Advances in Mathematical Methods and High Performance Computing / Advances in Mechanics and Mathematics Bd.41 (PDF)

Vinai K Singh is the Professor of Mathematics in the Department of Applied Mathematics, Inderprastha Engineering College Ghaziabad, India. Dr. Singh holds a Ph. D degree. in Approximation Theory from Department of Applied Mathematics, Institute of Technology, Banaras Hindu University (Now IIT BHU), Varanasi, India. He has been actively engaged in research activity since 1997. His areas of research interest include functional analysis, approximation theory, and different kinds of positive operators. He is author of 3 book chapters and 6 books and over 29 research papers in the national and International Journals of repute. He referees articles for professional journals and serves as editorial member of many national and international journals.
> 50% are single authored) on applied mathematics, theoretical and computational mechanics, global optimization and operations research etc. His main research contributions include a canonical duality-triality theory, several mathematical models in engineering mechanics and material science, a series of complete solutions to a class of nonconvex/nonsmooth/discrete problems in nonlinear sciences, and some deterministic methods/algorithms for solving certain NPhard problems in global optimization and computational science. One application of this canonical duality theory in large deformation solid mechanics solved a 50-years open problem and leads to a pure complementary energy principle (i.e. the Gao Principle in the literature), which has broad applications in engineering mechanics and physics. One of the large deformed beam models he proposed in 1996 is now recognized as the nonlinear Gao beam which can be used to study postbuckling analysis and plays an important role in real-world applications. In discrete systems, this canonical duality theory shows that the NP-hard 0-1 integer programming problems are identical to a continuous unconstrained Lipschitzian global optimization problem which can be solved deterministically.