Browsing Mathematics (MA) by Title
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Decomposition of the tensor product of Hilbert modules via the jet construction and weakly homogeneous operators
Let ½ Cm be a bounded domain and K :£!C be a sesquianalytic function. We show that if ®,¯ È 0 be such that the functions K® and K¯, defined on £, are nonnegative definite kernels, then theMm(C) valued function ... 
Development of Efficient Computational Methods for Better Estimation of Optical Properties in Diffuse Optical Tomography
(20180402)Diffuse optical tomography (DOT) is one of the promising imaging modalities that pro vides functional information of the soft biological tissues invivo, such as breast and brain tissues. The near infrared (NIR) light ... 
Development Of NMR Methods For Metabolomics And Protein Resonance Assignments
(20170525)Nuclear Magnetic Resonance (NMR) spectroscopy is a quantitative, noninvasive and nondestructive technique useful in biological studies. By manipulating the magnetization of nuclei with nonzero spin, NMR gives insights ... 
Dilation Theory of Contractions and NevanlinnaPick Interpolation Problem
In this article, we give two different proofs of the existence of the minimal isometric dilation of a single contraction. Then using the existence of a unitary dilation of a contraction, we prove the `von Neumann's ... 
Dilations, Functoinal Model And A Complete Unitary Invariant Of A rcontraction.
(20130802)A pair of commuting bounded operators (S, P) for which the set r = {(z 1 +z 2,z 1z 2) : z 1 ≤1, z 2 ≤1} C2 is a spectral set, is called a rcontraction in the literature. For a contraction P and a bounded commutant ... 
Duality for Spaces of Holomorphic Functions into a Locally Convex Topological Vector Space
Consider an open subset O of the complex plane and a function f : O ÝÑ C. We understand the concept of holomorphicity of a complexvalued function. Suppose a function f defined on O takes values in a locally convex ... 
Dynamic Flow Rules in Continuum Viscoplasticity and Damage Models for Polycrystalline Solids
Modelling highly nonlinear, strongly temperature and ratedependent viscoplastic behaviour of polycrystalline solids (e.g., metals and metallic alloys) is one of the most challenging topics of contemporary research ... 
Dynamical Properties of Families of Holomorphic Mappings
(20180608)Thesis Abstract In the first part of the thesis, we study some dynamical properties of skew products of H´enon maps of C2 that are fibered over a compact metric space M . The problem reduces to understanding the dynamical ... 
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 ... 
Finite Element Analysis of Optimal Control Problems Governed by Certain PDEs
The primary goal of this thesis is to study finite element based \textit{a priori} and \textit{a posteriori} error analysis of optimal control problems of various kinds governed by linear elliptic PDEs of second order. ... 
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 ... 
Fourier coeffcients of modular forms and mass of pullbacks of Saito–Kurokawa lifts
In the first part of the talk we would discuss a topic about the Fourier coefficients of modular forms. Namely, we would focus on the question of distinguishing two modular forms by certain ‘arithmetically interesting’ ... 
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 ...