Mathematics (MA): Recent submissions
Now showing items 41-60 of 220
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Exact analytic solutions for some classes of partial differential equations
Exact solutions of linear partial differential equations with variable coefficients and those of nonlinear partial differential equations are dilEcult to obtain. The present thesis attempts to extend the existing methods ... -
Fredholm determinant and decay properties of eigenvalues of hilbert-schmidt integral operators
In this thesis, some properties of the eigenvalues of Hilbert-Schmidt integral operators (briefly H-S operators) are investigated. This thesis consists of three chapters. In the first two chapters, H-S operators of the ... -
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 ... -
Some analytic studies on generalized burgers equations
Thesis Summary: Analysis of Generalized Burgers Equations This thesis analyzes a class of nonlinear parabolic equations known as generalized Burgers equations. The study combines analytical techniques with numerical ... -
Finite section convolution integral operators structure of resolvent and solution of first kind equations
This thesis investigates the structure of the solutions of Fredholm integral equations of the first and second kinds with convolution kernels on finite intervals and some of its applications. The thesis is divided into ... -
On the reconstruction problems in graph theory
One of the most difficult unsolved problems in graph theory is the Reconstruction Conjecture. Harary even referred to problems like the Four Colour Problem (now a theorem), the Hamiltonian Circuit Problem, and the ... -
Some nonlinear elliptic equations involving nonlinearities of critical growth
We consider the following Neumann boundary value problem: ?Anu+??u?n?2u=f(x,u)?u?n?2in ?- A_n u + \lambda |u|^{n-2}u = f(x, u) |u|^{n-2} \quad \text{in } \Omega?An?u+??u?n?2u=f(x,u)?u?n?2in ? in a bounded domain ??Rn\Omega ... -
Spectral approximations
The problem of determining the nonzero eigenvalues, if any exist, of a linear operator on a Hilbert space, is a very important one in mathematics and physics. Even when the space is finite-dimensional, the actual ... -
Contractivity, Complete Contractivity and Curvature Inequalities
Let ???A\| \cdot \|_A???A? be a norm on Cm\mathbb{C}^mCm given by the formula ?(z1,…,zm)?A=?z1A1+?+zmAm?\|(z_1, \ldots, z_m)\|_A = \|z_1 A_1 + \cdots + z_m A_m\|?(z1?,…,zm?)?A?=?z1?A1?+?+zm?Am?? for some choice of an ... -
Numerical Techniques for reconstruction of objects from projections
In this dissertation we consider certain alternative procedures, viz., the g-inverse method as well as an iterative technique based on probabilistic estimation for the reconstruction of objects from their projections. ... -
Computation of Lyapunov spectrum and dynamic moment invariants
This thesis consists of two parts. The first part describes a new method of computing the Lyapunov exponents of continuous and discrete dynamical systems. Chaos is observed in a large class of systems and hence the problem ... -
Projective Modules and the Quillen Suslin Theorem
The notion of a module over a ring is a generalization of that of a vector space over a field k. The axioms are identical. But whereas every vector space possesses a basis, a module need not always have one. Modules ... -
Curves on Surfaces
This project report concerns the study of simple closed curves on surfaces. Specifically, we consider the question of when a closed curves on a torus can be deformed to a simple closed curve. We also consider applications ... -
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: ... -
Mapping class group dynamics, relative character varieties and hyperbolic cone surfaces
This thesis concerns the punctured surface group representations into $\pslr$ and $\pslc$. We study the action of mapping class group on the relative character varieties of punctured surface groups into $\pslr$ and $\pslc$. ... -
Some results on beta ensembles and on scaling limits of random graphs
This thesis is divided into two main parts, each of which can be studied independently of the other. The first part is devoted to the study of beta ensembles (β-ensembles). The main theme in β-ensembles, in this thesis, ... -
Positivity properties of the deformed Hermitian-Yang--Mills and related equations
In the first part of the talk, we briefly introduce the deformed Hermitian-Yang-Mills (dHYM) equation and discuss a result regarding the solvability of the twisted dHYM equation on compact Kähler three-folds with slightly ... -
Symmetric real-closed subsets of affine Kac-Moody Lie Algebras
In this thesis, we study some important classification problems related to affine Kac--Moody Lie algebras. First, we address the combinatorial problem of classifying symmetric real-closed subsets of affine root systems ... -
The Momentum Construction Method for Higher Extremal Kähler and Conical Higher cscK Metrics
This thesis consists of two parts. In both the parts we study two new notions of canonical K\"ahler metrics on compact K\"ahler manifolds which were introduced by Pingali, viz. `higher extremal K\"ahler metric' and ... -
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 ...