Browsing Mathematics (MA) by Title
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Algorithmic and Hardness Results for Fundamental FairDivision Problems
The theory of fair division addresses the fundamental problem of dividing a set of resources among the participating agents in a satisfactory or meaningfully fair manner. This thesis examines the key computational challenges ... 
An Algorithmic Approach To Crystallographic Coxeter Groups
(20130214)Coxeter group, named after H.S.M. Coxeter, is an abstract group that admits a formal description in terms of mirror symmetries. It turns out that the finite Coxeter groups are precisely the finite Euclidean reflection ... 
Analysis of Proportional Navigation Class of Guidance Law against Agile Targets
(20171212)Guidance is defined as the determination of a strategy for following a nominal path in the presence of onominal conditions, disturbances and uncertainties, and the strategy employed is called a guidance law. Variants of ... 
Analytic and Entire Vectors for Representations of Lie Groups
(20180101)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 ... 
Analytic Continuation In Several Complex Variables
(20140630)We wish to study those domains in Cn,for n ≥ 2, the socalled domains of holomorphy, which are in some sense the maximal domains of existence of the holomorphic functions defined on them. We demonstrate that this study ... 
Analytic Models, Dilations, Wandering Subspaces and Inner Functions
This thesis concerns dilation theory, analytic models, joint invariant subspaces, reproducing kernelHilbert spaces and multipliers associated to commuting tuples of bounded linear operators on Hilbert spaces. The main ... 
Analyzing Credit Risk Models In A Regime Switching Market
(20160425)Recently, the financial world witnessed a series of major defaults by several institutions and investment banks. Therefore, it is not at all surprising that credit risk analysis have turned out to be one of the most important ... 
Asymptotic Lower Bound for Quasi Transitive Codes over Cubic Finite Fields
(20180714)Algebraic geometric codes were first introduced by V.D.Goppa . They were well recognized and developed by Tsfasman, Vladut and Zink because they have parameters better than GilbertVarshmov bound and thus giving rise to ... 
Betti Numbers, Grobner Basis And Syzygies For Certain Affine Monomial Curves
(Indian Institute of Science, 20070330)Let e > 3 and mo,... ,me_i be positive integers with gcd(m0,... ,me_i) = 1, which form an almost arithmetic sequence, i.e., some e  1 of these form an arithmetic progression. We further assume that m0,... ,mc_1 generate ... 
BorsukUlam Theorem And Its Equivalent Formulations
(20110928) 
Bounded Analytic Functions On The Unit Disc
(20110809)In this thesis, we have dealt primarily with two function algebras. The first one is the space of all holomorphic functions on the unit disc D in the complex plane which are continuous up to the boundary, denoted by A(D). ... 
The CaratheodoryFejer Interpolation Problems and the VonNeumann inequality
(20180530)The validity of the vonNeumann inequality for commuting $n$  tuples of $3\times 3$ matrices remains open for $n\geq 3$. We give a partial answer to this question, which is used to obtain a necessary condition for the ... 
Central and Peripheral Correlates of Motor Planning
(20180211)A hallmark of human behaviour is that we can either couple or decouple our thoughts, decision and motor plans from actions. Previous studies have reported evidence of gating of information between intention and action that ... 
Characterization of Brain Signals Across Scales Using Temporally Modulated Visual Stimuli
Electrical signals from the brain can be recorded at several different scales, ranging from spiking activity to local field potential (LFP) in animals to scalp electroencephalogram (EEG) in humans. Each signal represents ... 
Characters of classical groups twisted by roots of unity
This thesis focuses on the study of specialized characters of irreducible polynomial representations of the complex classical Lie groups of types A, B, C and D. We study various specializations where the characters are ... 
Compactness Theorems for The Spaces of Distance Measure Spaces and Riemann Surface Laminations
(20180218)Gromov’s compactness theorem for metric spaces, a compactness theorem for the space of compact metric spaces equipped with the GromovHausdorﬀ distance, is a theorem with many applications. In this thesis, we give a ... 
Computation of Sparse Representations of High Dimensional Time Series Data and Experimental Applications
Obtaining a sparse representation of high dimensional data is often the first step towards its further analysis. Conventional Vector Autoregressive (VAR) modelling methods applied to such data results in noisy, nonsparse ... 
Computational Studies on Structures and Functions of Single and Multidomain Proteins
(20180525)Proteins are essential for the growth, survival and maintenance of the cell. Understanding the functional roles of proteins helps to decipher the working of macromolecular assemblies and cellular machinery of living ... 
A computational systems biology approach for elucidating molecular features of primary and metastatic melanoma
Malignant melanoma, a cancer arising from melanocytes, is reported to have one of the fastest growing incidence rates worldwide, and is considered to be one of the most aggressive human malignancies. According to the ...