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Dilation Theory of Contractions and Nevanlinna-Pick Interpolation Problem
In this article, we give two different proofs of the existence of the minimal isometric dilation of a single contraction. Then using the existence of a unitary dilation of a contraction, we prove the `von Neumann's ...
Homogeneous Operators and Some Irreducible Representations of the Mobius Group
In this report, after recalling the definition of the M¨obius group, we define homogeneous operators,
that is, operators T with the property '(T) is unitarily equivalent to T for all ' in the M¨obius group and prove some ...
Dynamic Flow Rules in Continuum Visco-plasticity and Damage Models for Poly-crystalline Solids
Modelling highly non-linear, strongly temperature- and rate-dependent visco-plastic behaviour of poly-crystalline solids (e.g., metals and metallic alloys) is one of the most challenging topics of contemporary research ...
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 ...
Graph Spectral Methods for Analysis of Protein Structures
Network representation of protein structures is an information-rich mode of examining protein structure, dynamics and its interactions with biomolecules. Graph spectral methods are extremely useful and powerful in analysing ...
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, non-sparse ...
Computational Studies on Structures and Functions of Single and Multi-domain Proteins
(2018-05-25)
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 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 ...
Central and Peripheral Correlates of Motor Planning
(2018-02-11)
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 ...
Kinetic Theory Based Numerical Schemes for Incompressible Flows
(2018-02-07)
Turbulence is an open and challenging problem for mathematical approaches, physical modeling and numerical simulations. Numerical solutions contribute significantly to the understand of the nature and effects of turbulence. ...