Mathematics (MA)
Recent Submissions
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Computations in linear algebra: a new look at residue arithmetic.
The dissertation deals with error-free and approximate computations of some problems in linear algebra, with an emphasis on a modified residue arithmetic developed here. It is divided into five chapters:Chapter 1 The ... -
Numerical study of natural convection boundary layer flows
This thesis presents a numerical study of some laminar natural convection boundary layer flows in isothermal and non-isothermal media. It consists of five chapters. The first is an introductory one; the remaining four are ... -
Ergodic and adaptive control of markov processes.
We address the problem of controlling two classes of Markov processes, viz., Markov chains and diffusion processes. Our main goal is to minimize a long-run average cost criterion (or ergodic cost criterion) associated with ... -
Boundary element method applied to fluid flow problems
This research work is a study of fluid flow problems by the Boundary (Finite) Element Method. The widely used Finite Element Method has the advantages of its flexibility in choosing the shape and size of the elements, the ... -
some nonlinear surface wave propagation problems
This thesis contains the results of investigations of some nonlinear surface wave propagation problems. It is divided into six chapters, of which Chapter I is the general introduction and the concluding remarks constitute ... -
Some results on finite section linear integral operators
This thesis deals mainly with some spectral properties of finite section linear integral operators from L2[0,t]L^2[0,t]L2[0,t] into itself, defined as Ttf(x)=?0tK(x,y)f(y)?dyT_t f(x) = \int_0^t K(x,y) f(y) \, dyTt?f(x)=? ... -
Enumerative considerations of SDR's and latin rectangles
The art of counting is interesting but often 120000103 a difficult task. It requires computational skills^ ' .. ability to recognise similar patterns and a little mastery of general principles and simplification ... -
Some boundary value problems in elasticity with and without magnetic field
In our paper, in order to solve the problem we need the knowledge of three analytic functions 4>(z), and f^(z).. In the case of plane magneto-elasticity we arrive at a homogeneous biharmonic equation, as is the case ... -
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 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 ... -
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 ... -
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 ... -
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 ... -
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 ... -
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 ... -
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. ...
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