Browsing Mathematics (MA) by Title
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The Space of Metric Measure Spaces
(20180522)This thesis is broadly divided in two parts. In the first part we give a survey of various distances between metric spaces, namely the uniform distance, Lipschitz distance, Hausdor distance and the Gramoz Hausdor distance. ... 
Sparse bounds for various spherical maximal functions
Harmonic analysis mainly deals with the qualitative and quantitative properties of functions and transforms of those functions. It has applications in various areas of Mathematics like PDE, Differential geometry, Ergodic ... 
Spectral Theory And Root Bases Associated With Multiparameter Eigenvalue Problems
(20100601)Consider (1) yn1+ q1y1 = (λr11 + µr12)y1 on [0, 1] y’1(0) = cot α1 and = y’1(1) = a1λ + b1 y1(0) y1(1) ... 
Stabilization Schemes for Convection Dominated Scalar Problems with Different Time Discretizations in Time dependent Domains
(20180521)Problems governed by partial differential equations (PDEs) in deformable domains, t Rd; d = 2; 3; are of fundamental importance in science and engineering. They are of particular relevance in the design of many engineering ... 
Stochastic Differential Games In A Bounded Domain
(20121121) 
Structural Bioinformatics of Ligand Recognition in Proteins : A largescale Analysis and Applications in Drug Discovery
Biological processes are governed by highly specific macromolecular interactions. Understanding the precise mechanism of ligand recognition in proteins is essential for deriving features responsible for such recognition ... 
Structural connectivity correlates of human cognition explored with diffusion MRI and tractography
Intact structural connectivity among brain regions is critical to cognition. Structural connectivity forms the substratum for information flow between brain regions, and its plasticity is a hallmark of learning in the ... 
Studies on Dynamic Plasticity of Ligand Binding Sites in Proteins
Molecular recognition between proteins and their associated ligands constitutes ligandinduced protein rewiring thereby enabling the formation of a stable proteinligand complex. The studies presented in this thesis address ... 
Study of Higher Order SplitStep Methods for Stiff Stochastic Differential Equations
(20180406)Stochastic differential equations(SDEs) play an important role in many branches of engineering and science including economics, finance, chemistry, biology, mechanics etc. SDEs (with mdimensional Wiener process) arising ... 
Study of Optimal Control Problems in a Domain with Rugose Boundary and Homogenization
(20171210)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 ... 
A Study of Some Conformal Metrics and Invariants on Planar Domains
The main aim of this thesis is to explain the behaviour of some conformal metrics and invariants near a smooth boundary point of a domain in the complex plane. We will be interested in the invariants associated to the ... 
A Study Of The Metric Induced By The Robin Function
(20130913)Let D be a smoothly bounded domain in Cn , n> 1. For each point p _ D, we have the Green function G(z, p) associated to the standard sumofsquares Laplacian Δ with pole at p and the Robin constant __ Λ(p) = lim G(z, p) ... 
A Study On Solutions Of Singular Integral Equations
(20120531) 
Subnormality and Moment Sequences
(20180307)In this report we survey some recent developments of relationship between Hausdorﬀ moment sequences and subnormality of an unilateral weighted shift operator. Although discrete convolution of two Haudorﬀ moment sequences ... 
Time Series Analysis Of Neurobiological Signals
(20110928) 
Total variation cutoff for random walks on some finite groups
This thesis studies mixing times for three random walk models. Specifically, these are random walks on the alternating group, the group of signed permutations and the complete monomial group. The details for the models are ... 
Toward Computationally Efficient Models for Nearinfrared and Photoacoustic Tomographic Imaging
(20171128)Near Infrared (NIR) and Photoacoustic (PA) Imaging are promising imaging modalities that provides functional information of the soft biological tissues invivo, with applications in breast and brain tissue imaging. These ... 
Trace Estimate For The Determinant Operator And K Homogeneous Operators
Let $\boldsymbol T=(T_1, \ldots , T_d)$ be a $d$ tuple of commuting operators on a Hilbert space $\mathcal H$. Assume that $\boldsymbol T$ is hyponormal, that is, $\big [\!\!\big [ \boldsymbol T^*, \boldsymbol T \big ]\!\! ... 
Unfolding Operators in Various Oscillatory Domains : Homogenization of Optimal Control Problems
(20180613)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 ...