Browsing Mathematics (MA) by Title
Now showing items 61-80 of 159
-
Homogenization of PDEs on oscillating boundary domains with L1 data and optimal control problems
This thesis comprehensively studies the homogenization of partial differential equations (PDEs) and optimal control problems with oscillating coefficients in oscillating domains. After the introduction, the thesis is divided ... -
Inferences on Structure and Function of Proteins from Sequence Data : Development of Methods and Applications
(2018-07-23)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
(2014-06-30)The curvature of a contraction T in the Cowen-Douglas 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. ... -
Interaction of distinguished varieties and the Nevanlinna-Pick interpolation problem in some domains
This thesis explores the interplay between complex geometry and operator theory, focusing on characterizing certain objects from algebraic geometry. Two concepts that have been of prime importance in recent times in the ... -
An Introduction to Minimal Surfaces
(2017-12-10)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 ... -
Invariants Associated with Complete Nevanlinna-Pick Spaces
The broad aim of this thesis is to study certain tuples of bounded operators that satisfy an operator inequality arising from a complete Nevanlinna-Pick kernel. Specifically, we focus on two invariants of these operator ... -
Irreducible Representations Of The Symmetric Group And The General Linear Group
(2013-01-31)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
(2014-04-07)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
(2018-02-07)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. ... -
Learning Filters, Filterbanks, Wavelets and Multiscale Representations
The problem of filter design is ubiquitous. Frequency selective filters are used in speech/audio processing, image analysis, convolutional neural networks for tasks such as denoising, deblurring/deconvolution, enhancement, ... -
Local Projection Stabilization Methods for the Oseen Problem
Finite element approximation of fluid flow problems with dominant convection exhibit spurious oscillations. To eliminate these nonphysical oscillations one needs to incorporate stabilizations that can curb the effect of ... -
Lp-Asymptotics of Fourier Transform Of Fractal Measures
(2018-06-08)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 ... -
Maps Between Non-compact Surfaces
This thesis focuses on studying proper maps between two non-compact surfaces with a particular emphasis on the topological rigidity and the Hopfian property. Topological rigidity is the property that every homotopy equivalence ... -
Matchings Between Point Processes
(2014-06-20) -
Mechanising knot Theory
(2018-01-31)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
(2018-06-11)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
(2018-01-03)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 ... -
Multi-scale Modelling of HLA Diversity and Its Effect on Cytotoxic Immune Responses in Influenza H1N1 Infection
(2018-06-06)Cytotoxic T-lymphocytes (CTLs) are important components of the adaptive immune system and function by scanning the intracellular environment so as to detect and de-stroy infected cells. CTL responses play a major role in ...