Proceedings of the International Conference on Frontiers in Mathematics, 26-28 March, 2015

Proceedings of the
International Conference on Frontiers in
Mathematics, 26-28 March, 2015
Department of Mathematics
Gauhati University
Guwahati-781014
Assam, India
EDITORS
R. K. Deka
H. K. Sarmah
N. Ahmed
Copyright © 2015 by the Department of Mathematics, Gauhati University, Guwahati.
Published in 2015 by Pratul Bhattacharyya, Shri Ganesh Printers, Noonmati, Guwahati
ISBN: 978-81-928118-9-5
ISBN: 978-81-928118-9-5
ICFM 2015
The First International Conference on Frontiers in Mathematics, ICFM 2015 took place from Thursday
March 26th to Saturday March 28th 2015 at the Department of Mathematics, Gauhati University,
Guwahati, Assam (India).
The conference was an event of high repute for the presence of eleven plenary speakers of which three
plenery speakers from USA, China and Taiwan as well as seventeen invited speakers from institutes of
repute from our own country, India.
There were 211 registered delegates from different states of India and union territories, namely Kerala,
Mumbai, Tirupati, Bangalore, Chennai, Pondicherry, Lucknow, Aurangabad, Bhubaneswar, Jaipur,
Dhanbad, West Bengal, Pune, Varanasi, Amravati, Bilaspur, Patna, Jaunpur, Andhra Pradesh, Allahabad,
Rohtak, Darjeeling and from all north eastern states.
Token amounts of reimbursement were given to participants coming from outside our home state. To a
total number of 45 participants were given partial reimbursement. However, participants travelled in
sleeper class were given full reimbursement.
Special thanks go to Prof. Kandarpa Das, Director, Institute of distance and open learning (IDOL) for
providing comfortable infrastructural facilities for holding technical sessions in the IDOL building.
We thank the authors for their contributions. We also take this opportunity to thank all those whose
efforts contributed to the success of the conference, including the Organising Committee of the
conference, the participants, and the faculty and administrative staff of the Mathematics Department,
Gauhati University who enthusiastically carried out various responsibilities for the conference. Thanks
are also due to Department of Science and Technology, Gauhati University and Oil India Limited, Noida
for financial support to the conference.
At last I acknowledge the help from Dr. Bhaben Chandra Neog, Principal, Jagiroad College and Shri
Ganesh Printers for their help in making this publication possible.
R. K. Deka
Organizing Secretary, ICFM-2015
ISBN: 978-81-928118-9-5
Organising Committee
Chief Patron:
Dr. M. Hazarika, Vice Chancellor, Gauhati University
President:
Secretary:
Prof. T. K. Dutta, Gauhati University
Prof. (Mrs.) H. K. Saikia, Gauhati University
Organizing Secretary: Prof. R. K. Deka, Gauhati University
/Convenor
Co-Convenor:
Prof. H. K. Sarmah, Gauhati University
Treasurer:
Prof. N. Ahmed, Gauhati University
Assistant Treasurer: Dr. (Mrs.) K. Das, Gauhati University
Members:
1. Prof. B. C. Kalita, Gauhati University
2. Prof. K. C. Choudhury, Gauhati University
3. Prof. N. R. Das, Gauhati University
4. Prof. (Ms.) K. Patra, Gauhati University
5. Prof. (Mrs.) R. Choudhury, Gauhati University
6. Dr. (Mrs.) N. Goswami, Gauhati University
7. Dr. H. Dutta, Gauhati University
8. Prof. K. Das, Director, IDOL, Gauhati University
9. Prof. G. Choudhury, IASST, Guwahati
10. Dr. D. Sarma, Cotton College
11. Dr. B. C. Neog, Jagiroad College
12. Dr. S. K. Das, J. B. College
13. Dr. J. Changmai, Digboi College
14. Dr. K. K. Das, Gauhati University
15. Dr. S. K. Sinha, Downtown University
16. Dr. R. Das, Arya Vidyapeeth College
17. Dr. (Mrs.) A. Bhattacharyya, B. Barooah College
18. Dr. A. Paul, Bodoland University
Publicity/Communication:
Dr. Ridip Dev Choudhury, Faculty Member, IDOL, GU.
Mr. Khurshid Alam Borbora, Faculty Member, IDOL, GU
Sponsored by
University Grants Commission, New Delhi
Department of Science & Technology, New Delhi
Oild India Limited, Noida
Gauhati University
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Plenary Lecture I
Finite-Volume and Discontinuous Galerkin Methods for Numerical Solution of
Maxwell Equation of Electromagnetics
Prof. Ramesh K. Agarwal,
Department of Mechanical and Aerospace Engineering
Washington University
Campus Box 1185, St. Louis, MO 63130-4899
Email: [email protected]
Abstract: It will be shown that the majority of partial differential equations of computational physics can
be recast in hyperbolic conservation law form. As a result, the very well developed finite-volume and
discontinuous Galerkin numerical methods can be employed for their solution. The computational
methodology includes mesh generation and higher-order accurate numerical algorithms that can be
applied to obtain accurate and efficient solution of these equations. This talk will demonstrate the
effectiveness of this unified numerical approach by solving the Maxwell equations for electromagnetic
scattering
Brief Biography of the Speaker: Professor Ramesh K. Agarwal is the William Palm Professor of
Engineering in the department of Mechanical Engineering and Materials Science at Washington
University in St. Louis. From 1994 to 2001, he was the Sam Bloomfield Distinguished Professor and
Executive Director of the National Institute for Aviation Research at Wichita State University in Kansas.
From 1978 to 1994, he was the Program Director and McDonnell Douglas Fellow at McDonnell Douglas
Research Laboratories in St. Louis. Dr. Agarwal received Ph.D in Aeronautical Sciences from Stanford
University in 1975, M.S. in Aeronautical Engineering from the University of Minnesota in 1969 and B.S.
in Mechanical Engineering from Indian Institute of Technology, Kharagpur, India in 1968. Over a period
of 35+ years, Professor Agarwal has worked in various areas of Computational Science and Engineering Computational Fluid Dynamics (CFD), Computational Materials Science and Manufacturing,
Computational Electromagnetics (CEM), and Multidisciplinary Design and Optimization. He is the
author and coauthor of over 460 publications. He has given many plenary, keynote and invited lectures at
various national and international conferences worldwide in over fifty countries. Professor Agarwal
continues to serve on many academic, government, and industrial advisory committees. Dr. Agarwal is a
Fellow of sixteen societies including the Institute of Electrical and Electronics Engineers (IEEE),
American Association for Advancement of Science (AAAS), American Institute of Aeronautics and
Astronautics (AIAA), American Physical Society (APS), American Society of Mechanical Engineers
(ASME), Royal Aeronautical Society, Chinese Society of Aeronautics and Astronautics (CSAA), Society
of Manufacturing Engineers (SME) and American Society for Engineering Education (ASEE). He has
received many prestigious honors and national/international awards from various professional societies
and organizations for his research contributions.
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Plenary Lecture II
Locally reduced rings and PP rings
Prof. K. P. Shum
Institute of Mathematics, Yunnan University
Kunming, Yunnan, China
Email: [email protected]
Abstract: A ring $R$ is said to be a reduced rings if it does not contain any non trivial nilpotent
elements. A ring $R$ is said to be a pp ring if all principle ideals generalted by an element of $R$ can
be regarded as a projective module over $R$. The class of pp rings can be regarded
as a generalized class of regular rings and the class of PP rings also contains the class of Baer rings
and the class of semi hereditary rings as its subclasses. In this talk, we will introduce the concept of
locally reduced rings and prove that when will a locally reduced rings be a reduced ring. Some
generalized pp rings will be particularly discussed and the relationships between the reduced rings
and the pp rings will be considered and investigated.
Brief Biography of the Speaker: Msc ( Leeds, England ), PhD (Alberta, Canada ), Hon Director of Math
( Gomel, Russia ). Lecturer to Chair Professor, Department of Matehmatics, The Chinese University
of Hong Kong (1971-2002). Chair Research Professor, Faculty of Science, The Chinese University of
Hong Kong, (2002-2007). Honorary Professor of Mathematics, University of Hong Kong (2008-2011).
Chief editor, Asian European Journal of Mathematics, Since 1998. Chief editor, Journal of semigroup
theory and applications, Since 2011. Chief editor, Southeast Asian Bulletin of Mathematics, Since 1976.
Member of Advisory board of IMO. since 2012. Chairman, Federation of Hong Kong higher Education
Institutes staffs associations since 1996.
Plenary Lecture III
Stability of two dimensional collapsible channel flow at high Reynolds number
using interactive boundary layer theory
Prof. N. M. Bujurke
INSA Honorary Scientist,
Professor of Mathematics (Rtd.)
Department of Mathematics,
Karnatak University,
Dharwad- 580 003
E-mail: [email protected]
ISBN: 978-81-928118-9-5
Abstract: The stability of two-dimensional high Reynolds number flow in a parallel sided
channel, of which part of one wall is a flexible membrane under longitudinal tension, is studied.
Far upstream the flow is parallel Poiseuille flow at Reynolds number Re . The width of the
channel is a and the length of the membrane is a , where 1  Re 1 / 2    Re , and
Re  U a /  * , U is average fluid velocity and  ,  * are fluid density and viscosity
respectively. The flow comprise the inviscid core flow and viscous boundary layers on both
walls coupled to each other and to the membrane deformation interactively. Lineralized unsteady
interactive boundary layer theory is used to investigate the instability of steady unidirectional
flows for zero external pressure for a range of values of tension T * (of the membrane). An
unexpected finding is that the flow is always unstable with a growth rate increasing with T * . In
other words the stability problem is ill posed with pressure difference ( 0) prescribed at the
upstream end. However, when the pressure difference is held fixed ( 0) at the downstream end
of the membrane or little further downstream, the problem is well posed and all solutions are
stable. The Physical mechanism underlying these findings are explored using a simple inviscid
model: the crucial factor in the fluid dynamics is the vorticity gradient across the incoming
Poiseuille flow.
Brief Biography of the Speaker: Fellow, National Academy of Sciences, India (FNASc), Fellow,
Indian National Science Academy, India (FNA), INSA Senior Scientist, (from 2005 to 2007), UGC
Emeritus Fellow, (from 2007 to 2009), INSA Senior Scientist, (from 2009 to March 2012), INSA
Honorary Scientist from 24th April 2012. Commonwealth Academic Staff Fellow in DAMTP
(Department of Applied
Mathematical and Theoretical Physics), University of Cambridge, 1985-86. Sr.
Visitor (DAMTP) University of Cambridge during 1990, 1998,2003 and 2012 for the collaborative
Research with Prof. T.J. Pedley, FRS, G. I. Taylor Professor and Head, DAMTP. He has eighty
publications in reputed journals, jointly with his students and other collaborators published by Academic
Press, Elsevier, Springer, OUP, CUP, John Wiley, Pergomen and others.
Plenary Lecture IV
Integrable Motion of Space Curves in Self Consistent Potentials: Spin Systems and Soliton
Equations
Prof. M. Lakshmanan
Prof. of Eminence & DAE Raja Ramanna Fellow
Centre for Nonlinear Dynamics, Bharathidasan University, Tiruchirapalli
Email: [email protected]
Abstract: Dynamics of several interesting physical systems such as the motion of vortex filaments,
superfluid 4^He, spin motion in a ferromagnetic chain, etc. can all be mapped onto a moving space curve
in R^3 described by Serret-Frenet equations, along with suitable time evolution equations. The resulting
compatibility condition leads to nonlinear evolution equations for the curvature and torsion. These can be
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associated with well known integrable soliton equations such as the nonlinear Schroedinger, modified
Korteweg-de Vries, and nonintegrable Ginzburg-Landau equations, and generalizations. These equations
can also be related to moving surfaces. Recently progress has been made in generalizing this approach by
considering curves evolving in the presence of self consistent vector potentials and identifying generalized
spin evolution equations with potentials and generalized soliton equations. I will review some of these
aspects.
Brief biography of the speaker: Professor M. Lakshmanan is one of the world leaders in the frontier
field of 'Nonlinear Dynamics'. Professor Lakshmanan has written over 300 research articles in
internationally reputed scientific journals and published 8 books through reputed publishers in the area of
Nonlinear Dynamics/Theoretical Physics. He has received some of the highest awards in the country,
including S. S. Bhatnagar Prize in Physical Sciences (1989), U. G. C. Hari Om Trust Meghnad Saha
Award in Theoretical Sciences (1990), Tamilnadu Scientist Award (1994), Biren Roy Memorial Lecture
Award of Indian National Science Academy (1998), 76th Indian Science Congress Madurai Kamaraj
University Distinguished Scientist Award (2004), Goyal Prize in Physics (2005) and Professor V. V.
Narlikar Memorial Lecture Award, INSA (2006). He has been a recipient of several prestigious
international fellowships, including Alexander von Humboldt Foundation Fellowship (Germany, 1997677, 1982), Eindhoven University Postdoctoral Fellowship (Holland, 1978). Swedish Guest Research
Fellowship (1981, 2000), and Japan Society of Promotion of Science Fellowship (1984-85, 2002, 2006)
and ICTP Senior Associateship (2002-08). He is also a member of the Editorial Boards of several
prestigious Theoretical Physics Journals, including the Proceedings of Royal Society of London A.
Professor Lakshmanan has been recently honoured with a D. Sc. (honoris causa) by the University of
Burdwan for his deep contributions to Nonlinear Dynamics. Professor Lakshmanan is a Fellow of all the
three Academies of Science of India and is an elected Foreign Member of the Royal Academy of
Sciences, Uppsala, Sweden. He has been recently elected as a Fellow of the Academy of Sciences of the
Developing Countries (FTWAS 2009). He has held visiting positions in many prestigious institutions all
around the world including Bulgaria, Canada, China, France, Finland, Germany, Greece, Holland, Italy,
Japan, Poland, Spain, Soviet Union and Ukraine.
Plenary Lecture V
Mathematics: Future and Prospects
Prof. P. Kandaswamy, Bharathiar University, Coimbatore
Email: [email protected]
Abstract: The future of Mathematics in India will see an unbelievable development in Mathematical
Biology, Financial Mathematics and Ballistics. These three areas hold the future and prospects for Indian
Mathematics. In this talk the present status of these three new areas and the possible requirements will be
discussed. Few examples like Mathematical Immunology, Portfolio Optimization and Ballistic Defence
Missile System will be discussed.
Brief biography of the speaker: Professor and Head Department of Mathematics; Director, School of
Mathematics and Statistics; Dean, Research Coordinator UGC DRS Center for Fluid Dynamics,
Bharathiar University, Coimbatore. Member Program Advisory Committee, Department of Science and
Technology, Government of India and Visiting Professor, Energy Conversion Research Center,
Department of Mechanical Engineering, Doshisha University, Kyoto, Japan. Fellow of the National
Academy of Sciences, India; UGC National Associate, India; INSA- JSPS Fellow, Japan; INSA-Royal
Society International Scientist; Exchange Fellow, UK; William Mong Award, The University of Hong
Kong, Hong Kong. He has published more than 100 papers.
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Plenary Lecture VI
Scientific Computing and Recent Perspective on Error Metrics
Prof. Tapan K. Sengupta
Department of Aerospace Engineering
IIT Kanpur, Kanpur-208 016
Email: [email protected]
Abstract: With the growing power of hardware and diversity of architectures, there are many claims
about direct numerical simulations (DNS) from all around. While such claims are mostly qualitative in
nature, it is now imperative to develop metrics for testing all such claims quantitatively. In the last
decade, we, at HighPerformance Computing Laboratory (IIT Kanpur), have introduced global spectral
analysis (GSA) tool for testing space-time discretization schemes. With GSA we have not only been able
to show the incorrectness of von Neumann error and stability analysis, we have firmly established the
correct error evolution for the benchmark problem of 1D convection equation. It is indeed a very
successful tool and many such DNS methods have been examined about the true scope. With the help of
GSA we have proposed a large numbers of high accuracy computing methods, mainly focusing on spatial
discretization, although GSA is a tool for space-time discretization methods.
In recent times, we have been focusing on space-time resolution and error minimization aspect of
scientific computing with time discretization as the main key. Historically, many so-called higher order
time integration methods have been used which uses more than two time levels, e.g. the Adams-Bashforth
method, mid-point leapfrog method etc. In this talk we will talk about some prominent published
problems of DNS where these methods have been used with dire consequences. It is now time to rectify
these mistakes once for all. In the talk, we will discuss about all these recent changes sweeping the field.
Time permitting, we will also discuss about mixed implicit-explicit (IMEX) time integration methods and
how such methods are used in DNS of transitional and turbulent flows with incorrect results proliferating.
The High Performance Computing Laboratory (IIT Kanpur) is leading these research and will be
showcased as to how DNS has been developed to solve the turbulence problem from first principle.
Brief biography of the speaker: B. Tech. (Aeronautical Engg.): Indian Institute of Technology,
Kharagpur (1979), M.E. (Aerospace Engg.): Indian Institute of Science, Bangalore (1981). Ph. D.
(Aerospace Engg.): Georgia Institute of Technology, Atlanta (USA) (1984) and Senior Research
Associate: University Engineering Dept., Univ. of Cambridge, Cambridge (UK) 1988-1990. Senior
Visiting Fellow- Dept. of Mechanical Engineering, National Univ. of Singapore, Singapore. Senior
Associate (2005 –2011), International Centre of Theoretical Physics, Trieste, Italy. Regional Editor,
Computers & Fluids, Elsevier, USA (Up to October, 2014). Pandit R. Dwivedi Chair Professor of
Aerospace Engineering, IIT Kanpur (Up to Dec. 2014). Visiting Faculty, Technical Univ. Munich,
Germany May-June, 2001. Visiting Professor, Ecole Polytechnique, Montreal, Canada June-July, 2012.
Visiting Professor, McGill University, Montreal, Canada May – July, 2013. Senior Research Associate,
Flow Transition and Receptivity (1988-1990), Univ. of Cambridge, UK. Visiting Faculty in 2001
Summer, Dept of Mech. & Aero. Eng., Technical Univ. Munich, Germany; Visiting Professor, Ecole
Ploytechnique, Montreal Genie Mecanique in 2012 summer; Visiting Professor, McGill University,
Montreal Mechanical Engg. In 2013 summer. Prof. Sengupta authored five books and published more
than 133 papers.
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Plenary Lecture VII
HIV Infection Models With Immune Response
Prof. Peeyush Chandra
IIT, Kanpur
Email: [email protected]
Abstract: AIDS (Acquired Immunodeficiency Syndrome), which results from the deterioration of immune system,
is caused by HIV (Human Immunodeficiency Virus). HIV belongs to the family of retrovirus. It attcks the cells of
human immune system that contains CD 4 protein on their surface and havocs the most CD 4+ T cells. On detection
of the invasion of virus, immune response starts and the hman body reacts to it by simulating CD 4+ T cells which
inturn stimulate the CD 8+ T cells. These CD 8+ T cells, also known as cytotoxic T lymphocytes (CTLs), try to
clear the infected CD 4+ T cells by proliferating and surrounding the infected cell to kill. Here, we shall consider
mathematical models for the effect of immune response on the dynamics of HIV. Further, delay in the activation of
CTLs as well as in immune response is accounted in model. The stability analys is performed. It is found that in the
presence of time delays the system exhibits rich dynamics.
Brief biography of the speaker: Biofluid Mechanics, Mathematical Modelling in Epidemiology, Fluid Mechanics
(Low Reynolds number flow) Lubrication Theory, Magnetic Fluids, Mathematical Ecology. Fellow of National
Academy of Sciences, India; President (Apr 2009-Mar 2010), Indian Mathematical Society; President (2012),
Indian Society of Theoretical and Applied Mechanics (ISTAM); Distinguished Service Award of Vijnana Parishad
of India, 2012; Sanjay Mittal Chair Professor Dec. 2011 - Dec. 2014; Member, PAC (MS), DST, New Delhi. (200407, 2007- 11); Member, Mathematical Sciences Research Committee, CSIR, Mar. 2015 - Mar. 2018; Editor
(Maths.), National Academy Science Letters, 1981-82; Editorial Board: (i) Proc.(A), National Academy Science,
India 2005; Prof. P.L. Bhatnagar Memorial Award Lecture in the 67th Annaul Conf. of IMS, Aligarh, 2002. He
authored 3 books and published more than 90 papers.
Plenary Lecture VIII
Homoclinic chaos and Mixed-mode oscillation
Prof. Shyamal Dana
Emeritus Scientist
Central Instrumentation, CSIR-Indian Institute of Chemical Biology
Jadavpur, Kolkata-700032, India
Email: [email protected]
ISBN: 978-81-928118-9-5
Abstract: In this talk I like to introduce a global bifurcation such as homoclinic chaos in a 3D nonlinear
system and its origin via a sequence of mixed-mode oscillation. I will describe, in details, how to observe
this phenomenon when a single parameter is tuned slowly. I will elaborate experimental experience in
electronic circuit that reveals the intricate details of homoclinic chaos.
Brief biography of the speaker: FIELD OF RESEARCH: Experimental chaos and synchronization.
Visiting Scholar, Abdus Salam ICTP,Trieste,Italy. Visiting Scientist, Elizabeth City State University,
USA for three months during Oct.1998-Jan.1999, two months during June-July, 2000 and one month
during August, 2001 sponsored by the NASA Glen Research Centre, Cleveland, Ohio, USA.Visiting
Scientist, Academia Sinica, Taipei, Taiwan: Three visits (One month each) in October, 2005; January
2006, June, 2006 sponsored by the Academia Sinica, Taiwan. Visiting Scientist, University of Medicine
and Pharmacy, Iasi, Romania under the Indo-Romanian collaboration for one month each in OctoberNovember, 2007 and June, 2008 and July 2009 sponsored by the DST, India and Ministry of Education
and Research, Romania. Visiting Scholar, Dept. of Physics, University of Agriculture, Abeokuta, Nigeria,
April, 2012 sponsored by the Abdus Salam ICTP,Trieste, Italy. More than 48 learned publications and
one book published by Springer.
Plenary Lecture IX
Finite group action and nature of its fixed point set: Recent developments
Prof. S. S. Khare, Pro Vice Chancellor, NEHU, Shillong
Email: [email protected]
Abstract: A closed manifold (compact, smooth and without boundary) Mn1 is said to be bordic to another
closed manifold Mn2 , if there exists a compact smooth manifold Wn+1 with the boundary of Wn+1 being
diffeomorphic to Mn1 U Mn2. Closed manifolds can be classified with help of Stiefel Whitney numbers (in
unoriented case) and with the help of Pontrajagin numbers as well (in oriented case). The objective of this
talk is to give an account of classification of G-manifolds up to G-bordism through its fixed point set with
special emphasis on fixed point sets like RPn, (S1)n and RPm U RPn etc.
Brief biography of the speaker: B. Sc.- Gold Medallist from Allahabad University (1966).
M.Sc.Silver Medallist from Allahabad University (1968).
Lecturer - Allahabad University from 1968 to
1971.
Lecturer - Gorakhpur University from 1972 to 1975.
Lecturer - NEHU from 1976
to1977.
Reader - NEHU from 1978 to 1985.
Professor - NEHU from 1986 till superannuation i.e.
2012.
Chief Proctor - 1997-98,
Dean School of Physical Sciences from 1998 to 2000,
Pro Vice
Chancellor from 2001 to 2010.
NBHM Visiting Professor from 2012 to 2014.
Fulbright Fellowship for
USA in 1986.
Commonwealth Academic Staff Fellowship 1987 for UK.
Fellow of National Academic
of Sciences in 1994.
He authored 30
books.
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Plenary Lecture X
From Euclidean geometry to manifold theory and some basic property of the
curvature tensors in Riemannian geometry
Prof. U. C. De, University of Calcutta
Email: [email protected]
Abstract. In the present talk we explain how the notion of manifolds come from Euclidean geometry.
Next some basic properties of curvature tensors in Riemannian geometry have been discussed. In
particular, 2-dimensional and 3-dimensional Riemannian space have been considered.
Brief biography of the speaker: Professor, Department of Mathematics, University of Kalyani (1998
June, 2009) and presently U.G.C. Professor in the Department of Pure Mathematics, Calcutta University
since 2009. More than 293 papers. Visiting Professorship in University of Debrecen, Hungary
; Chuo
University (twice), Japan; Dumlupinar University(thrice), Turkey; Balikesir University, Turkey; Uludag
University, Turkey
and Kuwait University, Kuwait.
Plenary Lecture XI
Poincare map for 3D chaotic attractor
Prof. D. K. Bhattacharyya
Ex Professor Emeritus UGC, Rabindra Bharati University
Abstract: The problem is discussed in two cases (i) 3D chaotic attractor of a 3D dynamical system and
(ii) 3D reconstructed chaotic attractor of a time series. 2D section of the attractor with a transversal plane
is called a Poincare section. The locus of points on the 2D section is called a Poincare map. In order that
the Poincare map is able to explain fully the chaotic dynamics of the original attractor, it has to be chaotic
too. But the section is subjective. Sometimes a particular plane of section gives rise to such a map that it
is able to explain the chaotic dynamics of the chaotic attractor, whereas there are sections for which the
corresponding Poincare map does not do so. Thus to find a suitable 2D Poincare map for a 3D attractor is
really a problem. Another natural question is to ascertain the proper dimension of the Poincare map. This
question arises as we already know that Lorenz map is 1-dimensional. But it can explain 3D chaotic
attractor of Lorenz system. Thus Poincare map may also be 1-dimensional.But the result is not a general
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one. It is shown that a 2D Poincare map may be reduced to a 1-dimensional one, under a very special
choice of the section, but the chaotic nature of the map may cease to exist. Hence for a given 3D chaotic
attractor, Poincare map is a 2D map, which is obtained only under a suitable choice of the plane of
section.
Brief biography of the speaker: Dilip Kumar Bhattacharya, the UGC Emeritus professor of Rabindra
Bharati Univerity, Kolkata retired from Calcutta University as Professor and Head from the department of
Pure Mathematics in 2008. Then he served as an AICTE Emeritus Professor in the School of Bio-science
and Engineering, Jadavpur University from 2008-10. He got his undergraduate and post-graduate degree
from Presidency College and Department of Pure Mathematics, Calcutta University. He also obtained his
Ph.D degree from Calcutta University, India. He is a good researcher having nearly ninety publications in
peer-reviewed National and International Journals of repute. He has a varied interest in his field of
research. He originally worked on basics of pure mathematics including modern algebra, functional
analysis and manifold theory. Then he switched on to mathematical modeling and control in Biology and
medicine. Afterwards he was interested in nonlinear dynamical system and chaos theory and studied the
effect of music and meditation on mind. Presently he is applying nonlinear time series analysis and fuzzy
set theory and its modification in the field of DNA and protein sequencing in bioinformatics. He is a
fellow of the International Academy of Physical Sciences.
Invited Lecture I
Mathematical problems in continuum mechanics at the mico/nanoscale
Prof. Huei Chu Weng
Department of Mechanical Engineering, Chung Yuan Christian University
Chungli 32023, Taiwan, ROC
Email: [email protected]
Abstract: Recent advances in micro/nanoscience and technology have promoted a rapid development in
micro/nanofluidic devices. The importance of micro/nanoscale flow and heat transfer arises from the new
applications in these devices. A fundamental understanding of micro/nanoscale physical aspects, which
may deviate from macroscale ones, is required for further progress. In this talk, some mechanics problems
for rarefied gases at the micro/nanoscale, which now have several accepted continuum modeling methods,
will be shown, and some mathematical problems awaiting solutions will be discussed. Hope the methods
of classical continuum mechanics have a chance to be extended to render them applicable to the whole
micro/nanoscale.
Brief biography of the speaker: Interests: Smart Nanomaterial Science, Micro/Nanoscale ThermalFluid Science, Power and Energy Science. Editor: Advances in Mathematical Physics (2014.6 - present;
Lead Guest Editor); Nanosciences and Nanotechnologies (2011.12 - present; EB Member); Journal of the
Chinese Society of Mechanical Engineers (2010.3 - present; EB Member). Distinguished Young
Engineering Professor Award, 2014 CSME (Chinese Society of Mechanical Engineers); Young
Engineering Professor Awards (2014.12); Excellent Tutoring Award, 2014 CYCU (Chung Yuan
Christian University); Tutoring Awards (2014.10); Excellent Compilation Award, 2013; K-12 Energy
Seed Teacher Training & Joint Textbook Compilation Awards (2013.11)
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Invited Lecture II
Waves on the surface of a conducting falling liquid film in presence of
electromagnetic field
Prof. B. S. Dandapat
Sikkim Manipal Technical University
Email: [email protected]
Abstract: Waves that occur at the surface of a thin conducting liquid film flowing down an inclined plane
in presence of electromagnetic field are investigated. Using the method of integral relations an evolution
equation is derived under the assumption of small magnetic Reynolds number. A quasi-stationary wave
approximation helps to analyze the evolution equation and it is possible to show the existence for two
types of waves depending on flow rate. Linear stability analysis predicts the contribution of different
terms in the wave mechanism. It is found that the wave process stabilizes as the Hartmann number M <
MC increases for a fixed electrical parameter E. It is also found that the flow field destabilizes for E > 0.
For negative E electric field stabilizes the wave process so long ̟ 𝜔
̅̅̅( 3 + 𝐸̅ 𝑀2 , where 𝐸̅ = −E > 0) > 0.
However, for 𝜔
̅ < 0 the electric field destabilizes the flow. At 𝐸̅𝐶 , ̅̅̅
𝜔 = 0, the basic flow ceases. At small
flow rate, Kuramoto-Sivashinsky equation is deduced from the evolution equation. At high flow rate,
phase speed increases with the decrease of the surface tension.
Brief biography of the speaker: Professor B. S. Dandapat received his Ph.D. degree from IIT Kharagpur
in the year 1978. He has joined as a lecturer at the Indian Statistical Institute, Calcutta in the year 1979.
He became Professor in the year 1991. Professor Dandapat, elected as a Fellow of the National Academy
of Sciences, India in year 1998. He has published more than 80 research papers in the leading
international journals like JFM, Physics of Fluids, Archive of Rational Mech. Analysis, International J. of
Heat & Mass Transfer, International J. Nonlinear Mechanics, ZAMP, ZAMM, Fluid Dynamics Research,
AIAA Journal, J. Appl. Mech. (Trans ASME) etc. Many of his research findings are cited in different text
books and research monographs published by leading publishers like Springer, Academic Press etc.
Currently he is an active Editorial Board member of 5 international Journals. Professor Dandapat has
worked as visiting professor in the University of Paris, France; Institute of Thermophysics, Novosibirsk,
Russia; Norwegian Technical University, Trondheim, Norway. He has visited several foreign countries
like USA, Canada, Germany, China etc. to deliver invited talks at different conferences and under
different assignments. After retirement from ISI, Kolkata in 2008, he is working at Sikkim Manipal
Institute of Technology, Sikkim.
Invited Lecture III
Stability of thermal convection in a vertical layer of porous medium
Prof. I.S. Shivakumara
Professor of Mathematics & Coordinator
UGC-CAS Programme
Department of Mathematics
Central College Campus, Bangalore University,
Bangalore - 560 001
E-mail: [email protected]
Abstract: The study of natural convection in a vertical porous layer whose side walls are maintained at
different fixed temperatures can be regarded as one of the classical problems of thermal convection in
porous media. In this talk, the stability of thermal convection in a vertical porous layer would be
reviewed. In particular, the results will be presented for couple stress fluids obtained through a modified
Orr-Sommerfeld equation derived and solved numerically. The critical Reynolds number Rec , the critical
wave number  c and the critical wave speed cc computed for wide ranges of couple stress parameter
would be used to analyze the stability of the system.
ISBN: 978-81-928118-9-5
Brief biography of the speaker: Recipient of the “PRESIDENT OF INDIA CASH AWARD” for the
best paper presentation at the 26th Congress of the Indian Society of Theoretical and Applied Mechanics
(ISTAM) held at Coimbatore Institute of Technology, Coimbatore–1981. The “PRESIDENT OF INDIA
CASH AWARD” was won for the second time at the 27th Congress of Indian Society of Theoretical and
Applied Mechanics (ISTAM) held at Jadavapur University, Calcutta–1982. Recipient of “YOUNG
SCIENTIST AWARD” Instituted by the Karnataka Association for Advancement of Science (KAAS),
Bangalore, Karnataka–1986. FIRST PRIZE for the best research paper presentation at the III SERC
School held at Indian Institute of Tropical Meteorology, Pune–1996. Recipient of “C. L. CHANDNA
INTERNATIONAL MATHEMATICS AWARD” from Canada for distinguished and outstanding
contributions to mathematics research and teaching-1998. Elected Fellow of the NATIONAL
ACADEMY OF SCIENCES, India - 2001. (F.N.A.Sc.). Bestowed with UGC NATIONAL HARI OM
ASHRAM TRUST AWARDS entitled “MEGHNAD SAHA AWARD” for outstanding scholarly
contributions in Theoretical science–2010 Nominated by the DEPARTMENT OF SCIENCE AND
TECHNOLOGY, GOVT. OF INDIA, NEW DELHI AS AN EXPERT FROM INDIA to deliver an
invited talk in the “International Conference on Application of Fluid Dynamics (ICAFD -2012)”
organized by the University of Botswana, Gaborone, Botswana- 2012. Visited Max-Planck Institute,
Bremen, Germany as a visiting Scientist under the German Science Council Programme (DFG)-2000.
Visited Department of Computational Science and Engineering, Yonsei University, Seoul, South Korea
as a visiting Scientist under World Class University (WCU) Program-2009. Visited School of Mechanical
Engineering, Yonsei University, Seoul, South Korea as a visiting Professor under Brain Korea (BK 21)
Program-2010. Visited School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong
University, Shanghai, China as a visiting Scientist–2011. Visited Department of Mechanical Engineering,
The Hong Kong University, Hong Kong as a visiting Professor–2011. He has published more than 159
papers in learned journals.
Invited Lecture IV
Nonlinear Analysis of Natural Convection under Modulation
Prof. B. S. Bhadauria
Banaras Hindu University
Email: [email protected]
Abstract: In the presentation, I would like to talk about the weak nonlinear analysis of natural convection
in a horizontal fluid layer/porous medium. In addition to a steady temperature difference across the layer,
a time-dependent periodic temperature is applied at the boundaries and the effect of modulation on the
convective flow is investigated. Also time-dependent gravity field, which can be realized by oscillating
the layer vertically, is considered. The whole system of equations is reduced to a well known amplitude
equation that is Ginzburg-Landau equation. Heat transfer is quantified in terms of the Nusselt number,
which is obtained as function of amplitude of convection. Effect of various system parameters is obtained
on heat and transfer.
ISBN: 978-81-928118-9-5
Brief biography of the speaker: Joined Eritrea Institute of Technology, Asmara, Eritrea, Africa as
Associate Professor. Nominated as one of the Vice-Presidents of the International Society “FORUM
FOR INTERDISCIPLINARY MATHEMATICS” of scholars working in mathematical sciences, April
2013. Visited Universiti of Kebangsaan Malaysia during October 24-28, 2011 and June 04- 22, 2012
where he was invited as visiting Professor to the School of Mathematical Sciences, Faculty of
Science and Technology for collaborative research work. Won Best Research Paper award during
Indian Mathematical Society Conference organized by the Department of Mathematics, at Indian
Institute of Technology, Roorkee during 26-29 December 2005. Presently, he is in the department
of Mathematics, Banaras Hindu University as Professor.
Invited Lecture V
Modelling of Groundwater Mound in an Aquifer in Response to Precipitation
Recharge am and the Effects of Bed Slope near Open Tidal Water
Prof. S. K. Das
Department of Applied Mathematics
Defence Institute of Advanced Technology (DIAT), (Deemed University)
Girinagar, Pune-411025, India
Email: [email protected]
Abstract: Groundwater flow problems have received considerable attention in recent years due to
growing scarcity and fast depletion of groundwater in various parts of the world. The mathematical
models for simultaneous groundwater and surface water interaction are useful to estimate, optimize and
planning of groundwater resource through conjunctive use systems. Many aquifers that are hydraulically
connected with nearby water bodies are usually heterogeneous and unconfined. Evaluating the formation
of groundwater mound due to recharge becomes important for large-scale land reclamation projects. The
study deals with the transient semi-analytical solution of linearized Boussinesq equations characterizing
the development of groundwater mound in an unconfined two-dimensional heterogeneous aquifer under
vertical recharge conditions. The finite aquifer consists of two rectangular basins surrounded by open
water bodies and shares a common impermeable or permeable boundary at the mid plane. The region
wise development of the groundwater mound indicates that the effect of heterogeneity becomes
significant for small time duration whereas for long time it becomes insignificant. This result can have
application in land reclamation problems in the presence of localized recharge where the reclamation
displaces the ground water divide and changes the ground water conditions in the entire region. In the
other scenario leaky confined aquifer with constant groundwater head is considered in response to sea
tide. The evaluation of water-table fluctuation in a coastal aquifer is important for various hydro
geological, ecological and environmental engineering problems which can help to understand significant
impact on the environmental and ecological conditions in the coastal areas. The groundwater head
distribution with varying slopes considering tidal boundaries is discussed for the diurnal tide and semidiurnal tide and the effect of leakage on groundwater head fluctuation with varying slope is also analyzed.
It is observed that with the increase in slope and time groundwater head fluctuations decreases for a
specific leakage.
ISBN: 978-81-928118-9-5
Brief biodata of the speaker: Dr. Das has received prestigious United Nation Development Program
(UNDP) Fellowship to pursue Post-doctoral research (1991-92) at the University of Minnesota (St.
Anthony Falls Hydraulic Lab), Minneapolis, USA. He has also received National Science Council (NSC)
Fellowship (2002-2003) as a Visiting Research Scientist to work at the National Taiwan University,
Taipei, Taiwan. He is also a recipient of prestigious Japan Society for the Promotion of Science (JSPS)
Fellowship as a visiting professor to conduct collaborative research at the Tohoku University (2009),
Japan. He was also Invited speaker for Russian-Indian Workshop and for project collaboration with
ICAD-RAS, RICCR, Moscow (2011) funded by Department of Science and Technology (DST) &
Russian Federation for Basic Research (RFBR). During his Doctoral studies, he has also received
Fellowships from UGC, DAE, IIT (Institute fellowship) and CSIR (SRF-Individual). He has published
75 research papers in various journals and conferences and 5 contributed article in books.
Invited Lecture VI
Reflection and transmission of plane dilatational wave from the microstretch
fluid/solid interface
Prof. S. K. Tomar
Department of Mathematics
(Centre for Advanced Study in Mathematics)
Panjab University, Chandigarh - 160 014 (UT)
E-mail: [email protected]
Abstract: This work is concerned with the study of reflection and transmission phenomena of
longitudinal plane wave striking obliquely at a plane interface between a microstretch elastic solid half
space and a microstretch liquid half space. 3M theory of micro-continuum materials has been employed
for addressing the mathematical analysis. We have analyzed the problem when a longitudinal plane wave
is incidences obliquely at the interface after propagating through the solid half space. Appropriate
boundary conditions have been formulated and the equations providing the amplitude ratios of various
reflected and transmitted waves have been presented in closed form. It is found that the reflection
coefficients are functions of angle of incidence, frequency of the incident wave and elastic properties of
the half spaces. To study the problem in greater details, numerical calculations have been carried out for a
specific model. The computed results obtained have been depicted graphically for better understanding of
the phenomena investigated. Several special cases have been reduced from the present formulation.
Brief biography of the speaker: Prof. Tomar has been bestowed with P. L. Bhatnagar Memorial Award
at the 80th Annual Conference of Indian Mathematical Society. Prof Tomar delivered 28th P. L.
Bhatnagar Memorial Award Lecture on the topic titled “Wave propagation in local and nonlocal
microstretch elastic media” at the Annual Conference, which was held at Indian School of Mines,
Dhanbad, Jharkhand from December 27-30, 2014. Prof. Tomar has more than 86 research articles
published in the journal of international repute.
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Invited Lecture VII
Stochastic Mortality Modeling and Forecasting for Indian Population with
Applications in Actuarial Science
Prof. Ramkrishna L. Shinde
Head, Department of Statistics and Actuarial Science,
Director, School of Mathematical Sciences,
North Maharashtra University, Jalgaon-425 001, India.
E-mail: [email protected], [email protected]
Abstract: Since early 1990s a number of stochastic models have been developed to analyze mortality
improvements throughout the world. The most popular stochastic mortality model was proposed by Lee
and Carter in 1992. Subsequently other stochastic mortality models have been proposed in the actuarial
literature as extensions of Lee and Carter model as Renshaw and Haberman (RH, 2006), Currie (2006),
Cairns-Blake-Dowd (CBD, 2006) and three extensions of CBD, two models by Plat (2009) and O'Hare
and Li(2012). An overview of these models is discussed. We have quantitatively compared these ten
stochastic mortality models on Indian population for explaining improvement in the mortality rates of
India. We have applied these ten models on yearly mortality data of Indian population obtained from
Sample Registration System, India for the period 1995-2013. By using R-codes these models are fitted for
the ages 20-99 years. On the basis of Bayes Information Criteria we observed that Plat's first model is the
best fitted model for Indian male as well as female populations. We have forecasted the future mortality
rates for Indian population using time series models for time dependent parameters of the fitted model. As
an application of results derived, actuarial quantities such as life annuities and premium of whole life and
term life insurance for Indian population are also presented. The produced empirical results can be
greatly useful for insurance industry and for making governmental policies.
Brief biography of the speaker: Thrust areas of research: Statistical Process Control, Life Insurance,
Crop Insurance, Health Statistics, Reliability Theory, Distribution Theory of Runs, Scans & Patterns and
their applications. Department of Mathematics and Statistics, University of Calgary, Canada during JulyAugust, 2010, May-June 2011 and May-June 2012 (Visiting Professor).
ISBN: 978-81-928118-9-5
Invited Lecture VIII
Finite difference solutions of free convective flow over moving vertical surface
Prof. P. Loganathan,
Department of Mathematics, College of Engineering
Anna University, Chennai - 600 025
Email: [email protected]
Abstract: The study of unsteady boundary layer flow over moving vertical surfaces has important
geophysical and engineering applications. Momentum, Heat and Mass transfer from a heated moving
material to a quiescent ambient medium occur in many manufacturing processes such as hot rolling, hot
extrusion, wire drawing and continuous casting. For example, as a result of volcanic activities or tectonic
movements, magnetic intrusion may occur at shallow depths in the earth crust. The intrusive magma may
take the form of a cylindrical shape. If the intrusive magma is trapped in a quiver, free convective flow
can be generated in the ground water adjacent to the hot intrusive. A study of temperature distribution
around the intrusive will aid in an assessment and the evaluation of geothermal resources during
geophysical exploration. However, in many industrial applications, the flow past a moving semi-infinite
vertical surface plays an important role. A finite-difference method is used to study the heat-transfer
response of an incompressible, laminar, natural convection, and unsteady flow along semi-infinite vertical
surfaces with different boundary conditions. The governing boundary layer equations are converted into a
non-dimensional form. The dimensionless, unsteady, coupled and non-linear governing equations are
solved by an implicit finite difference scheme of Crank-Nicolson type is employed to solve the equations.
The finite difference scheme is stable and accurate. Graphical results for the velocity, temperature,
concentration, local and average skin-friction, Nusselt number and Sherwood number are illustrated and
discussed for various physical parametric values.
Brief biography of the speaker: Current Area of Research: Computational Fluid Dynamics; Natural
Convection over vertical/inclined surfaces. He has more than 64 publications in Journals, namely,
International Journal of Heat and Mass Transfer, Nuclear Engineering and Design, Heat and mass
transfer, Journal of Engineering Physics and Thermophysics, Acta mechanica, Non-linear Analysis:
Hybrid systems, Forschung im Ingenieurwesen, Applied Mathematics and Mechanics, Meccanica.
Awarded with Senior Research Fellowship by CSIR, New Delhi, India.
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Invited Lecture IX
Turbulent scaling laws and symmetries
Prof. G. C. Layek
Department of Mathematics
The University of Burdwan
Email id: [email protected]
Abstract: The aim of the talk is to establish turbulent scaling laws and symmetries mathematically under
the framework of self preserving turbulent flow hypothesis. Lie symmetry group of continuous
transformations is employed on the non-linear partial differential equation derived from Heisenberg’s
integro-differential equation of energy spectrum. This unifies all invariant solutions in the system.
Turbulence scaling laws and group invariant energy spectrum depend upon one translation and two
scaling group parameters. The group operators with respect to their group parameters form a Lie algebra
of dimension three under the composition of commutator, Lie bracket. The flow statistics of turbulent
fluid at statistically equilibrium stage are obtained from this group theoretic analysis. A self –similar
equation is obtained, its order is further reduced by one by differential invariant method. It is interesting
to note that the present group invariant solution coincided with the self similar solution hypothesized by
Heisenberg when the ratio of dilation group parameters c1 and c2 is -1/2. It has been established that in
the limit of infinite Reynolds number (kinematic fluid viscosity  0 ), the self-similarity maintains for
any values of dilation group parameters. The initial and asymptotic states and energy spectra for different
values of group parameters are discussed.
Brief biography of the speaker: G.C. LAYEK is professor at the Department of Mathematics, The
University of Burdwan, West Bengal. He did his PhD from Indian Institute of Technology Kharagpur and
did his post-doctoral studies at Indian Statistical Institute, Kolkata. His areas of research are theoretical
fluid dynamics of viscous fluid, fluid turbulence and chaotic systems. Professor Layek has published
several research papers with international journals of repute and has visited several international
universities including Saint Petersburg State University, Kazan State Technological University, Russia,
for collaborative research work and teaching. He authored a book, “An Introduction to Dynamical
Systems and Chaos”, published by Springer. Prof. Layek has more than 100 publications.
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Invited Lecture X
Application of Some Random Fixed Point Theorem for Ćirić Type Contractive
Mapping
Prof. M. Saha
Department of Mathematics
The University of Burdwan, Burdwan-713104
E-mail: [email protected]
Abstract: The aim of this paper is to prove a random fixed point theorem in a separable Banach space
equipped with a complete probability measure for a certain class of contractive mappings namely Ćirić
Type Contractive Mapping. The main finding of this paper is to establish some random fixed point
theorems with its application to a random nonlinear integral equation.
Brief biography of the speaker: University Gold Medal awarded in M.Sc. in Pure Mathematics. More
than 54 publications.
Invited Lecture XI
Concerning quasi-uniformity and different topological properties via strong quasiuniform covers
Prof. M. N. Mukherjee, University of Calcutta
Email: [email protected]
Abstract: The development of uniform space is a natural one from topological spaces through quasiuniform spaces, and every topological space is quasi-uniformizable. Again, it is well known that a
uniform space can be characterized by means of uniform covers. However, a quasi-uniform space cannot
be characterized by quasi-uniform covers. Nevertheless, we have introduced a type of covers, termed
strong quasi-uniform covers, which has enabled us to ultimately obtain the desired axiomatic formulation
of quasi-uniformity. As application of this result, it is natural to expect characterizations of different
topological properties in terms of strong quasi-uniform covers, and we have been able to achieve the same
for several cases.
Brief biography of the speaker: Gold medalist in M.Sc. Research Papers – 149. Authored 8 books.
ISBN: 978-81-928118-9-5
Invited Lecture XII
On the dynamics of holomorphic correspondences on the sphere
Dr. G. Bharali
Department of Mathematics, IISc, Bangalore-560012
Email: [email protected]
Abstract: We shall discuss an equidistribution result for holomorphic correspondences on the 2-sphere.
Our result is motivated by a result of Dinh and Sibony in which, essentially, they construct for
correspondences the equivalent of Brolin's invariant measure for polynomial maps. However, their
construction works for the so-called correspondences of “large topological degree”. For a correspondence
𝐹 on the 2-sphere, this means that 𝑑𝑡𝑜𝑝 (𝐹) > 𝑑𝑡𝑜𝑝 (𝐹 𝑡 ). Here, 𝑑𝑡𝑜𝑝 denotes the topological degree, and
𝐹 𝑡 denotes the transpose of 𝐹. However, most interesting correspondences on the 2-sphere are not of large
topological degree. This is most notably the case for the correspondences introduced by Bullet and his
collaborators ― for which 𝑑𝑡𝑜𝑝 (𝐹) = 𝑑𝑡𝑜𝑝 (𝐹 𝑡 ). When 𝐹 is not of large topological degree, we show that
one can construct an invariant measure in the style of Brolin provided 𝐹 satisfies some constraints. These
constraints are rather natural, which we shall see via examples. We shall end with an outline of our
construction.
Brief biography of the speaker: Born on May 13, 1974, In Guwahati. M.Sc. (Integrated) from IIT,
Kanpur in 1997. Ph.D. from the university of Wisconsin-Madison, 2002. Assistant Professor (Visiting),
Department of Mathematics, University of Michigan, 2002-2005. Assistant Professor, Department of
Mathematics, IISc, Bangalore from Sep. 2005-Sep. 2011. Young associate of the Indian Academy of
Sciences, 2006-2009. Associate of the International Centre for Theoretical Physics, 2007. Awarded the
INSA medal for young scientists, 2009. Tenured at the Department of Mathematics, IISc, Bangalore,
2010. Associate Professor, Department of Mathematics, IISc, Bangalore, 2011-present. Guest associate
professor, Department of Mathematics, Norwegian University of Science and Technology, Trondhelm,
Aug. 2012-June 2013 (on sabatical). Awarded one of the 2014 Swarnajayanti Felloships in March 2015.
More than 21 publications.
Invited Lecture XIII
Black holes in dark energy backgrounds
Prof. Ng. Ibohal
Mathematics Department, Manipur University
Imphal 795003, Manipur
E-mail: [email protected]
Abstract: We discuss an exact solution of Einstein's field equations describing the Schwarzschild black
hole in dark energy background. It is also regarded as an embedded solution that the Schwarzschild black
hole is embedded into the dark energy space producing Schwarzschild-dark energy black hole. It is found
that the space-time geometry of Schwarzschild-dark energy solution is non-vacuum Petrov type $D$ in
the classification of space-times. We study the energy conditions (like weak, strong and dominant
ISBN: 978-81-928118-9-5
conditions) for the energy-momentum tensor of the Schwarzschild-dark energy solution. We also find that
the energy-momentum tensor of the Schwarzschild-dark energy solution violates the strong energy
condition due to the negative pressure leading to a repulsive gravitational force of the matter field in the
space-time. It is shown that the time-like vector field for an observer in the Schwarzschild-dark energy
space is expanding, accelerating, shearing and non-rotating. We investigate the surface gravity and the
area of the horizons for the Schwarzschild-dark energy black hole. We also extend the study in the case of
charged black hole in dark energy back grounds as Reissner-Nordstrom-dark energy black hole.
Brief biography of the speaker: Born on 1st March 1954 in Khurkhul Village, Imphal, Manipur. Did
graduation from Gauhati University in 1975; M. Sc. (1978) from J. N. U. Imphal Centre, Ph. D. (1984)
from Shivaji University, Kolhapur; Post Doctoral Research for 2 years from 1st September 1984 to 30
October 1986 in Mathematics Department of Aberdeen University, Aberdeen, U. K.; Worked as Pool
Officer from January 1987 to July 1988 in Mathematics Department, Manipur University, Imphal; Joint
Manipur University in 1988 as Assistant Professor, Associate Professor from 1997, Professor from 2011:
Published about 30 research papers in Indian and Foreign journals.
Invited Lecture XIV
Sructured Spectral Perturbation Theory for Hamiltonian Matrices
Prof. R. Alam
Department of Mathematics, IIT, Guwahati
Email: [email protected]
Abstract: Structured eigenvalue problems arise in many applications in science and engineering. For
example, the passivation analysis of an LTI system in Control Theory gives rise to a Hamiltonian
eigenvalue problem. The spectrum of a structured matrix inherits a spectral symmetry, which signifies a
characteristic property of the physical problem and has an important role to play in applications. Often it
is necessary, due to approximations and errors in the data, to perturb a structured matrix A by a structured
matrix ∆A so that the spectrum of A + ∆A has certain desired properties. On the other hand, the evolution
of eigenvalues of A under small structured perturbations plays an important role in various applications as
well as in the accuracy assessment of computed eigenvalues obtained by structured preserving algorithms.
We discuss spectral perturbations theory for Hamiltonian matrices and analyze evolution of eigenvalues
under Hamiltonian perturbations. We demonstrate that the structured spectral perturbation theory is
substantially different from the classical unstructured spectral perturbation theory for matrices.
Brief biography of the speaker: M.Sc from IIT Kharagpur in 1991 and Ph.D. from IIT, Mumbai, 1996.
BOYSCAST Fellowship (2003) awarded by the DST, Govt. of India. Visiting Fellow, TIFR,
Bangalore, June 1994. Visiting Faculty, Department of Mathematics, The University of Manchester, U.
K., March 2003 - March 2004. Visiting Professor, Equipe d'Analyse Numerique, Universite Jean Monnet
de Saint Etienne, France, June 01-30, 1997.
ISBN: 978-81-928118-9-5
Invited Lecture XV
Inverse of graphs and some eigenvalue properties
Prof. S. Pati
Department of Mathematics, IIT, Guwahati
Email: [email protected]
Abstract: C. D. Godsil and D. Cvetkovic introduced the notion of graph inverse in 1985. If the adjacency
matrix A(G) is nonsingular, then we say G is nonsingular. We say G has an inverse if A(G) -1 is signature
similar to the adjacency matrix of an weighted graph. Godsil has provided a class of connected bipartite
graphs with a unique perfect matching which have inverses. Our primary aim is to supply a much larger
class. A nonsingular graph G has the reciprocal eigenvalue property (R) if 1/λ is an eigenvalue of A(G)
for each eigenvalue λ of A(G). When that happens with equal multiplicities, then we say G has the strong
reciprocal eigenvalue property (SR). For trees, we know that property (R) is equivalent to property (SR).
This means, the class of trees with property (R) is precisely the same as that of the trees with property
(SR). A natural question is to find out larger class of graphs where these two are equivalent. We supply a
natural larger class graphs than the nonsingular trees, on which these are equivalent.
Brief biography of the speaker: Ph.D. form ISI, Delhi. more than 32 publications and authored one
book.
Invited Lecture XVI
Multilateral value for TU Games : The Role of a Parasite Player
Dr. S. Borkotoky
Department of Mathematics, Dibrugarh University
Email: [email protected]
Abstract: A value of a TU Cooperative game represents an assessment by a player of her gains for
participating in a coalition. One of the most important values in the literature of TU games is the Shapley
value. It is indeed an aggregation of the marginal contributions of a player based on her bilateral
interactions. In this paper we introduce a new value for TU Cooperative games. The notion of multilateral
interaction of a player is proposed that accounts not only for the player's own inclusion or exclusion in a
ISBN: 978-81-928118-9-5
coalition as considered in computing the Shapley value but also for her influence on her peers in their
decision of joining or leaving the coalition together. We characterize this value by the axioms of linearity,
anonymity, efficiency and a new axiom: the axiom of parasite player. A parasite player extracts worths
of other players. Our model makes her role less significant in presence of multilateral interactions.
Brief biography of the speaker: M.Sc. (Delhi Univ.) , M.Phil. (Delhi Univ.) , Ph.D (Dib Univ.).
Published 20 Articles in Reputed Journals and 5 Book Articles including Science Direct, Springer and
Taylor & Francis etc. Written 6 Review Articles in Math Review of American Mathematical Society
(MathSci.net). Awarded with the Indo-US Science and Technology Fellowship 2011 to do Post Doctoral
research in Network Games at Louisiana State University, USA during 2011-12. Visiting faculty at
Beijing Institute of Technology, Beijing, China during 2014. Visited as invited speaker the Univ. of
Western Australia, Perth; Indiana University, Bloomington, USA, University of Illinois at Chicago, USA;
Paris Mines Tech, Paris, Univ. of Sao Paulo, Brazil.
Invited Lecture XVII
Structured eigenvalue distributions and associated distance problems
Dr. Sreemayee Bora
Department of Mathematics, IIT, Guwahati
Email: [email protected]
Abstract: Matrices and matrix polynomials with special structure arise in a number of applications in
science and engineering. Often the structure leads to symmetries in the distribution of their eigenvalues.
For example the eigenvalues of matrix pencils where both matrices are Hermitian occur in pairs (λ, l ) 
C2 whereas matrix pencils where one of the matrices is Hermitian and the other skew-Hermitian give rise
to pairings of the form (λ, − l )  C2 in their eigenvalues. However, in both cases the eigenvalue pairings
break down for certain critical eigenvalues like real eigenvalues in the first instance and purely imaginary
eigenvalues in the second instance. The presence of critical eigenvalues can result in computational
difficulties and other implications for the underlying dynamical system that gives rise to these problems.
Therefore, in certain cases, given a structured eigenvalue problem with no critical eigenvalues, it is
important to know the nearest problem with the same structure which has such eigenvalues with respect
to a specified norm. On the other hand, given a structured eigenvalue problem with only critical
eigenvalues, it may also be important to know the nearest problem with the same eigenvalue symmetry,
which has at least one non-critical eigenvalue.
A distinguishing feature of critical eigenvalues is that they are associated with additional invariants called
sign characteristic or eigenvalue type which is positive, negative or mixed and this influences their
behaviour under structure preserving perturbations to the data. In this talk we focus on a few structured
eigenvalue problems and some associated distance problems. In particular, we highlight the role of the
eigenvalue type in the solutions to the distance problems.
Brief biography of the speaker: Worked as Research Assistant Professor in the research group of
Professor Volker Mehrmann in the Institut Fu r̈ Mathematik, Technische Universit ä t Berlin, Germany.
Visiting Fellow at Swiss Federal Institute of Technology, Zurich (ETH Zurich) with fellowship from Indo
Swiss Bilateral Research Initiative (ISBRI) of Ecole Polytechnique F ́ed ́erale de Lausanne (EPFL),
Switzerland. Received University gold medal and V. D. Thawani Award for topping the list of successful
candidates in the M. Sc. examination in Mathematics of Gauhati University in 1996.
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Contributed Papers
Paper 1:
IFP modules which are PS-armendariz
M. Buhphang
1-3
Paper 2: Operation on intuitionistic fuzzy soft multi sets
A. Mukherjee and A. K. Das
4-8
Paper 3: Rainfall frequency analysis of north east India
Abhijit Bhuyan
9-11
Paper 4: Montone convergence theorem for Henstock-Kurzweil integral
Anil Pedgaonkar
12-15
Paper
Paper
5:
A study of an improved renormalization group method in non-linear oscillation
Aniruddha Palit
16-23
6:
Solitary wave solutions of nth order K-P equation in hot adiabatic dusty plasma
having non-thermal ions with trapped electrons
Apul N. Dev, Manoj K. Deka and Jnanjyoti Sarma
24-32
Paper 7: On conjugate quadratic fields whose class numbers are divisible by 3
Azizul Hoque and Helen K. Saikia
33-34
Paper 8:
Mathematical modeling on the ill-effect of parthenium hysterophorus linn in
human health: a case study of Tezpur- sub division in Sonitpur district, Assam.
Barnali Das Deka
35-38
Paper 9:
Different acoustic feature parameters ZCR, STE, LPC and MFCC analysis of
assamese vowel phonemes
Bhargab Medhi and P. H. Talukdar
39-43
Paper 10: Multi-item integrated inventory model with fuzzy credit period and fuzzy space
constraints
Bibhas Chandra Das, Barun Das and Shyamal Kumar Mondal
44-50
Paper 11: Anisotropic bulk viscous cosmological models with variable cosmological term
Chandra Rekha Mahanta, Azizur Rahman Sheikh and Sangita Kakoti
51-55
Paper 12: Shear stress distribution at the wall of omega(  ) shaped stenotic tapered artery in
the presence of catheter and velocity slip-effects of polar fluid
D. Srikanth, J. V. Ramana Reddy and Vssnvg Krishna Murthy
56-59
Paper 13: A model for topological relations of fuzzy region with holes and fuzzy point
Dibyajyoti Hazarika
60-64
ISBN: 978-81-928118-9-5
Paper 14: Some fixed points theorems on tensor product spaces
Dipankar Das and Nilakshi Goswami
65-68
Paper 15: Magnetic field effect on oscillatory flow of blood in a stenosed artery
G. C. Hazarika and Barnali Sharma
69-73
Paper 16: On ℱ −torsion pure injective modules
Himashree Kalita and Helen K. Saikia
74-77
Paper 17: Designing a data cube for NSL-KDD data set to improve the quality of network
intrusion detection
Jamal Hussain and Pranjal Kalita
78-81
Paper 18: Early decelerating and late time accelerating bianchi type-v cosmological model
with quadratic equation of state in general relativity
K. S. Adhav, S. L. Munde and M. A. Purandare
82-86
Paper
Paper
19: Generalization of semigroups and monoids
Kh. Herachandra Singh
87-90
20: Sequence dynamical systems
Khundrakpam Binod Mangang
91-93
Paper 21: Soliton propagation in weakly inhomogenous plasmas with nonthermal electrons
L. B. Gogoi and P. N. Deka
94-98
Paper 22: Thermodynamic performance analysis of active and passive solar heater
M. Bardalai, S. Shukla, A.K. Shukla, R. Saraj, G. Tripathy and S. Kumar 99-102
Paper
23: Identicalness of N-norms
M.P. Singh and S. Romen Meite
103-107
Paper 24: An empirical comparison of brand switching behaviour of rural and urban
consumer: A Markovian approach
Manash Pratim Kashyap and Dibyojyoti Bhattacharjee
108-112
Paper 25: A numerical investigation on manetohydrodynamic flow in a rectangular duct
with strong transverse magnetic field and moving insulating walls
Muhim Chutia and P. N. Deka
113-118
Paper 26: TL-moments approach rainfall frequency analysis: a case study for the north east
India
Munindra Borah, Dhruba Jyoti Bora and Rubul Bora
119-122
Paper 27: Internal heat generation and viscous dissipation effects on nanofluids over a
moving vertical plate with convective boundary condition
N. Bhaskar Reddy, T. Poornima and P. Sreenivasulu
123-129
ISBN: 978-81-928118-9-5
Paper 28: A new proof of a modular equation for Ramanujan’s cubic continued
fraction and related results
Nayandeep Deka Baruah and Kanan Kumari Ojah
130-134
Paper 29: Effect of limiter in the computation of viscous supersonic flow over a flat plate
P. Kalita and A. K. Dass
135-141
Paper
30: Fluid flow studies of a compact rotary flue gas air preheater
P. P. Dutta and N. Baruah
142-145
Paper 31: Influence of magnetic field and viscous dissipation on nanofluids past a nonlinear
stretching sheet with radiation and uniform heat source
P. Sreenivasulu, T. Poornima and N. Bhaskar Reddy
146-153
Paper 32: Cyclic codes from the two-prime Whiteman’s generalized cyclotomic sequences
with order 6
Priti Kumari
154-157
Paper 33: Transient free convection MHD flow past a vertical plate immersed in porous
medium with exponentially decaying wall temperature and radiation
R. K. Deka, Nityajyoti Kalita and Ashish Paul
158-161
Paper 34: Modified K-dV equation for dust acoustic solitary waves in dusty plasma
R. K. Kalita, A. N. Dev and J. Sarma
162-167
Paper 35: Effect of rotation on covective flow through porous medium past an impulsively
started infinite vertical plate
R. M. Lahurikar and P. P. Ubale Patil
168-171
Paper
36: Difference triple sequences defined by orlicz function
Rupanjali Goswami
172-176
Paper 37: MHD flow and heat transfer of a dusty visco–elastic liquid down an inclined
channel in porous medium under variable viscosity and pressure
S. Chakraborty and Nripen Medhi
177-183
Paper
38: Higher order accurate heat transfer results in a rotating fluid at low Reynolds
numbers
S. Damodaran, S. Vimala, R. Sivakumar and T. V. S. Sekhar
184-188
Paper
39: Some triple sequence spaces based on difference operator  2
S. Debnath and B. C. Das
Paper
189-191
40: On some sequence spaces of regular matrix of interval numbers based on
fibonacci numbers
S. Debnath and S. Saha
192-193
ISBN: 978-81-928118-9-5
Paper 41: A note on primal ideals and decomposition in c(x)
S. Dutta
Paper
42: Food bolus transport through esophagus
S. Maiti
Paper 43: Peristaltic transport of blood: wave propagation in small blood vessel
S. Maiti, S. K. Tiwari and J. C. Misra
Paper
44:
194-195
196-199
200-203
Effect of chemical reaction on an unsteady MHD free convective flow past a
porous plate with ramped temperature
S. Sinha
204-210
Paper 45: Thermal radiation effect on MHD stagnation point flow of a carreau fluid with
convective boundary condition
S. Suneetha, K. Gangadhar and N. Bhaskar Reddy
211-216
Paper 46: Love wave propagation in a porous layer over a prestressed anisotropic half space
Shishir Gupta and Smita
217-220
Paper
Paper
47: Some aspects of special fuzzy boolean algebra
Sisir Kumar Rajbongshi and Dwiraj Talukdar
221-224
48: Symbolic method for polynomial interpolation with stieltjes conditions
Srinivasarao Thota and Shiv Datt Kumar
225-228
Paper 49: Study of blood flow using power law & Harschel-Bulkley non-Newtonian fluid
model through elastic artery
Surendra Kumar
229-234
Paper 50: Temperature–dependent viscosity effect on MHD mixed convective dissipating
flow of cylinder-shaped Cu-water nanofluid past a vertical moving surface
T. Poornima, P. Sreenivasulu and N. Bhaskar Reddy
235-242
Paper 51: Mass transfer effect on flow past impulsively started infinite plate in a rotating
dissipative fluid with constant heat flux.
V. B. Bhalerao and R. M. Lahurikar
243-247
ISBN: 978-81-928118-9-5