PROCEEDINGs of National Seminar on Application of Mathematics in Technology and Management (NSAMTM 2016)

Transcription

1 PROCEEDINGS OF NATIONAL SEMINAR ON APPLICATION OF MATHEMATICS IN TECHNOLOGY AND MANAGEMENT 8-9 September, 2016

2 Proceedings of National Seminar on Application of Mathematics in Technology and Management 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 International E - Publication

3 International E - Publication 427, Palhar Nagar, RAPTC, VIP-Road, Indore (MP) INDIA Phone: , Mobile: contact@isca.co.in, Website: First Impression: 2017 Copyright Reserved 2017 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted, in any form or by any means of electronic, mechanical, photocopying, reordering or otherwise, without the prior permission of the publisher. ISBN: 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.

4 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

5 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 teachinglearning. 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.

6 Mission, Vision and Objective of the Institute Quality Policy Mission Vision 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. 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 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.

7 Preface Mathematics plays a key role in the development of various branches of science, technology and Management as well as in the understanding of real world problems. It is the Science of pattern, order and relationship. The language and logic of our technological world is none other than Mathematics. Mathematical power is the ability to explore and to use a variety of mathematical methods to solve engineering problems effectively. The main purpose of the two day National Seminar on Application of Mathematics in Technology and Management is to bring academicians, researchers and students in a single platform in order to have the opportunity to interact and exchange ideas among themselves, discuss issues of common concern, establish contacts, and gather information in the interdisciplinary field of research. The invited lectures by eminent speakers from reputed University and Institutions, paper reading sessions and interactive sessions has enormously increased the interest of the participants in academic value addition as well as R&D activities. Young researchers got the opportunity to demonstrate their own works and have suggestions from experts. Many of the contributions are closely related to the need for mathematical modelling and Simulation of Physical, Engineering as well as Managerial phenomena. The seminar is specially designed to focus on the recent developments in Mathematics and its applications in real world complex decision making environment and also to encourage academicians, researchers and students to develop various competencies and enhance their self efficacy in different Mathematical techniques. The overall environment in the Seminar naturally motivated the students to study mathematics with deeper interest and in acquiring new skills to solve difficult technical problems. We have the pleasure to welcome the guests of Honour, the eminent speakers and several outstanding researchers from different Universities/Institutions of repute. We would like to take the Proud privilege to thank our Managing Director, Principal, Registrar, HOD of Department of BS& HU, the organising chair of the Seminar, the organizing committee, the reviewers, all colleagues and friends, the entire cast and crew who helped us to organize this Seminar. September 2016, kolkata Dr. Debjani Chakraborti TIC (Mathematics) and Assistant Professor, Department of BS & HU

8 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

9 Message from Chairman, JIS Group "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 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

10 Message from Chairman, BOG, JIS Group 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, 8th -9 th September, 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 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

11 Message from Managing Director, JIS Group 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. I am extremely delighted to share through this message my enthusiasm about the National Seminar on Application of Mathematics in Technology and Management, 8 th - 9 th September 2016 at Narula Institute of Technology, Agarpara, Kolkata, India. The National Seminar promises to be a forum of research scholars and professionals from within the country and outside and will certainly provide a platform for the sharing of experience and the exchange of opinions on technological advancements. I am sure that this event will draw talent from all over the globe and create a great learning experience for all participants, delegates and guests. I appreciate the efforts taken by the Organizing Committee of the NSAMTM 2016 and all the eminent persons involved. I wish them great success. Mr. Taranjit Singh.. page 3.

12 Message from the Principal (Seminar Chair) 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. I also extends my sincere thanks to our Managing Director Mr. Taranjit Singh for motivating us to organize the event successfully. I would like to appreciate the collective efforts put in by the members of different Committees and staff members of the Institute for making NSAMTM-2016 a grand success without whom it would have been very difficult for us to arrange the event. I also offer my thanks to all the participants for their immense support and active participation with sincerity and punctuality. I appreciate the effective assistance of every faculty and staff of the institute in direct and indirect manner to make NSAMTM-2016 a grand success. I hope, every individual will be satisfied and will enjoy the seminar to a great extent. Prof. (Dr.) M. R. Kanjilal....page 4.

13 Message from the Organizing Chair 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 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

14 Message from the convener 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. 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 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 I thank all the HODs of all the respective departments, the plenary speakers, the tutorial speakers and the delegates for their enthusiastic participation in this Seminar. I also convey my sincere thanks to all the people who have given their precious time in organizing this grand occasion. Dr. Debjani Chakraborti.. page 6.

15 LIST OF COMMITTEE MEMBERS Chief Patron: Sardar Jodh Singh (Chairman, JIS Group, India) Patrons: Sardar Taranjit Singh (MD, JIS Group) Prof.(Dr.)S.M.Chatterjee, Chairman,BOG Mr. S.S. DuttaGupta (Director,JIS Group) Prof. (Dr.) Asit Guha (Advisor, JIS Group) Mr. U. S. Mukherjee (Deputy Director, JIS Group) Mr. Simarpreet Singh (Director, JIS Group) Mrs. Manpreet Kaur (CEO, JIS Group) Ms. Jaspreet Kaur (Trustee Member, JIS Group) Seminar Chair: Prof.(Dr.) M.R.Kanjilal (Principal, NiT, Agarpara) Advisory Committee: Prof. B.B. Pal, Kalyani University Prof. M. N. Mukherjee, Calcutta University Prof. P.K. Roy, Jadavpur University Prof. S. Sen, Calcutta University Prof. N. C. Ghosh, Rabindra Bharati University Prof. S. Gupta, IIT(ISM), Dhanbad Prof. S. Kar, NIT Durgapur Prof. D. K. Bhattacharjee, Jadavpur University Prof. A. Dutta, ISI Kolkata Prof. A. Sengupta, Calcutta Medical College Prof. J.K. Das (Advisor R&D), NiT, Agarpara.. page 7..

16 Organising Chair: Dr. Sumit Nandi, HOD, BS & HU Convener: Dr. Debjani Chakraborti, TIC (Mathematics) & Asst. Professor, BS&HU Secretary: Dr. Susmita Karan, TIC (Physics) & Asst. Professor, BS&HU Joint Secretary: Dr. Nikhilesh Sil, Asst. Professor, BS&HU Dr. Raju Dutta, Asst. Professor, BS&HU Organising Committee: Dr. Pijush Basak, Asst. Professor, BS&HU Dr. Sarbani Ganguly, TIC (Chemistry) & Asst. Professor, BS&HU Dr. Leena Sarkar Bhaduri, TIC (English) & Asst. Professor, BS&H Ms. Sharmistha Basu, Asst. Professor, BS&HU Dr. Rupa Bhattacharyya, Asst. Prof, BS&HU. Ms. Rajasi Ray, Asst. Prof, BS&HU Ms. Nidhi Singh, Registrar, NiT Mr. Ratan Das, Site Supervisor, NiT Mr. Nilanjan Mitra, Accounts, NiT Mr. Partha Das, TEQIP Cell, NiT. page 8

17 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.... page 9

18 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. page 10

19 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.... page 11

20 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. page 12..

21 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. page 13

22 A Bio-Inspired Computation Based Approach to Non-Linear HIV Dynamics Debjani Chakraborti 1, Sumit Nandi 2 1 Department of Basic Science & Humanities (Mathematics), Narula Institute of Technology, Kolkata , India 2 Department of Basic Science & Humanities (Chemistry), Narula Institute of Technology, Kolkata , India Id: debjani.chakraborti@gmail.com 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... page 14..

23 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 Id: 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

24 Importance of Benchmark Function in Bio-Inspired Optimization Sangita Roy Department of Electronics and Communication Engineering, Narula Institute of Technology, Kolkata , India Id: 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.... page 16

25 Mathematical Model of Energy Consumption for Deploying Nodes in Sensor Network Raju Dutta Department of Basic Science & Humanities (Mathematics), Narula Institute of Technology, Kolkata , India Id: 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... page 17

26 Statistical Analyses in Drug Design and Environmental Chemistry Indrani Sarkar Department of Basic Science & Humanities (Physics), Narula Institute of Technology, Kolkata , India Id: 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.. page 18

27 Application of Business Mathematics in Management Nidhi Singh Registrar, Narula Institute of Technology, Kolkata , India Id: 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.. page 19

28 A Critical Review on Space Weather D. K. Tripathi Department of Basic Science & Humanities (Physics), Narula Institute of Technology, Kolkata , India Id: 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.....page 20.

29 Mathematical Modelling of Image Formation through Atmosphere Saurav Kumar Datta, Mainak Hore, Sangita Roy Department of Electronics and Communication Engineering, Narula Institute of Technology, Kolkata , India Id: 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 page 21

30 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 Id: hiranmoymondal@yahoo.co.in 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... page 22..

31 Comparing Antiloosening Ability BetweenM16 and 5/8 Inch BSW Threaded Fasteners Bikash Panja 1, Santanu Das 2 1 Department of Mechanical Engineering, Narula Institute of Technology, Kolkata , India. 2 Department of Mechanical Engineering, Kalyani Govt. Engg. College, Kalyani , India. Id: panja86@gmail.com 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 (60 0 ) 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.

32 Novelty in Vegard s Law Susmita Karan Department of Basic Science & Humanities (Physics), Narula Institute of Technology, Kolkata , India Id:susmita2108@gmail.com 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 [(NH 4 ) 2 SO 4 ] and potassium sulphate [K 2 SO 4 ] where, ammonium ions (NH 4 + ) 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, [(NH 4 ) 1-x K x ] 2 SO 4 have been collected using a Philips microprocessor controlled X-ray Diffractometer (APD 1710) and nickel filtered CuK radiation ( = Å) with an output power of 36 kv and 25 ma from a stabilized Philips X-ray Generator PW 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 NH 4 + 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..

33 Formula for getting Prime Numbers Abhijit Pandey Department of Computer Science and Engineering, Narula Institute of Technology, Kolkata , India Id: : 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.. page 25...

34 Analysis of Piezo-resistive Sensor data by multiple regression method Bansari Deb Majumde, Debatra Choudhury, Tirthankar Saha, Yekta Roy Department of Electronics and Instrumentation Engineering, Narula Institute of Technology, Kolkata , India Id: 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. page 26...

35 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 , West Bengal, India Id: 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 stockdependent 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... page 27.

36 A Mathematical Approach to Digital Humanities Rajasi Ray 1, Debjani Chakraborti 2 Department of Basic Science & Humanities (English), Narula Institute of Technology, Kolkata , India Department of Basic Science & Humanities (Mathematics), Narula Institute of Technology, Kolkata , India Id: rajasi.ray@gmail.com 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

37 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 , India 2 Department of Mechanical Engineering, Narula Institute of Technology, Kolkata , India Emai Id: banerjee.sudip71@gmail.com 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 (R a ) with the help of L 27 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 T on T off 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..... page 29

38 The role of Mathematics behind football science and Technology Debatra Choudhury, Tirthankar Saha, Bansari Deb Majumder, Yekta Roy Department of Electronics and Instrumentation Engineering, Narula Institute of Technology, Kolkata , India Id: 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..... page 30

39 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 Id: 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 invitro-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 page 31..

40 An Exact Approach for Transportation-p-Facility Location Problem Soumen Kumar Das, Sankar Kumar Roy Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University, Midnapore , West Bengal, India Id: 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 (Tp-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..... page 32

41 Migration of the Susceptible Prey can Stabilize the System: A Mathematical Approach Nikhilesh Sil Department of Basic Science & Humanities (Mathematics), Narula Institute of Technology, Kolkata , India Id: sil.nikhilesh@gmail.com 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.... page 33.

42 Solution of matrix games with generalized trapezoidal fuzzy payoffs Jishu Jana, Sankar Kumar Roy Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University, Midnapore , West Bengal, India Id: 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.... page 34.

43 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 , India Id: 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 selfdriven 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.... page 35.

44 The Missing Fundamental Element: Memristor S. Mandal, S. Roy, S. K. Pandey, S. Kumar Department of Mathematics, JIS College of Engineering, Kalyani, Nadia, India Id: 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]... page 36.

45 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 The physical structure of HP memristor, consists of a two-layer thin film of TiO 2, 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 ( nm) and w the doped region length. Figure:3. HP memristor.... page 37

46 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.. page 38

47 Fractional Calculus --- Threshold of a New Era of Science Arnab Gupta Department of Mathematics, Prabhu Jagatbandhu College, Howrah, Bengal. arnab.gupta@prabhujagatbandhucollege.edu.in The concept of calculus (differential and integral), often called infinitesimal calculus was first given by Sir Issac Newton ( ) 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 30 th September, 1695, n d y L Hospitals wrote to Leibnit z asking him about the derivative of when n=1/2 and for y=x. n dx 1/ 2 d y 2 x Leibnitz replied that = and responded : this is an apparent paradox from which one 1/ 2 dx 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 Most of the applications and physical manifestations of fractional calculus related to science and technology have been found in 20 th and 21 st 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 timedependent viscous- diffusion fluid problems (Kulish V.V. et. al., 2002) are worth mentioning...page 39..

48 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 d evolution equation as: f ( t) Bf ( t), where tr denotes time and B is an operator on Banach dt 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 d equation: f ( t) Bf ( t), where the order of the derivative is fractional or complex order. The dt 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=L 0 +Ru+Nu=G (1) L 0 : 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 L 0 ; this can also be fractional linear operator i.e. Ru..., where a 0,a 1, a 2,.,a m-1 are constants. N: non- linear part which will be decomposed into infinite sum of adomain polynomial (this term may be linear or constant) i.e. Nu ( ) ( ) ( ) ( )... ( ) G(x): sum of all external stimulus source/ sink. However, R and N generates internal stimuli and when it get balanced with the external stimulus G then the process of the parameter remains static without any growth or decay. Otherwise, the process parameter will have a solution as infinite (or finite) decomposed modes; generated by the system itself to oppose stimulus generated internally by previous mode.... page 40.

49 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 L 0 is the fractional differential operator in the sense of Riemann-Liouville (RL), then the initial conditions should be in fractional order say, u m (0), u m-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 21 st century, and so it is a threshold of new era of science. Keywords: Fractional Calculus, Infinitesimal calculus, fluxion, Banach space.. page 41

50 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 , W.B., INDIA Id: banani89roy@gmail.com : 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... page

51 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 , India amitindu1999@gmail.com 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. Electrohydraulic actuation system, real time control.... page 43.

52 Modified Android App and Website to Reduce Terror Attacks in Railway Arijit Manna Department of computer science and engineering, Narula Institute of Technology, Kolkata , India Id: 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 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.... page 44.

53 Application of Mathematics in Management Juin Ghosh Sarkar MCKV Institute of Engineering, Liluah, Howrah, West Bengal, India Id: 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... page 45..

54 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 , West Bengal, India. Id: la.ankan@gmail.com 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.... page

55 Ground Deformation during Aseismic Periods Under the Action of Tectonic Forces Subrata Kr. Debnath 1, Sanjay Sen 2 1 Department of Mathematics, Department of Basic Science and Humanities, MeghnadSaha Institute of Technology,Nazirabad.P.O. Uchhepota, Via- Sonarpur, Kolkata , India. 2 Department of Applied Mathematics, University of Calcutta, 92, APC Road, Kolkata , India. E- mail Id: dr.sanjaysen@rediffmail.com 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..... page 47...

56 Mathematical Analysis through Packet Transmission of Modified PEGASIS in WSN Raju Dutta Department of Basic Science & Humanities (Mathematics), Narula Institute of Technology, Kolkata , India Id: 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.. page 48

57 Visualizing imaginary roots of a polynomial Damodar Prasad Goswami, Sharmistha Sikdar Department of Basic Science & Humanities (Mathematics), Narula Institute of Technology, Kolkata , India Id: goswami.damodar@gmail.com 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.... page

58 Realizing Mathematical Truths with Computer Algebra Systems (CAS) Amitava Jana Department of Mathematics Education Pailan College of Education, Pailan, Kolkata, India Id: 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.. page 50...

59 Application of Mathematics in Management Kalipada Senapati MCKV Institute of Engineering, Liluah, Howrah, West Bengal, India Id: 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.. page 51...

60 Implementation of Golden Ratio to the Modern Science and Technology Neha Mukherjee, Dibyendu Sur Department of Electronics and Instrumentation Engineering, Narula Institute of Technology, Kolkata , India 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... page 52...

61 Visualizing multiplicity of roots in a polynomials Damodar Prasad Goswami, Krisnendu Sarkar Department of Basic Science & Humanities (Mathematics), Narula Institute of Technology, Kolkata , India Id: goswami.damodar@gmail.com 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.. page 53...

62 Parametric Optimization of MRR in Electrical Discharge Machining Akhtarujjaman Sarkar Department of Mechanical Engineering, Narula Institute of Technology, Kolkata , India Id: 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 L 9 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... page 54..

63 Response of R/C Asymmetric Rectangular Community Structures under Near Fault Ground Motion Considering Equal Eccentricity Goutam Roy 1, P.K.Das 2 1 Department of Mechanical Engineering, Narula Institute of Technology, Kolkata , India 2 Department of AE & AM, IIEST, Shibpur,711103, Howrah, West Bengal, India Id:goutammlp@gmail.com 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.... page 55..

64 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... page 56..

65 Role of Mathematics in Business Decisions: The current scenario and emergence of a new horizon of studies Soma Bose Biswas 1, Nidhi Singh 2 1 Department of Business Administration, Narula Institute of Technology, Kolkata , India 2 Registrar, Narula Institute of Technology, Kolkata , India Id: soma_mba@rediffmail.com 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. page 57

66 Optimization of enzyme catalysed polyester condensation - A mathematical study Rupa Bhattacharyya, Sumit Nandi Department of Basic Science & Humanities (Chemistry), Narula Institute of Technology, Kolkata , India Id: ruparupa1974@gmail.com 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 k 1 k 2 S 1 + S 2 + E S 1 E + S 2 E + S 1 S 2 E P+E k -1 Where S 1 = monomer 1 = polybasic acid S 2 = monomer 2 = polyhydric alcohol E = enzyme P = polymer k 1, k -1, k 2 = 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... page 58..

67 A Kinetic Study for the Synthesis of Diisobutyl Adipate by Candida Antarctica Sarbani Ganguly, Sumit Nandi Department of Basic Science & Humanities (Chemistry), Narula Institute of Technology, Kolkata , India Id: 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....page 59.

68 A Problem on Farm Planning: A Mathematical Approach Debjani Chakraborti 1, Papun Biswas 2 1 Department of Basic Science & Humanities (Mathematics), Narula Institute of Technology, Kolkata , India 2 Department of Electrical Engineering, JIS College of Engineering, Kalyani , India Id: debjani.chakraborti@gmail.com 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.. page 60

69 GLIMPSES OF NSAMTM-2016