Tentative Academic Programme (as on 23-11-2011) of the ensuing IMS Conference 2011 at SRTM University, Nanded. 1. Plenary Lectures : • Raman Parimala. (Dept. of Mathematics, Emory University, USA) : on "Trace forms". • Dinesh Singh (VC, Delhi University, Delhi) • Ravi Kulkarni. (IIT Mumbai, Powai, Mumbai) : 2. IMS Memorial Award Lectures : • 25th P. L. Bhatnagar Memorial Award Lecture will be delivered by Rama Bhargava (IIT Roorkee, Roorkee) on To be announced . • 22nd V. Ramaswamy Aiyer Memorial Award Lecture will be delivered by Prof Geetha S. Rao (Chennai) “ Tools and Techniques in Approximation Theory ”. • 22nd Srinivasa Ramanujan Memorial Award Lecture will be delivered by B. Ramakrishnan (HRI, Allahabad) on “ Modular forms of half-integral weight ” • 22nd Hansraj Gupta Memorial Award Lecture will be delivered by Ajai Choudhry (Dean, Foreign Service Institute, New Delhi) “ Some diophantine problems concerning perfect powers of integers ” * 10th Ganesh Prasad Memorial Award Lecture will be delivered by Gadadhar Mishra (IISc, Bangalore) “ Differentiation (?)! ” 3. Half an hour Invited Talks : 1. Chanchal Kumar (IISER, Mohali) : on " Alexander Duals of Monomial ideals" 2. Vinayak Joshi (University of Pune, Pune) : "On zero divisor graphs of posets" Abstract: Beck [1988] introduced the notion of coloring in a commutative ring $R$ as follows. Let $G$ be a simple graph whose vertices are the elements of $R$ and two vertices $x$ and $y$ are adjacent if $xy=0$. $G$ is known as the zero divisor graph of $R$. He conjectured that $\chi(G) = Clique(G)$. Anderson and Naseer [1993] gave an example of a commutative local ring $R$ with 32 elements for which $\chi(G) > Clique(G)$. This concept of zero divisor graph is also studied in other algebraic as well as in ordered structures such as near rings, semigroups, semilattices, posets etc. This talk will provide background and discuss key issues of the theory of zero divisor graphs of posets. Mainly, we will be interested in the basic notions and properties of zero divisor graphs such as diameter, girth, a solution of a form of Beck's Conjecture, realization of zero divisor graphs of a general poset and in particular, a Boolean poset. 3. U. C. De (University of Calcutta, Kolkata) : on " Certain generalizations of Einstein manifolds with applications to relativity" 4. S. S. Khare (NEHU, Shillong) : on " span of some specific manifolds " 5. V. Lokesh (Acharya Inst. of Technology, Bangalore) : on “An Excursion on Mathematical means” 6. S. K. Khanduja (Mohali, Chandigarh) : on “Irreducible polynomials” 7. R. K.Yadav (Jodhpur University, Jodhpur) : on To be announced 8. M. M. Tripathi (BHU, Varanasi) : on “Chen-Ricci inequalities for Riemannian submanifolds” 09. K. Srinivasa : (IMSc, Chennai): “On the zeros of Riemann zeta-function: some recent results” Abstract: The study of the zeros of the Riemann zeta function, $\zeta(s), s= \sigma + it$, is an important problem in analytic number theory. G. H. Hardy was the first to show that $\zeta(s)$ has infinitely many zeros on the line critical line $\sigma =1/2$ and the famous unsolved Riemann Hypothesis says that in fact all the complex zeros of $\zeta(s)$ are on the critical line. We shall discuss an extension of Hardy's result to a class of more general Dirichlet series. This is a joint work with A. Mukhopadhyay and R. Krishnan. 11. G. S. Khadekar (RTM Nagpur University, Nagpur) : on “The Universe : What is man ?” 12. Cenap Ozel (Turkey, cenap.ozel@gmail.com) : on “fredholm maps and complex cobordism of Hilbert manifdolds" 13. S. M. Padhye (Sri RLT PG College of Science, Akola) : on “Atsuji Spaces, L-spaces, Uniformly approachable spaces and compactness related concepts" Abstract. The concept of compactness in analysis has been crucial and its characterizations in different spaces have fruitful applications. A simple property of compact metric spaces that every real valued continuous function is uniformly continuous has been exploited. Several generalizations of spaces having the property that every continuous function is uniformly continuous have been known .The talk is likely to discuss such spaces called Atsuji spaces or uniformly continuous spaces studied originally by M.Atsuji(1958)[ ],Norman Levine(1955)[ ] and their interrelated properties. Such spaces have to be in general uniform spaces to enable a function to be uniformly continuous. Several generalizations of these spaces such as Lebesgue spaces , Uniformly approachable spaces, weakly uniformly approachable spaces will be discussed. One more property of comact metric spaces that the product of any two uniformly continuous functions is uniformly continuous can also be expected to have connection with uniformly continuous sets. These generalizations may also have some connections with compactifications, e.g. Stone Cech compactification of uniform/topological spaces. The related results, answered questions and unanswered questions are discussed. 4. Symposia : 1. On “ Functions of Matrix Argument and Applications” Convener : A. M. Mathai. (Center for Math. Sciences, Pala). Speakers : (i). R K Kumbhat on "Applications of Special Functions of Matrix Arguments" (ii). Hans J. Haubold (Chief Scientist, Outer Space Division, United Nations, Vienna Office, Vienna , Austria) on "Anomalous Distributions in Physics: Statistics versus Probability". (iii). Seema S. Nair (DST-SRF at CMS, Pala) on "Fractional Calculus and Matrix-variate Statistical Distributions" (iv) A.M. Mathai on "Functions of Matrix Argument and Applications". 2. On “Extremal Graph Theory” Convener: B. N. Waphare (University of Pune, Pune). Speakers : (i). B. N. Waphare (Pune University) on "To be announced" (ii). S. Arumugam (Kalasalingam University, Krishnan Koil) on "To be announced" . (iii). Ambat Vijay kumar (Cochin University of science and technology, Cochin) on "To be announced" . (iv) H. S. Ramane (Karnatak Law Society's Gogte Institute of Technology, Belgaum) on "To be announced". (v) Y. M. Borse (Pune University,Pune) on "To be announced". 3. On “Ramanujan-yesterday and today” Convener : M. A. Pathan. (AMU, Aligarh). Speakers : (i). A. K. Agarwal (P.U.Chandigarh) on "New partition theoretic interpretations of Rogers-Ramanujan identities" Abstract: The generating function for a restricted partition function is derived. This in conjunction with two identities of Rogers provide new partition theoretic interpretations of Rogers-Ramanujan identities. (ii). P. N. Rathie (Universidade de Brasilia, Brazil) on "To be announced" . (iii). R. Y. Denis (DDU, University,Gorakhpur) on "Applications of WP Bailey pairs" . Abstract: In this paper author has established many intersting transformation formulae for q-series and some very useful identities by making use of WP Bailey pair. (iv) S.N.Singh (P.U.Jaunpur) on Transformation formulae for elliptic Hypergeometric series. Abstract: In this paper, making use of certain summation formulae for truncated poly-basic elliptic hypergeometric series, we have established some very general transformation formulae for poly-basic elliptic hypergeometric series. (v) M. I. Qureshi (J.M.I.,New Delhi) on "To be announced". (vi) M. S. Mahadev Naika (Bangalore University) on "To be announced". Abstract: On page 44 of his lost notebook, S. Ramanujan recorded continued fractions of different orders as follows: Order 4: a=0, b=±1, (2 cases). On page 290 of his second notebook, Ramanujan recorded several identities for the continued fraction of order four also known as Ramanujan-Selberg continued fraction. Oder 5: a=0, b=0, (1 case). Only continued fraction proved and published by Ramanujan is the famous Rogers-Ramanujan continued fraction which is known as continued fraction of order 5. Order 6: a=±1, b=±1, (4 cases). On page 366 of his lost notebook, Ramanujan recorded cubic continued fraction and several identities satisfied by them. Ramanujan cubic continued fraction is also known as continued fraction of order 6. Order 8: a=±1, b=0. (2 cases). On page 229 of his second notebook, Ramanujan recorded the continued fraction of order eight (also known as amanujan-Gollnitz-Gordon continued fraction) along with two identities satisfied by them. We make a survey on the results of Ramanujan-Selberg continued fractions, Rogers-Ramanujan continued fraction, Ramanujan’s cubic continued fractions, Ramanujan-Gollnitz-Gordon continued fractions and Continued fraction of Order 12. (vii) S. Ahmad Ali (B.B.D.University,Lucknow) on "On q-Series Transformations and Ramanujan’s Partial Theta Function Identities". Abstract: In the ‘Lost’ Notebook, Ramanujan wrote many amazing identities for partial theta functions. Agarwal (Advan. Math., 53, 1984, p. 291) indicated the possibility of making a systematic study of three and four term relations of 3?2’s to generalize most of the partial theta function identities of Ramanujan in ‘Lost’ Notebook. In the present work, we have produced a new partial theta function identity which contains Ramanujan’s identity as its particular case. 4. On “ Analysis and related fields” Convener : Rajiv Srivastava (IBSc, Agra). Speakers : (i). A. P. Singh (CURAJ, Ajmer) on "Some applications of approximation theory in complex dynamics" Abstract. Let f be a transcendental entire function. The set F = f z 2 C : (fn)n2N is normal in some neighbourhood of z g is called the Fatou set or the set of normality and its complement C F denoted by J is called the Julia set. If Un \ Um = _ for n 6= m where Un denotes the component of F(f) which contains fn(U), then U is called wandering domain, else U is called a pre-periodic domain, and if Un = U for some n 2 N, then U is called periodic domain. We use here, approximations of continuous functions by entire functions on Carleman sets to obtain results on the periodic and wandering domains of entire functions. (ii). S. S. Bhoosnurmath (Dharwad) on "Role of hyperbolic matrics in complex analysis" . Abstract. Euler was the first to find the relation between analytic functions and the partial differential equations. Further, by introducing complex differential operators, Laplacian gets a new shape and it leads to a new characterization of analytic functions. Using the notion of partial derivatives a new metric is defined on the complex domain following the ideas of Riemann. This new development gives newer depths and insights into classical complex analysis. The simplest of examples is the extension and generalisation of Liouville’s theorem. A dramatic development here is the deletion of boundeness in Liouville’s theorem. Further , it leads to a very simple and elegant proof of Picard’s theorem. Apart from Poincare metric , Caratheodory metric and Kobayashi metric lead to another metric version of Riemann Mapping theorem. (iii). Indrajit Lahiri (Kalyani, WB) on "Nevanlinna's five and four value theorems and allied results" . Abstract. The five and four value theorems of the Finnish mathematician Prof. Rolf Nevanlinna are two outstanding results in the history of Complex Analysis. In fact, these are the two theorems which initiated the modern theory of uniqueness of meromorphic functions. In the talk we discuss the five and four value theorems and the course of research motivated by these results. (iv) S. P. Tiwari (ISM, Dhanbad) on "Rough Sets, Relations and Topologies". Abstract. Rough set theory, firstly proposed by Pawlak has now developed significantly due to its importance for the study of intelligent systems having insufficient and incomplete information. In rough set introduced by Pawlak, the key role is played by equivalence relations. In literature several generalizations of rough set have been made by replacing the equivalence relation by an arbitrary relation. Simultaneously, the relation of rough sets with topologies is also studied. The counterpart of this situation has also been investigated for fuzzy rough sets (a notion which is formulated in terms of a fuzzy relation on a set), resulting in a few nice studies of the relationships between fuzzy preorders and fuzzy topologies. Sometimes, such studies have been carried out within the context of rough set theory and sometime independent of it. In any case, a closer examination of these relationship makes it clear that the context of (fuzzy) rough set theory is only incidental and it has no bearing on the relationship between (fuzzy) relations and (fuzzy) topologies. (v) Poonam Sharma (Lucknow) on "Involvement of Wright's Generalized Hypergeometric (Wgh) Functions in Geometric Function Theory (GFT)". Abstract: The introduction part of the talk focuses on the class S of univalent functions and the Bieberbach conjecture. Attention to various generalized forms of hypergeometric functions in GFT is to paid. Building on Hohlov's work on convolutional operators involving Gauss Hypergeometric functions, several generalized hypergeometric functions including Wgh functions are discussed in the context of Dziok-Srivastava as well as Dziok-Raina operators. Due to the importance of hypergeometric functions in applied sciences, the results of several geometric function theorists on class S and its sub-classes involving these operators are elaborated. While concluding, areas of potential research directions involving convergence of Wgh functions, through Dziok-Raina operators are explored. (vi) Rajiv K. Srivastava (Agra) on "Bicomplex Analysis: State of Art". Abstract. Bicomplex Analysis has been a center of attraction of contemporary Analysts due to its multi disciplinary applications besides its interesting and convenient techniques. Bicomplex Analysis has recently found applications in Signal processing, Spiral wave theory and Quantum mechanics etc. Hence attempts are being made to strengthen the Analysis of the Bicomplex Space. Our school of researchers has recently contributed substantially towards development of Bicomplex Analysis with a Topological viewpoint. 5. On “ Topology” Convener : V. Kannan. (Hyderabad Uni.) : Speakers : (i). M. Rajagopalan (Tennesee) on "To be announced" (ii). T K S Moothathu (HYderabad) on "To be announced" . (iii). T. K. Das ( M S University of Baroda) on "To be announced" . (iv) V. Kannan (Hyderabad) on "To be announced". (v) Suprabha Kulkarni (Nanded) on "To be announced". (vi) Zohreh Vajiry. (Nanded) on "To be announced". 6. On “Modeling and Uncertainty Analysis” Convener : D. Datta (BARC, Mumbai) : Speakers : (i). K. Karmeshu on "Nonlinear Stochastic modeling, power law and entropy " (ii). (Mrs) Smita Naik on "To be announced" . (iii). Shankar Kukar Roy on "Game theory under uncertain environment" . (iv) Prallahad on "To be announced". (v) Tanmoy Som / Uma Basu on "To be announced". (vi) S. V. Ingale on "To be announced". 7. Special Session : There will be a special Session of one-and-half hour for SAARC mathematicians. Speakers : (i). K. Karmeshu on "Nonlinear Stochastic modeling, power law and entropy " (ii). Mofiz Ahmed. (Bangla Desh) on "To be announced" . (iii). Saraswati Acharya on "To be announced" , and (iv) D. B. Gurung (Dept. of Neural Sciences (Mathematics), Kathmandu, University, Nepal) on "Time Dependent Temperature Distribution in Layered Human Dermal Part" . Abstract : Skin temperature distribution of the man is a complex interaction of physical heat exchange processes and the potential for physiological adjustment. The paper developed application of finite element method with linear shape function in the study of temperature distribution in the five layers of dermal partStratum Corneum, Stratum Germinativum, Papillary Region, Reticular Region and Subcutaneous Tissues. The method is applied to obtain the solution of governing partial differential equation for one dimensional unsteady state bioheat transfer based numerical models of the five layers of dermal parts. The physical and physiological parameters in each layer that affect the heat regulation in human body is taken as a function of position dependent. The loss of heat from the outer surface of the body to the environment is taken due to convection, radiation and sweat evaporation. The numerical result has been carried out using the CAS software MATLAB. The same program has been used to plot the graph at different cases. The graphs represent the comparative study of temperature stribution profiles in human layers as a function of internal and external parameters, such as temperature of the incoming arterial blood, blood flow, ambient temperature and heat exchange with the environment. Keywords: Finite Element Method, Bioheat Equation, Human dermal Part