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Mixed Norm Estimates in Dunkl Setting and Chaotic Behaviour of Heat Semigroups
(2018-01-03)
This thesis is divided into three parts. In the first part we study mixed norm estimates for Riesz transforms associated with various differential operators. First we prove the mixed norm estimates for the Riesz transforms ...
Study of Optimal Control Problems in a Domain with Rugose Boundary and Homogenization
(2017-12-10)
Mathematical theory of partial differential equations (PDEs) is a pretty old classical area with wide range of applications to almost every branch of science and engineering. With the advanced development of functional ...
Mechanising knot Theory
(2018-01-31)
Mechanisation of Mathematics refers to use of computers to generate or check proofs in Mathematics. It involves translation of relevant mathematical theories from one system of logic to another, to render these theories ...
Shortest Length Geodesics on Closed Hyperbolic Surfaces
(2018-01-31)
Given a hyperbolic surface, the set of all closed geodesics whose length is minimal form a graph on the surface, in fact a so called fat graph, which we call the systolic graph. The central question that we study in this ...
Shift-like Automorphisms of Ck
(2018-01-03)
We use transcendental shift-like automorphisms of Ck, k > 2 to construct two examples of non-degenerate entire mappings with prescribed ranges. The first example exhibits an entire mapping of Ck, k>2 whose range avoids a ...
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 ...