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Analytic and Entire Vectors for Representations of Lie Groups
(2018-01-01)
We start with the recollection of basic results about differential manifolds and Lie groups. We also recall some preliminary terminologies in Lie algebra. Then we define the Lie algebra corresponding to a Lie group. In the ...
Unfolding Operators in Various Oscillatory Domains : Homogenization of Optimal Control Problems
(2018-06-13)
In this thesis, we study homogenization of optimal control problems in various oscillatory domains. Specifically, we consider four types of domains given in Figure 1 below.
Figure 1: Oscillating Domains
The thesis is ...
Minimal Crystallizations of 3- and 4- Manifolds
(2018-06-11)
A simplicial cell complex K is the face poset of a regular CW complex W such that the boundary complex of each cell is isomorphic to the boundary complex of a simplex of same dimension. If a topological space X is homeomorphic ...
Novel Upwind and Central Schemes for Various Hyperbolic Systems
(2018-05-21)
The class of hyperbolic conservation laws model the phenomena of non-linear wave propagation, including the presence and propagation of discontinuities and expansion waves. Such nonlinear systems can generate discontinuities ...
Homogeneous Operators
(2018-06-13)
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 ...
Lp-Asymptotics of Fourier Transform Of Fractal Measures
(2018-06-08)
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 ...
Finite Element Analysis of Interior and Boundary Control Problems
(2018-06-18)
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 ...
The Pick-Nevanlinna Interpolation Problem : Complex-analytic Methods in Special Domains
(2018-06-13)
The Pick–Nevanlinna interpolation problem, in its fullest generality, is as follows:
Given domains D1, D2 in complex Euclidean spaces, and a set f¹ zi; wiº : 1 i N g D1 D2, where zi are distinct and N 2 š+, N 2, find ...
Stabilization Schemes for Convection Dominated Scalar Problems with Different Time Discretizations in Time dependent Domains
(2018-05-21)
Problems governed by partial differential equations (PDEs) in deformable domains, t Rd; d = 2; 3; are of fundamental importance in science and engineering. They are of particular relevance in the design of many engineering ...
On an ODE Associated to the Ricci Flow
(2018-04-18)
We discuss two topics in this talk. First we study compact Ricci-flat four dimensional manifolds without boundary and obtain point wise restrictions on curvature( not involving global quantities such as volume and diameter) ...