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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 ...
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 ...