Browsing Mathematics (MA) by Title
Now showing items 105-124 of 154
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Positivity preservers forbidden to operate on diagonal blocks
The question of which functions acting entrywise preserve positive semidefiniteness has a long history, beginning with the Schur product theorem [Crelle 1911], which implies that absolutely monotonic functions (i.e., ... -
A Posteriori Error Analysis of Discontinuous Galerkin Methods for Elliptic Variational Inequalities
(2018-02-15)The main emphasis of this thesis is to study a posteriori error analysis of discontinuous Galerkin (DG) methods for the elliptic variational inequalities. The DG methods have become very pop-ular in the last two decades ... -
Quasi-analytic Functions, Spherical Means, and Uncertainty Principles on Heisenberg Groups and Symmetric Spaces
This thesis has two parts. The first part revolves around certain theorems related to an uncertainty principle and quasi-analyticity. In contrast, the second part reflects a different mathematical theme, focusing on the ... -
Recognition of Structures, Functions and Interactions of Proteins of Pathogens : Implications in Drug Discovery
(2018-07-14)Significant advancements in genome sequencing techniques and other high-throughput initiatives have resulted in the availability of complete sequences of genomes of a large number of organisms, which provide an opportunity ... -
Relative Symplectic Caps, Fibered Knots And 4-Genus
(2014-04-07)The 4-genus of a knot in S3 is an important measure of complexity, related to the unknotting number. A fundamental result used to study the 4-genus and related invariants of homology classes is the Thom conjecture, proved ... -
Representations of Special Compact Linear Groups of Order Two : Construction, Representation Growth, Group Algebras and Branching Laws
Let o be the ring of integers of a non-Archimedean local field such that the residue field has characteristic p: Let p be the maximal ideal of o: For Char¹oº = 0; let e be the ramification index of o: i.e., 2o = pe: Let ... -
Ricci Flow And Isotropic Curvature
(2014-09-03)This thesis consists of two parts. In the first part, we study certain Ricci flow invariant nonnegative curvature conditions as given by B. Wilking. We begin by proving that any such nonnegative curvature implies nonnegative ... -
Riemann Roch Theorem For Algebraic Curves
(2011-09-28) -
Riesz Transforms Associated With Heisenberg Groups And Grushin Operators
(2015-12-08)We characterise the higher order Riesz transforms on the Heisenberg group and also show that they satisfy dimension-free bounds under some assumptions on the multipliers. We also prove the boundedness of the higher order ... -
Rigidity And Regularity Of Holomorphic Mappings
(2015-07-16)We deal with two themes that are illustrative of the rigidity and regularity of holomorphic mappings. The first one concerns the regularity of continuous CR mappings between smooth pseudo convex, finite type hypersurfaces ... -
Risk-Sensitive Stochastic Control and Differential Games
This thesis studies risk-sensitive stochastic optimal control and differential game problems. First, we study risk-sensitive stochastic differential games for controlled reflecting diffusion processes in a smooth bounded ... -
Role of gamma oscillations in processing of natural stimuli
Gamma oscillations (~30-80 Hz) are a prominent signature of electrophysiological signals recorded from the brain with proposed roles in various cognitive functions such as attention and visual perception. Although gamma ... -
The Role Of Potential Theory In Complex Dynamics
(2014-04-07)Potential theory is the name given to the broad field of analysis encompassing such topics as harmonic and subharmonic functions, the Dirichlet problem, Green’s functions, potentials and capacity. In this text, our main ... -
Semi-Markov Processes In Dynamic Games And Finance
(2010-07-01)Two different sets of problems are addressed in this thesis. The first one is on partially observed semi-Markov Games (POSMG) and the second one is on semi-Markov modulated financial market model. In this thesis we study ... -
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 ... -
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 ... -
Single and Multi-player Stochastic Dynamic Optimization
(2018-04-06)In this thesis we investigate single and multi-player stochastic dynamic optimization prob-lems. We consider both discrete and continuous time processes. In the multi-player setup we investigate zero-sum games with both ...