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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 ...
A Study On Solutions Of Singular Integral Equations
(2012-05-31)
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 ...