Browsing Mathematics (MA) by Title
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Quasianalytic 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 quasianalyticity. 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
(20180714)Significant advancements in genome sequencing techniques and other highthroughput 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 4Genus
(20140407)The 4genus of a knot in S3 is an important measure of complexity, related to the unknotting number. A fundamental result used to study the 4genus 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 nonArchimedean 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
(20140903)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
(20110928) 
Riesz Transforms Associated With Heisenberg Groups And Grushin Operators
(20151208)We characterise the higher order Riesz transforms on the Heisenberg group and also show that they satisfy dimensionfree bounds under some assumptions on the multipliers. We also prove the boundedness of the higher order ... 
Rigidity And Regularity Of Holomorphic Mappings
(20150716)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 ... 
RiskSensitive Stochastic Control and Differential Games
This thesis studies risksensitive stochastic optimal control and differential game problems. First, we study risksensitive stochastic differential games for controlled reflecting diffusion processes in a smooth bounded ... 
Role of gamma oscillations in processing of natural stimuli
Gamma oscillations (~3080 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
(20140407)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 ... 
SemiMarkov Processes In Dynamic Games And Finance
(20100701)Two different sets of problems are addressed in this thesis. The first one is on partially observed semiMarkov Games (POSMG) and the second one is on semiMarkov modulated financial market model. In this thesis we study ... 
Shiftlike Automorphisms of Ck
(20180103)We use transcendental shiftlike automorphisms of Ck, k > 2 to construct two examples of nondegenerate 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
(20180131)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 Multiplayer Stochastic Dynamic Optimization
(20180406)In this thesis we investigate single and multiplayer stochastic dynamic optimization problems. We consider both discrete and continuous time processes. In the multiplayer setup we investigate zerosum games with both ... 
Software Quality Testing And Remedies
(20130118) 
Some Aspects Of The First Passage Time Problem In Neuroscience
(20110808)In the stochastic modeling of neurons, the first passage time problem arises as a natural object of study when considering the inter spike interval distribution. In this report, we study some aspects of this problem as it ... 
Some Descriptions Of The Envelopes Of Holomorphy Of Domains in Cn
(20110809)It is well known that there exist domains Ω in Cn,n ≥ 2, such that all holomorphic functions in Ω continue analytically beyond the boundary. We wish to study this remarkable phenomenon. The first chapter seeks to motivate ...