Browsing Mathematics (MA) by Title
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Inferences on Structure and Function of Proteins from Sequence Data : Development of Methods and Applications
(20180723)Structural and functional annotation of sequences of putative proteins encoded in the newly sequenced genomes pose an important challenge. While much progress has been made towards high throughput experimental techniques ... 
Infinitely Divisible Metrics, Curvature Inequalities And Curvature Formulae
(20140630)The curvature of a contraction T in the CowenDouglas class is bounded above by the curvature of the backward shift operator. However, in general, an operator satisfying the curvature inequality need not be contractive. ... 
An Introduction to Minimal Surfaces
(20171210)In the first chapter of this report, our aim is to introduce harmonic maps between Riemann surfaces using the Energy integral of a map. Once we have the desired prerequisites, we move on to show how to continuously deform ... 
Irreducible Representations Of The Symmetric Group And The General Linear Group
(20130131)Representation theory is the study of abstract algebraic structures by representing their elements as linear transformations or matrices. It provides a bridge between the abstract symbolic mathematics and its explicit ... 
Joint Eigenfunctions On The Heisenberg Group And Support Theorems On Rn
(20140407)This work is concerned with two different problems in harmonic analysis, one on the Heisenberg group and other on Rn, as described in the following two paragraphs respectively. Let Hn be the (2n + 1)dimensional Heisenberg ... 
Kinetic Theory Based Numerical Schemes for Incompressible Flows
(20180207)Turbulence is an open and challenging problem for mathematical approaches, physical modeling and numerical simulations. Numerical solutions contribute significantly to the understand of the nature and effects of turbulence. ... 
LpAsymptotics of Fourier Transform Of Fractal Measures
(20180608)One of the basic questions in harmonic analysis is to study the decay properties of the Fourier transform of measures or distributions supported on thin sets in Rn. When the support is a smooth enough manifold, an almost ... 
Matchings Between Point Processes
(20140620) 
Mechanising knot Theory
(20180131)Mechanisation of Mathematics refers to use of computers to generate or check proofs in Mathematics. It involves translation of relevant mathematical theories from one system of logic to another, to render these theories ... 
Minimal Crystallizations of 3 and 4 Manifolds
(20180611)A simplicial cell complex K is the face poset of a regular CW complex W such that the boundary complex of each cell is isomorphic to the boundary complex of a simplex of same dimension. If a topological space X is homeomorphic ... 
Mixed Norm Estimates in Dunkl Setting and Chaotic Behaviour of Heat Semigroups
(20180103)This thesis is divided into three parts. In the first part we study mixed norm estimates for Riesz transforms associated with various differential operators. First we prove the mixed norm estimates for the Riesz transforms ... 
Multiscale Modelling of HLA Diversity and Its Effect on Cytotoxic Immune Responses in Influenza H1N1 Infection
(20180606)Cytotoxic Tlymphocytes (CTLs) are important components of the adaptive immune system and function by scanning the intracellular environment so as to detect and destroy infected cells. CTL responses play a major role in ... 
A Multiscale Modeling Study of Iron Homeostasis in Mycrobacterium Tuberculosis
(20180510)Mycobacterium tuberculosis (M.tb), the causative agent of tuberculosis (TB), has remained the largest killer among infectious diseases for over a century. The increasing emergence of drug resistant varieties such as the ... 
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 ...