8-9 september, 2016 - isca 978-93-84659-98-1.pdf · technology, computer applications, dental...
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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PROCEEDINGS OF NATIONAL SEMINAR ON APPLICATION OF
MATHEMATICS IN TECHNOLOGY AND MANAGEMENT
(NSAMTM 2016)
8-9 September, 2016
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Proceedings of National Seminar on Application of
Mathematics in Technology and Management
(NSAMTM 2016)
8-9 September, 2016
UNDER TECHNICAL EDUCATION QUALITY IMPROVEMENT PROGRAMME
TEQIP-1.1, PHASE-II
Editor
Dr. Debjani Chakraborti
TIC (Mathematics) & Asst. Professor, BS&HU (Mathematics)
Narula Institute of Technology, Kolkata
Organized by
Department of Basic Science &Humanities
(Mathematics)
Narula Institute of Technology (An Autonomous Institute under MAKAUT)
81, Nilgunj Road, Agarpara,
Kolkata –700 109
2017
International E - Publication www.isca.co.in
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International E - Publication 427, Palhar Nagar, RAPTC, VIP-Road, Indore-452005 (MP) INDIA
Phone: +91-731-2616100, Mobile: +91-80570-83382
E-mail: [email protected] , Website: www.isca.co.in
First Impression: 2017
© Copyright Reserved
2017
All rights reserved. No part of this publication may be reproduced, stored in a
retrieval system or transmitted, in any form or by any means of electronic,
mechanical, photocopying, reordering or otherwise, without the prior permission
of the publisher.
ISBN: 978-93-84659-98-1
DISCLAIMER
The author is solely responsible for the contents of the abstract papers compiled in this volume.
The publishers or editor will not take any responsibility for the same in any manner. Errors, if
any, are purely unintentional and readers are requested to communicate such errors to the editors
or publishers to avoid discrepancies in future.
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About JIS Group
JIS Group Educational initiative is the endeavour of Sardar Jodh Singhji, Chairman, JIS Group.
Through the years, with this enterprising zeal and vision the empire of JIS Group spanned in the
fields of Education, Dairy business, Telecommunication, Transportation, Infrastructure,
Logistics, Healthcare and Social service. His aspiration to serve society by imparting knowledge,
education and employment culminated into JIS Group Educational Initiatives. This is one of the
majestic entrepreneurial endeavours in Eastern India, creating facilities for higher education,
Research, industry and creating jobs for thousands of people.
JIS Group Educational Initiatives has heralded new age education in West Bengal by
imparting futuristic undergraduate and post graduate programmes. Spread across several
sprawling campuses, JIS Group Educational Initiatives has colleges in Engineering, Dental,
Pharmaceutical Sciences, Management Science and Polytechnic. The objective was to create an
opportunity for students from Eastern India by providing a high standard Education and
Research platform in Engineering, Dental Science, Pharmacy, Hospitality management etc.
The journey commenced with a mission
“Igniting Minds, Empowering Lives”
“Learning is the beginning of wealth.
Learning is the beginning of health.
Learning is the beginning of spirituality,
searching and learning is
where the miracle process all begins”
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ABOUT THE INSTITUTE
Narula Institute of Technology is a leading Engineering & Management college, located at
Agarpara in West Bengal. Approved by All India Council for Technical Education (AICTE)
and affiliated to MAULANA ABUL KALAM AZAD University of Technology (MAKAUT). The
college offers NBA accredited degree programmes in engineering. The four year B.Tech course
is imparted in the streams like CSE, ECE, EE, CE, IT, EIE & ME. The institute provides a
brilliant platform for pursuing higher studies through PG courses like M.Tech (CSE, ECE, VLSI
& Micro Electronics, EE- Power System, CE- Structural engineering), MBA and MCA. It has
expanded to include diploma programs in EE, CE and ETC under the affiliation of West Bengal
State Council of Technical Education. The Institute is eligible for receiving Central assistance
under the recognition of 2(f) & 12(B) under UGC Act. The institute is also accredited by
National Assessment and Accreditation Council (NAAC). The college has also received the
notable World Bank Assisted and MHRD approved TEQIP (Phase II) grant for the advancement
of Technical Education and is a one-stop venue for promoting a vibrant and sustainable
atmosphere for teaching-learning. The Institute has the Quality policy: Maintaining Excellence
in Quality Education.
Academic success is the key for laying the foundation for the students and therefore the
College emphasizes on quality academic delivery in their stride towards excellence. The College
has also significantly reinforced their outreach initiatives by facilitating faculty development
programme, knowledge exchange sessions, and procuring funded projects from Government to
foster synergy between academia, business, industry and the community.
The institute boasts of a powerful R & D cell with immense contribution from the scholarly
faculty members. There is an enormous repository of International and National Journal
publications which have drawn nationwide attention. The college is in collaboration with
Oracle, INFOSYS, TCS, NIT Sikkim, IIT-KGP, AIT Bangkok and other organizations of repute.
The students get an opportunity to interact with foreign experts all across the globe through
seminars, conferences and special teaching-learning sessions. The student chapter plays a
crucial role in organizing informative technical events within the campus. At present there are
five student chapters in our college: IETE student forum of Electronics & Communication
Engineering Department, ICE & ASCE of Civil Engineering Department, CSI of Computer
Science Engineering, Information Technology & MCA Department and Institute of Engineers of
Electrical Engineering Department.
NIT is a one-stop venue for promoting a vibrant and sustainable atmosphere for teaching-
learning. Besides academics, the students get an exposure to the world of co-curricular activities
which help them in shaping their personality. Thus, the cornerstone of the successful evolution of
Narula Institute of Technology lies in its meticulous tutoring and mentoring of the future
professionals of the industry as well as of academia and citizens of the society where the
Institute's success has always been directly proportional to the success of the students.
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Mission, Vision and Objective
of the Institute
Quality Policy Best standards and practices of good governance, to be put in place to bring in
transparency of operations and improve credibility at all levels
Industry-ready professionals to be developed through Interactive Teaching-Learning
Process, Corporate exposure and project work
Higher Studies/research for Faculty & Staff to be encouraged for up gradation of
knowledge which would, inter alia, include participation in TEQIPs, Seminar,
workshop etc
Appropriate Laboratory facilities would be developed in selected areas to provide
fillip for R&D
Industrial consultancy to be carried out in an effective manner through Industry
Institute Partnership cell (IIPC) for developing a sense of accomplishment
Appropriate Laboratory facilities would be developed in selected areas to provide
fillip for R&D
NBA accreditation for all AICTE approved programmes to be obtained at the earliest
and maintained on a long –term basis.
Mission
To impart high quality Engineering and Mnagement education to the budding
Professionals.
Provide the ambience needed for developing requisite skills to make a mark of
excellence in Education, Business and Industry
Vision
To become an institute of repute and bring about change in the sphere of technical
education Worldwide by offering a full range of programmes of global standard, and
to transform the students into globally competent personalities
To create an environment to empower the students with solid foundation in
mathematical, scientific, engineering, managerial, entrepreneurial fundamentals and
incorporate research based curriculum thorough establishing continuous wide
network with the industries in order to initiate long term academic excellence in the
institution.
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Preface
Mathematics plays a key role in the development of various branches of science, technology and
Management as well as in the understanding of real world problems. It is the Science of pattern,
order and relationship. The language and logic of our technological world is none other than
Mathematics. Mathematical power is the ability to explore and to use a variety of mathematical
methods to solve engineering problems effectively.
The main purpose of the two day National Seminar on Application of Mathematics in Technology
and Management is to bring academicians, researchers and students in a single platform in
order to have the opportunity to interact and exchange ideas among themselves, discuss issues
of common concern, establish contacts, and gather information in the interdisciplinary field of
research. The invited lectures by eminent speakers from reputed University and Institutions,
paper reading sessions and interactive sessions has enormously increased the interest of the
participants in academic value addition as well as R&D activities. Young researchers got the
opportunity to demonstrate their own works and have suggestions from experts. Many of the
contributions are closely related to the need for mathematical modelling and Simulation of
Physical, Engineering as well as Managerial phenomena. The seminar is specially designed to
focus on the recent developments in Mathematics and its applications in real world complex
decision making environment and also to encourage academicians, researchers and students to
develop various competencies and enhance their self–efficacy in different Mathematical
techniques. The overall environment in the Seminar naturally motivated the students to study
mathematics with deeper interest and in acquiring new skills to solve difficult technical
problems.
We have the pleasure to welcome the guests of Honour, the eminent speakers and several
outstanding researchers from different Universities/Institutions of repute. We would like to take
the Proud privilege to thank our Managing Director, Principal, Registrar, HOD of Department
of BS& HU, the organising chair of the Seminar, the organizing committee, the reviewers, all
colleagues and friends, the entire cast and crew who helped us to organize this Seminar.
September 2016, kolkata
Dr. Debjani Chakraborti
TIC (Mathematics) and Assistant Professor, Department of BS & HU
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Table of Contents
MESSAGE FROM CHAIRMAN JIS GROUP
1
MESSAGE FROM CHAIRMAN BOG JIS GROUP
2
MESSAGE FROM MANAGING DIRECTOR JIS GROUP
3
MESSAGE FROM PRINCIPAL (SEMINAR CHAIR)
4
MESSAGE FROM ORGANIZING CHAIR
5
MESSAGE FROM CONVENER
6
COMMITTEE MEMBERS
7
INVITED SPEAKERS
9
LIST OF ABSTRACTS
10
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Message from Chairman, JIS
Group
industry ready professionals for successful careers. In this process the Group intends to unite all
dimensions of Education from Undergraduate to Post Graduate Programmes in Engineering and
Technology, Computer Applications, Dental Science, Pharmacy, Hospitality, diverse streams of
Management and so on under the same umbrella in order to comprehensively and collectively
optimize the reach of Educational Initiatives in every strata and corner of society towards a better
future. Our educational Initiatives believes that creating an academic foundation for social,
cultural, scientific, economic and technological development in our Nation can mature into
Global Interface by giving way to education exchange in the International territory as well.
Therefore, our focus is to achieve unparalleled excellence that will bring development to our
society and mankind by optimizing their potential, thereby establishing the observation of the
renowned Journalist Sydney J. Harris on the role the purpose of education which is to “turn
mirrors into windows”.
Sardar Jodh Singh
…….…………………………………………………....page 1………………………………………………………
"Vision looks inward and becomes duty. Vision looks
outward and becomes aspiration. Vision looks upward
and becomes faith."
I always experienced a yearning to acknowledge my
responsibilities and reciprocate by contributing to the
growth and development of our society. Years ago when
I visited my son's school, I perceived that the best way to
advance society is by fostering education and it was at
that moment that the dream and vision of JIS Group
Educational Initiatives was conceived. Now, when this
vision of duty, aspiration and faith has become a reality,
it is a proud moment for me and my team to see
thousands of students pursuing higher education in JIS
Group of Colleges and equipping themselves to become
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Message from Chairman, BOG,
JIS Group
innovation is the keynote to success in today’s globalised market driven economy. It is not only
important to invent ideas but also to be able to convert them into productive outcomes in
consumer’s society. Innovation and invention are quite different things. While invention is
largely a personal pursuit, innovation is much more akin to social pursuit. Innovation warrants
attention because it contributes immensely to social and industrial development.
I am confident that this Seminar will come up with new findings, strategies and innovations
on various issues laid out by the Organizers and will brain storm the mindset of the participating
researchers. I expect further this Seminar to identify the state -of -art and future directions in the
mentioned areas so as to ensure demand driven and productive research to fulfil the societal
needs and desire. This Seminar must depict a future line transforming the concepts in the
published papers into patenting and commercialization of the products.
Prof. (Dr.) Sparsha Mani Chatterjee
…….………………………………………..…………page 2…………………………………………………………
I am happy to observe that the Basic Science and Humanities
Department of NiT has been organizing the National Seminar
on Application of Mathematics in Technology and
Management (NSAMTM 2016), 8th -9th
September, 2016.
This Seminar in terms of its areas and tracks is a
comprehensive one providing a platform from multiple
disciplines of engineering and technology to participate and
contribute. This Seminar will definitely be a significant
attempt to assemble the leading experts and learners in the
field. Understanding the differences between invention and
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Message from Managing
Director, JIS Group
I am extremely delighted to share through this message my enthusiasm about the National
Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016), 8th
-
9th
September 2016 at Narula Institute of Technology, Agarpara, Kolkata, India. The National
Seminar promises to be a forum of research scholars and professionals from within the country
and outside and will certainly provide a platform for the sharing of experience and the exchange
of opinions on technological advancements.
I am sure that this event will draw talent from all over the globe and create a great learning
experience for all participants, delegates and guests. I appreciate the efforts taken by the
Organizing Committee of the NSAMTM 2016 and all the eminent persons involved. I wish them
great success.
Mr. Taranjit Singh
…….………………………………………………….…page 3……………………………………………………….
I am chasing a dream that my father (Sardar Jodh Singh)
cherished, to empower lives through knowledge and
education. In this regard we have established the JIS
educational initiative which is now one of the leading private
educational service providers in India. JIS educational
initiative has 25 educational institutes to its credit and holds
an average of 25,000 students who have enrolled in diverse
academic programmes. We have also created new standards in
quality self-financed education and laid the foundation of the
JIS University.
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Message from the Principal
(Seminar Chair)
I also extends my sincere thanks to our Managing Director Mr. Taranjit Singh for motivating us
to organize the event successfully. I would like to appreciate the collective efforts put in by the
members of different Committees and staff members of the Institute for making NSAMTM-2016
a grand success without whom it would have been very difficult for us to arrange the event.
I also offer my thanks to all the participants for their immense support and active participation
with sincerity and punctuality. I appreciate the effective assistance of every faculty and staff of
the institute in direct and indirect manner to make NSAMTM-2016 a grand success.
I hope, every individual will be satisfied and will enjoy the seminar to a great extent.
Prof. (Dr.) M. R. Kanjilal
…….………………………………………..………….page 4……………………………………………………….
On behalf of the Organizing Committee, I
welcome all to the National Seminar on
Application of Mathematics in Technology and
Management (NSAMTM-2016), to be held
during 8-9, September, 2016, at the Campus of
Narula Institute of Technology, which is
sponsored by TEQIP.
National Seminar is a gathering of
academicians, researchers and students from
several part of our country in a single platform
in order to have the opportunity to interact and
share ideas among themselves.
On behalf of the Organizing Committee, I
would like to convey my sincere thanks to
TEQIP for sponsoring the event.
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Message from the Organizing Chair
The eminent speakers from different disciplines as resource persons are invited to share their
valuable research and ideas among students during the 2-day Seminar to raise the interest of the
students on research activity.
Our Principal and the committee members of nsamtm 2016 gave their best effort to
materialize the smooth functioning of the two day Seminar. We find immense satisfaction after
the successful completion of the Programme. We hope to organize such programme in future to
benefit our students as well as the Nation by providing future Researchers.
I hope, every participant will be benefitted and will enjoy the seminar to the most.
Dr. Sumit Nandi
…….……………………………………………………page 5………………………………………………………
I consider conducting NSAMTM-2016 a very
challenging job on behalf of the Organizing
Committee of the National Seminar. The main
aim to arrange this two day National Seminar
is to bring academicians, researchers and
students in a single platform in order to have
the opportunity to interact and share ideas
among themselves. To make the program most
fruitful, the availability of the suitable speakers
was our high concern. We are really thankful
that the speakers showed their enthusiasm and
lend their valuable time to educate our
participants in regards to NSAMTM-2016.
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Message from the convener
I am very much thankful to TEQIP for sponsoring this program, without whose generous financial
support, it would not have been possible to organize such an event. I, on behalf of the entire team of
organizing committee wish to extend a very hearty vote of thanks and deep gratitude to our
honourable Managing Director Mr. Taranjit Singh for motivating us and giving us such a platform to
organize such effective program for teaching and research fraternity. I extend my whole hearted vote
of thanks and deep gratitude to our friend, philosopher and guide, our honourable Principal Prof.
(Dr.) M. R. Kanjilal for extending her unfailing support towards our initiative to organize this
Seminar. I am very much thankful to our HOD Dr. Sumit Nandi for his continuous support and
advices which have greatly helped towards the successful organization of NSAMTM-2016. I would
like to place on record our hearty thanks to our registrar Ms. Nidhi Singh for her perfect logistic
support towards organizing the Seminar. I am thankful to the NSAMTM-2016 steering committee
members for their whole hearted support and for working relentlessly for the past few weeks in order
to achieve grand success in NSAMTM-2016. I thank all the HODs of all the respective departments,
the plenary speakers, the tutorial speakers and the delegates for their enthusiastic participation in this
Seminar. I also convey my sincere thanks to all the people who have given their precious time in
organizing this grand occasion.
Dr. Debjani Chakraborti
…….………………………………………………….…page 6……………………………………………………….
I feel honoured and privileged to get the
opportunity to propose a vote of thanks on this
grand inaugural occasion of the Seminar of
Mathematics, NSAMTM-2016 at Narula
Institute of Technology. September 8, 2016 is
indeed a very memorable day for all the
members of the Basic Science & Humanities
department. As we usher the opening of the
National Seminar in the presence of the
honourable Principal and the dignitaries. I, on
behalf of Organizing Committee convey deep
regards and heartfelt thanks to the respected
dignitaries, participants and fellow colleagues.
I am thankful to all the participants across
West Bengal for coming to Narula Institute of
Technology to attend the Seminar.
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LIST OF COMMITTEE MEMBERS
Chief Patron:
Sardar Jodh Singh (Chairman, JIS Group, India)
Patrons:
Sardar Taranjit Singh (MD, JIS Group)
Prof.(Dr.)S.M.Chatterjee, Chairman,BOG
Mr. S.S. DuttaGupta (Director,JIS Group)
Prof. (Dr.) Asit Guha (Advisor, JIS Group)
Mr. U. S. Mukherjee (Deputy Director, JIS Group)
Mr. Simarpreet Singh (Director, JIS Group)
Mrs. Manpreet Kaur (CEO, JIS Group)
Ms. Jaspreet Kaur (Trustee Member, JIS Group)
Seminar Chair:
Prof.(Dr.) M.R.Kanjilal (Principal, NiT, Agarpara)
Advisory Committee:
Prof. B.B. Pal, Kalyani University
Prof. M. N. Mukherjee, Calcutta University
Prof. P.K. Roy, Jadavpur University
Prof. S. Sen, Calcutta University
Prof. N. C. Ghosh, Rabindra Bharati University
Prof. S. Gupta, IIT(ISM), Dhanbad
Prof. S. Kar, NIT Durgapur
Prof. D. K. Bhattacharjee, Jadavpur University
Prof. A. Dutta, ISI Kolkata
Prof. A. Sengupta, Calcutta Medical College
Prof. J.K. Das (Advisor R&D), NiT, Agarpara
…….……………………………………….…………page 7………………………………………………………..
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Organising Chair: Dr. Sumit Nandi, HOD, BS & HU
Convener: Dr. Debjani Chakraborti , TIC (Mathematics) & Asst. Professor, BS&HU
Secretary: Dr. Susmita Karan, TIC (Physics) & Asst. Professor, BS&HU
Joint Secretary: Dr. Nikhilesh Sil , Asst. Professor, BS&HU
Dr. Raju Dutta, Asst. Professor, BS&HU
Organising Committee:
Dr. Pijush Basak , Asst. Professor, BS&HU
Dr. Sarbani Ganguly, TIC (Chemistry) & Asst. Professor, BS&HU
Dr. Leena Sarkar Bhaduri, TIC (English) & Asst. Professor, BS&H
Ms. Sharmistha Basu, Asst. Professor, BS&HU
Dr. Rupa Bhattacharyya, Asst. Prof, BS&HU.
Ms. Rajasi Ray, Asst. Prof, BS&HU
Ms. Nidhi Singh, Registrar, NiT
Mr. Ratan Das, Site Supervisor, NiT
Mr. Nilanjan Mitra, Accounts, NiT
Mr. Partha Das, TEQIP Cell, NiT
…….…………………………………page 8…………………………………………
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INVITED SPEAKERS
Distinguished Speakers:
Prof. Joydev Chattopadyay, Indian Statistical Institute, Kolkata
Prof. Ashok Dutta, Indian Statistical Institute, Kolkata
Prof. Priti Kumar Roy, Jadavpur University, Kolkata
Prof. Sankar Kumar Roy, Vidyasagar Universiety, Midnapur
Prof. Arnab Sengupta, Calcutta Medical College, Kolkata
Prof. Samarjit Kar, National Institute of Technology, Durgapur
Prof. Dilip Kumar Bhattacharya, Calcutta University, Kolkata
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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LIST OF ABSTRACTS
1. A Bio-Inspired Computation Based Approach to Non-Linear HIV Dynamics 14
Debjani Chakraborti and Sumit Nandi
2. Mathematical Modelling of pore Formers Based Osmotic Drug Delivery 15 Gopa Roy Biswas, Sutapa Biswas Majee and Shubham Mukherjee
3. Importance of Benchmark Function in Bio-Inspired Optimization 16
Sangita Roy
4. Mathematical Model of Energy Consumption for Deploying Nodes in Sensor 17
Network
Raju Dutta
5. Statistical Analyses in Drug Design and Environmental Chemistry 18
Indrani Sarkar
6. Application of Business Mathematics in Management 19
Nidhi Singh
7. A Critical review on Space weather 20 Dhananjay Kumar Tripathi
8. Mathematical Modelling of Image Formation through Atmosphere 21
Saurav Kumar Datta, Mainak Hore and Sangita Roy
9. Effects of MHD convection Radiative Heat and Mass Transfer
of Nanofluids over a Nonlinear Stretching Sheet 22
Hiranmoy Mondal and Precious Sibanda
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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10. Comparing Antiloosening Ability Between M16 and 5/8 Inch 23
BSW Threaded Fasteners
Bikash Panja and Santanu Das
11. Novelty in Vegard’s law 24
Susmita Karan
12. Formula for getting Prime Numbers 25
Abhijit Pandey
13. Analysis of Piezo-resistive Sensor data by multiple regression method 26 Bansari Deb Majumder,
Debatra Choudhury, Tirthankar Saha
and Yekta Roy
14. A deteriorating inventory model with variable holding cost and shortage 27
under two levels of trade credit policy
Magfura Pervin and Sankar Kumar Roy
15. A Mathematical Approach to Digital Humanities 28
Rajasi Ray and Debjani Chakraborti
16. Study of Roughness for EN 47 spring steel in WEDM 29
Sudip Banerjee, BikashPanja and Soupayan Mitra
17. The role of Mathematics behind football science and Technology 30 Debatra Choudhury, Tirthankar Saha, Bansari Deb Majumder and Yekta Roy
18. Artificial neural network in dissolution profiling and establishing IVIVC of 31
pharmaceutical solid dosage forms
Sutapa Biswas Majee and Gopa Roy Biswas
19. An Exact Approach for Transportation-p-Facility Location Problem 32
Soumen Kumar Das and Sankar Kumar Roy
20. Migration of the Susceptible Prey can Stabilize the System: 33
A Mathematical Approach
Nikhilesh Sil
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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21. Solution of matrix games with generalized trapezoidal fuzzy payoffs 34
Jishu Jana and Sankar Kumar Roy
22. Mathematics and Computer Science to give Sixth-Sense to Machines 35
Rakesh Anand and Abhijit Pandey
23. The Missing Fundamental Element: Memristor 36 S.Mandal, S. Roy, S. K. Pandey and S. Kumar
24. Fractional Calculus--- Threshold of a New Era of Science 39
Arnab Gupta
25. Analysis of a Fishery Model with Harvesting including Prey Refuge 42
Banani Roy and Sankar Kumar Roy
26. Design of a direct neural controller with pid compensation for an 43
electrohydraulic actuation system by simulation and real-time experiment
Amit Datta
27. Modified android app and website to reduce terror attacks in railway 44 Arijit Manna
28. Application of Mathematics in Management 45 Juin Ghosh Sarkar
29. Triangular intuitionistic fuzzy matrix games and a new ranking approach 46
Ankan Bhaumik and Sankar Kumar Roy
30. Ground deformation during aseismic periods under the action 47
of tectonic forces
Subrata Kr. Debnath and Sanjay Sen
31. Mathematical Analysis through Packet Transmission of Modified 48
PEGASIS in WSN
Raju Dutta
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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32. Visualizing imaginary roots of a polynomial 49 Damodar Prasad Goswami and Sharmistha Sikdar
33. Realizing Mathematical Truths with Computer Algebra Systems (CAS) 50
Amitava Jana
34. Application of Mathematics in Management 51
Kalipada Senapati
35. Implementation of Golden Ratio to the Modern Science and Technology 52
Neha Mukherjee and Dibyendu Sur
36. Visualizing multiplicity of roots in a polynomials 53
Damodar Prasad Goswami and Krisnendu Sarkar
37. Parametric optimization of MRR in electrical discharge machining 54
Akhtarujjaman Sarkar
38. Response of R/C Asymmetric Rectangular Community Structures 55
under Near Fault Ground Motion Considering Equal Eccentricity
Goutam Roy and P.K.Das
39. Role of Mathematics in Business Decisions: The current scenario 57
and emergence of a new horizon of studies
Soma Bose Biswas and Nidhi Singh
40. Optimization of enzyme catalysed polyester condensation – 58
A mathematical study
Rupa Bhattacharyya and Sumit Nandi
41. A Kinetic Study for the Synthesis of Diisobutyl Adipate 59
by Candida Antarctica
Sarbani Ganguly and Sumit Nandi
42. A problem on Farm Planning: A Mathematical Approach 60
Debjani Chakraborti and Papun Biswas
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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A Bio-Inspired Computation Based Approach to Non-Linear
HIV Dynamics
Debjani Chakraborti1, Sumit Nandi
2
1Department of Basic Science & Humanities (Mathematics), Narula Institute of Technology,
Kolkata 700109, India 2Department of Basic Science & Humanities (Chemistry), Narula Institute of Technology,
Kolkata 700109, India
Email Id: [email protected]
Abstract
Mathematical models of the epidemiological and immunological dynamics of human
immunodeficiency virus (HIV) have proven valuable for understanding the HIV pathogenesis.
As the millennium unfolds the impact of HIV/AIDS on international, national and community
security has become significant. The spread of HIV is complex and nonlinear in nature, so
accurate dynamic models are difficult to construct. To improve therapeutic treatment for HIV, a
simple and effective computer model of nonlinear HIV dynamics is needed to facilitate analysis
of its pathogenesis. This article presents how genetic algorithm (GA) based fuzzy dynamical
system can be used to control the HIV disease.
Keywords: HIV, CD4+ T Cell, Fuzzy differential equations, nonlinear programming.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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Mathematical Modelling of Pore Formers Base Dosmotic
Drug Delivery
Gopa Roy Biswas, Sutapa Biswas Majee, Shubham Mukherjee
Division of Pharmaceutica, NSHM College of Pharmaceutical Technology, NSHM Knowledge
Campus, Kolkata-Group of Institutions, Kolkata 700 053.
Email Id: [email protected]
Abstract
Mathematical modeling of controlled drug delivery is a challenging area in novel drug delivery
approach. One such controlled way can be achieved by developing osmoticallyactive drug
delivery devices. There are so many methods available of preparing osmotic drug delivery
systems. One form is with hydrophilic polymer membranes in the presence of water soluble pore
forming materials. Coming in contact with aqueous media, pore former dissolves and leaches out
from the system leading to the formation of microporous membrane around. Drug comes out by
the process of diffusion through the micropores. The examples of pore forming agents employed
in controlled release dosage forms are carbohydrates like glucose, fructose, mannose, alkaline
earth metals such as calcium chloride, calcium nitrate, Alkaline metal salts like sodium chloride,
sodium bromide, potassium chloride etc. As drug release occurs through the pores, concentration
of pore formeris of great importance here. Depending on the nature of the polymer, drug and
pore formers used, the drug release kinetics can be of zero order or non zero order. That can be
well explained by the mathematical modelling.
Keywords: Mathematical modeling, Drug delivery, Micropores.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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Importance of Benchmark Function in Bio-Inspired
Optimization
Sangita Roy
Department of Electronics and Communication Engineering, Narula Institute of Technology,
Kolkata 700109, India
Email Id: [email protected]
Abstract
Bench Mark Functions (Test Functions) are the artificial bed for testing optimization algorithms.
These BMF (TF) are both single modal as well as multi modal. They give an idea how the
optimization algorithm behavioural pattern deviated depending on the BMFs. There are
numerous test functions. Here only Bio-Inspired Optimization Algorithm Cuckoo Search
Algorithm (CSA) has been observed. CS is a robust and fast Optimizing Algorithm due to its
number of parameters involved. This has been proved through TFs. In this work Ackley, Beale,
Booth, Easom, Levy, Matyas, Rosenbrock, Sphere functions have been used as BMF.
Keywords: Benchmark Function, Bio-Inspired Optimization, Algorithm Cuckoo Search.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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Mathematical Model of Energy Consumption for Deploying
Nodes in Sensor Network
Raju Dutta
Department of Basic Science & Humanities (Mathematics), Narula Institute of Technology,
Kolkata 700109, India
Email Id: [email protected]
Abstract
Wireless Sensor Networks (WSN) provides network access for mobile users. Therefore, most traffic
flows in WSNs are to and from the sensor node and base station of the networks without wired
connection. Power consumption is one of the most important issue in the sensor network. Energy
constraints have a significant impact on the design and operation of wireless sensor networks. This paper
describes a mathematical model for the power consumption of mobile node in wireless sensor networks.
A wireless sensor network having multiple BSs (data sink nodes) and mobile nodes are considered. Each
source node must send all its locally generated data to the other nodes and vice –versa. To maximize
mobile node’s lifetime, it is essential to have optimum monitored region and radio range of each source
node of WSNs. To find an optimal solution a mathematical model, which is proposed for optimal power
consumption in terms of ratio of whole energy of sensor nodes to energy consumption speed of sensor
nodes in any area should be constant. Through extensive simulation of the model we achieved the results
of the model which is shown below and implies that this model has excellent performance and provides a
near-optimal solution.
Keywords: Sensor Node, Energy Consumption, Sensor’s Life time, Base Station, WSNs.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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Statistical Analyses in Drug Design and Environmental
Chemistry
Indrani Sarkar
Department of Basic Science & Humanities (Physics), Narula Institute of Technology, Kolkata
700109, India
Email Id: [email protected]
Abstract
The biological response produced by a molecule can be a function of its physicochemical
properties. Structure-activity data analysis was dominated by the use of simple and multiple
regression analyses to produce quantitative models. Multivariate methods have been increasingly
infiltrating the field in order to produce qualitative or semi-quantitative models. Principal
components analysis (PCA) is the most popular multivariate technique for finding the underlying
dominant features among a matrix, in association with data reduction. PCA has been used to
compare molecular properties, find structure-property relationships for pesticides, rank
chemicals and identify toxicity syndromes. It has been successfully used to model
carcinogenicity of drugs. Nonlinear mapping (NLM) is a display method producing a two
dimensional plot in which the distances between points are a good representation of the distances
between points in the original high-dimensional space. Successful applications of NLM include
the analysis of anti filarial activity, the classification of antibiotics and the antiviral activity of
bicyclicamines against Influenza A. Kohonen topology-preserving mapping is a neural network
method for representing the clustering of samples on a map. It has been used in pharmacology.
When the molecules are classified into different groups (e.g.; carcinogens and non-carcinogens),
it is possible to obtain semi-quantitative models by means of discriminate analyses (DAs). DAs
have been used to find structure activity relationships in pharmacology, acute toxicity and
carcinogenicity. At present the most widely employed statistical method in QSAR studies is
regression analysis where a search is performed for a quantitative relationship between a
biological activity and molecular descriptors. Numerous models have been obtained only using
simple regression analysis. Partial Least Squares regression is particularly valuable when the
candidate molecular descriptors are numerous. While the activity and molecular descriptors are
obtained in a rather straightforward way, problems still remain for selecting a suitable statistical
tool, especially when the training of the user in statistics is not sufficient.
Keywords: Drug design, structure-activity relationship, multiple regression analysis.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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Application of Business Mathematics in Management
Nidhi Singh
Registrar, Narula Institute of Technology, Kolkata 700109, India
Email Id: [email protected]
Abstract
Management can be defined as a set of activities including planning,
decision making, organizing, leading and controlling directed at an organization’s resource with
the aim of achieving organizational goals in an efficient and effective manner. Mathematics is an
important subject and knowledge of it enhances a person's reasoning, problem-solving skills, and
in general, the ability to think.
Mathematics that is used by commercial enterprises to record daily transactions,
forecast demand and supply as well as other commercial operations are known as business
mathematics. Business mathematics is essential to keep track of an organization day to day
operation. The importance of business mathematics are to record daily transaction of business, to
forecast production, to forecast sales volume, to calculate profit or loss: Organizations uses
business mathematics to calculate their total cost (TC), total revenue (TR) and total profit (TP)
from the operation, to reduce wastage.
Mathematics plays a major role in business management because it helps maximize profit by
using techniques such as analyzing production costs, determining ideal pricing, discerning sales
patterns and projecting future sales. Having strong skills in mathematics means an individual can
analyze all of a company's finances and make changes to save the company money and time, and
ultimately make a higher profit.
Keywords: Business Mathematics, Business Management, finance.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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A Critical Review on Space Weather
D. K. Tripathi
Department of Basic Science & Humanities (Physics), Narula Institute of Technology, Kolkata
700109, India
Email Id: [email protected]
Abstract
The Sun is the epicentre of space weather events. It affects the Earth and its environment in a
variety of ways. The space between the Sun and the planets is filled by tenuous magnetized
plasma, which is a mixture of ions and electrons flowing away from the Sun. Actually, the Sun’s
outer atmosphere is so hot that not even the Sun’s gravity can prevent it from continuously
evaporating. The escaping plasma carries the solar magnetic field along with it, out to the
boundary of the heliosphere where its dominance finally ends in interstellar space. Solar activity
includes phenomena related to solar flares and Coronal mass ejections, and their recurrence in
time and space. Solar activity varies with the well known 11-year cycle due to which an 11-year
activity cycle is there in the geomagnetic phenomena. As the orientation of the magnetic dipole
axis relative to the Sun–Earth line changes over the course of the year, the activity is largest
during the equinoxes when the dipole is tilted along the Earth’s orbital track and the projection of
the IMF to the geomagnetic field maximizes. The activity level is at minimum during the
solstices when the projection of the IMF onto the Earth’s field is on average a minimum. In this
paper the development in the recent decades on the subject is briefly discussed.
Keywords: Space weather, solar magnetic field, geomagnetic phenomena.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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Mathematical Modelling of Image Formation through
Atmosphere
Saurav Kumar Datta, Mainak Hore, Sangita Roy
Department of Electronics and Communication Engineering, Narula Institute of Technology,
Kolkata 700109, India
Email Id: [email protected]
Abstract
Image formation model due to atmospheric scattering is given by H Koschmieder in 1924.Where
I(x) is the original hazy image intensity, x is the pixel index, J(x) is the scene radiance. A is the
global atmospheric light and t is the un-deflected scene transmission light that reaches the
camera or the observer directly. The transmission t(x) denotes the field depth of the scene
objects. In a homogeneous medium the transmission is expressed as shown in as ( )
is the scattering coefficient of the medium. The above equation indicates that the scene radiance
is attenuated exponentially with the scene depth d. d is known as optical thickness. It is a
challenge to retrieve the original image from degraded image.
Keywords: Mathematical Modelling, atmospheric scattering, Image formation model.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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Effects of MHD convection Radiative Heat and Mass
Transfer of Nanofluids over a Nonlinear Stretching Sheet
Hiranmoy Mondal, Precious Sibanda
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal,
South Africa
Email Id: [email protected]
Abstract
The problem of mixed convection boundary layer flow of nanofluids over a non-linear stretching
sheet in presence of magnetic field parameter and suction parameter is investigated numerically
in this paper. The resulting non-linear partial differential equations with associated boundary
condition are solved numerical using modified spectral quasi-linearisation method (SQLM). The
SQLM is a generalization of the Newton-Raphson method for solving nonlinear boundary value
problems. Present results showed an excellent agreement with the previously published work in
absence of magnetic field, thermal radiation and suction. The physics of the problem is well
explored for the embedded material parameters through tables and graphs. The effects of various
physical parameters are analyzed in details. It is found that thermal radiation greatly effects the
velocity and temperature distributions in the boundary layer.
Keywords: Nanofluids, nonlinear stretching sheet, conjugate effects, boundary layer flow.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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Comparing Antiloosening Ability BetweenM16 and 5/8 Inch
BSW Threaded Fasteners
Bikash Panja
1, Santanu Das
2
1Department of Mechanical Engineering, Narula Institute of Technology, Kolkata 700109, India.
2Department of Mechanical Engineering, Kalyani Govt. Engg. College, Kalyani 741235, India.
Email Id: [email protected]
Abstract
A designer often considers providing a reliable threaded joint, due to its distinct advantages.
However, threaded fasteners have the problem of loosening under hostile vibrating conditions,
which leads to decreasing the clamping force and failure of the system at the end. The
mechanism of loosening process of screw fasteners is first reviewed in this work. It is found that
two factors are the main reasons for loosening of screw fasteners. One is relative slip between
the bolt and nut threads, causing torsion on bolt. Second is the relative slip between the bearing
surface of the nut, or bolt, and the surface of the fastened material, thereby slackening the
fasteners. In present experimental work, anti-loosening ability has been investigated for various
threaded fasteners, such as conventional nut, nylock nut, adhesive bonded nut, flat washer, spring
washer, inside serrated washer, outside serrated washer and new concept of hybrid double nut
(first one conventional nut and then nylock nut) with conventional metric and BSW bolts.
Different initial clamping forces under accelerated vibrating conditions were resorted to for the
test on an indigenously made testing rig. A hybrid double nut and adhesive bonded nut show
better anti-loosening characteristics compared to other fasteners. Also, the BSW threaded
fasteners have better anti-loosening effects compared to metric threaded fasteners. The reason
may be that the metric thread has higher angle of thread (600) compared to BSW thread (55
0).
Due to less slip along the flank due less angle of thread better resistance to loosening is obtained
in BSW threads.
Keywords: Bolt, nut, washer, Metric and BSW fasteners, loosening, anti-looseners, vibration.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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Novelty in Vegard’s Law
Susmita Karan
Department of Basic Science & Humanities (Physics), Narula Institute of Technology, Kolkata
700109, India
Email Id:[email protected]
Abstract The accurate measurement of lattice constants of mixed crystals has been contributed to the
understanding of a number of factors, which influences the stability and several properties of the
system. In case of simple crystalline structures, knowledge of precise values of lattice constants
provides a direct measure of inter atomic distances and thereby inter atomic binding forces.
Lattice constants are also required for the calculation of other physical properties such as
compressibility, lattice energy, refractive energy etc. A value of atomic density determined by X-
ray can also be compared with that obtained from other macroscopic methods to gather
knowledge of the defects present inside the crystal. This again demands a correct measurement
of lattice constants. In case of some multi-component systems, namely alloys and mixed crystals
with anionic and cationic substitutions, the values of lattice constants for several compositions
can be predicted by Vegard’s law where the dependency is linear. This law is established
empirically and affords a simple but reliable tool for the measurement. In the present study,
experiments has been done on solution grown mixed crystals of ammonium sulphate
[(NH4)2SO4] and potassium sulphate [K2SO4] where, ammonium ions (NH4 +) gradually been
replaced by potassium (K+) ions over entire range of composition. Structural characterization of
the entire system has been done by X-ray diffraction studies. Powder diffraction data for the
mixed system, [(NH4 )1-x Kx]2SO4 have been collected using a Philips microprocessor controlled
X-ray Diffractometer (APD 1710) and nickel filtered CuK radiation ( = 1.5405 Å) with an
output power of 36 kV and 25 mA from a stabilized Philips X-ray Generator PW 1130. Lattice
constants a, b and c are measured experimentally using computer program POWD and compared
them with those calculated from Vegard’s law. It is found that both the values are very close with
a constant deviation. So we may conclude that the variation of lattice constants with molar
concentrations satisfy Vegard’s law of linear dependence over the entire range of composition.
The replacement of NH4 +
ion by K+
induces strain in the system thereby reducing the cell
volume with the increase in K+ ion concentration. Thus the simple but elegant Vegard’s law
plays an important role in predicting the unknown structure of the solid solution.
Keywords: Crystallography; Powder Diffraction; Lattice Constant; Solid Solution; Mixed
Crystals of Ammonium-Potassium Sulphate.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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Formula for getting Prime Numbers
Abhijit Pandey
Department of Computer Science and Engineering, Narula Institute of Technology, Kolkata
700109, India
Email Id: [email protected]
Abstract:
In order to find a general formula for getting a prime numbers a pattern has been discussed. If
two consecutive prime numbers are added and the immediate prime number before the numbers
is subtracted from the sum of the primes then in most of cases the next prime number will be
obtained. But there are some cases where prime number is not obtained by this pattern. But if we
add some numbers with that result then one of them becomes a prime number. There are some
cases where this pattern may not be applicable or the immediate prime number is not obtain
easily i.e. a prime number is missed out from the sequence or list. Instead of this exception, the
pattern can be used to solve the problem for getting a prime number. The choices of some
numbers are providing some interesting results. So, it can also be seen that nothing is random in
universe. This number for stabilization of an atom is also not random but depends on
mathematics.
Keyword: Randomness, Prime number, Pattern in prime numbers.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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Analysis of Piezo-resistive Sensor data by multiple
regression method
Bansari Deb Majumde, Debatra Choudhury, Tirthankar Saha, Yekta Roy
Department of Electronics and Instrumentation Engineering, Narula Institute of Technology,
Kolkata 700109, India
Email Id: [email protected]
Abstract
Piezo-resistive material is a sensor which occupies minimum space. It is a function of both
pressure and temperature variable. The output of this sensor is sensitive to both these variables
when excited by an electrical signal. Multiple regression analysis is one of the effective
mathematical tools which give more sophisticated research hypothesis. Here, this analytical
method has been used to determine different sensing variables from the aggregated output
response of the sensor. This mathematical method is widely used for signal processing purpose at
various domains. Further artificial neural network (ANN) can be added to this multiple
regression model for sensor data extraction and fusion which will help to develop smart sensors.
Keyword: Multiple regression method, signal processing artificial neural network smart
sensors
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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A deteriorating inventory model with variable holding cost
and shortage under two levels of trade credit policy
Magfura Pervin, Sankar Kumar Roy
Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar
University, Midnapore-721102, West Bengal, India
Email Id: [email protected]
Abstract
In this study, we develop a deterministic inventory model for deteriorating items which follows a
constant rate with respect to time. Keeping in mind the competition of modern age, the stock-
dependent demand rate is included in the formulated model. Shortages are allowed to this model
and when stock on hand is zero, the retailer offers a price discount to customers who are willing
to back-order their demands. Here, the supplier as well as the retailer adopts the trade credit
policy for their customers in order to promote the market competition. The retailer can earn
revenue and interest after the customer pays for the amount of purchasing cost to the retailer until
the end of the trade credit period offered by the supplier. Besides this, the traditional parameter
of holding cost is considered here as time-dependent. Thereafter, we present a solution
technique to find the optimal order quantity so that the total cost per unit time is minimized. The
results are discussed by the help of a numerical example to validate the proposed model. A
sensitivity analysis of the optimal solutions for the parameters is also provided in order to
stabilize our model.
Keywords: Inventory, Stock Dependant Demand, Deterioration, Trade credit period.
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PROCEEDINGs of
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A Mathematical Approach to Digital Humanities
Rajasi Ray1, Debjani Chakraborti
2
Department of Basic Science & Humanities (English), Narula Institute of Technology, Kolkata
700109, India
Department of Basic Science & Humanities (Mathematics), Narula Institute of Technology,
Kolkata 700109, India
Email Id: [email protected]
Abstract
Digital Humanities is about the intersection of humanities and digital technology. The activities
undertaken by Digital Humanities (DH) scholars include not only the attempts to understand and
examine, but also to envision and enhance this intersection. Human experience, of course,
remains the central concern. The influence, therefore, flows from the humanities to digital and
not vice versa. With the digital turn, that has entered into its full swing with the World Wide
Web, the social media, the blogosphere, and digital libraries, the process of knowledge creation
and use has become further distributed and participatory.
The intersection of humanities with digital technology has become inevitable and the speedy
transfer of cultural material to the digital alongside ever-growing digital material which needs to
be tapped by humanities scholars for gaining fuller understanding of human experience. This can
be done in three ways: 1. by integrating digital technology into the activities of humanities
scholarship, 2. by using digital methods for the analysis of large cultural data sets and, 3. by
using different mathematical tools /software such as MATHEMATICA, LINGO/LINDO etc. and
Soft Computing techniques like Artificial Neural Network, Genetic Algorithm etc.
Preservation and dissemination of knowledge have been the main objectives of the university
system. Prior to the establishment of universities, these functions were carried out through oral
tradition. ‘Guru-Shishya’ tradition in the Indian context is one of the well-known examples of
the oral tradition that carried forward the objectives of education mentioned above for several
centuries. With the invention of the printing press, written ‘text’ occupied the central place in
education. The print media enabled standardization. With the digital turn that began discretely in
the 1940s and got accelerated with the invention of the Internet (1983) and development of
websites (1989), the cultural material began to be transferred to the digital media. By 2014, with
about four trillion pages available on websites and innumerable images circulated and
appropriated at a viral rate, we are fast heading towards a post-print era. Human activities are
getting technologically-mediated.
Keywords: Digital Humanities, digital technology, mathematical software.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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Study of Roughness for EN 47 spring steel in WEDM
Sudip Banerjee
1, BikashPanja
2, Soupayan Mitra
3
1,3 Department of Mechanical Engineering, Jalpaiguri Govt. Engg. College, Jalpaiguri-735102,
India 2Department of Mechanical Engineering, Narula Institute of Technology, Kolkata 700109, India
Emai Id: [email protected]
Abstract
WEDM (Wire-cut Electro discharge machining) is a unique adoption of EDM, generally used to
machine intricate shapes and complex geometry of difficult-to-machine materials like zirconium,
titanium etc. It is an indispensable thermal machining process for achieving higher degree of
dimensional accuracy. Here EN47 spring steel is taken as work piece, which is used in aerospace
industries, automotive industries, steering knuckles and disc spring of heavily bolted sections.
The present study investigates the effect of process parameters, i.e. pulse-on time, pulse-off time,
wire feed and gap voltage on surface roughness (Ra) with the help of L27 orthogonal array based
Taguchi optimization technique. The S/N ratio analysis and Analysis of variance is done to find
the optimal condition and significant parameters respectively. According to the S/N ratio
analysis, Pulse-on time gives more contribution whereas wire feed has moderate contribution in
controlling surface roughness of EN 47 spring steel. The ANOVA table shows that among the
interactions Ton×Toff has highest contribution within the specific test range. The confirmation test
shows that there is around 20% reduction in surface roughness from initial to optimal condition.
The surface morphology and composition analysis is done with the help of scanning electron
microscope and chemical analysis.
Keywords: WEDM, EN47 spring steel, Surface roughness, Taguchi Method.
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The role of Mathematics behind football science and
Technology
Debatra Choudhury, Tirthankar Saha, Bansari Deb Majumder, Yekta Roy
Department of Electronics and Instrumentation Engineering, Narula Institute of Technology,
Kolkata 700109, India
Email Id: [email protected]
Abstract
Good kicking technique is an important part of a football player. Therefore, understanding the
biomechanics of football kicking and its projection when a kick is made is much more important.
Many factors affect the outcome of a kick. Basic factors affecting the trajectory of the ball
include the launch angle and velocity of the kick. A much more complicated factor, often
ignored by math and physics classes is the force due to air resistance. Finally, the factor most
memorable to the kicker that affects the outcome of a kick is the wind. In this study we explore
the launch angle and initial velocity of a kick, the force due to air resistance on a football, and
the effect that wind has on the trajectory of a football. The boundary layer of football is laminar
which is changing to turbulent at different spots and shows how quickly a ball is moving. This
transition is influenced by the surface roughness of the ball due to stiches. Angular velocity is
maximized first by the thigh, then by the shank and finally by the foot. When the boundary layer
of a football undergoes transition from laminar to turbulent flow, a drag crisis occurs whereby
the drag coefficient (cd) rapidly decreases. When a football player kicks a ball off- centre it
causes the ball to spin. The direction and the speed of the spin will determine how much the ball
curves during flight. The curve of the ball during flight is known as the Magnus effect.
Keywords: Launch angle, Velocity of the kick, Angular velocity, Magnus effect.
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PROCEEDINGs of
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Artificial Neural Network in Dissolution Profiling and
Establishing IVIVC of Pharmaceutical Solid Dosage Forms
Sutapa Biswas Majee, Gopa Roy Biswas
Division of Pharmaceutica, NSHM College of Pharmaceutical Technology, NSHM Knowledge
Campus, Kolkata-Group of Institutions, Kolkata 700 053.
Email Id: [email protected]
Abstract
Artificial neural networks (ANNs) can be considered superior and flexible to classical modeling
approaches during handling of data sets exhibiting non-linear relationships and hence useful for
data fitting, analysis and prediction in the field of optimization and formulation development
studies of different dosage forms, through profiling of dissolution data and establishment of in-
vitro-in-vivo correlation (IVIVC). This empirical modeling tool has been employed to study the
effect of input variables such as polymer weight fractions, ratio of polymers, drug/surfactant
ratio, level of penetration enhancer etc. on the output variables such as percentage of drug
released at various pre-defined time points, and also to predict release of drugs of varying
aqueous solubility from hydrodynamically balanced gastroretentive drug delivery systems, to
achieve desired target dissolution profile and bioavailability profiles from controlled release
matrix tablets, controlled porosity osmotic pump tablets, drug-loaded alginate microparticles,
transdermal drug delivery systems as well as from drug-cationic surfactant-modified zeolites
physical mixtures. It has also been utilized to predict dissolution profiles of -rheanite and α-
cristobalite from silica-calcium phosphate biphasic graft material. An optimized ANN is
constructed and trained through selection of optimal number of hidden layers and neuron number
in each layer. Suitability of the model was selected on the basis of cross-validation studies where
similarity factor was determined for a pair of predicted and reference dissolution profiles. IVIVC
can be established using dissolution data as inputs and pharmacokinetic data from patients
enrolled in crossover study as outputs. In vivo plasma profile of a particular drug from a dosage
form can also be predicted from in vitro profiles constructed using dissolution specifications.
Although non-linear modeling ability of ANN enables quality prediction and acts as efficient
data-mining and analytical tool, the success of ANN as a modeling tool depends essentially on
specification of inputs, ANN configuration variables, format of input-output relationship and
training.
Keywords: Artificial neural networks, IVIVC, Non-linear modeling.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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An Exact Approach for Transportation-p-Facility Location
Problem
Soumen Kumar Das, Sankar Kumar Roy
Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar
University, Midnapore-721102, West Bengal, India
Email Id: [email protected]
Abstract
This paper analyses a connection between the transportation problem and the facility location
problem; and the new form, here, is treated as the transportation-p-facility location problem (T-
p-FLP). The T-p-FLP is a generalization of the classical transportation problem where we
impose the p-number of facilities such that the total transportation cost will be minimized. The
iterative approachis applied to T-p-FLP to extract the results of our proposed problem. A
numerical exampleis included to show the efficiency of our proposed study with reality.
.
Keywords: Transportation-p-facility location problem, Iterative Approach.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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Migration of the Susceptible Prey can Stabilize the System:
A Mathematical Approach
Nikhilesh Sil
Department of Basic Science & Humanities (Mathematics), Narula Institute of Technology,
Kolkata 700109, India
Email Id: [email protected]
Abstract
A predator-prey system is considered, in a two-patch environment where the prey population is
divided into two parts: susceptible prey and infected prey. Here we consider the migration of the
susceptible prey and predator between those patches. Predator-prey system with infection in the
susceptible prey is well studied but the analysis of this system with migration of the susceptible
prey and the predator is not yet been explored. Here we take the advantage of two different time
scales and apply the aggregation procedure. Here we assume migration of the predator is
constant, whereas the migration of the prey is dependent on the predator density. We wish to
observe the migratory effect of susceptible prey through stability of our proposed slow-fast
system. Our results depict that migration of the susceptible prey can stabilize the system within
the two-patch environment.
Keywords: Migration, Predator, Prey, Two-patch environment, Slow-fast system.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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Solution of matrix games with generalized trapezoidal fuzzy
payoffs
Jishu Jana, Sankar Kumar Roy
Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar
University, Midnapore-721102, West Bengal, India
Email Id: [email protected]
Abstract
There are several methods available in the literature for solving the matrix game in fuzzy
environment. But in this article, we propose how to solve matrix games with generalized
trapezoidal payoffs. It is shown that once linear ranking function is chosen then Fuzzy Game
Problem (FGP) is converted into crisp one and then, is solved easily by the suggested method.
The validity and capability of Fuzzy Game Problem is illustrated with a numerical example.
Keywords: Matrix Game, Generalized Fuzzy Number, Ranking Function.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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Mathematics and Computer Science to give Sixth-Sense to
Machines
Rakesh Anand, Abhijit Pandey
Department of Computer Science and Engineering, Narula Institute of Technology, Kolkata
700109, India
Email Id: [email protected]
Abstract
Sixth sense is much related to predicting future by using the observed present conditions. This
can be achieved by using Mathematics with the help of developed technology. By observing
present conditions and calculating the probability of events of future, machines will be able to
predict the probable events of future which in turn will make them take decisions like human do.
With help of computer programming the concept of permutation and combination along with
probability can be implemented in computers. The algorithm will be set to decide the event with
highest probability to be the most likely event to happen in future. This will help to design self-
driven cars, trains and much more. The priority of events will be set in order to make the
decision like humans make. An algorithm written in any programming language can be used for
it with the present events as input which will be taken through sensing devices like camera,
microphone etc. and as well as user input by humans can be taken.
Keywords: Sixth sense, Probability of events, Programming language.
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PROCEEDINGs of
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The Missing Fundamental Element: Memristor
S. Mandal, S. Roy, S. K. Pandey, S. Kumar
Department of Mathematics, JIS College of Engineering, Kalyani, Nadia, India
Email Id: [email protected]
Abstract
Traditionally there are only three fundamental circuit elements:
(a) Capacitor
(b) Inductor
(c) Resistor These three basic two terminals circuit elements are defined in terms of a relationship between
two of the four fundamental circuit variables, namely, the current i, the voltage v, the charge q,
and the flux linkage .
( ) ∫ ( )
∫ ( )
(1)
( ) ∫ ( )
∫ ( )
(2)
Out of the six possible combinations of these four variables, five have led to well-known
relationships {( ) ( ) ( ) ( ) ( )} But there is no relationship in between ( ).
In the year 1971, the father of non-linear circuit theory Leon O Chuawas postulated the
memristor (MemoryResistor) as the fourth basic element of electrical circuit.
Figure 1.-J J YANG/HP LABS [2]
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Any two terminal deviceswhich exhibits a pinched hysteresis loop [Fig. 2]in the V-I plane when
driven by any bipolar periodic voltage or current waveform, for any initial conditions, is a
memristor.
Figure: 2. Sodium ion channel memristor and its pinched hysteresis loop[3]
For all passive memristorsthe generalized forms are defined as follows:
( ) (3)
( ) (4)
Where denotes n state variables which do not depend on
any external voltage or current.
In 1976, Chuaet al. described about memristive devices essential for the dynamics. A
memristive device has been fabricated by Williamsgroup, HPPhotonic Technology Lab in the
year of 2008. The physical structure of HP memristor, consists of a two-layer thin film of TiO2,
sandwiched between platinum contacts. One of the layers is doped with oxygen vacancies and
thus it behaves as a semiconductor. The second, undoped region has an insulating property, as
shown in Fig: 3, where D represents the device length (≈ 10 - 30 nm) and w the doped region
length.
Figure:3. HP memristor
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Memristors have unique properties namely Dense, Non-Volatility, Fast, High Endurance. It
serves as non-volatile analog memory. Locally passive memristors have been used for switching
electromagnetic devices and for field programmable logic arrays and learning. The memristor
bridge weighting circuit is able to perform synaptic operation for neural cell.
In the year 1952, Hodgkin & Huxley had erroneously named two circuit elements
associated with the Potassium ion and the Sodium ion as time-varying conductance in there
model. Leon Chua et al. solved many hitherto unsolved paradox associated with the Hodgkin-
Huxley time varying potassium conductance is in fact a first order memristor and the Hodgkin-
Huxley time varying Sodium conductance is in fact a second order memristor.
Memristive synapses are obviously becoming reality, but their real competitive advantage
against mainstream technologies (such as CMOS-based floating-gate memories) has yet to be
evaluated.
Keywords: Capacitor, Inductor, Resistor, Memristor.
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Fractional Calculus --- Threshold of a New Era of Science
Arnab Gupta
Department of Mathematics, Prabhu Jagatbandhu College, Howrah, Bengal.
EMail: [email protected]
Abstract
The concept of “calculus” (differential and integral), often called infinitesimal calculus was first
given by Sir Issac Newton (1642-1727) in 1666 where he expressed the differentiation as fluxion
(rate of change) of a given fluent (flow or motion of a body) and integration as an inverse
problem which states that given fluxion, to find the fluent. Later on, Barron Gottfried Wilhelm
Von Leibnitz (or Leibnitz), who born in Leipzig on July 1, 1646 have enlightened the idea of
calculus in a modified form. The idea of fractional calculus (or often called non-integer calculus)
was first introduced in the year 1695 by L’Hospitals. In a letter dated 30th
September, 1695,
L’Hospitals wrote to Leibnit’z asking him about the derivative of n
n
dx
yd when n=1/2 and for y=x.
Leibnitz replied that 2/1
2/1
dx
yd =
x2 and responded : “this is an apparent paradox from which one
day useful consequence will be drawn”.
Many authors have developed and defined the concept of fractional integrals and derivatives
(often called differintegrals) in their own way. Of them, the name of Riemann- Liouville (RL),
Weyl and Grunwald-Letnikov are worth mentioning. However, Caputo (1967) reformulated the
more “classic” definition of the Riemann-Liouville fractional derivative in order to use integer
order initial condition to solve fractional order differential equation. It is in 1996, Kolwankar
and Gangal reformulated again, the Riemann-Liouville fractional derivative in order to
differentiate nowhere differentiable fractal functions. However, the first text books regarding
fractional calculus was written by K.B. Oldham and J. Spanier in the year 1974. Most of the
applications and physical manifestations of fractional calculus related to science and technology
have been found in 20th
and 21st century. The applications like, Abel’s fractional integral
equation of Tatochrome (1823), Modelling of speech signals (Assaleh K. et. al., 2007),
Modelling of cardiac tissue electrode interface (Magin R.L., 2008), Fractional differentiation of
edge detection related to image processing (Mathieu B et. al., 2003), the solution of time-
dependent viscous- diffusion fluid problems (Kulish V.V. et. al., 2002) are worth mentioning.
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Some other applications are sound waves propagation in rigid porous materials (Fellah Z.E.A.
et. al, 2002), lateral and longitudinal control of autonomous vessels (Su´arez J.I et. al., 2004),
ultrasonic wave propagation in human cancellous bone (Sebaa N. et. al., 2006), applications in
viscous elasticity (Soczkiewicz E., 2002), polymer science (Doglus, J.F.), fractal phenomena
(Rocco Andear et. al.,1999).
Any problems from physics and engineering can be formulated as initial problem for dynamical
evolution equation as: )()( tBftfdt
d , where tR denotes time and B is an operator on Banach
space. This classical equation of evolution represents basic symmetry, principle of locality and
irreversibility. The generalized form of the above evolution equation is a fractional differential
equation: )()( tBftfdt
d
, where the order of the derivative is fractional or complex order. The
order of the fractional derivative α where 0<α<1 classifies and quantifies the influence of past
history, which have inbuilt integration meaning that the operation is non-local and requires
information about the past states.For unity value of the fractional order (or integer of order one)
the influence of past history is minimal, in the sense that, then the process evolution enters only
through the present state and for small value of α corresponds to a strong influence of past
history.
The present paper highlights the concept of an extraordinary differential equation
Fu=L0+Ru+Nu=G (1)
L0: highest order derivative (may be positive integer or fractional order), which is invertible i.e.
( )
dx
( ), which is linear operator.
R: linear differential (remainder) operator of order less than that of L0; this can also be fractional
linear operator i.e.
Ru
......
, where a0,a1, a2,….,am-1 are constants.
N: non- linear part which will be decomposed into infinite sum of adomain polynomial (this term
may be linear or constant) i.e.
Nu ( ) ( ) ( ) ( ) ..... ( )
G(x): sum of all external stimulus source/ sink. However, R and N generates internal stimuli and
when it get balanced with the external stimulus G then the process of the parameter remains
static without any growth or decay. Otherwise, the process parameter will have a solution as
infinite (or finite) decomposed modes; generated by the system itself to oppose stimulus
generated internally by previous mode.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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The proposed solution to this problem is a new approach called Adomain Decomposition
Method (ADM). The major advantages of ADM is that, it is free from rounding off errors, does
not involve any discretization and does not require large computer memory. Moreover, ADM is
close to physical reality and visualize the reaction system by decomposing the total gross
reactions from zeroth to infinity mode. The sum of all these modes is the solution of (1).
However, if L0 is the fractional differential operator in the sense of Riemann-Liouville (RL),
then the initial conditions should be in fractional order say, um
(0), um-1
(0) for m to be fractional.
These states are hard to visualize. But with this ADM, the RL formulation does not need these
fractional initial states instead requires u(0), u(1)
(0), u(2)
(0) etc.; the integer order states gives the
solution and thus physically understandable. As an application of extraordinary differential
equation, the paper discusses some aspects of fractional based calculus in electrical engineering
viz., Resistance- Capacitor circuit (RC circuit). The current into the line is half the applied
voltage. Thus, the circuit with semi-infinite lossy transmission line acts as half order element
connected to a CRO probe. The paper also demonstrated that using capabilities of
MATHEMATICA software, the total current for the said problem can be evaluated. In reality, it
is slightly deviated when past states i.e. the fractional order element say α=1/4, 1/3, 1/2 is taken
into consideration. In fact, just before shutting down (Voltage drop) the total current can be
evaluated as the actual scenario is that the current into the line is equal to αth derivative of
applied voltage.
The beauty of this subject is that fractional derivatives (and integrals) are not a local (or a point)
property (or quantity) rather, it tells us about the history and non-local distributed effects.
Perhaps, the fractional calculus is the calculus of 21st century, and so it is a threshold of new era
of science.
Keywords: Fractional Calculus, Infinitesimal calculus, fluxion, Banach space. …….……………………………………………………page 41………………………………………………………
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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Analysis of a Fishery Model with Harvesting including Prey
Refuge
Banani Roy, Sankar Kumar Roy
Department of Applied Mathematics with Oceanology and Computer Programming,
Vidyasagar University, Midnapore 721102, W.B., INDIA
Email Id: [email protected]
Abstract:
In this article, a prey-predator system with Holling type II functional response for the predator
population including prey refuge region is analyzed. Also a harvesting effort is considered on
predator population. The equilibria of the proposed system are determined. Local and global
stabilities for the system are discussed. The density-dependent mortality rate for the prey,
predator and super predator is considered. We use the analytic approach to derive the global
asymptotic stabilities of the system. The maximal predator per capita consumption rate is
considered as a bifurcation parameter to evaluate Hopf bifurcation in the neighborhood of
interior equilibrium point. Also, we use fishing effort to harvest predator population of the
system as a control to develop a dynamic framework to investigate the optimal utilization of the
resource, sustainability properties of the stock and the resource rent is earned from the resource.
Finally, we present some numerical simulations to verify the analytic results and the system is
analyzed through graphical illustrations.
Keywords: Prey-predator model, Harvesting, Time delay, Local stability, Hopf bifurcation,
Optimal control.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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Design of a Direct Neural Controller with Pid Compensation
for an Electrohydraulic Actuation System by Simulation and
Real-time Experiment
Amit Datta
Department of Mechanical Engineering, Narula Institute of Technology, Kolkata 700109, India
Email: [email protected]
Abstract
The present work attempts to develop an artificial neural network based controller for closed
loop control of a rugged electrohydraulic actuation system. A theoretical formulation has been
proposed that ensures the stability of the controller based on an assumed mathematical model of
the nonlinear electrohydraulic actuation system. Sinusoid demands at different speeds have been
tested to assess the effectiveness of the controller. This control design is based on Direct Neural
Controller with modified back propagation learning algorithm. Real-time experiments have been
performed using NI Systems with Labview interface
Keywords: Electrohydraulic, Jacobian, back propagation, DNC, PID compensation. Electro-
hydraulic actuation system, real time control.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
………………………………………………………………………………………………………………………………
Modified Android App and Website to Reduce Terror
Attacks in Railway
Arijit Manna
Department of computer science and engineering, Narula Institute of Technology, Kolkata
700109, India
E-mail Id: [email protected]
Abstract
Nowadays, terror attacks are one of the most important cases in our country. And it is growing
up day by day. Here I want to modify an android app and a website which provide us the update
of an express train’s next halt station time. I want to implement the app in android studio and the
website in (.net) compiler. This app will reduce the number of terror attack that’s why I have to
tie up with tie with Government. We have to give our name, address, valid email id and any id
card number(voter id, adhar id and pan id), issued by Government after verifying of our details
we will be successfully registered to the app and we will receive a confirmation mail, which will
indicate I am a successful registered user and my user id and password will be given there. After
completing these steps then we will be able to access the app to get the updates of that particular
express trains in which we want to travel. A terrorist also has to complete these steps, at the time
of id verification he/she will be caught.
In other side, if a terror attack has been happened then we can easily reach to the people of the
particular place where the attacks took place those who have used the app to get the updates
through their device IP address, then enlist their name and start a hard investigation on it.
I want to request to the government to seize all kinds of app and websites which do not
maintain the registration by using id proof.
Keywords: Terror Attacks, Express trains, Android Studio,(.Net), Id card Number, Hard
Investigation, seize.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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Application of Mathematics in Management
Juin Ghosh Sarkar
MCKV Institute of Engineering, Liluah, Howrah, West Bengal, India
Email Id: [email protected]
Abstract
This paper attempts to initiate a discussion on relevance and application of mathematics in
management. Management as defined by an eminent management guru Mary Parker Follet is
“getting the work done by people”. So in order to get the work done from the subordinates a lot
of calculation is required at each and every hierarchy of management in an organistion so that the
work can be properly planned and implemented. I would like to segregate the concept of
management into five broad mathematical areas: accountancy, financial management, statistics,
operations research and operations management.
Keyword: Mathematics, Management, Accountancy, Financial Management, Statistics,
Operations Research and Operations Management.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
………………………………………………………………………………………………………………………………
Triangular intuitionistic fuzzy matrixgames and a new
ranking approach
Ankan Bhaumik, Sankar Kumar Roy
Department of Applied Mathematics withOceanology and Computer Programming
Vidyasagar University, Midnapore-721102, West Bengal, India.
E-mail Id: [email protected]
Abstract
In this article, we consider a matrix game whose payoffs as triangular intuitionist fuzzy numbers
and we apply robust ranking technique to solve the matrix game. Score function approaches, and
accuracy function approaches of different types are used in matrix games earlier but robust
ranking technique to solve matrix game is rare in use. For validation of the proposed technique
numerical examples are included with a conclusive discussion.
Keywords: Matrix games, Intuitionistic fuzzy number, Ranking function.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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Ground Deformation during Aseismic Periods Under the
Action of Tectonic Forces
Subrata Kr. Debnath1, Sanjay Sen
2
1Department of Mathematics, Department of Basic Science and Humanities, MeghnadSaha
Institute of Technology ,Nazirabad.P.O. Uchhepota, Via- Sonarpur, Kolkata-700150, India.
2Department of Applied Mathematics, University of Calcutta, 92, APC Road, Kolkata 700009,
India.
E- mail Id: [email protected]
Abstract Small ground deformations are observed in seismically active regions during the aseismic
periods in between two major seismic events. Different tectonic phenomena, such as
mantle convection, etc. are supposed to be the main reason behind the generation of
tectonic forces which, in turn, lead to accumulation of stresses and strains in the region.
The nature of these tectonic forces may be investigated by developing suitable
mathematical model using the observed data on the aseismic ground deformations. We
consider a two – layer model representing the Lithosphere-Asthenosphere System.A
movement of strike -slip nature across the fault situated in the first layer occurs when the
accumulated stress due to various tectonic reasons e.g. mantle convection etc, exceeds the local
frictional and cohesive forces across the fault. The movement is assumed to be slipping in nature,
expressions for displacements, stresses and strains are obtained by suitable mathematical
methods involving integral transformation , integral equation and Green’s function method. The
values of the model parameters are used from updated field observations. It is observed that due
to the movement across the fault, there are regions where stress get accumulated and in some
other regions stress is released. A detailed study of these expressions may give some ideas
about the nature of stress accumulation/release in the system which may be helpful for effective
earthquake prediction programme.
Keywords: Aseismic period , Long Strike-slip fault , Tectonic force , Stress-strain,
Accumulation and Earthquake Prediction.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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Mathematical Analysis through Packet Transmission of
Modified PEGASIS in WSN
Raju Dutta
Department of Basic Science & Humanities (Mathematics), Narula Institute of Technology,
Kolkata 700109, India
Email Id: [email protected]
Abstract
Network lifetime is the prime factor in wireless sensor networks which consists nodes with
limited energy. Gathering information efficiently in critical situation in sensor network for a long
period of time is required efficient protocols. The LEACH and PEGASIS (Power-Efficient
Gathering in Sensor Information Systems) protocols are perfect solutions to this problem which
minimize the overall energy dissipation by the nodes in the network. The LEACH protocol
randomizes cluster heads for achieve equal energy dissemination, whereas the PEGASIS
protocol forms a chain of cluster heads taking rounds in transmitting to the base station. In this
paper, we propose an energy efficient protocol which enhances the performance of PEGASIS. In
Modified PEGASIS, each node communicates only with a close neighbor node with minimum
distance and transmits data to the base station, thus reducing the amount of energy spent per
round. For this protocol it will combine few parameters such as Distance and Residual Energy
for each node. The proposed system will increase the overall communication and increase the
network life. Simulation results show that Modified PEGASIS performs better than PEGASIS,
LEACH-C, and LEACH.
Keywords: Wireless Sensor Network, Unequal Cluster, Energy-Aware Clusters, Packet
Transmissions.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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Visualizing imaginary roots of a polynomial
Damodar Prasad Goswami, Sharmistha Sikdar
Department of Basic Science & Humanities (Mathematics), Narula Institute of Technology,
Kolkata 700109, India
E-mail Id: [email protected]
Abstract
Real roots are visible from the graph of any polynomial because it is the point of intersection of
the curve with the x-axis. But what about the complex ones? Can we see them? Unfortunately
not. Complex roots lie in the x-y plane and are two dimensional in nature. So they cannot be seen
in this way. Our question is, can we make them visible by any method? So far we could not find
any such procedure in the literature. Only one method is available which works only for
quadratic equations. This method becomes inapplicable if the degree of the equation increases
more than two.
In this study we have tried to capture the complex roots from graphs but so far we could not
achieve our desired goal and solve the problem completely. We have only succeeded to make
them visible if they are purely imaginary in nature, that is, there is no real part associated with
the root. We have elaborated it with some graphs along with necessary mathematical
explanations.
Keywords: Imaginary Roots, Polynomial, Quadratic equations.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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Realizing Mathematical Truths with Computer Algebra
Systems (CAS)
Amitava Jana
Department of Mathematics Education Pailan College of Education, Pailan, Kolkata, India
Email Id: [email protected]
Abstract
Computer algebra systems allow us to perform symbolic computation with computer. It not only
facilitates complicated calculations but can also be used as a powerful tool for teaching and
learning mathematics. It can be used by the teachers in the classroom for hands on experiment as
well as by the students to visualize mathematical results and get a realistic view of abstract
concepts in mathematics.
In this short exposition, we have used it to visualize certain mathematical results, which not only
give us delighted and helpful learning; it generates new insights in exploring the wonderful
mathematical world.
With some specific numerical examples, we have shown how this approach can enlighten us
with new way of looking at some standard mathematical facts and can be utilized for teaching
mathematics at different levels and complexity.
Keywords: Computer Algebra Systems, symbolic computation, mathematical world.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
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Application of Mathematics in Management
Kalipada Senapati
MCKV Institute of Engineering, Liluah, Howrah, West Bengal, India
Email Id: [email protected]
Abstract
This paper demonstrates thenumerous applications of mathematical tools and techniques in field
of management.Due to the ever-growing complexities in management caused by continuously
changing business environment, decision making has become cumbersome anf hazardous. The
past decades have witnessed versatile use of mathematical tools in management science across
all management functions like strategic business, engineering economics, human resource,
production and operations, accounts and finance, marketing, and retail and logistics
management. All these tools are directly or indirectly drawn from the fundamental theories of
mathematics, statistics and computer learned programs. Hence, application of mathematics is
inevitable in every function of management and in any kind of industry or organization – be it a
sophisticated software company, a heavy manufacturing industry, or a modern marketing
organization.
Policy making is invariably a strategic decision making process. Generally, business experts
prefer calculated decisions in positions of multiple alternatives. A variety of tools are followed in
engineering economic analysis in order to make a practical feasible solution with minimum risk.
Modern techniques of OR (Operations Research), as well as statistical and quantitative methods
have been extensively used in management for decades. This paper attempts to explain the
applications of mathematics in diverse functions of management with a special consideration on
engineering economics decision making.
Keywords : Mathematics, Management, Decision making, planning, forecasting,
Engineering economics.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
………………………………………………………………………………………………………………………………
Implementation of Golden Ratio to the Modern Science and
Technology
Neha Mukherjee, Dibyendu Sur
Department of Electronics and Instrumentation Engineering, Narula Institute of Technology,
Kolkata 700109, India
Email Id:[email protected]
Abstract
Golden ratio (φ) can be interpreted as a ratio of two integer numbers. The condition that needs to
be satisfied to qualify the ratio as a Golden ratio is that the ratio should be equal to their addition
divided by the biggest of the numbers. The historical evaluation and derivation methodology of
the Golden ratio are evaluated. The utilizations of Golden ratio in natural phenomena, scientific
and mathematical explanations, geometric calculations, art, architecture and technologies have
also been discussed in this paper. Detailed correlations between Golden ratio alongside
astronomical and biological aspects have also been addressed in this paper.
Keywords : Golden Ratio, Modern Science, mathematical calculations.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
………………………………………………………………………………………………………………………………
Visualizing multiplicity of roots in a polynomials
Damodar Prasad Goswami, Krisnendu Sarkar
Department of Basic Science & Humanities (Mathematics), Narula Institute of Technology,
Kolkata 700109, India
E-mail Id: [email protected]
Abstract
We know that any real root of a polynomial with real coefficients can be determined from its
graphical representation because it is the point where the curve intersects the x-axis. Importance
of this method lies in the fact that any polynomial equation of degree greater than four cannot be
solved analytically by any procedure. So, numerical solutions are the only way out. But
numerical solutions are generally lengthy and involve clumsy manipulations with decimal
numbers as they usually follow iterative scheme. On the other hand, if we simply plot the
function and look at it, all the real roots become visible at a single glance. If the equation has
three real roots for example, the curve intersects the x-axis three times at three different places.
But difficulty arises when the roots occur in multiples. For example, if the root 7 occurs three
times in an equation, how can we determine it from its graph? We can easily determine the root 7
but not the multiplicity because the graph always cuts x-axis at the point 7 whatever be its
multiplicity. In this paper, we have developed a method to get qualitative information about the
multiplicity from its pictorial representation. We could not determine the exact order but found a
consistent pattern with its increasing or decreasing tend. Moreover, the graph readily tells us
whether the degree of multiplicity is even or odd. We believe that this observation puts us a step
ahead in visualizing mathematical facts and feel them more realistically. A simple mathematical
explanation has also been provided to clarify the visual pattern.
Keywords : Multiplicity of roots, polynomials, mathematical calculations.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
………………………………………………………………………………………………………………………………
Parametric Optimization of MRR in Electrical Discharge
Machining
Akhtarujjaman Sarkar
Department of Mechanical Engineering, Narula Institute of Technology, Kolkata 700109, India
Email Id: [email protected]
Abstract
Electrical Discharge Machining or EDM is a machining method primarily used for hard metals
or those that would be impossible to machine with traditional techniques. So, Electro Discharge
machining (EDM) is one of the important non-traditional machining processes which are used
for machining difficult to machine materials like composites and inter-metallic materials. In this
process, the material removal mechanism uses the electrical energy and turns it into thermal
energy through a series of discrete electrical discharges occurring between the electrode and
work piece immersed in an insulating dielectric fluid. In this paper the machining experiments
were carried out on Mild Steel and Aluminum as Work-piece by using Copper and Graphite as
Electrode. Experiments are carried out by utilizing the combination of three process parameters
namely, Electrode speed, Current and Depth of cut. In this experimental study, it has inspected
the best combination of work-piece and Electrode which gives the maximum Material Removal
Rate (MRR). Furthermore, a mathematical model has been developed using polynomial
regression method to predict the material removal rate with considered control parameters by
conducting a designed experiment based on the Taguchi L9 orthogonal array. The developed
model has shown high prediction accuracy. A Computer program has been done in “C” language
on the basis of the proposed model. The program consists three parts each for analyzing the
variation of control parameters with the output parameter (MRR). The S/N Ratio has been done
to find out the influence of control parameters on MRR and also the optimal setting of control
parameters for maximum MRR. The test results analyzed using computer simulation and S/N
ratio, again analyzed by ANOVA (analysis of variance) for identifying the significant factors and
their relative contribution on the MRR. The conclusion carried out from this work is the increase
in Current and electrode speed leads to the increase in the material removal rate, but increase in
depth of cut leads to decrease in MRR. And Current is the most significant control factor among
the considered parameters within their considered ranges.
Keywords: EDM, MRR, Taguchi Method, S/N ratio, ANOVA.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
………………………………………………………………………………………………………………………………
Response of R/C Asymmetric Rectangular Community
Structures under Near Fault Ground Motion Considering
Equal Eccentricity
Goutam Roy1, P.K.Das
2
1Department of Mechanical Engineering, Narula Institute of Technology, Kolkata 700109, India
2Department of AE & AM, IIEST, Shibpur,711103, Howrah , West Bengal, India
Email Id:[email protected]
Abstract
Seismic vulnerability of asymmetric R/C structures is repeatedly reported by different seismic
damage surveys conducted all over the world and it is also pointed out that such damage is more
severe in R/C structures due to progressive strength and stiffness degradation of R/C structural
elements. Community structures like auditoriums generally have load resisting elements
distributed only near the boundary region of the structures leaving a large empty space at the
central region. These types of structures may have small to medium natural periods due to their
comparatively less height than other type of residential or official building structures.
Investigation of response of such systems under near-fault ground excitation are of great
importance as there may be a huge gathering of people inside an auditoriums and amount of
energy input to the structural systems will be much more in near-fault ground motions are than
their far-field counter parts.
It is observed that R/C structural systems with bidirectional asymmetry can have different
seismic responses depending upon orientation of the same, at different positions due to
functional requirements, even if its structural design and components are identical due to
presence of two different torsional moments of additive and cancelling nature. The present
research effort is conducted to study the effect of shape of the R/C community structural systems
in terms of variation of aspect ratio on response of bi-directionally asymmetric of equal
eccentricity systems under near-fault motions and a general trend of behaviour is also obtained
for such non- square shaped R/C community structures.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
………………………………………………………………………………………………………………………………
Shaped structural system under near-fault and far field ground excitation either in real or
simulated form. The present research effort is conducted to study the effect of shape of the R/C
community structural systems in terms of variation of aspect ratio on response of bi-directionally
asymmetric systems considering equal eccentricity under near-fault motions and a general trend
of behaviour is also obtained for such non- square shaped R/C community structures.
Keywords: Aspect ratio, asymmetric, time period ratio.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
………………………………………………………………………………………………………………………………
Role of Mathematics in Business Decisions: The current
scenario and emergence of a new horizon of studies
Soma Bose Biswas1, Nidhi Singh
2
1Department of Business Administration, Narula Institute of Technology, Kolkata 700109, India
2Registrar, Narula Institute of Technology, Kolkata 700109, India
Email Id: [email protected]
Abstract
There is a saying that Mathematics is the mother of all social sciences. It is evident from the
theories, practices and through the development of management as science that a systematic and
profound mathematical background results in harnessing coherent managerial thought process
while taking business decisions. Though the elements using mathematics in management in
ancient world is evident from folk tales, historical writings or the proofs obtained from
excavations such as graphic records, etc., the development modern management owe its origin to
classical school of thoughts. The genesis of using mathematics as a tool to take decision started
during the World War II to solve military problems and emerged a separate branch of studies as
“Quantitative School of thoughts” and “Management Science”. With the passage of time it
encouraged the managers to use mathematics, statistics, and operations research to take
managerial decisions. The paper investigated about the historical pattern of using mathematics in
business decisions. The recent trends of practicing mathematical models and tools in
management are also another major objective to study. The current research examines the recent
syllabi used by different universities in management teaching and identified the lacuna. It
highlights the emerging mathematical tools used in the business decisions and suggests a
direction to incorporate contemporary mathematical tools in management courses to prepare
more practical and industry ready professionals.
Key words: Quantitative Techniques, Management decisions, Mathematical tools,
Mathematical Software
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
………………………………………………………………………………………………………………………………
Optimization of enzyme catalysed polyester condensation - A
mathematical study
Rupa Bhattacharyya, Sumit Nandi
Department of Basic Science & Humanities (Chemistry), Narula Institute of Technology,
Kolkata 700109, India
Email Id: [email protected]
Abstract Enzyme kinetics, on the foundation of mathematical paraphernalia, explains fundamental aspects related
to chemical and biochemical processes in reality. Mathematical modeling based on this idea is proving to
be worthy nowadays in predicting the feasibility and optimality of chemical reaction processes. In recent
decades, enzyme-catalyzed polymerization (enzymatic polymerization) has been of increasing importance
as a new trend in macromolecular science. Enzyme catalysis has provided a new synthetic strategy for
useful polymers, most of which are difficult to produce by conventional chemical catalysts. In enzymatic
polymerization, the product polymers can be obtained under mild reaction conditions without
using toxic reagents. Therefore, enzymatic polymerization has a large potential as an
environmentally friendly synthetic process of polymeric materials, providing a good example to
achieve green polymer chemistry. In the present study, mathematical modeling is done over enzyme
catalyzed polyester condensation reaction wherein the aim of the model was of product optimization.
Polyester is formed by polycondensation process from polybasic acid and polyhydric alcohol via
successive elimination of water in each step. The kinetic reaction of polyester synthesis by enzymes can
be depicted by
k1 k2
S1 + S2 + E S1E + S2E + S1S2E P+E
k-1
Where S1 = monomer 1 = polybasic acid
S2 = monomer 2 = polyhydric alcohol
E = enzyme
P = polymer
k1, k-1, k2 = rate constants.
Present mathematical study proposes to optimize the reaction parameters including the monomer ratio and
molecular weight which in turn determines the engineering properties of the polymer and its ultimate use.
Keywords: Polyester, enzymes, modeling, optimization.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
………………………………………………………………………………………………………………………………
A Kinetic Study for the Synthesis of Diisobutyl Adipate by
Candida Antarctica
Sarbani Ganguly, Sumit Nandi
Department of Basic Science & Humanities (Chemistry), Narula Institute of Technology,
Kolkata 700109, India
Email Id: sarbaniganguly@gmail
Abstract
During the past years, there has been an increased interest in replacing chemical catalysts by
biocatalysts i.e. microbial enzymes as a whole or in isolated form to synthesize different
oleochemicals. Diisobutyldipate i.e. diester of adipic acid and di-isobutylalcohol have varied
industrial applications as fragrance stabilizer, plasticizer, emollient, masking agent, skin
conditioner, solvent etc. The present work aimed the kinetic study for the synthesis of
diisobutyldipate using adipic acid and di-isobutylalcohol under the catalyzing action of non
specific lipase NS 435 (Source: Candida Antarctica). Different reaction parameters like lipase
concentrations, temperature, stirring speed and substrate concentrations were studied using
different solvents where isooctane was found to be most suitable. Adipic acid concentration was
varied with fixed concentration of Isobutyl alcohol with the mole ratio of 1:1 to 8:1 and vice
versa. The activity of immobilized lipase was found to be maximum at lipase concentration of
10% of substrate (w/w) and at the reaction temperature of 45ºC. Kinetics of the reaction was
studied on analysing the effect of substrate concentration on rate of esterification using Ping-
Pong Bi-Bi mechanism which shows an inhibition by isobutyl alcohol at higher concentration.
The Kinetic parameter values were estimated by non-linear regression analysis.
Keywords: Immobilized, Diisobutyladipate, Candida Antarctica, Esterification.
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PROCEEDINGs of
National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)
………………………………………………………………………………………………………………………………
A Problem on Farm Planning: A Mathematical Approach
Debjani Chakraborti
1, Papun Biswas
2
1Department of Basic Science & Humanities (Mathematics), Narula Institute of Technology,
Kolkata 700109, India 2 Department of Electrical Engineering, JIS College of Engineering, Kalyani-741235, India
Email Id: [email protected]
Abstract
This paper describes how genetic algorithm (GA) can be efficiently used to fuzzy goal
programming (FGP) formulation of irrigation water and arable land allocation problems of
several seasonal crops in agricultural system.
In the proposed approach, utilization of total cultivable land, different productive resources,
achievement of target levels of production of seasonal crops and expected profit from farm are
fuzzily described.
In the model formulation of the problem, the concept of tolerant membership functions in
fuzzy sets for measuring the degree of optimality of crop-production by utilizing the productive
resources is considered.
In the solution process, achievement of the defined membership goals to the highest degree
(unity) to the extent possible on the basis of priorities of objectives is determined by employing
GA scheme in the decision making environment.
A case example is considered to demonstrate the potential use of the approach.
Keywords: Genetic algorithm, fuzzy goal programming, agricultural system, membership
function.
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GLIMPSES OF NSAMTM-2016