The monodromy groups of the n-th order hypergeometric differential equations are characterized as the subgroups of the general linear group GL(n), which are generated by the companion matrices of two monic co-prime polynomials f (x) and g(x) of degree n.

My research interest lies in the field of linear and nonlinear wave propagation. More specifically, my interest is in the study of partial differential equations of hyperbolic type. Most of the systems of PDEs (of practical interest) are not solvable exactly to get closed form solutions and therefore an approximation procedure needs to be adopted. Also, since the solution spaces of these systems are often vast (for instance the space of BV functions in the case of hyperbolic system of conservation laws), any qualitative analysis becomes more challenging.

"Plates are plane structural elements with a small thickness compared to the planar dimensions. De-pending on the length to thickness ratios, plates are classified into moderately thick, thin and very thin plates. One of my primary research interests has been to employ finite element methods to determine approximations to deformation and stresses in thin and very thin plates when they are subject to loads. A Kirchoff model is used for the thin elastic plates and this leads to fourth order elliptic equations with the transverse displacement as the unknown variable.

(1) Asymptotic analysis of PDEs: Most of the physical phenomena are modeled by Hyperbolic PDEs and in many of them feature multiple characteristics. Roughly it corresponds to studying crossings of eigenvalues of operators parametrized by a vectorial parameter. We are studying some of such situations.

(2) Conservation laws: We are studying the question of convergence generalized viscous approximations to entropy solutions of hyperbolic conservation laws.

Extension of Recent Contributions for Wider Applications in Computational Biology/Drug Discovery/Immunoinformatics/Automated Pulse-Diagnostics

(1) ParaDes: AI Software for Epitope-Paratope Designing (Copyright: GoI No. SW-698/2002) deploying knowledge-based correlation mapping on Hopfield Network.

(2) Efficient ab-initio Protein Structure Prediction using AI & Nonparametric Statistics.[Web-server: www.math.iitb.ac.in/~epropainor/ ]

My research area is Reliability Theory. Currently, I have been working on research problems that deal with Multi-state coherent systems. These systems are such that their components and systems themselves can be in one of (M + 1) possible states 0, 1, 2, • • • , M at any given time, where the extreme states 0 and M represent completely failed and completely working states respectively, and others are intermediate states that decrease in performance level as the system or a component makes a transition from state i to (i − 1), i = M, (M − 1), • • • , 1.