Browsing Mathematics (MA) by Title
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Geometric invariants for a class of submodules of analytic Hilbert modules
Let $\Omega \subseteq \mathbb C^m$ be a bounded connected open set and $\mathcal H \subseteq \mathcal O(\Omega)$ be an analytic Hilbert module, i.e., the Hilbert space $\mathcal H$ possesses a reproducing kernel $K$, the ... 
Goldman Bracket : Center, Geometric Intersection Number & Length Equivalent Curves
(20171130)Goldman [Gol86] introduced a Lie algebra structure on the free vector space generated by the free homotopy classes of oriented closed curves in any orientable surface F . This Lie bracket is known as the Goldman bracket ... 
Graph Spectral Methods for Analysis of Protein Structures
Network representation of protein structures is an informationrich mode of examining protein structure, dynamics and its interactions with biomolecules. Graph spectral methods are extremely useful and powerful in analysing ... 
The Green's Function, the Bergman Kernel and Quadrature Domains in Cn
(20180608)In the ﬁrst part of this thesis, we prove two density theorems for quadrature domains in Cn ,n≥2. It is shown that quadrature domains are dense in the class of all product domains of the form D×Ωwhere D⊂Cn−1 is a smoothly ... 
Grothendieck Inequality
(20160620)Grothendieck published an extraordinary paper entitled ”Resume de la theorie metrique des pro¬duits tensoriels topologiques” in 1953. The main result of this paper is the inequality which is commonly known as Grothendieck ... 
HandMovement Prediction Using LFP Data
(20110808)The last decade has seen a surge in the development of BrainMachine Interfaces (BMI) as assistive neural devices for paralysis patients. Current BMI research typically involves a subject performing movements by controlling ... 
Homogeneous Operators
(20180613)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 Optimal Control Problems in a Domain with Oscillating Boundary
(20171127)Mathematical theory of homogenization of partial differential equations is relatively a new area of research (3040 years or so) though the physical and engineering applications were well known. It has tremendous applications ... 
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)