In the first part of this thesis, we study critical points of random polynomials. We choose two deterministic sequences of complex numbers, whose empirical measures converge to the same probability measure in complex plane. ...

A pair of commuting bounded operators (S; P ) acting on a Hilbert space, is called a -contraction, if it has the symmetrised bides = f(z1 + z2; z1z2) : jz1j 1; jz2j 1g C2 as a spectral set. For every -contraction (S; P ), ...

The last decade has seen a surge in the development of Brain-Machine Interfaces (BMI) as assistive neural devices for paralysis patients. Current BMI research typically involves a subject performing movements by controlling ...

Guidance is defined as the determination of a strategy for following a nominal path in the presence of o-nominal conditions, disturbances and uncertainties, and the strategy employed is called a guidance law. Variants of ...

Mathematical theory of partial differential equations (PDEs) is a pretty old classical area with wide range of applications to almost every branch of science and engineering. With the advanced development of functional ...

The aim of this dissertation is to give explicit descriptions of the set of proper holomorphic mappings between two complex manifolds with reasonable restrictions on the domain and target spaces. Without any restrictions, ...

In this thesis we have investigated two different types of problems in multivariable operator theory. The first one deals with the defect sequence for contractive tuples and maximal con-tractive tuples. These condone deals ...

Goldman [Gol86] introduced a Lie algebra structure on the free vector space generated by the free homotopy classes of oriented closed curves in any orientable surface F . This Lie bracket is known as the Goldman bracket ...

Mathematical theory of homogenization of partial differential equations is relatively a new area of research (30-40 years or so) though the physical and engineering applications were well known. It has tremendous applications ...