Springer Proceedings in Mathematics & Statistics

Volume 139

Springer Proceedings in Mathematics & Statistics

This book series features volumes composed of selected contributions fromworkshops and conferences in all areas of current research in mathematics andstatistics, including operation research and optimization. In addition to an overallevaluation of the interest, scientific quality, and timeliness of each proposal at thehands of the publisher, individual contributions are all refereed to the high qualitystandards of leading journals in the field. Thus, this series provides the researchcommunity with well-edited, authoritative reports on developments in the mostexciting areas of mathematical and statistical research today.

More information about this series at http://www.springer.com/series/10533

Ram N. Mohapatra • Dipanwita Roy ChowdhuryDebasis GiriEditors

Mathematics and ComputingICMC, Haldia, India, January 2015

123

EditorsRam N. MohapatraDepartment of MathematicsUniversity of Central FloridaOrlando, FLUSA

Dipanwita Roy ChowdhuryDepartment of Computer Scienceand Engineering

Indian Institute of Technology KharagpurKharagpur, West BengalIndia

Debasis GiriDepartment of Computer Scienceand Engineering

Haldia Institute of TechnologyHaldia, West BengalIndia

ISSN 2194-1009 ISSN 2194-1017 (electronic)Springer Proceedings in Mathematics & StatisticsISBN 978-81-322-2451-8 ISBN 978-81-322-2452-5 (eBook)DOI 10.1007/978-81-322-2452-5

Library of Congress Control Number: 2015939433

Springer New Delhi Heidelberg New York Dordrecht London© Springer India 2015This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or partof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmissionor information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilarmethodology now known or hereafter developed.The use of general descriptive names, registered names, trademarks, service marks, etc. in thispublication does not imply, even in the absence of a specific statement, that such names are exempt fromthe relevant protective laws and regulations and therefore free for general use.The publisher, the authors and the editors are safe to assume that the advice and information in thisbook are believed to be true and accurate at the date of publication. Neither the publisher nor theauthors or the editors give a warranty, express or implied, with respect to the material contained herein orfor any errors or omissions that may have been made.

Printed on acid-free paper

Springer (India) Pvt. Ltd. is part of Springer Science+Business Media (www.springer.com)

Preface

The Second International Conference on Mathematics and Computing (ICMC2015) was held at the Haldia Institute of Technology, Haldia, from January 5 to 10,2015. Haldia is a city and a municipality in Purba Medinipur in the Indian state ofWest Bengal, and Haldia Institute of Technology is a premier institution that givestraining to engineers and computer scientists. It has gained reputation through itsinstitutional dedication to teaching and research.

In response to the call for papers for ICMC 2015, a total of 69 papers weresubmitted for presentation and inclusion in the proceedings of the conference.These papers were evaluated and ranked on the basis of their significance, novelty,and technical quality by at least two reviewers per paper. After a careful and blindrefereeing process, 34 papers were selected for inclusion in the conference pro-ceedings. The papers cover current research in cryptography, abstract algebra,functional analysis, Pal and fractal approximation, fluid dynamics, fuzzy modelingand optimization, and statistics. ICMC 2015 saw eminent personalities both fromIndia and abroad (USA, France, Russia, Japan, Turkey, China, and Indonesia) whodelivered invited addresses, workshop lectures, and tutorial talks. Speakers fromIndia were recognized leaders from government, industry, and academic institutionslike Defense Research and Development Organization (DRDO), New Delhi; IndianInstitute of Sciences (IISc), Bangalore; Indian Statistical Institute (ISI), Kolkata;Indian Institute of Technology (IIT) Kharagpur; and IIT Madras. All of them areinvolved in research dealing with the current issues of interest related to the themeof the conference. The conference hosted four tutorial talks by Prof. PeeyushChandra (IIT Kanpur), Dr. Prasanta Kumar Srivastava (IIT Patna), Dr. DhanonjoyDey (DRDO, New Delhi), and Prof. Ram N. Mohapatra (University of CentralFlorida, USA). There were four workshops, ranging over 2 days by Prof. Ram N.Mohapatra, Prof. Manoranjan Maiti (Vidyasagar University), Prof. C. Pandurangan(IIT Madras), and Prof. Abhijit Das (IIT Kharagpur). In addition to these, there wasone keynote talk by Prof. Heinrich Begehr (Freie Universitat Berlin, Germany) and11 invited talks by Prof. C.E Venimadhavan (IISc, Bangalore), Prof. Ekrem Savaş(Istanbul Commerce University, Turkey), Dr. P.K. Saxena (DRDO, New Delhi),Prof. Peeyush Chandra, Dr. Christina Boura (Versailles Saint-Quentin-en-Yvelines

v

University, France), Prof. Birendra Nath Mandal (ISI, Kolkata), Dr. Mridul Nandi(ISI, Kolkata), Prof. G.P. Kapoor (IIT Kanpur), Prof. P.D. Srivastava (IITKharagpur), Prof. Abhijit Das (IIT Kharagpur), and Prof. B.C. Tripathy (Institute ofAdvanced Study in Science and Technology, India).

A conference of this kind would not be possible to organize without the fullsupport from different people across different committees. All logistics and generalorganizational aspects were looked after by the organizing committee members whospent their time and energy in making the conference a reality. We also thank all thetechnical program committee members and external reviewers for thoroughlyreviewing the papers submitted to the conference and sending their constructivesuggestions within the deadlines. Our hearty thanks to Springer for agreeing topublish the proceedings.

We are indebted to DRDO, Department of Electronics and InformationTechnology (Ministry of Communication and Information Technology, theGovernment of India), Indian Space Research Organisation (ISRO), University ofCentral Florida, The International Society for Analysis, its Applications andComputation (ISAAC), Cryptology Research Society of India (CRSI), Science andEngineering Research Board (DST), and Haldia Institute of Technology for spon-soring/supporting the event. Their support has significantly helped in raising theprofile of the conference.

Last but not least, our sincere thanks go to all authors who submitted papers toICMC 2015 and to all speakers and participants. We sincerely hope that the readerswill find the proceedings stimulating and inspiring.

Ram N. MohapatraDipanwita Roy Chowdhury

Debasis Giri

vi Preface

Committee

PatronLakshman Seth, Chairman, Haldia Institute of Technology, Haldia, India

General Co-ChairsP.K. Saxena, SAG, DRDO, New Delhi, IndiaP.D. Srivastava, IIT Kharagpur, India

Workshop ChairPeeyush Chandra, IIT Kanpur, India

Program Co-ChairsRam N. Mohapatra, University of Central Florida, USADipanwita Roy Chowdhury, IIT Kharagpur, IndiaDebasis Giri, Haldia Institute of Technology, India

Program Committee Members

PC Member Organization

P.N. Agarwal Indian Institute of Technology Roorkee, India

Ravi P. Agarwal Texas A&M University, Kingsville, USA

Rafikul Alam Indian Institute of Technology Guwahati, India

Rana Barua Indian Statistical Institute Kolkata, India

Heinrich Begehr Freie Universitat Berlin, Germany

Amitava Bhattacharya Tata Institute of Fundamental Research, Mumbai, India

Somnath Bhattacharyya Indian Institute of Technology Kharagpur, India

Jaydeb Bhaumik Haldia Institute of Technology, India(continued)

vii

PC Member Organization

Leonid Bokut Sobolev Institute of Mathematics, Novosibirsk, Russia

Ioana Boureanu Akamai Technologies Limited, UK

Teodor Bulboaca Babes-Bolyai University, Cluj-Napoca, Romania

Sucheta Chakrabarty DRDO, Delhi, India

Kalyan Chakraborty Harish-Chandra Research Institute, Allahabad, India

Peeyush Chandra Indian Institute of Technology Kanpur, India

Janka Chlebikova University of Portsmouth, UK

Dipanwita RoyChowdhury

Indian Institute of Technology Kharagpur, India

Rifat Colak Firat University, Elazig, Turkey

Abhijit Das Indian Institute of Technology Kharagpur, India

Ashok Kumar Das IIIT Hyderabad, India

Kinkar Das Sungkyunkwan University, Korea

Manik Lal Das DAIICT, India

B.K. Dass University of Delhi, India

Biswa Datta Northern Illinois University, USA

Anilkumar Devarapu Albany State University, GA, USA

Dhananjoy Dey DRDO, Delhi, India

Jana Dittmann University of Magdeburg, Germany

Philippe Gaborit University of Limoges, France

Sugata Gangopadhyay Indian Institute of Technology Roorkee, India

Praveen Gauravaram Tata Consultancy Services, India

Debasis Giri Haldia Institute of Technology, Haldia 721657, India

Narendra Govil Auburn University, Alabama, USA

Shay Gueron University of Haifa, Israel

Indivar Gupta DRDO, Delhi, India

U.C. Gupta Indian Institute of Technology Kharagpur, India

Tian-Xiao He Illinois Weslyan University, USA

Aoi Honda Kyushu Institute of Technology, Japan

Don Hong Middle Tennessee State University, USA

Honggang Hu University of Science and Technology of China, China

N.J. Hunag Sichuan University, Chengdu, Republic of China

Peter Johnson Auburn University, Alabama, USA

Mohan S. Kankanhalli National University of Singapore, Singapore

G.P. Kapoor Indian Institute of Technology Kanpur, India

Sandip Karmakar IIIT Guwahati, India

K.V. Krishna Indian Institute of Technology. Guwahati, India

Somesh Kumar Indian Institute of Technology Kharagpur, India

Shanta Laishram Indian Statistical Institute, Delhi, India

Duan Li The Chinese University of Hong Kong, Hong Kong

Shijun Liao Shanghai Jiao Tong University, China(continued)

viii Committee

PC Member Organization

Jiqiang Lu Institute for Infocomm Research (I2R), Singapore

Manoranjan Maiti Vidyasagar University, India

Soumen Maity IISER, Pune, India

Birendra Nath Manda Indian Statistical Institute Kolkata, India

Keith Martin Royal Holloway, University of London

Edgar Martinez-Moro University of Valladolid, Spain

Miodrag Mihaljevic Serbian Academy of Science and Arts, Belgrade, Serbia

P.R. Mishra DRDO, Delhi, India

Tapan Misra Space Applications Centre, ISRO, Ahmedabad, India

Ram N. Mohapatra University of Central Florida, USA

Shyamal Mondal Vidyasagar University, India

DebdeepMukhopadhyay

IIT Kharagpur, India

M. Mursaleen Aligarh Muslim University, India

Sukumar Nandi Indian Institute of Technology Guwahati, India

Vilem Novak University of Ostrava, Czech Republic

S. Padhi Birla Institute of Technology Mesra, India

Madhumangal Pal Vidyasagar University, India

Saibal K. Pal DRDO, Delhi, India

Kolin Paul Indian Institute of Technology Delhi, India

Svetla Petkova-Nikova KU Leuven, ESAT-COSIC, Belgium

Rajesh Pillai DRDO, Delhi, India

V. Sree Hari Rao IDRBT, India

Bimal Roy Indian Statistical Institute, Kolkata, India

Kouichi Sakurai Kyushu University, Fukuoka, Japan

Suman Sanyal Marshall University, West Virginia

Santanu Sarkar Chennai Mathematical Institute, India

P.K. Saxena DRDO, Delhi, India

G.P. Raja Sekhar Indian Institute of Technology Kharagpur, India

S. Samarendra Singh Manipur University, India

Seong Han Shin National Institute of Advanced Industrial Science and Technology,Japan

P.D. Srivastava Indian Institute of Technology Kharagpur, India

S. Sundar Indian Institute of Technology Madras, India

Pamini Thangarajah Mount Royal University, Calgary, Alberta, Canada

P. Vellaisamy Indian Institute of Technology Bombay, India

C.E. Veni Madhavan Indian Institute of Science, Bangalore, India

Ram U. Verma Texas A&M University-Kingsville, USA

V. Vetrivel Indian Institute of Technology Madras, India

Konstantin Volkov Kingston University, UK

Bixiang Wang New Mexico Institute of Mining and Technology, USA

Yao Zhao Beijing Jiao Tong University, China

Committee ix

Additional Reviewers

Organizing Committee

Asish LahiriA.K. DeyAnjan MishraDebasis GiriJaydeb BhaumikSk. SahnawajSudipta Kumar BasuDebasis DasSoumen PaulTarun Kumar GhoshApratim MitraSubhabrata BarmanSourav Mandal

Reviewer Organization

Abhijit Datta Banik Indian Institute of Technology Bhubaneswar, India

Rajesh Deo Institute of Information Security, India

Manish Kant Dubey SAG, DRDO, Delhi, India

Kishan Gupta Indian Statistical Institute Kolkata, India

Dipak Kumar Jana Haldia Institute of Technology, India

Louis Yang Liu Michigan State University, USA

Mukund Madhav Mishra University of Delhi, India

Seiichiro Mizoguchi Kyushu University, Japan

Kirill Morozov Kyushu University, Japan

Chandal Nahak Indian Institute of TechnologyKharagpur, India

Harika Narumanchi Jawaharlal Nehru Technological University, India

Ameeya Nayak Indian Institute of Technology Roorkee, India

Gayatri Ramesh University of Central Florida, USA

David Rollins University of Central Florida, USA

Sujit Samanta National Institute of Technology Raipur, India

Joe Sawada University of Guelph, Canada

Shalabh Indian Institute of Technology Kanpur, India

Juan Jacobo Simon Pinero Universidad de Murcia, Espaa

Yogesh Tripathi Indian Institute of Technology Patna, India

x Committee

Subhankar JoardarSusmit MaityPalash RoySk. Arif AhmedBidesh ChakrabortyMrinmoy SenJayeeta MajumderMihir Baran Bera

Message from the General Chairs

As we all are aware mathematics has always been a discipline of interest not only totheoreticians but also to all practitioners, irrespective of their specific profession. Beit science, technology, economics, commerce, or even sociology, new mathematicalprinciples and models have been emerging and helping in new research and indrawing inferences from practical data as well as through logic. The past fewdecades have seen enormous growth in applications of mathematics in differentareas multidisciplinary in nature. Cryptography and signal processing are suchareas, which have got more focus recently due to the need for securing commu-nication while connecting with others. With emerging computing facilities andspeeds, a phenomenal growth has happened in the problem solving area. Earlier,some observations were made and conjectures were drawn which remained con-jectures till somebody could either prove it theoretically or found counter examples.But today, we can write algorithms and use computers for long calculations, ver-ifications, or for generation of huge amounts of data. With available computingcapabilities, we can find factors of very large integers of the size of hundreds ofdigits; we can find inverses of very large size matrices and solve a large set of linearequations, and so on. Thus, mathematics and computations have become moreintegrated areas of research these days, and it was thought to organize an eventwhere thoughts may be shared by researchers and new challenging problems couldbe deliberated for solving these.

Apart from many other interdisciplinary areas of research, cryptography hasemerged as one of the most important areas of research with discrete mathematics asa base. Several research groups are actively pursuing research on different aspects ofcryptology not only in terms of new crypto-primitives and algorithms, but a wholelot of concepts related to authentication, integrity, and security proofs/protocols,many times with open and competitive evaluation mechanism to evolve standards.

As conferences, seminars, and workshops are the mechanisms to share knowl-edge and new research results that give us a chance to get new innovative ideas forfuturistic needs as threats and computational capabilities of adversaries are ever-increasing, it was thought appropriate to organize the present conference focused onmathematics and computations covering theoretical as well as practical aspects ofresearch, cryptography being one of them.

Committee xi

Eminent personalities working in mathematical sciences and related areas wereinvited from abroad as well as from within the country to deliver invited talks andtutorials for participants. The talks by these speakers covered a wide spectrum,namely number theoretic concepts, cryptography, algebraic concepts, and appli-cations. The conference was spread over 6 days (January 5–10, 2015) with the first2 days dedicated to workshops and the next one day dedicated to tutorials. Themain conference was planned with special talks by experts and paper presentationsin each session.

We hope that the conference met the aspirations of the participants and itsobjective of ideas and current research being shared and new targets/problemsidentified in the domain of cryptography, computational number theory, algebra,frame theory, optimizations, fuzzy logic, stochastic processes, compressive sensing,functional analysis, complex variables, etc., so that researchers and students wouldget new directions to pursue their future research.

P.K. SaxenaP.D. Srivastava

Message from the Program Chairs

It is a great pleasure for us to organize the Second International Conference onMathematics and Computing 2015 held from January 5 to 10, 2015 at the HaldiaInstitute of Technology, Purba Medinipur, West Bengal, India. Our main goal wasto provide an opportunity to the participants to learn about contemporary researchin mathematics and computing and exchange ideas among themselves and withexperts present in the conference as workshop presenters, tutorial presenters, andthe plenary as well as invited speakers. With this aim in mind, we carefully selectedthe invited speakers and the speakers for the workshops and tutorials. It is oursincere hope that the conference would help the participants in their research andtraining and open new avenues for work for those who are either starting theirresearch or are looking for extending their area of research to a different area ofcurrent research in mathematics and computing.

The below table shows the workshops held on January 5–6, 2015.

Title of the workshop Name of the speaker Duration of the workshop

Signcryption in standard model Prof. C. Pandu Rangan 3 h and 45 min

Elliptic curve cryptography Prof. Abhijit Das 3 h and 45 min

Riesz bases and frames Prof. Ram N. Mohapatra 3 h and 45 min

Conventional and metaheuristicoptimization techniques

Prof. Manoranjan Maiti 3 h and 45 min

xii Committee

The below table shows the tutorials held on January 7, 2015.

The conference began after a formal opening ceremony on January 8. There wasone keynote 90-min talk by Prof. Heinrich Begehr and seven invited 1-h talks byProf. Peeyush Chandra, Prof. C.E. Venni Madhavan, Dr. P.K. Saxena, Prof. EkremSavaş, Prof. Abhijit Das, Dr. Christina Boura, Dr. Mridul Nanadi, Prof. BirendraNath Mandal, Prof. P.D. Srivastava, Prof. G.B. Kapoor, and Prof. Binod ChandraTripathy. There were 32 contributed half-hour talks. Our speakers/contributorscame from Germany, France, Japan, Turkey, Indonesia, India, China, and USA.After an initial call for papers, 69 papers were submitted for presentation at theconference. All submitted papers were sent to external referees and after refereeing,34 papers were recommended for presentation. The proceedings of the conferencecontains 34 papers published by Springer. We are grateful to the speakers, par-ticipants, referees, organizers, sponsors, and funding agencies (from DRDO,University of Central Florida, DeitY-DIT, ISRO, CRSI, ISAAC, SERB-DST,Haldia Institute of Technology) for their support and help, without which it wouldhave been impossible to organize the conference, the workshops, and the tutorials.We owe our gratitude to the volunteers who worked behind the scene tirelessly intaking care of the details in making this conference a success.

Ram N. MohapatraDwipanita Roy Chowdhury

Debasis Giri

Title of the tutorial Name of the speaker Duration of the tutorial

Mathematical epidemiology Prof. Peeyush Chandra 2 h

Mathematical epidemiology Dr. Prasanta K. Srivastava 1 h and 45 min

A gentle introduction to blockciphers: design and analysis

Dr. Dhananjoy Dey 2 h

Some mathematical snapshots Prof. Ram N. Mohapatra 1 h and 45 min

Committee xiii

Contents

Integral Representations Related to Complex PartialDifferential Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Heinrich Begehr

Higher Order Hybrid Invexity Frameworks and DiscreteMultiobjective Fractional Programming Problems . . . . . . . . . . . . . . . . 19Ram U. Verma

A Study of Generalized Invex Functions on Riemannian Manifold . . . . 37S. Jana and C. Nahak

Second-order Symmetric Duality and Variational Problems. . . . . . . . . 49Saroj Kumar Padhan, Pramod Kumar Behera and R.N. Mohapatra

Efficient Portfolio for Interval Sharpe Ratio Model . . . . . . . . . . . . . . . 59Mrinal Jana, Pankaj Kumar and Geetanjali Panda

On Solvability for Certain Functional Equations Arisingin Dynamic Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Deepmala and A.K. Das

CASca:A CA Based Scalable Stream Cipher. . . . . . . . . . . . . . . . . . . . 95Shamit Ghosh and Dipanwita Roy Chowdhury

Improved Cryptographic Puzzle Based on Modular Exponentiation . . . 107Lakshmi Kuppusamy and Jothi Rangasamy

Computationally Secure Robust Multi-secret Sharingfor General Access Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123Angsuman Das, Partha Sarathi Roy and Avishek Adhikari

xv

Key Chain-Based Key Predistribution Protocols for SecuringWireless Sensor Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135Prasun Hazra, Debasis Giri and Ashok Kumar Das

IMSmining: A Tool for Imaging Mass Spectrometry DataBiomarker Selection and Classification . . . . . . . . . . . . . . . . . . . . . . . . 155Jingsai Liang, Don Hong, Fengqing (Zoe) Zhang and Jiancheng Zou

Pal Interpolation of Integral Types. . . . . . . . . . . . . . . . . . . . . . . . . . . 163Gayatri Ramesh

Positivity Preserving Rational Cubic Trigonometric FractalInterpolation Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187A.K.B. Chand and K.R. Tyada

A Monotonic Rational Fractal Interpolation Surfaceand Its Analytical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203A.K.B. Chand and N. Vijender

Toward a Unified Methodology for Fractal Extensionof Various Shape Preserving Spline Interpolants . . . . . . . . . . . . . . . . . 223S.K. Katiyar and A.K.B. Chand

Unistochastic Matrices and Related Problems . . . . . . . . . . . . . . . . . . . 239Aaron Carl Smith

Film Story Structure and Shot Type Analysis Using One-WayANOVA, Kruskal–Wallis Test, and Poisson Distribution Test . . . . . . . 251Udjianna Sekteria Pasaribu and Klara Ajeng Canyarasmi

Characterization of Total Very Excellent Trees . . . . . . . . . . . . . . . . . . 265N. Sridharan and S. Amutha

Quadratic Residue Cayley Graphs on Composite Modulus . . . . . . . . . 277Angsuman Das

A Dynamic Programming Algorithm for Solving Bi-ObjectiveFuzzy Knapsack Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289V.P. Singh and D. Chakraborty

A Fuzzy Random Periodic Review Inventory Model InvolvingControllable Back-Order Rate and Variable Lead-Time . . . . . . . . . . . 307Sushil Kumar Bhuiya and Debjani Chakraborty

xvi Contents

Supplier Selection Using Fuzzy Risk Analysis . . . . . . . . . . . . . . . . . . . 321Kartik Patra and Shyamal Kumar Mondal

The Control for Prey–Predator System with TimeDelay and Refuge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339Shashi Kant and Vivek Kumar

Evaluation of Solving Time for Multivariate Quadratic EquationSystem Using XL Algorithm Over Small Finite Fields on GPU . . . . . . 349Satoshi Tanaka, Chen-Mou Cheng and Kouichi Sakurai

Hierarchical Visual Secret Sharing Scheme Using Steganography . . . . 363Biswapati Jana, Amita Samanta and Debasis Giri

Covering Arrays of Strength Four and Software Testing . . . . . . . . . . . 391Yasmeen Akhtar, Soumen Maity and Reshma C. Chandrasekharan

Amplitude Equation for a Nonlinear Three DimensionalConvective Flow in a Mushy Layer . . . . . . . . . . . . . . . . . . . . . . . . . . 399Dambaru Bhatta and Daniel N. Riahi

Effect of Variable Bottom Topography on Water WaveIncident on a Finite Dock. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411Harpreet Dhillon and Sudeshna Banerjea

Electrokinetic Effects on Solute Mixing Near a ConductingObstacle Within a Microchannel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427S. Bera and S. Bhattacharyya

Distribution of Primitive Polynomials Over GF(2) with Respectto Their Weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441Prasanna Raghaw Mishra, Indivar Gupta and Navneet Gaba

Medial Left Bipotent Seminear-Rings . . . . . . . . . . . . . . . . . . . . . . . . . 451R. Perumal and P. Chinnaraj

Subcentral Automorphisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459R.G. Ghumde and S.H. Ghate

On Symmetric Laplace Integral of Order n . . . . . . . . . . . . . . . . . . . . 467S. Ray and A. Garai

A Sequence Space and Uniform (A;ϕ)—Statistical Convergence . . . . . 481Ekrem Savaş

Contents xvii

Editors and Contributors

About the Editors

Ram N. Mohapatra is Professor of Mathematics, University of Central Florida,Orlando, USA. He received his PhD degree from the University of Jabalpur, India,in 1968. Earlier, he taught at Sambalpur University in India, American University inBeirut, Lebanon, University of Alberta, and York University, Canada, prior tocoming to Orlando. His area of research is Mathematical Analysis and he is theauthor of two books, two edited monographs, and over 120 research papers. Hereferees articles for professional journals and serves as a member of the editorialboard of a number of journals.

Dipanwita Roy Chowdhury is Professor at the Department of Computer Scienceand Engineering, Indian Institute of Technology (IIT) Kharagpur, India. She is alsothe chairman of Kalpana Chawla Space Technology Cell, IIT Kharagpur. ProfessorRoy Chowdhury is PhD from IIT Kharagpur and M.Tech. in Computer Sciencefrom the University of Calcutta. Her topics of research interest are cryptography,error-correcting code, and cellular automata. She has published more than 150research papers in several international journals and conference proceedings.Professor Roy Chowdhury is the recipient of INSA Young Scientist Award andassociate of Indian Academy of Science. She is a fellow of Indian NationalAcademy of Engineers (INAE).

Debasis Giri is Professor at the Department of Computer Science and Engineering,Haldia Institute of Technology, India. His topics of interest are discrete mathe-matics, cryptography, information security, coding theory, advanced algorithms,design and analysis of algorithms, and formal languages and automata theory. Hisresearch interests include cryptography, network security, security in wirelesssensor networks, and security in VANETs. Dr. Giri had delivered several talks andguest lectures at various universities and conferences. He is supervisor of three PhDresearch scholars, and has guided many B.Tech. and M.Tech. students. He isassociate editor of the Journal of Security and Communication Networks (Wiley),

xix

and the Journal of Electrical and Computer Engineering Innovations. Further, he isthe editorial board member and reviewer of many reputed international journals. Heis also a program committee member of many international conferences. He is a lifemember of Cryptology Research Society of India. He received his PhD on“Cryptanalysis and improvement of protocols for digital signature, smartcardauthentication and access control” from Indian Institute of Technology (IIT)Kharagpur. He did both his M.Tech. and M.Sc. from IIT Kharagpur. He secured10th position in all India rank with percentile score 98.42 in the Graduate AptitudeTest in Engineering (GATE) examination in 1999. Dr. Giri has published more than30 technical papers in several international journals and proceedings.

Contributors

Avishek Adhikari Department of Pure Mathematics, University of Calcutta,Kolkata, India

Yasmeen Akhtar Indian Institute of Science Education and Research, Pune, India

S. Amutha Ramanujan Centre for Higher Mathematics, Alagappa University,Karaikudi, TamilNadu, India

Sudeshna Banerjea Department of Mathematics, Jadavpur University, Kolkata,India

Heinrich Begehr Mathematical Institute, Free University Berlin, Berlin, Germany

Pramod Kumar Behera Department of Mathematics, Veer Surendra SaiUniversity of Technology, Burla, India

S. Bera Department of Mathematics, Indian Institute of Technology Kharagpur,Kharagpur, India

Dambaru Bhatta The University of Texas, Edinburg, TX, USA

S. Bhattacharyya Department of Mathematics, Indian Institute of TechnologyKharagpur, Kharagpur, India

Sushil Kumar Bhuiya Department of Mathematics, Indian Institute ofTechnology Kharagpur, Kharagpur, India

Klara Ajeng Canyarasmi Institut Teknologi Bandung, Bandung, Indonesia

Debjani Chakraborty Department of Mathematics, Indian Institute ofTechnology Kharagpur, Kharagpur, India

A.K.B. Chand Department of Mathematics, Indian Institute of TechnologyMadras, Chennai, Tamil Nadu, India

Reshma C. Chandrasekharan Indian Institute of Science Education andResearch, Pune, India

xx Editors and Contributors

Chen-Mou Cheng Kyushu University, Fukuoka, Japan; National TaiwanUniversity, Taipei, Taiwan

P. Chinnaraj Department of Mathematics, Park College of Engineering andTechnology, Coimbatore, Tamilnadu, India

Dipanwita Roy Chowdhury Department of Computer Science and Engineering,Indian Institute of Technology Karagpur, Kharagpur, India

A.K. Das SQC & OR Unit, Indian Statistical Institute, Kolkata, India

Angsuman Das Department of Mathematics, St. Xavier’s College, Kolkata, India

Ashok Kumar Das Center for Security, Theory and Algorithmic Research,International Institute of Information Technology, Hyderabad, India

Deepmala SQC & OR Unit, Indian Statistical Institute, Kolkata, India

Harpreet Dhillon Department of Mathematics, Jadavpur University, Kolkata,India

Navneet Gaba Scientific Analysis Group, Defence Research and DevelopmentOrganization, Delhi, India

A. Garai Memari College, Memari, Burdwan, West Bengal, India

S.H. Ghate Department of Mathematics, R.T.M. Nagpur University, Nagpur,India

Shamit Ghosh Department of Computer Science and Engineering, Indian Instituteof Technology Karagpur, Kharagpur, India

R.G. Ghumde Department of Mathematics, Ramdeobaba College of Engineeringand Management, Nagpur, India

Debasis Giri Department of Computer Science and Engineering, Haldia Instituteof Technology, Haldia, India

Indivar Gupta Scientific Analysis Group, Defence Research and DevelopmentOrganization, Delhi, India

Prasun Hazra Paladion Networks, Bangalore, India

Don Hong Computational Science Program, Middle Tennessee State University,Murfreesboro, TN, USA; College of Sciences, North China University ofTechnology, Beijing, China

Biswapati Jana Department of Computer Science, Vidyasagar University, WestBengal, India

Mrinal Jana Department of Mathematics, Indian Institute of TechnologyKharagpur, Kharagpur, India

Editors and Contributors xxi

S. Jana Department of Mathematics, Indian Institute of Technology Kharagpur,Kharagpur, India

Shashi Kant Department of Applied Mathematics, Delhi TechnologicalUniversity, Delhi, India

S.K. Katiyar Department of Mathematics, Indian Institute of Technology Madras,Chennai, India

Pankaj Kumar Department of Mathematics, Indian Institute of TechnologyKharagpur, Kharagpur, India

Vivek Kumar Department of Applied Mathematics, Delhi TechnologicalUniversity, Delhi, India

Lakshmi Kuppusamy Society For Electronic Transactions and Security, MGRKnowledge City, Chennai, Tamilnadu, India

Jingsai Liang Computational Science Program, Middle Tennessee StateUniversity, Murfreesboro, TN, USA

Soumen Maity Indian Institute of Science Education and Research, Pune, India

Prasanna Raghaw Mishra Scientific Analysis Group, Defence Research andDevelopment Organization, Delhi, India

R.N. Mohapatra Department of Mathematics, University of Central Florida,Orlando, FL, USA

Shyamal Kumar Mondal Department of Applied Mathematics with Oceanologyand Computer Programming, Vidyasagar University, Midnapore, India

C. Nahak Department of Mathematics, Indian Institute of Technology Kharagpur,Kharagpur, India

Saroj Kumar Padhan Department of Mathematics, Veer Surendra Sai Universityof Technology, Burla, India

Geetanjali Panda Department of Mathematics, Indian Institute of TechnologyKharagpur, Kharagpur, India

Udjianna Sekteria Pasaribu Institut Teknologi Bandung, Bandung, Indonesia

Kartik Patra Department of Mathematics, Sikkim Manipal Institute ofTechnology, Sikkim Manipal University, East Sikkim, India

R. Perumal Department of Mathematics, Kumaraguru College of Technology,Coimbatore, Tamilnadu, India

Gayatri Ramesh University of Central Florida, Orlando, FL, USA

Jothi Rangasamy Society For Electronic Transactions and Security, MGRKnowledge City, Chennai, Tamilnadu, India

xxii Editors and Contributors

S. Ray Visva Bharati, Santiniketan, West Bengal, India

Daniel N. Riahi The University of Texas, Edinburg, TX, USA

Partha Sarathi Roy Department of Pure Mathematics, University of Calcutta,Kolkata, India

Kouichi Sakurai Institute of Systems, Information Technologies andNanotechnologies, Fukuoka, Japan; Kyushu University, Fukuoka, Japan

Amita Samanta Department of Computer Science, Vidyasagar University, WestBengal, India

Ekrem Savaş Istanbul Commerce University, Department of Mathematics,Istanbul, Turkey

V.P. Singh Department of Mathematics, Indian Institute of TechnologyKharagpur, Kharagpur, India

Aaron Carl Smith Department of Mathematics, University of Central Florida,Orlando, FL, USA

N. Sridharan Department of Mathematics, Alagappa University, Karaikudi,TamilNadu, India

Satoshi Tanaka Institute of Systems, Information Technologies andNanotechnologies, Fukuoka, Japan; Kyushu University, Fukuoka, Japan

K.R. Tyada Department of Mathematics, Indian Institute of Technology Madras,Chennai, India

Ram U. Verma Department of Mathematics, Texas State University, San Marcos,TX, USA

N. Vijender Department of Mathematics, VIT University, Chennai, India

Fengqing (Zoe) Zhang Department of Psychology, Drexel University,Philadelphia, PA, USA

Jiancheng Zou Computational Science Program, Middle Tennessee StateUniversity, Murfreesboro, TN, USA; College of Sciences, North China Universityof Technology, Beijing, China

Editors and Contributors xxiii