8-9 september, 2016 - isca 978-93-84659-98-1.pdf · technology, computer applications, dental...

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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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

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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


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

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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

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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.


…….………………………………………………….…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

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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

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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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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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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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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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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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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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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.


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.

…….……………………………………………………page 15………………………………………………………

mailto:[email protected]

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Importance of Benchmark Function in Bio-Inspired

Optimization

Sangita Roy

Department of Electronics and Communication Engineering, Narula Institute of Technology,



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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Mathematical Model of Energy Consumption for Deploying

Nodes in Sensor Network

Raju Dutta

Department of Basic Science & Humanities (Mathematics), Narula Institute of Technology,



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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Statistical Analyses in Drug Design and Environmental

Chemistry

Indrani Sarkar

Department of Basic Science & Humanities (Physics), Narula Institute of Technology, Kolkata

700109, India


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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Application of Business Mathematics in Management

Nidhi Singh

Registrar, Narula Institute of Technology, Kolkata 700109, India


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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A Critical Review on Space Weather

D. K. Tripathi


700109, India


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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Mathematical Modelling of Image Formation through

Atmosphere

Saurav Kumar Datta, Mainak Hore, Sangita Roy

Department of Electronics and Communication Engineering, Narula Institute of Technology,



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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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


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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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.


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.

…….…………………...…………………………....…page 23…………………………………………………….


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Novelty in Vegard’s Law

Susmita Karan


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.

…….………………………………………………….…page 24……………………………………………………..

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Formula for getting Prime Numbers

Abhijit Pandey

Department of Computer Science and Engineering, Narula Institute of Technology, Kolkata

700109, India


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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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,



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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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


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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A Mathematical Approach to Digital Humanities

Rajasi Ray1, Debjani Chakraborti

2

Department of Basic Science & Humanities (English), Narula Institute of Technology, Kolkata

700109, India




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.

…….……………………………………………………page 28………………………………………………………

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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




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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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.


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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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



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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Migration of the Susceptible Prey can Stabilize the System:

A Mathematical Approach

Nikhilesh Sil




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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Solution of matrix games with generalized trapezoidal fuzzy

payoffs

Jishu Jana, Sankar Kumar Roy

Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar



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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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


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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The Missing Fundamental Element: Memristor

S. Mandal, S. Roy, S. K. Pandey, S. Kumar

Department of Mathematics, JIS College of Engineering, Kalyani, Nadia, India


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: nonlinear 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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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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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


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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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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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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Application of Mathematics in Management

Juin Ghosh Sarkar

MCKV Institute of Engineering, Liluah, Howrah, West Bengal, India


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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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.


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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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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Mathematical Analysis through Packet Transmission of

Modified PEGASIS in WSN

Raju Dutta




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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Visualizing imaginary roots of a polynomial

Damodar Prasad Goswami, Sharmistha Sikdar




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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Realizing Mathematical Truths with Computer Algebra

Systems (CAS)

Amitava Jana

Department of Mathematics Education Pailan College of Education, Pailan, Kolkata, India


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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Application of Mathematics in Management

Kalipada Senapati

MCKV Institute of Engineering, Liluah, Howrah, West Bengal, India


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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Implementation of Golden Ratio to the Modern Science and

Technology

Neha Mukherjee, Dibyendu Sur




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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Visualizing multiplicity of roots in a polynomials

Damodar Prasad Goswami, Krisnendu Sarkar




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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Parametric Optimization of MRR in Electrical Discharge

Machining

Akhtarujjaman Sarkar

Department of Mechanical Engineering, Narula Institute of Technology, Kolkata 700109, India


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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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


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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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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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


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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Optimization of enzyme catalysed polyester condensation - A

mathematical study

Rupa Bhattacharyya, Sumit Nandi

Department of Basic Science & Humanities (Chemistry), Narula Institute of Technology,



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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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,


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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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


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

8-9 september, 2016 - isca 978-93-84659-98-1.pdf · technology, computer applications, dental...

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