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Articles 1 - 12 of 12
Full-Text Articles in Physical Sciences and Mathematics
Model And Design-Based Analysis Of Complex Surveys., Joydip Mitra Dr.
Model And Design-Based Analysis Of Complex Surveys., Joydip Mitra Dr.
Doctoral Theses
We consider estimating the total Y of a variable y defined on a survey population. The survey is complex only in the sense that we admit sample selection with arbitrary probabilities. Our 'analysis' consists in examining efficacies of conf Idence intervals for the For this we need point estimators and or mean square error (MSE) variance { estimators, respectively say, total. the corresponding e and v. The distribution, resulting from repeated sampling, of the pivotal quantity d = (e-Y)/V 1s supposed to approximate that of standard normal deviate t or of Students t with (n-1) degrees of freedom, assuming large …
Studies On Design, Routing And Fault Tolerance Of Interconnection Network., Krishnendu Mukhopadhyay Dr.
Studies On Design, Routing And Fault Tolerance Of Interconnection Network., Krishnendu Mukhopadhyay Dr.
Doctoral Theses
A recent trend in computing is to distribute the computations among a set of processing elements. There are two basic appronches to this - one is to build a loosely-coupled system and the other is to form a tightly-coupled system [PS85].In a loosely-coupled system, the processors do not share common memory or a common clock; but sharing of important resources like data files, softwares, special hardware components etc., is possible without duplicating the resources themselves. The processing nodes may even be geographicully separated from each other and are connected through databuses, telephone/radio links, satellite, etc. Such loosely- coupled systems are …
Σary, Moorhead State University, Mathematics Department
Σary, Moorhead State University, Mathematics Department
Math Department Newsletters
No abstract provided.
Retiling A Colored Hexagonal Plane, Kari Kelton
Retiling A Colored Hexagonal Plane, Kari Kelton
Mahurin Honors College Capstone Experience/Thesis Projects
No abstract provided.
Markov Dilation Of Nonconservative Quantum Dynamical Semigroups And Quantum Boundary Theory., B. V. Rajarama Bhat Dr.
Markov Dilation Of Nonconservative Quantum Dynamical Semigroups And Quantum Boundary Theory., B. V. Rajarama Bhat Dr.
Doctoral Theses
In classical probability theory, based on Kolmogorov consistency theorem, one can associate a Markov process to any one parameter semigroup of stochastic matrices or transition probability operators. It is indeed the foundation for the theory of Markov processes. Here a quantum version of this theorem has been established. This effectively answers some of the questions raised by P. A. Meyer in his book (see page 220 of (Me).It is widely agreed upon that irreversible dynamics in the quantum setting is de- scribed by contractive semigroups of completely positive maps on C" algebras ([Kr). (AL]). In other words these semigroups, known …
Multivalued Approach For Uncertainty Management., Deba Prasad Mandal Dr.
Multivalued Approach For Uncertainty Management., Deba Prasad Mandal Dr.
Doctoral Theses
Real life problems are rarely free from uncertainty which usually emerges from the deficiencies of information available from a situation. The defi- ciencies may result from incomplete, imprecise, not fully reliable, vague or contradictory information depending on the problem. Management of uncer- tainty in a decision making system has been an important research problem for many years.Until the inception of the concept of fuzzy set theory in 1965 (1), the theory of probability and statistics was the primary mathematical tool for modeling uncertainty in a system/situation. Fuzzy set theory has shown enormous proinise in handling uncertaintics to a reasonable extent …
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 …
Some Limit Theorem On Conditional U-Statistics And Censored Data Non Parametric Regression., Arusharka Sen Dr.
Some Limit Theorem On Conditional U-Statistics And Censored Data Non Parametric Regression., Arusharka Sen Dr.
Doctoral Theses
In Statistics, a classical problem is that of estimating the regression function which is defined as m{t) := E(Y|X = ), te R, for two random variables X and Y such that EY < 0o. The estimators are constructed iased on a sample {(Xi, Yi.)}, 1sis n,n 2 1, from the distribution of (X, Y). Throughout this thesis, we assume X and Y to be real-valued for the sake of convenience. The classical approach to this problem is to assume a parametrized, polynomial form for nt-), i.e., m(t) := Bo + E-1 P,ti, p 21, and obtain estimates of the unknown paraineters Bo, Bj,, 1sjsp. Later, with the development of techıniques for non-parametrie density estimation, it was sought to extend these techniques to regression estimation. Heuristically, the two problems can be seen to be related as follows : let fi(-) be the marginal density of X and note that E1(X S x) = h(t)dt, z € R, whereas EY 1(X Sx) = m(t)fi(t)dt, x E MR. (1.0.2) In other wordds, (1.0.1) can be looked upon as a special case of (1.0.2), with Y = 1. + similarity, as we shall see later on, has been the underlying theme in Chapters 2 and 4 of the present work.) The following non-parametric regression estimator was proposed independently by Nadaraya (1964) and Watson (1964): "(): := m.(Y,)/m.(1, ), te R, (1.0.3) where m,(Y, t) = (nan)- E-, Y;K((t - X:)/an). (1.0.4) m,(1,1) (na,)-E, K((I - X)/a,). Here K(), the so-called kernel function, is chosen to satiafy various analytical conditions (typically, K(-) is taken to be a density function), and a, 1 0 are the bandwidths which go to zero sufficiently slowly (e.g., na,0o as n00) in order to ensure consistency of the estimator mW (). The intuition behind such an estimator is that m,(Y,) is an estimator of mt-)fi() while m,(1,) cstimates the density fa(-). See Prakasa Rao (1983), Chapters 1-4. for an introduction to non-parametric density and regression estimation. Now, m(t) is a functional of the conditional distribution of Y, given X = t. A natu- ral generalisation of the regression estimation problem seems to be the estimation of the following functionals: mh(t1,....tk) := E{h(Y1,.....Yk) | X1, = t1.,Xk. = tk), (t....) € R*, k 2 1, (1.0.5) where h: R*- R is such that Elh(Y...., Y) < 0. A similar generalisation led Hoelfding (1948) from the sample mcan to the theory of so-called U-statistics, in the uncondilional set-up. The estimation of (1.0.5) were considerexl, for the first time in published form, in Stute (1991) where the following conditional U-statistics were proposed as estimators;where Fn(-) := n-1E, 1(Xi; < ) denotes the empirical distribution function (c.d.f Bochynek discussed the asymptotic normality of conditional U- and V-statistics and pei formed simulation studies on them. Stute (1991) established weak and strong pointwis consistency and asymptotic normality of U(t). Liero (1991) studied uniform strong con sistency of conditional U-statistics and established asymptotic normality of the integrate squared error (ISE) statistic:for suitable A c R* and weight function w(-). We quote the following examples to illustrate the possible use of conditional U-statistics See Stute (1991) and Bochynek (1987) for other examples. Throughout this thesis, our set up will be as foliows: {(Xn, Yn)}n>ı is a bi-variate i.i.d sequence, with (X1, Y1) having join density f(,-) and X, having marginal density fi(-). Consequently,
Discrete Singularity Method And Its Application To Incompressible Flows., S K. Venkatesan Dr.
Discrete Singularity Method And Its Application To Incompressible Flows., S K. Venkatesan Dr.
Doctoral Theses
The smooth flow of a fluid has sprung many surprises. A flow which at an instant of time is quite regular and orderly could produce on the slightest of disturbance a complex bewildering varieties of flows, broadly termed as turbulence. Direct numerical simulation of the Navier-Stokes equations have shown that it is quite possible that these turbulent flows are solutions of the Navier-Stokes equations. In fact it is by now well recognized that many non-linear systems produce chaos quite similar to turbulence. However the large number of scales and their complex interactions involved make turbulence difficult to understand. Direct numerical …
Study Of Moduli Of Bundles., Indranil Biswas Dr.
Study Of Moduli Of Bundles., Indranil Biswas Dr.
Doctoral Theses
Hitchin (Hi2) realized the importance of studying pairs (E,∅) where E is a vector bundle and ∅ is a homomorphism of E into EOL for a fixed line bundle L. When C is a smooth pro jective algebraic curve this has since been studied quite extensively. One can construct a covering of C in this situation and the given data can be completely recovered by this covering map and a line bundle on the covering curve (see Beauville, Narasimhan and Ramanan (BNR]). When L is the canonical bundle this procedure gives a completely integrable system on the cotangent bundle of …
Parametric Homotopy Principle Of Some Practical Differential Relations., Mahuya Datta Dr.
Parametric Homotopy Principle Of Some Practical Differential Relations., Mahuya Datta Dr.
Doctoral Theses
A system uf r-th order partial differential inequalities is a subspace in the space of r-jets of CT" maps between manifolds. The problem of homotopy classification of C solutions of such systems is stauliel in this thesis. The text roughly divides into two parts. In the first part, the problem is considered in an equivariant setting when the system is open and invariant under the action of a compact L.ie group, but may not be invariant under the action of the pseudogroup of equivariant local diffeomorphisms. The second part concerns a non-equivariant set-up without the openness condition on the systern. …
Hyperinvariant Subspaces Of The Harmonic Dirichlet Space, William T. Ross, Stefan Richter, Carl Sundberg
Hyperinvariant Subspaces Of The Harmonic Dirichlet Space, William T. Ross, Stefan Richter, Carl Sundberg
Department of Math & Statistics Faculty Publications
No abstract provided.