Browsing Mathematics (MA) by Title
Now showing items 78-97 of 257
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Herglotz representation, approximation by inner functions, and Hankel operators
This thesis can be broadly categorized under the theories of multi-variable operators and holomorphic functions, structured into two distinct parts. The first part investigates the relationship between two classical theorems: ... -
Hermitian Metrics and Singular Riemann Surface Foliations
The main aim of this thesis is to understand curvature properties of a given hermitian metric by restricting it to the leaves of a suitable singular Riemann surface foliation. We will specifically consider the complete ... -
Holomorphic mappings and Kobayashi geometry of domains
In this thesis, we study certain aspects of the geometry of the Kobayashi (pseudo)distance and the Kobayashi (pseudo)metric for domains in $\mathbb{C}^n$. We focus on the following themes: on the interaction between Kobayashi ... -
Homogeneous Operators
(2018-06-13)A bounded operator T on a complex separable Hilbert space is said to be homogeneous if '(T ) is unitarily equivalent to T for all ' in M•ob, where M•ob is the M•obius group. A complete description of all homogeneous weighted ... -
Homogeneous Operators and Some Irreducible Representations of the Mobius Group
In this report, after recalling the definition of the M¨obius group, we define homogeneous operators, that is, operators T with the property '(T) is unitarily equivalent to T for all ' in the M¨obius group and prove some ... -
Homogenization of certain PDEs and associated optimal control problems on various rough domains
This thesis is devoted to the study of the asymptotic behavior of partial differential equations (PDEs) and associated boundary and interior optimal control problems in various oscillatory domains. The present thesis ... -
Homogenization of Optimal Control Problems in a Domain with Oscillating Boundary
(2017-11-27)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 ... -
Homogenization of partial differential equations in perforated domain
Theory of homogenization in Partial Differential Equations has a variety of applications in many branches of science. In the present thesis, we study the homogenization of certain boundary value problems in a periodically ... -
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 ... -
Hydromagnetic surface waves
The ASW propagates as a dispersive wave along the boundaries of a bounded plasma column. At the interface of a plasma slab surrounded by two identical plasma media, two modes-symmetric and asymmetric-propagate with a phase ... -
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 ... -
Iterative and direct P;Adic algorithms for exact solution of numerical problems
In this chapter, we have described an O(n³), 2 < P < 3 algorithm for inverting integer matrices using p-adic computations. Some of the important aspects of this method are: (a) Absence of any convergence problems – the ...