Browsing Mathematics (MA) by Title
Now showing items 2847 of 118

Eigenvalues of Products of Random Matrices
(20180207)In this thesis, we study the exact eigenvalue distribution of product of independent rectangular complex Gaussian matrices and also that of product of independent truncated Haar unitary matrices and inverses of truncated ... 
Exploring Polynomial Convexity Of Certain Classes Of Sets
(20110718)Let K be a compact subset of Cn . The polynomially convex hull of K is defined as The compact set K is said to be polynomially convex if = K. A closed subset is said to be locally polynomially convex at if there ... 
Finite Element Analysis of Interior and Boundary Control Problems
(20180618)The primary goal of this thesis is to study finite element based a priori and a posteriori error estimates of optimal control problems of various kinds governed by linear elliptic PDEs (partial differential equations) of ... 
A Formal Proof of FeitHigman Theorem in Agda
(20180218)In this thesis we present a formalization of the combinatorial part of the proof of FeitHigman theorem on generalized polygons. Generalised polygons are abstract geometric structures that generalize ordinary polygons and ... 
Fourier Analysis On Number Fields And The Global Zeta Functions
(20140804)The study of zeta functions is one of the primary aspects of modern number theory. Hecke was the first to prove that the Dedekind zeta function of any algebraic number field has an analytic continuation over the whole plane ... 
Function Theory On NonCompact Riemann Surfaces
(20140630)The theory of Riemann surfaces is quite old, consequently it is well developed. Riemann surfaces originated in complex analysis as a means of dealing with the problem of multivalued functions. Such multivalued functions ... 
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. ...