the conservation properties of the proposed algorithm for both test

problems.

Keywords: Equal Width wave equation, Galerkin finite element method, Solitary wave, B-spline.

References

1. P. J. Morrison, J.D. Meiss, and J. R. Carey, (2000), Scattering of RLW Solitary Waves, Physica D. 11, 324-336.

2. D. Irk, (2012), B-Spline Galerkin Solutions for the Equal Width Equation, Physics of Wave Phenomena, 20(2), (2012), 1-9.

3. B. Saka, İ. Dağ, Y. Dereli and A. Korkmaz, (2008), Three different methods for numerical solution of the EW equation,

Engineering analysis with boundary elements, 23(7), 556-566.





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132

Operator Ideals defined by Using Block Sequence Spaces

Pınar Zengin Alp1 and Emrah Evren Kara2

1,2Department of Mathematics, Duzce University

[email protected]

[email protected]

Abstract

Two new classes of operators in block sequence space 𝑙𝑝(𝐸) are defined in this study. Also,

it is shown that these classes are quasi-Banach operator ideals with appropriate quasi-norms.

Keywords: Operator ideal, s-numbers, symmetric norming function.

References

1. D. Foroutannia, On the block sequence space lp (E) and related matrix transformations,TurkJ. Math., (39), 830-841, 2015.

2. N. Tita, On Stolz mappings, Math. Japonica 26 (4), 495.496, 1981.

3. P. Zengin Alp, M. ·Ilkhan, E. E. Kara, Generalized Stolz mappings, Konuralp J. Math., 5 (2), 12-18, 2017.





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133

A Note on Equivalent Quasinorms

Pınar Zengin Alp1 and Emrah Evren Kara2

1,2Department of Mathematics, Duzce University

[email protected]

[email protected]

Abstract

In this paper a new operator ideal is defined by using symmetric norming function and the sequence space lp (E). Also,

some equivalent quasinorms are defined on this class.

Keywords: Operator ideal, s-numbers, symmetric norming function.

References

1. D. Foroutannia, On the block sequence space lp (E) and related matrix transformations,TurkJ. Math., (39), 830-

841, 2015.

2. N.Tita, Some equivalent quasinorms on operator ideals, Spectral and Evolution Problems,Taurida National Univ.

Simferopol, 13, 103-108, 2002.

3. P. Zengin Alp, M. ·Ilkhan, E. E. Kara, Generalized Stolz mappings, Konuralp J. Math., 5 (2), 12-18, 2017.





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134

Smoothness moduli for some Banach function spaces

Ramazan Akgün

Department of Mathematics, Balikesir University,

[email protected]

Abstract

Based on the Steklov operator, we considered a modulus of smoothness of functions in some Banach function spaces,

which can be not translation invariant, and obtained the main properties of it. A constructive characterization of the Lipschitz

class is obtained using the Jackson type direct theorem and inverse theorem of trigonometric approximation. As application,

several examples of related (weighted) function spaces are given.

Keywords: Modululus of smoothness, Banach function space, Constructive characterization, Direct and inverse inequalities,

Muckenhoupt weight.

References

1. R. Akgün, Polynomial approximation in weighted Lebesgue spaces, East J. Approx., 17 (2011), no. 3, 253-266.

2. R. Akgün, Trigonometric approximation of functions in generalized Lebesgue spaces with variable exponent, Ukrainian Math.

J., 63 (2011), no. 1, 1-26.

3. R. Akgün, Polynomial approximation of functions in weighted Lebesgue and Smirnov spaces with nonstandard growth,

Georgian Math. J., 18 (2011), no. 2, 203-235.

4. C. Bennett and R. Sharpley, Interpolation of operators, Pure and Applied Mathematics, 129, Academic Press, Inc., Boston, MA,

1988.



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135

Musielak Orlicz Spaces and Approximation Problems

Ramazan Akgün

1Department of Mathematics, Balikesir University,

[email protected]

Abstract

In the present work we prove some direct and inverse theorems for approximation by trigonometric polynomials in

Musielak-Orlicz spaces. Furthermore we get a constructive chracterization of the generalized Lipschitz classes in these spaces.

Keywords: Musielak Orlicz Space, Direct and Inverse theorems, Lipschitz class, Trigonometric approximation.

References

1. R. Akgün, Trigonometric approximation of functions in generalized Lebesgue spaces with variable exponent, Ukrainian Math.

J., 63 (2011), no: 1 , pp. 1-26.

2. R. Akgün, Some convolution inequalities in Musielak Orlicz spaces, Proc. Inst. Math. Mech., NAS Azerbaijan, 42 (2016), No:

2, 279-291.

3. P. L. Butzer, R. J. Nessel, Fourier analysis and approximation, V: 1, Birkhauser Verlag, 1971.

4. J. Musielak, Orlicz spaces and modular spaces, Lecture Notes in Mathematics, 1034, Springer, 1983.

5. I. I. Sharapudinov, On the uniform boundedness in L^p(p=p(x)) of some families of convolution operators, Math. Notes, 59

(1996), no. 1-2, 205-212.

6. I. I. Sharapudinov, Some problems in approximation theory in the spaces L^p(x)(E), (Russian) Anal. Math. 33 (2007), no. 2,

135-153.

7. I. I. Sharapudinov, Approximation of smooth sunctions in L_2π^p(x) by Vallee-Poussin means, Izv. Saratov. Univ. Mat.

Mekh. Inform., 13 (2013), no. 1 (1), 45-49.

8. A. Zygmund, Trigonometric Series. Cambridge Univ. Press, Cambridge, 1968.




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136

On a space of -statistical continuous functions

Raziyya Hasanli1 and Cemil Karacam2

1Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan 2 Department of Mathematics, Yildiz Technical University, Istanbul, Turkey


Abstract

In this work, we give definitions of -statistical one-sided limits at a point and -statistical discontinuities of the first

and second kind in some measurable space with a measure. We consider the space baCst , of -statistical continuous

functions on some interval ba, . We prove that the space of continuous functions is strictly embedded in baCst , . Moreover,

we show that baCst , is not embedded in the Lebesgue space baLp , for ,0p , i.e. baLbaC pst ,\, . We also

make comparison between the concept of -statistical continuity at a point and the known concept of approximate continuity

(see, e.g., [1]).

It should be noted that the direct generalization of the concept of statistical convergence in continuous case was first

carried out by B.T.Bilalov and S.R.Sadigova [2]. They introduced the concepts of -statistical convergence and -statistical

fundamentality, proved their equivalence and studied some of their properties. They also introduced the concept of -

statistical continuity.

Keywords: -statistical discontinuities, -statistical continuity, the space of -statistical continuous functions

References

1. I. P. Natanson, Theory of functions of a real variable, "Nauka", Moscow, 1974, 480 p.

2. B.T. Bilalov, S.R. Sadigova, On -statistical convergence, Proceedings of the American Mathematical Society, 143(9)

(2015), 3869--3878.





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137

Lie Group Analysis of Some Evolution Equations

Saadet S. Özer

Department of Mathematics Engineering, Istanbul Technical University,

[email protected]

Abstract

Lie group analysis to differential equations has significant role in not only determining the solutions of differential

equations, but only understanding the behavior of them. Classification problem and invariant functions of differential

equations are such tools in order to examine the behavior of differential equations.

In the applications to differential equations, in addition to the Lie groups of classical symmetry transformations, recently,

Lie groups of equivalence transformations give more general information and have more powerfull tools for complicated

diferential equations. The idea of equivalence groups belongs to Ovsiannikov [2], but has been developed by many reserachers

in the last 20 years. Classification of differential equations and determining the invariant solutions have been examined via

equivalence groups of admissible transformations by many researchers.

In this study, we have studied some evolution type equations within the frame work of the Lie groups of equivalence

transformations. The infinitesimal generators are determined and some subgroups of the general transformation groups are

investigated in details. The explorations of special desired transformations are discussed. Applications to nonhomogenous

equations are also given as examples.

Keywords: Transfromation Groups, Lie Groups, Evolution Equations, Diffusion Equation, Heat Equation.

References

1. Olver, Peter J. Applications of Lie groups to differential equations. Vol. 107. Springer Science & Business Media, (2000).

2. Ovsiannikov, Lev Vasil'evich. Group analysis of differential equations. Academic Press, (2014).

3. Suhubi, Erdogan. Exterior analysis: using applications of differential forms. Elsevier, (2013).

4. Özer, Saadet. (2018). On the equivalence groups for (2+ 1) dimensional nonlinear diffusion equation. Nonlinear Analysis: Real World Applications 43, 155-166.




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138

A New Cubic Picture Fuzzy Information Aggregation and Its Application to Multi-Atribute

Decision Making Problem

Saleem Abdullah1 and Shahzaib Ashraf 1

1Department of Mathematics, Abdul Wali Khan University, Mardan, Pakistan

[email protected]

[email protected]

Abstract

Ranking fuzzy numbers is an important issue in decision making analysis, optimization, artificial intelligence and

operations research. Thus, many methods have been proposed for ranking fuzzy numbers in the literature. However most of

these methods have some limitations and shortcomings. In this paper, based on cubic picture fuzzy information's, a method

for ranking is proposed to overcome the existing shortcomings. Futher introduced some cubic picture fuzzy algebric and cubic

picture fuzzy algebraic* aggregated operators for aggregated the information. Finally, a mutli-atribute decision making

problem is given as a practical application to demonstrate the usage and applicability of the proposed ranking approach.

Keywords: Cubic Picture Fuzzy Set, Algebraic Aggregation Operators, Algebraic* Aggregation Operators, Multi-attribute

decision making problem.

References

1. K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96.

2. B. C. Cuong, Picture Fuzzy Sets- a new concept for computational intelligence problems, In Proceedings of the Third World

Congress on Information and Communication Technologies, (2013), 1-6.

3. Y. B. Jun, C. S. Kim and K. O. Yang, Cubic sets, Ann. Fuzzy Math. Inform. 4(1) (2012), 83–98.

4. W. Wang, X. Liu, Y. Qin, Interval-valued intuitionistic fuzzy aggregation operators, Journal of Systems Engineering and

Electronics, 23(4) (2012), 574–580.





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139

Inventory Without Backorder Using The Polygonal Fuzzy Numbers

İsmail Özcan and Salih Aytar

Department of Mathematics, Süleyman Demirel University,

[email protected]

[email protected]

Abstract

In this paper, by generalizing the signed distance defuzzfication method for the polygonal fuzzy numbers we apply

this new method to Yao and Wu’s [3] Economic Order Quantity (EOQ) model. Finally using Yao and Wu’s example we show

that our method gives more optimum results than triangular fuzzy model.

Keywords: Polygonal fuzzy number; Signed distance defuzzfication method; Economic order Quantity.

References

1. Báez-Sánchez A.D., Moretti A.C., Rojas-Medar M.A., On polygonal fuzzy sets and numbers, Fuzzy Sets and Systems 209 (2012)

54-65.

2. Yao J.-S., Wu K.K., Ranking fuzzy numbers based on decomposition principle and signed distance, Fuzzy Sets and Systems 116

(2000) 275-288.

3. Yao J. S. and Chiang J., Inventory without backorder with fuzzy total cost and fuzzy storing cost deffuzified by centroid and

singed distance, European Journal of Operational Research,148 (2003) 401-409.

This presentation was supported by grant 117F252 from TUBITAK (The Scientific and Technological Research Council of Türkiye).





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140

New Type Integral Inequalities for Fourth Times Differentiable Prequasiinvex Functions

İmdat İŞCAN1, Selahattin MADEN2 and Huriye KADAKAL3

1Department of Mathematics, Giresun University, Giresun, Turkey

[email protected], 2Department of Mathematics, Ordu University, Ordu, Turkey

[email protected] 3Institute of Science, Ordu University, Ordu, Turkey

[email protected]

Abstract

In this study, a new identity is given for functions defined on an open invex subset of set of real numbers, and by using

this identity and the Hölder and Power mean integral inequalities it is presented new type integral inequalities for functions

whose powers of fourth derivatives in absolute value are prequasiinvex functions.

Keywords: Invex set, Prequasiinvex function, Hölder and Power Mean Integral inequality.

References

1. Barani A, Ghazanfari A.G, Dragomir S.S. (2011). Hermite-Hadamard inequality through prequasiinvex functions,

RGMIA Research Report Collection, 14(48), 7 pp.

2. Barani A, Ghazanfari A.G, Dragomir S.S. (2012). Hermite-Hadamard inequality for functions whose derivatives

absolute values are preinvex, J. Inequal. Appl. 2012:247.

3. Dragomir S.S and Pearce C.E.M. (2000). Selected Topics on Hermite-Hadamard Inequalities and Applications,

RGMIA Monographs, Victoria University.

4. Ion D.A. (2007). Some estimates on the Hermite-Hadamard inequality through quasi-convex functions, Annals of

University of Craiova, Math. Comp. Sci. Ser. Volume 34, Pages 82-87.

5. İşcan İ. (2014). Ostrowski type inequalities for functions whose derivatives are preinvex, Bulletin of the Iranian

Mathematical Society, 40 (2), 373-386.

6. İşcan İ, Kadakal H and Kadakal M. (2017). Some New Integral Inequalities for n- Times Differentiable Quasi-

Convex Functions, Sigma Journal of Engineering and Natural Sciences, 35 (3), 363-368.

7. Latif M.A and Dragomir S.S. (2013). Some Hermite-Hadamard type inequalities for functions whose partial

derivatives in absloute value are preinvex on the co-oordinates, Facta Universitatis (NIŠ) Ser. Math. Inform, Vol.

28, No 3, 257-270.

8. Maden S, Kadakal H, Kadakal M and İşcan İ. (2017). Some new integral inequalities for n-times differentiable

convex functions, J. Nonlinear Sci. Appl. 10 (12), 6141-6148.

9. Matloka M. (2014). On some new inequalities for differentiable (h₁; h₂)-preinvex functions on the co-ordinates,

Mathematics and Statistics, 2(1), 6-14.

10. Mohan S.R, Neogy S.K. (1995). On invex sets and preinvex functions, J. Math. Anal. Appl. 189, 901-908.

11. Noor M.A. (2007). Hermite-Hadamard integral inequalities for log-preinvex functions, J. Math. Anal. Approx.

Theory, 2, 126-131.

12. Noor M. A. (2005). Invex equilibrium problems. J. Math. Anal. Appl. 302, 463-475.

13. Pini R. (1991). Invexity and generalized convexity. Optimization, 22, 513-525.

14. Weir T and Mond B. (1998). Preinvex functions in multiple objective optimization, J Math Anal Appl. 136, 29-38.

15. Yang X.M and Li D. (2001). On properties of preinvex functions. J. Math. Anal. Appl. 256, 229-241.






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141

New Type Integral Inequalities for n-Times Differentiable Preinvex Functions

İmdat İŞCAN1, Mahir KADAKAL1 and Selahattin MADEN2

1Department of Mathematics, Giresun University, Giresun, Turkey [email protected], [email protected]

2Department of Mathematics, Ordu University, Ordu, Turkey [email protected]

Abstract

In this paper, a new identity for functions defined on an open invex subset of set of real numbers is established. By

using this identity, Hölder and Power mean integral inequalities, we present new type integral inequalities for functions whose

powers of nth derivatives in absolute value are preinvex functions. This study is a generalization of studies given for functions

whose first, second and third derivatives are preinvex articles. We should especially mention the results obtained in special

cases coincide with the well-known results in the literature.

Keywords: Invex set, Preinvex function, Hölder and Power Mean Integral inequality

References

1. Antczak T. (2005). Mean value in invexity analysis, Nonl. Anal. 60, 1473-1484.

2. Barani A, Ghazanfari A.G, Dragomir S.S. (2011). Hermite-Hadamard inequality through prequasiinvex functions, RGMIA

Research Report Collection, 14(48), 7 pp.

3. Barani A, Ghazanfari A.G, Dragomir S.S. (2012). Hermite-Hadamard inequality for functions whose derivatives absolute values

are preinvex, J. Inequal. Appl. 2012:247.

4. Dragomir S.S and Pearce C.E.M. (2000). Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA

Monographs, Victoria University.

5. İşcan İ. (2014). Ostrowski type inequalities for functions whose derivatives are preinvex, Bulletin of the Iranian Mathematical

Society, 40 (2), 373-386.

6. Latif M.A and Dragomir S.S. (2013). Some Hermite-Hadamard type inequalities for functions whose partial derivatives in

absloute value are preinvex on the co-oordinates, Facta Universitatis (NIŠ) Ser. Math. Inform, Vol. 28, No 3, 257-270.

7. Matloka M. (2014). On some new inequalities for differentiable (h₁; h₂)-preinvex functions on the co-ordinates, Mathematics and

Statistics, 2(1), 6-14.

8. Mohan S.R, Neogy S.K. (1995). On invex sets and preinvex functions, J. Math. Anal. Appl. 189, 901-908.

9. Noor M.A. (2007). Hermite-Hadamard integral inequalities for log-preinvex functions, J. Math. Anal. Approx. Theory, 2, 126-

131.

10. Noor M. A. (2005). Invex equilibrium problems. J. Math. Anal. Appl. 302, 463-475.

11. Pini R. (1991). Invexity and generalized convexity. Optimization, 22, 513-525.

12. Weir T and Mond B. (1998). Preinvex functions in multiple objective optimization, J Math Anal Appl. 136, 29-38.

13. Yang X.M, Yang X.Q, Teo K.L. (2003). Generalized invexity and generalized invariant monotonicity, J. Optim. Theory. Appl.

117, 607-625.

14. Yang X.M and Li D. (2001). On properties of preinvex functions. J. Math. Anal. Appl. 256, 229-241.






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142

Some Results on Generalized Fibonacci and Lucas Quaternions

Semih Yılmaz1, Elif Tan2, and Murat Şahin3 1Department of Actuarial Sciences, Kırıkkale University,



[email protected]

Abstract

There are several works related to Fibonacci and Lucas quaternions over some special quaternion algebras [1-4]. In

this talk, we consider a generalization of Fibonacci and Lucas quaternions over the generalized quaternion algebra .

It is clear that for , it gives the real quaternion algebra, and for , it gives the split quaternion algebra.

We investigate some basic properties of these generalized quaternions.

Keywords: Generalized quaternion algebra, Fibonacci quaternions, Lucas quaternions.

References:

1. Akyigit M., Kösal H.H., Tosun M. Fibonacci generalized quaternions. Adv. Appl Clifford Algebras, 24 (3)

(2014), 631-641.

2. Bilgici G., Tokeser U., Unal Z. k-Fibonacci and k-Lucas generalized quaternions. Konuralp Journal of

Mathematics, 5(2) (2017), 102-113.

3. Flaut C., Shpakivskyi V. On generalized Fibonacci quaternions and Fibonacci Narayana quaternions. Adv. Appl.

Clifford Algebr. 23(3) (2013), 673-688.

4. Halici S., Karatas A. On a Generalization for Quaternion Sequences, Chaos, Solitons & Fractals 98 (2017), 178-

182.





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143

Investigation of Mathematical Problem Solving and Posing Processes of Primary School Students

Mustafa Doğan1 and Sevgi Akten2

1Department of Elementary Mathematics Education, Yildiz Technical University,

[email protected] 2Computer Science Teacher,

[email protected]

Abstract

Problem and problem solving concepts are mostly related to mathematics. Because Mathematics based on abstract

concepts, it is perceived as a difficult course to learn. Research shows that students who demonstrate problem solving behavior

are also successful in mathematics. The ability of the learner to solve complex problems, to develop their own solution

methods and to analyze and generalize them under certain assumptions shows that the learners can control their own learning.

The purpose of the study is to examine the processes of solving and posing mathematical problems of fourth grade

primary school students and to reveal the steps they have used in these processes. The research is based on a mixed method.

The data obtained from both quantitative and qualitative methods. The research was conducted with 100 primary school

students. A problem solving and problem posing achievement test were used for quantitative data. A total of 10 students

within the sample interviewed with a semi-structured interviews. The achievement test consisted five mathematical problems

and five problem posing areas. Th test were prepared by the researcher and overviewed with experts. Analysis of quantitative

data is used whether there is a realtionship between problem solving ability and problem posing ability of fourth grade

students. Analysis of qualitative data is shows that the studenst achieved the stages of understanding the problem and

implementing the plan, but the final stages of checking and evaluating of a problem are not achieved sufficiently.

Keywords: Primary Mathematics Education, Problem Solving, Problem Posing

References:

1. Alakoç, Z. (2003). Matematik Öğretiminde Teknolojik Modern Öğretim Yaklaşımları. The Turkish Online Journal of Educational

Technology, 2(1), 43-49.

2. Özsoy, G. (2005). Problem Çözme Becerisi İle Matematik Başarısı Arasındaki İlişki. Gazi Eğitim Fakültesi Dergisi, Cilt 25, Sayı

3(2005), 179-190.

3. Baki, A. (2001). Bilişim Teknolojisi Işığı Altında Matematik Eğitiminin Değerlendirilmesi. Milli Eğitim Dergisi. February, 2011.





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144

On weighted weak statistical convergence

Sinan ERCAN1

1Department of Mathematics, Firat University,

[email protected]

Abstract

The extended notion of weak statistical convergence on normed spaces is introduced in this paper. Further, some

properties of this mode of convergence are studied.

Keywords: Statistical convergence, weighted statistical convergence, weak convergence.

References

1. T. Šalăt, On statistically convergent sequences of real numbers, Math. Slovaca 30, (1980) 139-150.

2. J. Connor, M. Ganichev, V. Kadets, A characterization of Banach spaces with separable duals via weak statistical convergence,

J. Math. Anal. Appl., 244, (2000) 251-261.

3. V. K. Bhardwaj, I. Bala, On weak statistical convergence, Int. J. Math. Math. Sci. Art. ID 38530, (2007) 9 pp.

4. V. Karakaya, T. A. Chishti, Weighted statistical convergence, Iran. J. Sci. Technol. Trans. A Sci. 33, (2009) 219-223.

5. M. Mursaleen, V. Karakaya, M. Ertürk, F. Gürsoy, Weighted statistical convergence and its application to Korovkin type

aprroximation theorem, Appl. Math. Comput. 218, (2012) 9132-9137.




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145

Noncommutative Geometry and application to Differeneiel Schrödingre Equation

Zaiem slimane

1Department of physics, Hadj Lakhdar University,

[email protected]

Abstract

We obtain exact solution of the 2D schrödingre Differential equation with the central potentials [1,2,3] in

nocommuitative geometry space[4] using the pwer-series expansion method similar to the 2D Schrödingre equation with the

singular even-power and inverse-power potentials respectively in ordinare space. We derive the exact noncommutative energy

levels and show that the energy is shifted to m levels, as in the Zeeman effect..

Keywords: Nincommutative geometry, Schrödinger equation Zeeman effecte.

References

1. S. H. Dong, Phys. Scr. 64, 273(2001).

2. S. H. Dong, Phys. Scr. 65, 289(2002).

3. S. H. Dong, , G. H. San Phys. Scr. 70, 94(2004).

4. N. Seiberg and E. Witten, JHEP 9909 (1999), 032.




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146

A Note on Dual Codes of Pseudo-cyclic Codes

Sumeyra Bedir1 and Fatmanur Gursoy2



[email protected]

Abstract

Pseudo-cyclic codes, as a direct representation of shortened cyclic codes over finite fields, have been studied widely

in terms of their algebraic structure. The dual codes of pseudo-cyclic codes, which are known to be a special type of sequential

codes, have not yet been classified appropriately, since they do not preserve correspondence to polynomial rings and they do

not have an ideal structure. In this study, we present a method to explore the generators of sequential codes.

Keywords: Pseudo-cyclic codes, Sequential Codes, Duality, Linear codes.

References

1. A. Alahamdi, S. Dougherty, A. Leroy, and P. Sole, On the duality and the direction of polycyclic

codes, Advances in Mathematics of Communications, 10(4) (2016) 921–929.

2. S.R. Lopez-Permouth, B.R. Parra-Avila and S. Szabo, Dual generalizations of the concept of

cyclicity of codes, Adv. in Math. of Com., 3(3) (2009) 227–234.

3. M. Matsuoka, θ-polycyclic codes and θ-sequential codes over finite fields, Int. J.of Algebra, 5 (2011) 65 - 70.

4. W. W. Peterson and E. J. Jr Weldon, Error Correcting codes: second edition, MIT Press, 1972.





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147

Matrix Representations of Compressible Fluid Equations

Süleyman Demir1 and Murat Tanışlı1

1Department of Physics, Faculty of Science, Anadolu University

[email protected]

[email protected]

Abstract

In this work, the special matrices have been introduced for the reformulation of compressible fluid equations. After

a brief survey on biquaternionic matrices, the matrix representations of Maxwell type fluid equations have been presented in

order to simplify equation manipulations. Moreover, the corresponding matrix representations of compact field equation and

wave equation have been given.

Keywords: Quaternion, matrices, compressible fluids, Maxwell equations, wave equation.

References

1. T. Kambe, A new formulation of equations of compressible fluids by analogy with Maxwell’s equations, Fluid Dyn. Res. 42

(2010) 055502.

2. D. F. Scofield, P. Huq, Fluid dynamical Lorentz force law and Poynting theorem introduction,

Fluid Dyn. Res. 46 (2014) 055513.

3. D. F. Scofield, P. Huq, Fluid dynamical Lorentz force law and Poynting theorem derivation

and implications, Fluid Dyn. Res. 46 (2014) 055514.

4. S. Demir, A. Uymaz, M. Tanışlı, A new model for the reformulation of compressible fluid equations, Chinese J. Phys., 55 (2017)

115-126.

5. S. Demir, M. Tanışlı, Hyperbolic octonion formulation of the fluid Maxwell equations, J. Korean Phys. Soc. 68 (2016) 616–623.





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148

Estimates of Faber Polynomial Coefficients for Bi-univalent Functions Equipped with the

Jackson (p,q)-derivative Operator

Şahsene Altınkaya1 and Sibel Yalçın2

1Department of Mathematics, Uludag University,

[email protected] 1Department of Mathematics, Uludag University,

[email protected]

Abstract

We consider the Faber polynomials for classes which defined by using the Jackson (p,q)-derivative operator.

Furthermore, we obtain upper bounds for the general coefficients of such functions subject to a gap series condition as well

as obtaining bounds for their first two coefficients.

Keywords: Bi-univalent functions, Faber polynomials, Jackson (p,q)-derivative operator.

References

1. H. Airault, Remarks on Faber polynomials, Int. Math. Forum, 3 (2008) 449-456.

2. H. Airault and H. Bouali, Differential calculus on the Faber polynomials, Bulletin des Sciences Mathematiques, (2006) 179–222.

3. H. Airault and J. Ren, In algebra of differential operators and generating functions on the set of univalent functions, Bulletin des

Sciences Mathematiques, 126 (2002) 343–367.

4. R. Chakrabarti and R. Jagannathan, A (p,q)-oscillator realization of two-parameter quantum algebras, J. Phys. A: Math. Gen, 24

(1991) L711–L718.

5. P. Duren, Univalent Functions. New York: Grundlehren der Mathematischen Wissenschaften, Springer, 1983.





Istanbul / TURKEY


149

Analytical Solutions of the Biswas-Milovic and Gerdjikov-Ivanov Equations

Şerife Müge EGE

Department of Mathematics, Ege University,

[email protected]

Abstract

This study concentrates the dynamics of soliton propagation through optical fibers that are governed by Biswas-Milovic

and Gerdjikov–Ivanov equations. The extended Kudryashov strategy applied to extract the analytical soliton solution.

Acknowledgement: This research is supported by Ege University, Scientific Research Project (BAP), Project Number:

2016FEN054

Keywords: Biswas-Milovic equation, Gerdjikov-Ivanov equation, soliton solutions, extended Kudryashov method

References

1. N. Raza, M. Abdullah, A. R. Butt, Analytical soliton solutions of Biswas–Milovic equation in Kerr and non-Kerr

law media, Optik, 157 (2018) 993-1002.

2. A. Biswas, M. Ekici, A. Sonmezoglu, H. Triki, A. S. Alshomranib, Q. Zhou, S. P. Moshokoa, M. Belic, Optical

solitons for Gerdjikov–Ivanov model by extended trial equation scheme, Optik, 157 (2018) 1241-1248.

3. A. Biswas, M. Ekici, A. Sonmezoglu, F. B.Majid, H. Triki, Q. Zhou, S. P. Moshokoa, M. Belic,Optical soliton

perturbation for Gerdjikov-Ivanov equation by extended trial equation method. Optik, 158 (2018) 747-752.

4. S. M. Ege, E. Misirli, A new method for solving nonlinear fractional differential equations, New Trends in Mathematical Sciences,

5(1), (2017) 225-233.




Istanbul / TURKEY


150

Generalized Sylvester Polynomials of Three Variables

Nejla Özmen1 and Sule Soytürk2

1Department of Mathematics, DüzceUniversity,

[email protected]

2Department of Mathematics, DüzceUniversity

[email protected]

Abstract

In this study deals with some new properties for the Generalized Sylvester polynomials of three variables. The results

obtained here include various families of multilinear and multilateral generating functions and their miscellaneous properties.

We also derive an application giving certain families of bilateral generating functions for the Generalized Sylvester and the

Appell functions. At the end, we discuss some special cases for this theorem.

Keywords: Generalized Sylvester polynomials, generating function, multilinear and multilateral generating function,

recurrence relation, hypergeometric function.

References

1. H. M. Srivastava and J. L. Lavoie, A certain method of obtaining bilateral generating functions, Indag. Math. 78 (1975), 304-320.

2. A. K. Agarwal, R. Bhatia and H. L. Manocha, Alternative methods of obtaining differential operator representations, Indian J.

Pure Appl. Math. 13 (1982), 237-246.

3. S. J. Liu, S.D. Lin, H. M. Srivastava and M. M. Wong, Bilateral generating functions for the Erkus-Srivastava polynomials and

the generalized Lauricella functions. Appl. Math. Comput. 218 (2012) 7685-7693.

4. N. Ozmen, E. Erkus-Duman, On the Poisson-Charlier polynomials, Serdica Math. J. 41 (2015) 457-470.

5. N. Ozmen, E. Erkus-Duman, Some families of generating functions for the generalized Cesàro polynomials, J. Comput. Anal.

Appl., 25(4) (2018) 670-683.





Istanbul / TURKEY


151

Statistical Hypo-Convergence in Sequence of Functions

Şükrü Tortop1 1Department of Mathematics, Afyon Kocatepe University,

[email protected]

Abstract

In this paper, we define statistical hypo-convergence in metric spaces as an alternative to statistical pointwise and uniform

statistical convergence. We show that this type of convergence provides a useful tool for solving stochastic optimization and

variational problems. Also, its characterizations with level sets are obtained and the cases where functions are monotone

increasing or decreasing are examined.

Keywords: Statistical hypo-convergence, hypographs, upper semicontinuity, level sets.

References

1. H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951) 241–244.

2. J. A. Fridy, C. Orhan, Statistical limit superior and limit inferior, Proc. Amer. Math. Soc.

125 (1997) 3625–3631.

3. G. D. Maso, An introduction to Γ-convergence, vol.8. Boston (1993).

4. R.T. Rockafellar, R.J-B. Wets, Variational Analysis. (2009).




Istanbul / TURKEY


152

On the special case of the Riemann boundary value problem

Tatsiana Urbanovich1,2 and Zahir Muradoglu1

1Department of Mathematics, Kocaeli University, Izmit, Turkey 2Department of Higher Mathematics, Polotsk State University, Belarus


Abstract

Let Γ be a simple smooth closed contour dividing the plane of the complex variable into the interior domain 𝐷+ and the

exterior domain 𝐷−. Let F be a finite set of points of the contour Γ and let 𝛼 = (𝛼𝜏, 𝜏 ∊ 𝐹) be a family of complex numbers,

(𝑧) = ∏ (𝑧 − 𝜏)𝛼𝜏 ,𝜏∊𝐹 𝑧 ∊ 𝐷+. Let 𝜆+ = (𝜆𝜏+, 𝜏 ∊ 𝐹) and 𝜆− = (𝜆𝜏

−, 𝜏 ∊ 𝐹) be families of complex numbers. The problem is

to find a function 𝛷(𝑧) ∊ 𝐻𝜆±(𝐷±, 𝐹) that is analytic outside Γ, vanishes at infinity, and satisfies the boundary condition

𝛷+(𝑡) − 𝐴(𝑡)𝐺0(𝑡)𝛷−(𝑡) = 𝑔(𝑡), 𝑡 ∊ 𝛤, (1) where 𝑔(𝑡) ∊ 𝐻𝜆+(𝛤, 𝐹) and 𝐺0(𝑡) ∊ 𝐻0(𝛤, 𝐹) is an invertible function.

Theorem. Let 𝑋(𝑧) be specially constructed canonical function (see [1]). If the index 𝜅 ≥ 0, then the general solution to the

problem (1) is given by the formula

𝛷(𝑧) = 𝐴(𝑧)𝛹(𝑧), 𝑧 ∊ 𝐷+,

𝛹(𝑧), 𝑧 ∊ 𝐷−, (2)

𝛹(𝑧) = 𝑋(𝑧) (1

2𝜋𝑖∫

𝑔(𝑡)𝑑𝑡

𝐴(𝑡)𝑋+(𝑡)(𝑡−𝑧)+ 𝑃𝜅−1(𝑧)

𝛤). If 𝜅 < 0, then the solution to the problem (1) is unique and given by the

formula (2) provided that the orthogonality conditions are satisfied.

Remark. By reduction to problem (1), one can study the corresponding singular integral equation with Cauchy kernel in the

exceptional case [2]. In turn, the resulting solution can be used to study boundary value problems for equations of the mixed

type.

Acknowledgements. This work is supported by the Scientific and Technological Research Council of Turkey (TUBITAK

grant 2221 - "Fellowship Program for Visiting Scientists and Scientists on Sabbatical Leave").

Keywords: Riemann boundary value problem, singular integral equation

References

1. T. M. Urbanovich, Exceptional Case of the Linear Conjugation Problem in Weighted Hölder Classes, Differential Equations

51(12) (2015) 1669–1673.

2. T. M. Urbanovich, On the Exceptional Case of the Characteristic Singular Equation with Cauchy Kernel, Differential Equations

52(12) (2016) 1650–1654.





Istanbul / TURKEY


153

Eigenparameter Dependent Discontinuity Condition in Weighted Lebesque Spaces

Telman Gasymov,1 Selim Yavuz2 and Nigar Ahmedzade 1

1Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan 2 Yıldız Technical University, Istanbul, Turkey

[email protected], [email protected], [email protected]

Abstract

In this paper is studied the spectral problem for a discontinuous second order differential operator with a spectral

parameter in transmission conditions. The basicity of eigenfunctions of the spectral problem in weighted Lebesgue spaces is

proved.

We consider a model eigenvalue problem for the discontinuous second order differential operator

),1;3/1()(0;1/3x , y(x))( xy (1)

with boundary conditions

,3/13/103/1,03/103/1,010 myyyyyyy (2)

where is the spectral parameter, m is a non-zero complex number. Such spectral problems arise when the problem of

vibrations of a loaded string with fixed ends is solved by applying the Fourier method [1].

In [2] asymptotic formulas for the eigenvalues and eigenfunctions of the problem (1),(2) are obtained and the

completeness of the eigenfunctions is proved in CLp 1,0 .

Let

r

k

kkttt

1

,

,1,01

mkt be a weight function that satisfies the condition ,/1/1 qp k mk ,1 , where

.1/1/1 qp Let 1,0,pL be a weighted Lebesgue space with norm pLp

ff

, and consider the system

Nniniyy

;2,1,0 ˆˆ in CLp 1,0, , where 3/1,ˆ ,, myxyy nini , and xy ni, are the eigenfunctions of the problem (1),(2).

It is hold the following

Theorem. The system

Nniniyy

;2,1,0 ˆˆ forms a bases for space .1,1,0, pCLp

Keywords: spectral problem, eigenfunctions, basicity,weighted Lebesgue spaces.

References

1. A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics (Mosk. Gos. Univ., Moscow, 1999; Dover, New York,

(2011).

2. Gasymov T.B., G.V. Maharramova. On completeness of eigenfunctions of the spectral problem, Casp. J. of Appl. Math., Ecology

and Economics, 3(2) ( 2015), 66-76.






Istanbul / TURKEY


154

Variational Approximation for Modified Meyer-König and Zeller Operators

Tuğba Yurdakadim1 and Emre Taş2

1Department of Mathematics, Hitit University,

[email protected] 2Ahi Evran University

[email protected]

Abstract

In this talk, we introduce modified Meyer-König and Zeller operators which coincide with the classical Meyer-König and

Zeller operators if 𝝎(𝒙) = 𝒙. We provide sufficient conditions on the boundedness of the total variation of these operators

and we also present a result which deals with the variational approximation of the new modified operators.

Keywords: Meyer-König and Zeller operators, convergence in variation, functions of bounded variation.

References

1. U. Abel, V. Gupta & M. Ivan, The complete asymptotic expansion for a general Durrmeyer variant of the Meyer-König and Zeller

operators. Math. Comput. Modelling 40 (2004), 67-875.

2. C. Bardaro, P.L. Butzer, R.L. Stens & G. Vinti, Convergence in variation and rates of approximation for Bernstein-type

polynomials and singular convolution integrals. Analysis 23 (2003), 299-340.

3. O. Dogru & O. Duman, Statistical approximation of Meyer-K\önig and Zeller operators based on q-integers. Publ. Math. Debrecen

68 (2006), 199-214.

4. H.G. Ince Ilarslan & G. Bascanbaz Tunca, Convergence in variation for Bernstein-type operators. Mediterr. J. Math. 13 (2016),

2577-2592.





Istanbul / TURKEY


155

Hardy-Type Inequalities and Some Related Results

Tugce Unver1 1Department of Mathematics, Kirikkale University,

[email protected]

Abstract

The aim of this talk is to give the characterization of multidimensional reverse Hardy-type inequality for supremal

operator. Discretization tecnique will be used to obtain necessary and sufficient conditions.

We will also present some embedding results between weighted local Morrey-type spaces and weighted Lebesgue spaces,

as well as calculations of the associated spaces of weighted local Morrey-type spaces, based on using the characterization of

direct and reverse multidimensional Hardy-type inequalities.

Keywords: Hardy-type inequalities, discretization, Morrey-type spaces

References

1. Gogatishvili, A., Mustafayev, R. Ch. The multidimensional reverse Hardy inequalities. Math. Inequal. Appl. Vol. 15, No.

1 (2012) 1-14.

2. Kufner, A., Persson, L.-E, Samko, N. Weighted inequalities of Hardy type. Second Edition. World Scientific Publishing Co.

(2017) xx+459 pp. ISBN: 978-981-3140-64-6.

3. Mustafayev, R. Ch., Ünver, T. Embeddings between weighted local Morrey-type spaces and weighted Lebesgue spaces. J. Math.

Inequal. Vol. 9, No. 1 (2015) 277-296.

4. Mustafayev, R. Ch., Ünver, T. Reverse Hardy-type inequalities for supremal operators with measures. Math. Inequal. Appl. Vol.

18, No. 4 (2015) 1295-1311.



https://mathscinet.ams.org/mathscinet/search/author.html?mrauthid=254490


https://mathscinet.ams.org/mathscinet/search/journaldoc.html?id=5116

https://mathscinet.ams.org/mathscinet/search/publications.html?pg1=ISSI&s1=299868





https://mathscinet.ams.org/mathscinet/search/journaldoc.html?id=5116




Istanbul / TURKEY


156

A Spatial Curve Adjoining Another Spatial Curve Based on Bishop Frame

Vahide Bulut

Independent Scholar, Izmir,

[email protected]

Abstract

The adjoint approach is usually used to study on the coupler curves of crank-rocker linkages and the geometry of rigid

objects in spatial motion. In this paper, we expressed the adjoint approach between two spatial curves based on Bishop frame.

We present the velocity of the adjoint curve according to Type-1 and Type-2 Bishop frames of the original curve.

Keywords: Bishop frame, Serret-Frenet frame, adjoint curves.

References

1. Bishop, L.R., There is a more than one way to frame a curve, Amer. Math. Monthly. Vol 82, Issue 3, (1975), 246-251.

2. Hanson, A.J. and Ma, H.H., Parallel Transport Approach to Curve Framing, Tech. Math. Rep. 425, Indiana University Computer

Science Department, (1995).

3. Wang, D. and Xiao, D.Z., Distribution of coupler curves for crank-rocker linkages, Mechanism and Machine Theory, 28, (1993),

671-684.

4. Wang, D., Liu, J. and Xiao, D.Z., Kinematic differential geometry of a rigid body in spatial motion-I. A new adjoint approach

and instantaneous properties of a point trajectory in spatial kinematics, Mechanism and Machine Theory, 32, (1997), 419-432.




Istanbul / TURKEY


157

Theorem on Local Equiconvergence for Dirac Operator

Vali Kurbanov1and Afsana Abdullayeva2

1Institute of Mathematics and Mechanics of NAS of Azerbaijan,

[email protected] 2Azerbaijan State Pedagogical University

[email protected]

Abstract

The Dirac operator with real-valued potential is studied on the interval 2,0G . A theorem on component wise

equiconvergence on the compact of the interval G is proved.

Keywords: Dirac operator, eigen function, equiconvergence, orthogonal expansion.

Consider on the interval 2,0G the Dirac operator

TxyxyyyxPByDy 2,,' 1 ,

where xpxqxpdiagxPB ,,,01

10

and xq are real-valued functions from the class 1, GL .

Let 1kk xu be a complete orthonormed in GL2

2 system of eigen functions of the operator D , i.e. kkk uDu ,

where Rkkk

,

1 is the system of eigen values of this operator.

Let us introduce the partial sum of orthogonal expansion of the function GLxf p2 , 1p in the system

1kk xu :

fxfxfx ,,,, 21 ,

k

xuuffx ikk

i ,, , 2,1i , 0 , Txfxfxf 21 , , xuxuxu kkk21 , . By

2,1,, ifxS we denote a partial sum of trigonometric expansion of the function xf i .

Theorem. Let 1,,;1,2 GLxqxppGLxf p and the following conditions be fulfilled:

1,2

1,

1min

11 11

qpqs

.

Then on any compact GK the following equality is valid:

0,,lim kL

ii

S

fSf

.




Istanbul / TURKEY


158

Determination Young’s Modulus by Using Additional Data in The System Composed of The

Plates with Different Properties

Vildan Yazıcı and Zahir Muradoğlu

Department of Mathematics, Kocaeli University,

[email protected]

[email protected]

Abstract

Production of the materials with the best quality features is one of the important problems in engineering and mechanics.

Nowadays better to carry out computer experiments than laboratory experiments being carried out with large costs. By using

the 2i ig plasticity functions are defined as

2 2i i i,0

2 i2i i 1 2 i i ii,0 2 2 i

i i,0 i2i

G , 0 ,

g x , x , , 0,1 ,G , ,

the mathematical model of the problem of the bending of the system of plates formed by the plates with different mechanical

features that fill i regions is expressed by equation

2 2 2 2 2 22 2

i i i i i i2 2 2 2 2 21 1 2 2 2 1

2 22

i i i

1 2 1 2

ω ω ω ωg ν g ν

x x x x x x

ω2 g 1 ν q x ,

x x x x

where i,0 are the elasticity limits, i are the strain hardness parameters, iE are the Young's modulus, i are the Poisson

constants, i i iG E 2(1 ) are the shear modulus.

In this study, by using the additional conditions, a numerical algorithm was developed to find the Young’s module. This

module is an important feature of any plate in the system of plates. Based on computer experiments, we have developed the

new approach to find the Young’s module. Using our approach one can find the Young’s module faster than by another

method. Obtained results are given in tables and graphs and error analysis is done.

Keywords: Biharmonic equation, Elastic plate, Young’s modulus.

References

1. S.P. Timoshenko, J.N. Goodier, Theory of Elasticity, McGraw Hill, New York, 1970.





Istanbul / TURKEY


159

A Solution of Airy Differential Equation via Natural Transform

Yasin Ucakan1, Kevser Koklu2 and Seda Gulen3

1Department of Mathematical Engineering, Yildiz Technical University

[email protected] 2Department of Mathematical Engineering, Yildiz Technical University

[email protected] 3Department of Mathematics, Namik Kemal University

[email protected]

Abstract

Integral transformations and special functions have an important place in engineering mathematics. In addition to well-

known transformations such as Fourier, Laplace and Mellin, a new transformation called Natural Transformation which is

more general form of Laplace transformation, has brought a new breath to solve the problems that arise in engineering

applications. In this work the Airy differential equation which is important in physical sciences is solved by Natural Transform

and Airy function solutions are obtained.

Keywords: Airy function, Natural transform.

References

1. Z. H. Khan and W. A. Khan, N-Transform Properties and Applications, NUST Journal of Engineering Sciences, 1(1) (2008),

127–133.

2. F. B. M. Belgacem and R. Silambarasan, Theory of Natural Transform, Mathematics in Engineering, Science and Aerospace

Mesa., 3(3) (2012), 99-124.

3. K. Shah, M. Junaid, N. Ali, Extraction of Laplace, Sumudu, Fourier and Mellin transform from the Natural transform, Journal of

Applied Enviromental and Biological Sciences, 5(9) (2015), 1-10.

4. W. A. Geyi, A time-domain theory of waveguides, Progress in Electromagnetics Research (PIER) , 59 (2004), 267-297.

5. V. V. Borisov, Transient Electromagnetic Waves, Leningrad Univ. Press, Leningrad, 1987 (in Russian).






Istanbul / TURKEY


160

Componentwise uniform equiconvergence theorem for a third order differential operator

Yuliya G.Abbasova

Institute of Mathematics and Mechanics of NASA, Azerbaijan

[email protected]

Abstract

On a compact we study componentwise uniform equiconvergence of orthogonal expansion of a vector- function from

the class 𝑊1,𝑚1 (𝐺) , 𝐺 = (0,1)

in eigen vector- functions of a third order differential operator with trigonometric decomposition

and the rate of componentwise uniform equiconvergence on a compact is estimated.

Keywords:Eigen vector-function,equiconvergence,spectral expansion.

In the interval 𝑮 = (𝟎, 𝟏)

,we consider the operator

𝑳𝜳 = 𝜳(𝟑) + 𝑼𝟐(𝒙)𝜳(𝟏) + 𝑼𝟑(𝒙)𝜳

with matrix coefficients 𝑼𝒍(𝒙) = (𝒖𝒍𝒊𝒋(𝒙))𝒊,𝒋=𝟏𝒎 , 𝒍 = 𝟐, 𝟑 , 𝒘𝒉𝒆𝒓𝒆 𝒖𝒍𝒊𝒋(𝒙) 𝝐 𝑳𝟏(𝑮) a complex valued functions.

Assume that 𝜳𝒌(𝒙)𝒌=𝟏∞ is the complete system of vector eigenfunctions of the operator 𝑳 ortonormal in 𝑳𝟐

𝒎(𝑮) .By

𝝀𝒌𝒌=𝟏∞ we denote the corresponding system of eigen values.Moreover, we assume that 𝑹𝒆 𝝀𝒌 = 𝟎.Parallel with the spectral

parametr 𝝀𝒌, we consider a parametr 𝝁𝒌: 𝝁𝒌 = (−𝒊𝝀𝒌)𝟏

𝟑⁄ 𝒇𝒐𝒓 𝑰𝒎 𝝀𝒌 ≥ 𝟎 ; 𝝁𝒌 = (𝒊𝝀𝒌)𝟏

𝟑⁄ 𝒇𝒐𝒓 𝑰𝒎 𝝀𝒌 < 𝟎 (𝒔𝒆𝒆[𝟏], [𝟐])

We now introduce a partial sum of spectral expansion of the vector function 𝒇(𝒙)𝝐𝑾𝟏,𝒎𝟏 (𝑮) in the system

𝜳𝒌(𝒙)𝒌=𝟏∞ : 𝝈𝝂(𝒙, 𝒇) = (𝝈𝝂

𝟏(𝒙, 𝒇), 𝝈𝝂𝟐(𝒙, 𝒇), … , 𝝈𝝂

𝒎(𝒙, 𝒇)) , 𝝈𝝂𝒋 (𝒙, 𝒇) = ∑ (𝒇,𝝁𝒌≤𝝂 𝜳𝒌)𝜳𝒌

𝒋 (𝒙), 𝒋 = 𝟏, 𝒎 , 𝜳𝒌(𝒙) =

(𝜳𝒌𝟏(𝒙), 𝜳𝒌

𝟐(𝒙), … , 𝜳𝒌𝒎(𝒙)).

Denote by 𝑺𝝂(𝒙, 𝒇𝒋), 𝒋 = 𝟏, 𝒎 , the partial sum of trigonometric series of function 𝒇𝒋(𝒙).

Consider the difference ∆𝝂𝒋 (𝒙, 𝒇) = 𝝈𝒋(𝒙, 𝒇) − 𝑺𝝂(𝒙, 𝒇𝒋), 𝒋 = 𝟏, 𝒎 .

Theorem. Let the elements 𝒖𝟐𝒊𝒋(𝒙), 𝒋 = 𝟏, 𝒎 , of the 𝒊 - throw of the matrix 𝑼𝟐(𝒙) belong to the class 𝑳𝒑(𝑮), 𝒑 > 𝟏 and

𝒇(𝒙)𝝐𝑾𝟏,𝒎𝟏 (𝑮) .Then for any compact 𝑲 ⊂ 𝑮 the following estimation is valid:

‖∆𝝂𝒋 (•, 𝒇)‖

𝑪(𝑲)= 𝜪 (𝝂−𝟏

𝟐⁄ ) , 𝝂 → +∞ .

References:

1. V.A.Ilin and I.Joo.Estimation of difference of partial sums of expansions responding to two arbitrary non-negative self-adjoint

extensions of two Sturm-Liouville operators for absolutely continouns function,Differ.Uravn.15(7),1175-1193 (1979).

2. Yu.G.Abbasova and V.M.Kurbanov, Convergence of the spectral decomposition of a function from the class 𝑊1,𝑚1 (𝐺), 𝑝 > 1, in

the vector eigenfunctions of a differential operator of the third order,Ukr.Math.Zh.,Vol.69. 6, 2017, p.719-733.




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161

On the Solutions of reaction-diffusion equations

Zehra Pinar1 and Hüseyin Kocak2

1Department of Mathematics, Namık Kemal University,

[email protected] 2 Quantitative Methods Department, Pamukkale University

[email protected]

Abstract

In this study, the class of auxiliary equations is extended to classical Bernoulli equation which considered by various

researchers to a variable-coefficient Bernoulli type equation. The proposed variable-coefficient Bernoulli type auxiliary

equation produces many new solutions comparing to classical Bernoulli equation which produce two solutions only.

Consequently, the new exact travelling wave solutions of some Kuramoto-Sivashinsky equation in terms of these new

solutions of the variable-coefficient Bernoulli type equation is obtained.

Keywords: Kuramoto-Sivashinsky equation, Bernoulli equation,Auxiliary equation method.

References

1. N. K. Vitanov, Application of simplest equations of Bernoulli and Riccati kind for obtaining exact traveling-wave solutions for

a class of PDEs with polynomial nonlinearity, Commun Nonlinear Sci Numer Simulat 15 (2010) 2050–2060

2. M. Hayek, Exact and traveling-wave solutions for convection–diffusion–reaction equation with power-law nonlinearity,

Applied Mathematics and Computation 218 (2011) 2407–2420

3. Z. Pinar, H. Kocak, Exact solutions for the third-order dispersive-Fisher equations. Nonlinear Dyn 91(1) (2018) 421-426.





Istanbul / TURKEY


162

On Weighted Zorko Subspaces and Riesz type Theorems for Analytic Functions

Yusuf Zeren1 and Selim Yavuz1

1 Department of Mathematics, Yildiz Technical University, Istanbul, Turkey


Abstract

The concept of Morrey space was introduced by C. Morrey [1] in 1938 in the study of qualitative properties of the solutions

of elliptic type equations with BMO (Bounded Mean Oscillations) coefficients (see also [2;3]). There appeared lately a large

number of research works which considered many problems of the theory of differential equations, potential theory, maximal

and singular operator theory, approximation theory, etc in Morrey-type spaces (for more details see [1-9]). It should be noted

that the matter of approximation in Morrey-type spaces has only started to be studied recently (see, e.g., [5-8]), and many

problems in this field are still unsolved. This work is just dedicated to this field.

In this paper the weighted Morrey space is considered on the interval , and its Zorko subspace, in which the shift

operator is continuous, is defined. Some properties of the functions from this subspace are studied. Moreover, a new version

of the Riesz theorem on analytic functions from Hardy class is established.

Keywords: Morrey space, Riesz theorem, Hardy classes.

References

1. Morrey C. B. On the solutions of quasi-linear elliptic partial differential equations, Trans. Amer. Math. Soc. 43(1938), 207-226.

2. Anna L. Mazzucato, Decomposition of Besov-Morrey spaces, in ”Harmonic Analysis at Mount Holyoke”, American Mathematical

Society Contemporary Mathematics, 320(2003) 279-294.

3. Chen Y. Regularity of the solution to the Dirichlet problem in Morrey space, J. Partial Differ. Eqs. 15 (2002) 37–46.

4. N. Samko, Weight Hardy and singular operators in Morrey spaces, J. Math. Anal. Appl. 35(1) (2009) 183–188.

5. D. M. Israfilov and N. P. Tozman, Approximation by polynomials in Morrey–Smirnov classes, East J. Approx. 14(3) (2008) 255–

269.

6. D. M. Israfilov and N. P. Tozman, Approximation in Morrey–Smirnov classes, Azerbaijan J. Math. 1(1) (2011) 99–113.

7. Bilalov B.T., Quliyeva A.A. On basicity of exponential systems in Morrey-type spaces. International Journal of Mathematics. Vol.

25, No. 6 (2014) 1450054 (10 pages).

8. Bilalov B.T., Gasymov T.B., Quliyeva A.A., On solvability of Riemann boundary value problem in Morrey-Hardy classes, Turk.

J. Math., 40, (2016), 1085-1101

9. Adams D.R. Morrey spaces, Springer, 2016





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On a solvability for some variable exponent eigenvalue problem

Yusuf Zeren1 Lutfi Akin2 Kader Simsir3 and Caner Kazar4


[email protected] 2Department of Business Administration, Mardin Artuklu University

[email protected] 3Yildiz Technical University,

[email protected] 4Yildiz Technical University,

[email protected]

Abstract

Applying a new bounded ness and compactness results for Hardy's operator x

dttf0

)(

x

dttf )( and its conjugate

in variable exponent spaces ),0((.) lLp and the Mountain Pass Theorem approaches an existence result for the eigenvalue

problem:

))(( 2

1)(21)(2)(

xlxxayxlxyyyxq

xpxp (1)

with boundary conditions

0)()0( lyy (2)

.

have been stated. The exponent functions ),1(),0(:)(),( lxqxp are function from the class:

2

:1

ln)()(x

xyCx

xpyp . (3)

We search for a positive suolution of the problem (1 ) satisfying (2).

Theorem. Let 1 < 𝑝− < 𝑝(𝑥) ≤ 𝑞(𝑥) ≤ 𝑞+ < ∞ be measurable functions on (0, 𝑙) satisfying condition (3), moreover

they are such that

p

qp1

1

1

,

where

1,

11

p is a fixed number. Then for any fixed 𝜆 > 0 the problem (1), (2) has a nontrivial positive

solution.

Keywords: Montain Pass Theorem, variable exponent Lebesgue spaces, bounded and compact embedding, Hardy;s operator.

References:

1. F.I. Mamedov and Y. Zeren, A necessary and sufficient condition for Hardy's operator in the variable Lebesgue space, Abst. Appl.

Anal., 5/6, 2014, 7 pages.

2. F.I. Mamedov and S. Mammadli, Compactness for the weighted Hardy operator in variable exponent spaces, Compt. Rend. Math.,

355(3), 325-335, 2017.







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POSTER SESSION

Reconstruction Of Tomographic Images From Limited Projections Using Tvcim-P Algorithm

Abdessalem BENAMMAR1 Aicha ALLAG1,2, Redouane DRAI1

1Research Center in Industrial Technologies (CRTI),P.O.Box 64, Cheraga, Algiers, ALGERIA,

[email protected] 2University of Sciences and Technology Houari Boumédiène, USTHB, BP 32, El-Alia, DZ-16111 Algiers, ALGERIA

[email protected]

Abstract

Computed tomography (CT) has great impact in many fields such as medical applications, industrial inspection, etc...

Low dose constraints and Limited projection are common problems in a variety of tomographic reconstruction examples

which lead to wrong data. In this work, we propose a method of CT reconstruction based on the simultaneous iterative

reconstruction techniques SIRT improved by imposing positivity constraint in the total variation (TVcim-p). We test our

method with on Shepp-Logan phantom on different reconstruction methods. The results show that the proposed algorithm can

gives images with quality comparable to other algorithms.

Keywords: Computed tomography; Image Reconstruction; Total Variation Minimization; SIRT; Cimmino method.

References

1. D. Kim, S.J. Park, B. Jo, H. Kim, & H.J. Kim, "Investigation of sparse-angle view in cone beam computed tomography (CBCT)

reconstruction algorithm using a sinogram interpolation method", World Congress on Medical Physics and Biomedical

Engineering, June 7-12, 2015, Toronto, Canada.

2. Hong Shangguan, Quan Zhang, Yi Liu, Xueying Cui,Yunjiao Bai, Zhiguo Gui, "Low-dose CT statistical iterative reconstruction

viamodified MRF regularization", Computer methods and programs in biomedicine 123 (2016) 129–141.

3. Per Christian Hansen, Maria Saxild-Hansen, "AIR Tools — A MATLAB package of algebraic iterative reconstruction

methods", Journal of Computational and Applied Mathematics, V236, Issue 8, February 2012, Pages 2167-2178.





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165

On The Misconceptions of 10th Grade Students about Analytical Geometry

Ayten Özkan1, Erdoğan Mehmet Özkan1 1Department of Mathematics, Yildiz Technical University,

[email protected]

Abstract

Mathematics is the most important tool of science and technology and a part of everyday life. Mathematics education is an important factor in the rational approach of individuals to analytical thinking and problem solving problems. Misconceptions is one of the factors that complicate the mathematics education. The aim of this research is to determine the relationship between misconceptions and analytical concepts. In the first stage, an open-ended exam was applied to 2552 tenth-grade students studying at 19 high schools under İstanbul Provincial Directorate of National Education and 299 students from two high schools were tested in the second stage. In the last stage, In the last stage,10 students were interviewed. Errors and misconceptions of the students in the questions covering the analytic geometry were examined. At the end, it was concluded that knowledge levels, errors and misconceptions of students in the analytic geometry should be

identified to use proper instructional strategies. It is necessary to design different activities to improve the levels of students

who cannot comprehend the analytic geometry on the level of their classrooms. This will ensure that the whole classroom

achieves the same comprehension level. A decrease in errors and misconceptions will be observed and misconceptions will be

identified more easily. Eliminating the misconceptions is possible by getting beyond the traditional instructional methods and

keeping the teacher from the role of information transferer and the student from the role of passive listener.

Keywords: Morrey-type classes, harmonic functionsStatistical Convergence, λ- statistical convergence, Cintuitionistic fuzzy

2-normed space.

References:

1. Kazemi, F., Ghoraishi, M. Comparison of problem-based learning approach and traditional teaching on attitude, misconceptions

and mathematics performance of University Students. Procedia-Social and Behavioral Science, 46, 3852–3856, 2012.

2. Kustos, P., Zelkowski, J. Grade-continuum trajectories of four known probabilistic misconceptions: What are students’ perceptions

of self-efficacy in completing probability tasks?. The Journal of Mathematical Behaviory, 32(3) : 508–526, 2013

3. Lai, M. Y., Wong, J. P. Revisiting decimal misconceptions from a new perspective: The significance of whole number bias in the

Chinese culture. The Journal of Mathematical Behaviory, 47 , 96–108, 2017

4. Ozkan, A., Ozkan, E. M. Misconceptions and learning difficulties in radical numbers. Procedia-Social and Behavioral Science, 46,

462–447, 2012.




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166

Private Information Retrieval

Fatih Demirkale and Edanur Taştan

Department of Mathematics, Yildiz Technical University,

[email protected]

[email protected]

Abstract

In today’s world, it is quite easy to access to the information people want by means of the databases that are used in

public. On the other hand, this poses an important risk to users’ privacy because the servers of database know a lot things

about the users.

The goal of this poster is to lead lower communication complexity during the retrieval process. Therefore, we give a

definition of k-server Private Information Retrieval (PIR) protocol by replicating the database on k servers ( k ≥ 2) [1].

The main idea is that each server which has a copy the database does not figure out the specific record which the user

interested in. We also demonstrate an example of 2-server PIR protocol.

Keywords: Private Information Retrieval, complete privacy, communication complexity

≥≥

References

1. Benny Chor, Eyal Kushilevitz, Oded Goldreich, and Madhu Sudan. Private information retrieval. J. ACM, 45(6):965981,

1998.

2. Benny Chor, Oded Goldreich, Eyal Kushilevitz, and Madhu Sudan. Private information retrieval. In 36th Annual Symposium

on Foundations of Computer Science, Milwaukee, Wisconsin, 23-25 October 1995, pages 4150. IEEE Computer Society,

1995.


mailto:%20%20%[email protected]



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167

Some Classical Solutions of Dirac-Gursey Field Equation

Fatma Aydogmus1 and Eren Tosyali2

1Department of Physics, Istanbul University,


2Istanbul Bilgi University

[email protected]

Abstract

In this study, we consider the classical equation derived from the conformal invariant 4D pure spinor fermionic

system obtained by the Heisenberg’s ansatz. This classical field equation has particle-like solutions so-called instantons.

It is well known that instantons are classical solutions that originate from topological structure of vacuum in non-Abelian

gauge field theories with zero energy and finite action. We simulate the phase portraits and Poincare sections of the system

numerically.

References

1. P. A. M. Dirac, The quantum theory of the electron, Proc. R. Soc. London 23 (1928)

351–361, DOI:10.1098/rspa.1928.00.

2. W. Heisenberg, Zur quantentheorie nichtrenormierbarer wellengleichungen, Z. Nat.

9a (1954) 292.

3. F. Gursey, On a conform-invariant spinor wave equation, Nuovo Cimento 3 (1956)988 4. F. Aydogmus, Dynamics of excited instantons in the system of forced Gursey nonlinear

differential equations, J. Exp. Theor. Phys. 120(2) (2015) 210–216.

5. F. Aydogmus, Chaos in a 4D dissipative nonlinear fermionic model, J. Mod. Phys. C 26(7) (2015) 1550083

6. F. Aydogmus, Unstable Behaviours of Classical Solutions in Spinor-type Conformal

Invariant Fermionic Models, J. Exp. Theor. Phys. 125(5) (2017) 719–727..






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168

A New Topp-Leone Extended Weibull Distribution as a Sampling Distribution

Gamze Özel Kadılar1 and Cem Kadılar2

1,2Department of Statistics, Hacettepe University,


Abstract

In this article, a new extension of the Weibull distribution named as Topp-Leone extended Weibull distribution is proposed. Several statistical properties for the new distribution including quantile function, moments, moment generating function, and generating function are studied.. Distributional characteristics as an sampling distribution are given. The parameters are estimated by method of maximum likelihood. The effectiveness of proposed model is analysis with means of a simulation study.

Keywords: Weibull distribution, maximum likelihood estimation, Topp-Leone distribution, moments, simple random

sampling.

References

1. Afify, A. Z., Cordeiro, G. M., Yousof, H. M., Saboor, A., & Ortega, E. M. M. (2016). The Marshall-Olkin additive Weibull

distribution with variable shapes for the hazard rate. Hacettepe Journal of Mathematics and Statistics, Forthcoming.

2. Alzaatreh, A., Lee, C., & Famoye, F. A. (2013). A new method for generating families of continuous distributions, Metron

71, 63-79.

3. Aryal, G. R., & Tsokos, C. P. (2011). Transmuted Weibull distribution: a generalization of the Weibull probability

distribution. European Journal of Pure and Applied Mathematics, 4, 89-102.

4. Aryal, G., & Elbatal, I. (2015). On the Exponentiated Generalized Modified Weibull Distribution. Communications for

Statistical Applications and Methods, 22, 333-348.

5. Balakrishanan, N., Leiva, V., Sanhuzea, A., & Cabrera, E. (2009). Mixture inverse Gaussian distributions and its

transformations, moments and applications. Statistics, 43, 91-104.

6. Kadilar, C., Cingi, H. (2004). Ratio estimators in simple random sampling. Applied Mathematics and

Computation, 151, 893 – 902 .





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169

A Fuzzy Approach to the Estimation of PM Levels

Kardelen Kılıç1 and Filiz Kanbay2

1Department of Mathematics, Yildiz Technical University

[email protected] 2 Department of Mathematics, Yildiz Technical University

[email protected]

Abstract

In this study, Particulate Matter amounts emitted from the vessels passing through the Dardanelles are estimated by using

Fuzzy Inference System in MATLAB. The results are illustrated by surfaces.

Keywords: Fuzzy Inference System, Fuzzy, Emission, Surface.

References

1. A. Kilic, Marmara Denizi’nde Gemilerden Kaynaklanan Egzoz Emisyonları, Balıkesir Üniversitesi Fen Bilimleri Enstitüsü

Dergisi, 11(2009), 124-134.

2. U. Kesgin, N. Vardar, A Study on Exhaust gas Emissions from Ships in Turkish Straits, Atmospheric Environment,

35(2001), 1863-1870.

3. C. Deniz, Y. Durmusoglu, Estimating Shipping Emissions in the Region of the Sea of Marmara, Turkey Science of the

Total Environment, 390(2008), 255-261.

4. https://atlantis.udhb.gov.tr/istatistik/gemi_gecis.aspx

5. https://www.epa.gov/pm-pollution





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170

On Discrete Morse Theory

Mustafa Akkaya and İsmet Karaca

Department of Mathematics, Ege University,

[email protected]

[email protected]

Abstract

Discrete Morse theory is one of the practical methods in order to investigate the topology of a simplicial complex.

The main idea of this theory is to determine the critical points of a discrete function. This process can be done by searching

a discrete gradient vector field on a simplicial complex or the monotone decreasing graph property that gives rise to a

simplicial complex. The topology of this simplicial complex can be deduced from discrete gradient vector field. In this

poster, we focus on some examples explaining the main idea of this theory.

Keywords: CW-complex, discrete Morse theory, gradient vector fields, simplicial complexes.

References:

1. R. Diestel, Graph Theory, New York: Springer-Verlag (2005).

2. R. Forman, A User's Guide To Discrete Morse Theory, Seminarie Lotharingien de Combinatorie, 48:B48C (2002) 1-35.

3. K. P. Knudson, Morse Theory: Smooth and Discrete, World Scientific Publishing C.O. (2015).

4. J. Milnor, Morse Theory, Annals of Mathematics Studies Number 51 Princeton, New Jersey: Princeton University Press

(1963).





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171

Stability analysis of conformable fractional-order nonlinear systems Ghania Rebiai, Abdellatif Ben Makhlouf

Department of Mathematics, University of 8 Mai 1945 Guelma,BP 401, Guelma 24000. Algeria.


University of sfax,tunis

Abstract In this paper, we study the uniformly fractional exponential stability for some class of systems like class of perturbed

systems and class of nonlinear fractional-order equations with control using the Lyapunov-like function.

Keywords: Conformable, fractional derivative, factional practical exponential stability.

References

1. Abdeljawad,T.,\On conformable fractional calculus,"J. Comput.Appl.Math., vol. 279, pp 57-66, 2015

2. Batar_, H., Losada, J., Nieto, J J. and Shammakh, W. \Three-point boundary value problems for conformable fractional

di_erential equations," J. Funct. Spaces, pp.Art ID 706383, 6, 2015. 3. Ben Hamed, B.,Haj Salem,Z., Hammami, M.A.(2013). "Stability of nonlinear time- varying perturbe di_erential equations,"

Nonlinear Dynamics.,vol. 73,pp 1353-1365. 2013 4. Ben Makhlouf, A. and Hammami,M . A. \The convergence relation between ordinary and delay-integro-di_erential

equations,"In t. J. Dyn. Syst. Di_er. Equ., vol. 5, pp 236-247, 2015.





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172

Analysis of Judd–Ofelt theory to the rare earth ion Pr3+ doped KY3F10 single crystal

S. Khiari1,2 and M. Diaf2

1Université Chadli Bendjedid, 36000 W.El Tarf, Algeria

[email protected] 2Université Badji Mokhtar-Annaba, BP 12, 23000 Annaba, Algeria,

[email protected]

Abstract

Rare earth-doped fluoride single crystals are considered to be an important class of optical device materials due,

mainly, to their low phonon energies. Pr3+ doped fluoride and oxide crystals and glasses are being studied since a long

time for their UV emissions for scintillator and broad band laser applications, their visible ones for multicolor lasers in

high definition TV and medical applications, and their near-infrared one for fiber optics communications. Among the rare

earth, trivalent praseodymium ions (Pr3+) have potential for laser applications due to a large number of available energy

levels in the visible and near infrared domains.

Room temperature absorption spectra were recorded. Several absorption bands in the visible and near IR range were

observed and can be ascribed to the 4f–4f transitions of Pr3+. The Judd–Ofelt (J–O) [1-2] theory has been applied to the

analysis of the absorption spectra.

Based on the Judd – Ofelt theory, three intensity parameters were obtained. The spectroscopic parameters of this

crystal such as the oscillator strengths, radiative transition probabilities, radiative lifetimes as well as the branching ratios

were calculated.

The emission spectra have been also registered between 470 and 650 nm. Some important spectroscopic parameters

were obtained based on the Judd–Ofelt theory and the Fuchtbauer –Ladenburg formula. The discussions about the effect

of crystal structure on the spectroscopic properties of Pr3+ ions were given.

Keywords: rare earth trivalent ion (Pr3+), absorption spectra, Judd-Offelt Analysis, emission spectra.

References 1. B.R. Judd, Phys. Rev. 127 (1962) 750

2. G.S. Ofelt, J. Chem. Phys. 37 (1962) 511



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173

Note on A-Polynomial of Knots

SelinHatipoğlu*,İsmetKaraca, Ege University, Department of Mathematics, Bornova, 35100,Izmir, Turkey

*Corresponding author: [email protected]

Abstract

In this poster,our aim is to introduce the definition of the A-Polynomial which relates representations of the

fundamental group of a knot into special linear group. To calculate the A-Polynomial, we have to find the fundamental

group of knots. For this reason, we deal with the Wirtinger presentation for calculating fundamental group of knots

andsome properties of the A-polynomial. Finally, we mention de Rham’s Representation to understand the notions of

longitude and meridian of a knot.

Keywords:Knot,link,knot invariants,fundamental group of knots,Wirtinger presentation, matrix representation,A-

polynomial.

References

1. D. Bullockand W. L.Faro, TheKauffmanbracketskeinmodule of a twistknotexterior, AlgebraicandGeometricTopology, 5,

pp. 107-118, 2005.

2. D. Cooper and D. Long, Representationtheoryandthe A- polynomial of a knot, Chaos,SolitonsandFractals, 9 (4/5), pp. 749-

763, 1998.

3. R. Gelca, On therelationbetweenthe A-polynomialandtheJonespolynomial, Proceedings of theAmerican Mathematical

Society, 130 (4), pp. 1235-1241, 2002.

L. Kauffman, StatesmodelsandtheJonespolynomial, Topology, 26, pp. 395-407, 1987.



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174

A Fuzzy Approach to the Estimation of 𝑪𝑶𝟐 Emission Emitted from the Land and Sea

Transport

Yasemin Ergin1 and Filiz Kanbay2



[email protected]

Abstract

In this study, by using fuzzy the differences between the estimating emissions emitted from the land and sea

transport are examined. The estimating emissions are expressed surfaces and these results allow the analysis of the data

of the land and sea transport.

Keywords: Emission, Fuzzy, Fuzzy inference system, Surfaces.

References

1. A. Kilic, Marmara Denizi’nde Gemilerden Kaynaklanan Egzoz Emisyonları, Balıkesir Üniversitesi Fen Bilimleri Enstitüsü

Dergisi, 11(2009), 124-134

2. T. V. Ramachandra, Shwetmala, Emissions from India's transport sector: Statewise synthesis, Atmospheric Environment,

43(2009), 5510-5517.

3. U. Kesgin, N. Vardar, A Study on Exhaust Gas Emissions from Ships in Turkish Straits, Atmospheric Environment,

35(2001), 1863-1870.

4. S. Saija, D. Romano, A Methodology for The Estimation of Road Transport Air Emissions in Urban Areas of Italy,

Atmospheric Environment, 36(2002), 5377-5383.

5. https://www.normalbreathing.com/CO2.php





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INDEX

A

A. Hamdi2, 24 A. Nese Dernek1, 56 Abdellatif Ben Makhlouf, 171 Abdessalem BENAMMAR1, 164 Abdullah Ahmetoğlu2, 25 Abdurrahim Guliyev, 26 Abdurrahim Guliyev3, 43 Adem C. Cevikel1, 27, 28 Adem Cengiz Cevikel2, 125 Ahu Coşkun Özer2, 69 Ahu Ercan1, 42 Aicha ALLAG1,2, 164 Alaattin Akyar1, 29 Ali Aydoğdu1, 31 Ali Aydoğdu2, 32 Ali Demir1, 30 Ali Demir2, 111 Ali Huseynli, 33 Amiran Gogatishvili, 17, 18 Aydin Gezer2, 116 Ayhan Serbetci1, 38 Ayhan Şerbetçi, 34 Aykut Or1, 65 Aykut Or2, 66 Ayse Nese Dernek1, 72 Ayten Özkan1, 165

B

Başer Tambaş2, 35 Bilal Bilalov, 19 Birol Gündüz1, 123 Birol Gündüz2, 124 Burak Oğul1, 36, 37 Burcu Ungor2, 76

C

Canay Aykol1, 38 Caner Kazar, 5 Caner Kazar4, 163 Cem Kadılar2, 168 Cemil Karacam2, 136 Cennet Çimen1, 39 Ceren Sultan ELMALI1, 40 Coşkun Yakar2, 120 Cumali Ekici1, 86 Cumali Ekici3, 75 Cuneyt Yazici2, 102

D

Dağıstan Şimşek2,3, 36, 37 David Edmunds, 17, 18 Deniz Gökalp1, 41 Devrim Çakmak2, 25 Dogan Kaya1, 74 Dursun Irk1, 52, 107, 108, 131

E

Edanur Taştan, 166 Ekrem SAVAS, 20, 22 Elif Deniz, 5 Elif Deniz1, 43 Elif Tan1, 44 Elif Tan2, 142 Elif Tekin Tarım, 45 Elveda Gamze Memiş, 45 Emrah Evren Kara2, 109, 132, 133 Emrah Evren Kara3, 110 Emre Taş1, 46 Emre Taş2, 154 Engin Özkan1, 32 Engin Özkan2, 31 Erdal Gül1, 48 Erdoğan Mehmet Özkan1, 165 Eren Tosyali1, 49 Eren Tosyali2, 58, 167 Erhan Pişkin, 50 Ertugrul Ates 1, 51 Evren Topcu1, 52 Evren Topçu1, 107

F

Farman Mamedov1,3, 21 Faruk Dusunceli, 5, 53 Faruk Dusunceli1, 54 Faruk Düşünceli3, 98 Fateh Mebarek Oudina1, 100 Fatih Aylikci2, 56 Fatih Demirkale, 166 Fatih Karabacak1, 57 Fatih Sirin2, 33 Fatima Guliyeva, 59 Fatma Aydogmus1, 58, 167 Fatma Aydogmus2, 49 Fatma Solmaz2, 123 Fatma Yavcin, 60 Fatmanur Gursoy2, 146 Fedakar Çakır1, 61 Fidan Seyidova3, 33



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Fikriye Nuray Yılmaz, 62 Filiz Kanbay2, 169, 174 Filiz Karaman1, 67 Fuat Usta1, 63

G

G. Selin Savaşkan1, 66 G. Selin Savaşkan2, 65 Gamze Özel Kadılar1, 168 Ghania Rebiai, 171 Gizem S. Öztepe, 64 Godrick Oketch1, 67 Gözde Özyurt1, 68 Gulcin Bozkurt2, 72 Gulistan Iskandarova2, 74 Gülçin Bozkurt2, 73 Gülden Gün Polat1, 69 Gülşah Aydın Şekerci2, 75

H

H. Alsaoud1, 24 Hajiyeva Gunel Razim, 70 Handan Kose1, 76 Hasan Bayram1, 77 Hasan Es, 78 Hatice Çay2, 84, 85 Hatice Gülsün Akay, 87, 88 Hatice Tozak1, 75 Hatice Tozak2, 86 Hatice Yalman Kosunalp1, 79, 80 Huriye KADAKAL3, 140 Huseyin Tunc1, 83 Hussain Al-Qassem 1, 89 Hülya Burhanzade, 90 Hüseyin Kocak2, 91, 161

I

Ibrahim Senturk1, 92 Ilker Ustoglu 2, 51 Ilknur Temli2, 93

İ

İ.İlker Akça, 87 İlknur Özgüç, 94 İmdat İŞCAN1, 140, 141 İrem Küpeli Erken, 95 İsmail Özcan, 96, 139 İsmet Karaca, 170 İsmet Yıldız1, 29 İsmetKaraca, 173

K

Kader Simsir3, 163

Kadir Emir, 88 Kardelen Kılıç1, 169 Kevser Koklu2, 159

L

Leslie Cheng2, 89 Leyla Bugay1, 97 Lutfi Akin2, 54, 163 Lütfi Akın, 99 Lütfi Akın1, 98

M

M. Diaf2, 172 Mahir KADAKAL1, 141 Mardanov M.J., 112 Mehmet Albayrak2, 48 Mehmet Ercoban1, 102 Mehmet Gürdal1, 114 Mehmet Niyazi Çankaya1, 103, 104 Mehmet Onat, 101 Mehmet Şirin Demir, 105, 106 Melda Turhan1, 52, 107 Melikov T.K., 112 Melis Zorsahin Gorgulu1, 108 Merve İlkhan1, 109, 110 Merve Taştan1, 32 Metin Bayrak2, 30, 111 Mine Aylin Bayrak1, 111 Mine Aylin Bayrak2, 30 Mohammad Almahameed, 113 Mualla Birgül Huban1, 114 Muhammet Cihat Dağlı, 115 Murat Alan1, 118 Murat Altunbas1, 116 Murat Kirişci1, 81 Murat Koparan2, 61 Murat Sari1, 83 Murat Şahin3, 44, 142 Murat Tanışlı1, 147 Murat Turhan1, 117 Murat Yoğurtçu2, 118 Mushfiq Aliyev, 26 Mustafa Akkaya, 170 Mustafa Bayram Gücen1, 120 Mustafa Dede3, 86 Mustafa Doğan1, 143 Mustafa Fahri Aktaş1, 25 Mustafa Gezek, 5, 119 Mustafa Gülsu3, 79, 80 Muttalip Özavşar1, 84, 85 Mübariz T. Garayev2, 114 Müjdat Kaya, 121 Mümün Can, 115

N

Necip Şimşek2, 81, 110 Nejla Özmen1, 150



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Neslihan Uyanık3, 29 Neşe Dernek1, 73 Nigar Ahmedzade, 153 Nilgün Aygör, 122 Nuran Guzel, 60 Nurtilek Jamshitov4, 36

O

Osman Alagöz1, 124 Osman Alagöz3, 123 Oya Mert2, 29 Ozgur Yildirim1, 125

Ö

Ömer Faruk Doğan1, 126, 127 Ömer Ünsal1, 61 Özcan Sert1, 128 Özgür Yıldırım2, 27, 28

P

Peil Esengul kyzy4, 37 Pembe Ipek Al1, 129 Pembe Ipek Al2, 130 Pınar Keskin Yıldız1, 131 Pınar Zengin Alp1, 132, 133

R

Ramazan Akgün, 134, 135 Raziyya Hasanli1, 136 Redouane DRAI1, 164 Rukiye Öztürk Mert3, 130 Rukiye Öztürk3, 31

S

S. Khiari1,2, 172 Saadet S. Özer, 137 Sabina Sadigova1, 59 Saleem Abdullah1, 138 Salih Aytar, 96, 139 Salih Celik1, 93 Sayali Mammadli1, 21 Seda Gulen3, 159 Selahattin MADEN2, 140, 141 Selim Yavuz, 5 Selim Yavuz1, 162 Selim Yavuz2, 153 SelinHatipoğlu*, 173 Semih Yılmaz1, 142 Semih Yılmaz2, 44 Serpil Uslu1, 117 Sevgi Akten2, 143 Seyma Cetin2, 19 Sezgin Akbulut3, 124

Sezgin Akbulut4, 123 Shahzaib Ashraf 1, 138 Sibel Yalcin2, 77 Sibel Yalçın2, 148 Sinan ERCAN1, 144 Sufii Hamad Mussa1, 83 Sule Soytürk2, 150 Sumeyra Bedir1, 146 Süleyman Demir1, 147

Ş

Şahsene Altınkaya1, 148 Şerife Müge EGE, 149 Şerife Müge Ege2, 47 Şükrü Tortop1, 151

T

T.S. Al-Maadeed, 24 Tahsin Oner2, 92 Tamer UĞUR2, 40 Tatsiana Urbanovich1,2, 152 Telman Gasymov, 153 Tengiz Kopaliani, 17, 18 Teoman Özer 3, 69 Tugce Unver1, 155 Tuğba Yurdakadim1, 154 Tuğba Yurdakadim2, 46 Tuncer Kaya1, 35 Tülay Yıldırım2, 41

V

Vagif S. Guliyev1, 23 Vahide Bulut, 156 Vildan Yazıcı, 158

Y

Yalçın Öztürk2, 79, 80 Yasemin Alagöz2, 68 Yasemin Ergin1, 174 Yasin Ucakan1, 159 Yibiao Pan3, 89 Yuliya G.Abbasova, 160 Yusuf Zeren1, 162, 163 Yusuf Zeren2, 19, 21, 43, 98

Z

Zahir Muradoglu1, 152 Zahir Muradoğlu, 158 Zaiem slimane, 145 Zameddin I. Ismailov1,, 130 Zameddin I. Ismailov2, 129 Zehra Pinar1, 91, 161



Istanbul / TURKEY


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