Browsing Mathematics (MA) by Title
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Near Optimal Nonmalleable Codes and Leakage Resilient Secret Sharing Schemes
A wellstudied class of attacks on cryptosystems called "sidechannel attacks", stems from the additional access that an adversary can get due to the susceptibility of the hardware on which the cryptosystem (e.g., digital ... 
Nodal sets of random functions
This thesis is devoted to the study of nodal sets of random functions. The random functions and the specific aspect of their nodalset that we study fall into two broad categories: nodal component count of Gaussian Laplace ... 
Normal Spectrum of a Subnormal Operator
(20180321)Let H be a separable Hilbert space over the complex field. The class S := {NM : N is normal on H and M is an invariant subspace for Ng of subnormal operators. This notion was introduced by Halmos. The minimal normal ... 
Novel Upwind and Central Schemes for Various Hyperbolic Systems
(20180521)The class of hyperbolic conservation laws model the phenomena of nonlinear wave propagation, including the presence and propagation of discontinuities and expansion waves. Such nonlinear systems can generate discontinuities ... 
Numerical Methods for Elliptic Variational Inequalities in Higher Dimensions
The main emphasis of this thesis is on developing and implementing linear and quadratic finite element methods for 3dimensional (3D) elliptic obstacle problems. The study consists of a priori and a posteriori error ... 
Numerical Simulation Of Converging Nonlinear Wavefronts
(20130124) 
Numerical Study Of Regularization Methods For Elliptic Cauchy Problems
(20110630)Cauchy problems for elliptic partial differential equations arise in many important applications, such as, cardiography, nondestructive testing, heat transfer, sonic boom produced by a maneuvering aerofoil, etc. Elliptic ... 
On an ODE Associated to the Ricci Flow
(20180418)We discuss two topics in this talk. First we study compact Ricciflat four dimensional manifolds without boundary and obtain point wise restrictions on curvature( not involving global quantities such as volume and diameter) ... 
On certain invariant measures for correspondences, their analysis, and an application to recurrence
The aim of this dissertation is to analyse a certain class of dynamically interesting mea sures arising in holomorphic dynamics that goes beyond the classical framework of maps. We study measures associated with semigroups ... 
On commuting isometries and commuting isometric semigroups
This thesis consists of two parts commuting isometries and commuting isometric semigroups. In the first part, we study the Taylor joint spectrum for a pair of commuting isometries in certain cases. We show that the joint ... 
On Critical Points of Random Polynomials and Spectrum of Certain Products of Random Matrices
(20180730)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. ... 
On existence and regularity of some complex Hessian equations on Kahler and transverse Kahler manifolds
The thesis consists of two parts. In the first part of the thesis, we classify the convergence behaviour of rotationally symmetric solutions to the modified Jflow on the blowup of the complex projective space at a ... 
On regular subalgebras of symmetrizable KacMoody algebras and related combinatorics
In this thesis, we study two aspects of KacMoody algebras. One is to understand the subalgebras that can be embedded inside a KacMoody algebra as subalgebras generated by real root vectors. The other one is to explicitly ... 
On some canonical metrics on holomorphic vector bundles over Kahler manifolds
This thesis consists of two parts. In the first part, we introduce coupled Kähler Einstein and HermitianYangMills equations. It is shown that these equations have an interpretation in terms of a moment map. We identify ... 
On The Analytic Theory Of Explosions
(20120531) 
On the Geometry and Operator Theory of the Bidisc and the Symmetrized Bidisc
This work is concerned with the geometric and operator theoretic aspects of the bidisc and the symmetrized bidisc. First we have focused on the geometry of these two do mains. The symmetrized bidisc, a nonhomogeneous ... 
On the Kobayashi geometry of domains
In this thesis we study questions broadly related to the Kobayashi (pseudo)distance and (pseudo)metric on domains in ℂn. Specifically, we study the following subjects: Estimates for holomorphic images of subsets in convex ... 
On The PeakToAveragePowerRatio Of Affine Linear Codes
(20080125)Employing an error control code is one of the techniques to reduce the PeaktoAverage Power Ratio (PAPR) in an Orthogonal Frequency Division Multiplexing system; a well known class of such codes being the cosets of ... 
On the Stability of Certain Riemannian Functionals
(20180306)Given a compact smooth manifold Mn without boundary and n ≥ 3, the Lpnorm of the curvature tensor, defines a Riemannian functional on the space of Riemannian metrics with unit volume M1. Consider ...