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Full-Text Articles in Physical Sciences and Mathematics
Some Contributions To Free Probability And Random Matrices., Sukrit Chakraborty Dr.
Some Contributions To Free Probability And Random Matrices., Sukrit Chakraborty Dr.
Doctoral Theses
No abstract provided.
Commuting Isometries And Invariant Subspaces In Several Variables., Sankar T. R. Dr.
Commuting Isometries And Invariant Subspaces In Several Variables., Sankar T. R. Dr.
Doctoral Theses
A very general and fundamental problem in the theory of bounded linear operators on Hilbert spaces is to find invariants and representations of commuting families of isometries.In the case of single isometries this question has a complete and explicit answer: If V is an isometry on a Hilbert space â„‹, then there exists a Hilbert space Hu and a unitary operator U on â„‹u such that V on â„‹u and[ S ⊗ IW 0 0 U] ∈ B((l 2 (ℤ+) ⊗ W) ⊕ â„‹u),are unitarily equivalent, whereW = ker V∗ ,is the wandering subspace for V and S is the …
Characterization Of Eigenfunctions Of The Laplace-Beltrami Operator Through Radial Averages On Rank One Symmetric Spaces., Muna Naik Dr.
Characterization Of Eigenfunctions Of The Laplace-Beltrami Operator Through Radial Averages On Rank One Symmetric Spaces., Muna Naik Dr.
Doctoral Theses
Let X be a rank one Riemannian symmetric space of noncompact type and ∆ be the Laplace–Beltrami operator of X. The space X can be identified with the quotient space G/K where G is a connected noncompact semisimple Lie group of real rank one with finite centre and K is a maximal compact subgroup of G. Thus G acts naturally on X by left translations. Through this identification, a function or measure on X is radial (i.e. depends only on the distance from eK), when it is invariant under the left-action of K. We consider right-convolution operators Θ on functions …
Nonparametric Methods For Data In Infinite Dimensional Space., Anirvan Chakraborty Dr.
Nonparametric Methods For Data In Infinite Dimensional Space., Anirvan Chakraborty Dr.
Doctoral Theses
For univariate as well as finite dimensional multivariate data, there is an extensive literature on nonparametric statistical methods. One of the reasons for the popularity of nonparametric methods is that it is often difficult to justify the assumptions (e.g., Gaussian distribution of the data) made in the models used in parametric methods. Nonparametric procedures use more flexible models, which involve less assumptions. So, they are more robust against possible departures from the model assumptions, and are applicable to a wide variety of data. Nonparametric methods outperform their parametric competitors in many situations, where the assumptions required for the parametric methods …
Some Conjugacy Problems In Algebraic Groups., Anirban Bose Dr.
Some Conjugacy Problems In Algebraic Groups., Anirban Bose Dr.
Doctoral Theses
In this thesis we address two problems related to the study of algebraic groups and Lie groups. The first one deals with computation of an invariant called the genus number of a connected reductive algebraic group over an algebraically closed field and that of a compact connected Lie group. The second problem is about characterisation of real elements in exceptional groups of type F4 defined over an arbitrary field. Let G be a connected reductive algebraic group over an algebraically closed field or a compact connected Lie group. Let ZG(x) denote the centralizer of x ∈ G. Define the genus …
Spectral Properties Of Large Dimensional Random Circulant Type Matrices., Koushik Saha Dr.
Spectral Properties Of Large Dimensional Random Circulant Type Matrices., Koushik Saha Dr.
Doctoral Theses
Consider a sequence of matrices whose dimension increases to infinity. Suppose the entries of this sequence of matrices are random. These matrices with increasing dimension are called large dimensional random matrices (LDRM).Practices of random matrices, more precisely the properties of their eigenvalues, has emerged first from data analysis (beginning with Wishart (1928) [132]) and then from statistical models for heavy nuclei atoms (beginning with Wigner (1955) [130]). To insist on its physical applications, a mathematical theory of the spectrum of the random matrices began to emerge with the work of E. P. Wigner, F. J. Dyson, M. L. Mehta, C. …
Some Geometrical Aspects Of The Cone Linear Complementarity Problem., Madhur Malik Dr.
Some Geometrical Aspects Of The Cone Linear Complementarity Problem., Madhur Malik Dr.
Doctoral Theses
Cone Linear Complementarity ProblemLet V be a finite dimensional real inner product space and K be a closed convex cone in V. Given a linear transformation L : V → V and a vector q ∈ V the cone linear complementarity problem or linear complementarity problem over K, denoted as LCP(K, L, q), is to find a vector x ∈ K such thatL(x) + q ∈ K+ and hx, L(x) + qi = 0,where h., .i denotes an inner product on V and K is the dual cone of K defined as:K∗ := {y ∈ V : hx, yi ≥ …
Properties Of Some Matrix Classes In Linear Complementarity Theory., Arup Kumar Das Dr.
Properties Of Some Matrix Classes In Linear Complementarity Theory., Arup Kumar Das Dr.
Doctoral Theses
The linear complementarity problem is a fundamental problem that arises in optimization, game theory, economics, and engineering. It can be stated as follows:Given a square matrix A of order n with real entries and an n dimensional vector q, find n dimensional vectors w and z satisfying w − Az = q, w ≥ 0, z ≥ 0 (1.1.1) w t z = 0. (1.1.2)This problem is denoted as LCP(q, A). The name comes from the condition (1.1.2), the complementarity condition which requires that at least one variable in the pair (wj , zj ) should be equal to 0 …
Some Contributions To Semidefine Linear Complementary Problem., D. Sampangi Raman Dr.
Some Contributions To Semidefine Linear Complementary Problem., D. Sampangi Raman Dr.
Doctoral Theses
This thesis is composed of chapters 1 to 5. In Chapter 1, we formally define SDLCP and give some examples of SDLCP and show that SDLCP is a special case of variational inequality problem. Also we show that LCP is indeed a special case of SDLCP. Later section of this chapter deals with definitions and notations.In Chapter 2, we are concerned with the results which have been obtained in an effort to generalize the P-matrix condition of LCP to SDLCP. It is known that a matrix M is a P-matrix if and only if M does not re verse the …
Perturbed Laplacian Matrix And The Structure Of A Graph., Sukanta Pati Dr.
Perturbed Laplacian Matrix And The Structure Of A Graph., Sukanta Pati Dr.
Doctoral Theses
Laplacian matrices Let G be a connected simple graph with vertex set V = {1,2,.,n), edge set E and let each edge be associated with a positive number, the weight of the edge. The above graph is called a weighted graph. An unweighted graph is just a weighted graph with each of the edges bearing weight 1. All the graphs considered are weighted and simple, unless specified otherwise; all the matrices considered are real. The adjacency matrix A(G) related to this graph is defined as A(G) = (aij), whereaij, if (i, j] € E and the weight of the edge …
Some Problems In Estimating Finite Population Total And Variance In Survey Sampling., Saswati Bhattacharya Dr.
Some Problems In Estimating Finite Population Total And Variance In Survey Sampling., Saswati Bhattacharya Dr.
Doctoral Theses
The problem of drawing inference concerning the parameters of a finite population of identifiable units has been increasingly engaging the attention of statisticians. The central problem here is to devise a suitable method of selecting a sample from the population and to employ an appropriate estimator to estimate the finite population total or mean. A consider- able progress in this field of study has been made and many authors have contributed towards the development of the theory in this aspect of the problem of statistical inferenceNumerous papers have been written covering the first aspect of the problem, namely, method of …
Some Problems In Joint Spectral Theory., Tirthankar Bhattacharya Dr.
Some Problems In Joint Spectral Theory., Tirthankar Bhattacharya Dr.
Doctoral Theses
No abstract provided.
Hypergroup Graphs And Subfactors., A. K. Vijayarajan Dr.
Hypergroup Graphs And Subfactors., A. K. Vijayarajan Dr.
Doctoral Theses
The main theme of this t hesis is hypergroups. In this thesis the the- ory of hypergroups is applied to study the relation between certain graphs and subfactors of II, factors in the context of principal graphs associated with the inclusions of II, factors. More general classes of hypergroups are iutroduced, new examples of hypergroups associated to certain graphs are coustructed and classification of small order hypergroups is discussed.The text of the thesis is arranged in four chapters. The first chapter is on preliminaries of the theory of hypergroups, the second on the appli- cation of the theory of hyjrrgroups …
Coxeter Groups And Positive Matrices., Arbind Kumar Lal Dr.
Coxeter Groups And Positive Matrices., Arbind Kumar Lal Dr.
Doctoral Theses
In this thesis, we study positive matrices (matrices whose entries are nonnegative as well as matrices which are positive semidefinite) with Coxeter groups as the underlying theme. For an exposition on Coxeter groups see Humphreys (1990).A Cozeter system consists of a pair (W, s); where W is a group and S is a set which consists of the generators of the group W. The elements of the set S have only the relations of the form (ss')m(s.) 1; where m(s, s) 1, m(s, s') = m(s,s) 2 2 for s s in S. In case no relation occurs for a …
Some Contributions To Generalized Inverse And The Linear Complementarity Problem., N. Eagambaram Dr.
Some Contributions To Generalized Inverse And The Linear Complementarity Problem., N. Eagambaram Dr.
Doctoral Theses
A generalized inverse (g-inverse) of a matrix A is a solution x to the matrix equationA XA = A(1.1.1)A g-inverse of A can be defined alternatively as a matrix x such that x = Xb is a solution to the linear equation Ax -b for any b that makes - b consistent. There is a vast literature on g-inverse. For a number of results on g-inverses and their applications one may refer to the well known books in the literature by Rao and Mitra (1971); and by Ben Israel and Greville (1974).Another inverse that lies hidden in the definition of …
Some Spectral Properties Of Three And Four Body Scrodinger Operators By The Methods Of Time Dependent Scattering Theory., M. Krishna Dr.
Some Spectral Properties Of Three And Four Body Scrodinger Operators By The Methods Of Time Dependent Scattering Theory., M. Krishna Dr.
Doctoral Theses
In the present work we shall deal with the asymptotic completeness problem in three and four (Quantum Mechanical) particle scattering. This thesis is divided into three chapters. In the first chapter we give an introduction to Scattering Phencmenon and give a description of the N-particle completeness problem.Then we collect some results preliminary to the later chapters and some results that would complete a discussion of the problem.The second chapter consists of some technical results and a reduction of the asymptotic completeness problem in N-particlerscattering via time dependent methods. The last chapter has two sections. The first section deals with verifying …
Optimal Block Designs In One And Multi-Way Settings., Sunanda Bagchi Dr.
Optimal Block Designs In One And Multi-Way Settings., Sunanda Bagchi Dr.
Doctoral Theses
The study of optimality of block designs formally began with wald (1943) proving a very important optimality property, designated as D-optimality of Iatin Square. Desi gns in a given physical set up. Next Ehrenfield (1955) proved the E-optimality property of Latin Square Designs. Since then, the work in: the area has primarily consisted in evolving a number of useful opti- mality oriteria for oomparing block design in a reasonable set up given and oharacterizing and/or constructing desi gns saiisfying the so called optimality criteria developed. But it was not until 1958, when the theory was given a proper and precise …
Spectral And Scattering Theory For Schrodinger Operator With A Class Of Momentum Dependent Long Range Potentials., P. L. Muthuramalingam Dr.
Spectral And Scattering Theory For Schrodinger Operator With A Class Of Momentum Dependent Long Range Potentials., P. L. Muthuramalingam Dr.
Doctoral Theses
No abstract provided.
Estimation Of Spectral Variation., Rajendra Bhatia Dr.
Estimation Of Spectral Variation., Rajendra Bhatia Dr.
Doctoral Theses
The study of spectra occupies a central place in the theory of linear operators. One part of this study consists of obtaining a detailed and complete knowledge of the spectrum of a given lincar operator. The other part - perturbation theory - consists of using this knowledge to obtain information about the spectra of nearby operators.Apart from the intrinsic mathematical interest it has, perturbation theory is of great importance in the study of several physical problems. In fact, the theory came into existence with the work of Rayleigh on sound waves and that of Schrodinger on quantum mechanics. Later, their …
Extensions Of The Theory Of Positive Operators And Their Relationship To Minimax Games., T. E.S. Raghavan Dr.
Extensions Of The Theory Of Positive Operators And Their Relationship To Minimax Games., T. E.S. Raghavan Dr.
Doctoral Theses
The theory of positive matrices (matrioco with non- negative entries) nnd the the ory of positive operetors are used extensively in the study of vibrationa of mechanical eysteme l16], stochaatic proceuses (36] nd mathematical economics ((9] and L20].) It is well known from the claseical theoreme of Perron and Frobenius ((13), [14) and (25] that any non-eingul ar squere matrix with non-negative entries has a positive cigenvalue which ts maximal in modulus among al1 the eigenvalues of the matrix. Further for this positive eigenvalue, it has a non-null eigenvector with all components non-negative. If the matrix is also irroduc lble11) …