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Mathematical Sciences

Facilities

Laboratory:

The department is going to have its own state-of-the-art computing laboratory for under undergraduate programme. However, there is a research laboratory namely “Mathematical and Statistical Simulation” laboratory to facilitate computing and simulation work of the research scholars.  The Lab is equipped with high-end desktop including all necessary softwares related to mathematics and statistics. High performance computing facility is also available. The research interest includes statistical information theory, reliability theory, meshfree methods, computational finance, and numerical solutions of fractional partial differential equations. 

Information theory deals with problem of reliable transmission of messages or knowledge with economical techniques. The seminal work on information theory and its generalizations have been done in the literature to extend and enrich underlying information. Several generalized information-theoretic measures in bivariate setup have been investigated. Also, in the real life most of the observations are left, right and doubly truncated. Considering time as a prime variable of interest while analyzing a particular event, numerous measures of information and its generalized versions have been studied here for doubly truncated failure time. Another objective of statistics is the comparison of random quantities in some stochastic sense. As a result, several stochastic orders have been comprehensively discussed in the literature most of which are based on some reliability concepts for residual life and inactivity time at a fixed time. We also deal with several stochastic properties of residual life at random time and inactivity time at random time along with applications in reliability theory.

Computation with higher dimensional data is an important issue in many areas of science and engineering. Many numerical methods such as finite difference methods, finite element methods can either not handle such problems at all, or are limited to very special situations. Mesh-based methods are direct and usually easy to use, except for irregular domains or high accuracy control. So meshfree methods are often a better way to deal with many different application areas such as in mathematical finance, in optimization, in neural networks via a solution of partial differential equations. In the meshfree approach, rather than discretizing space, the solutions are approximated by a set of basis functions. The Radial Basis Function (RBF) method is one of the primary tools for interpolating multidimensional scattered data. The advantage of the RBF method is that it can be efficient, simple to implement, and easily adaptable to irregular domains or higher dimensions. The active research has been going on to solve fractional partial differential equations using RBF based meshfree method.