Browsing Mathematics (MA) by Title
Now showing items 52-71 of 163
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Hand-Movement Prediction Using LFP Data
(2011-08-08)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 ... -
Hardy's inequalities for Grushin operator and Hermite multipliers on Modulation spaces
This thesis consists of two broad themes. First one revolves around the Hardy's inequalities for the fractional power of Grushin operator $\G$ which is chased via two different approaches. In the first approach, we first ... -
Harmonic Map Heat Flow and Framed Surface-group Representations
This thesis concerns the construction of harmonic maps from certain non-compact surfaces into hyperbolic 3-space H3 with prescribed asymptotic behavior and has two parts. The focus of the first part is when the domain ... -
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 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 ...