Mathematics Commons^™

On The Existence And Symmetry Properties Of Finite Total Mass Solutions Of The Matukuma Equation, The Eddington Equation And Their Generalizations, Yi Li, Wei-Ming Ni

Mathematics and Statistics Faculty Publications

No abstract provided.

Remarks On A Semilinear Elliptic Equation On Rn, Yi Li

Yi Li

No abstract provided.

Remarks On A Semilinear Elliptic Equation On Rn, Yi Li

Mathematics and Statistics Faculty Publications

No abstract provided.

Spectral Measures, Orthogonal Polynomials, And Absolute Continuity, Joanne Dombrowski

Mathematics and Statistics Faculty Publications

This paper studies the spectral measure of an unbounded tridiagonal matrix operator for which the matrix entries satisfy a certain growth condition, and presents a sufficient condition for the existence of an absolutely continuous part. The results are related to a class of orthogonal polynomials with exponential weights.

On Conformal Scalar Curvature Equations In Rn, Yi Li, Wei-Ming Ni

Yi Li

No abstract provided.

On Conformal Scalar Curvature Equations In Rn, Yi Li, Wei-Ming Ni

Mathematics and Statistics Faculty Publications

No abstract provided.

Cyclic Operators, Commutators, And Absolutely Continuous Measures, Joanne Dombrowski

Mathematics and Statistics Faculty Publications

Commutator equations are used to study the relationship between the tridiagonal matrix structure of an unbounded cyclic selfadjoint operator and its spectrum. Sufficient conditions are given for absolute continuity. Results are related to the study of systems of orthogonal polyomials for which the measure of orthogonality is supported on an unbounded subset of the real line.

Orthogonal Polynomials, Measures And Recurrence Relations, Joanne Dombrowski, Paul Nevai

Mathematics and Statistics Faculty Publications

Properties of measures associated with orthogonal polynomials are investigated in terms of the coefficients of the three term recurrence formula satisfied by the orthogonal polynomials.

L(P) Estimates For Maximal Functions And Hilbert-Transforms Along Flat Convex Curves In R(2), Hasse Carlsson, Michael Christ, Antonio Cordoba, Javier Duoandikoetxea, Jose L. Rudio De Francia, Jim Vance, Stephen Wainger, David Weinberg

Mathematics and Statistics Faculty Publications

No abstract provided.

Cramer Type Large Deviations For Generalized Rank Statistics, Munsup Seoh, Stegan S. Ralescu, Madan L. Puri

Mathematics and Statistics Faculty Publications

A Cramer type large deviation theorem is proved under alternatives as well as under hypothesis for the generalized linear rank statistic which includes as special cases (unsigned) linear rank statistics, signed linear rank statistics, linear combination of functions of order statistics, and a rank combinatorial statistic.

Monte Carlo Simulation Of The Game Of Twenty-One, Douglas E. Loer

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The purpose of this paper is to demonstrate the application of computer simulation to the game of Twenty-One to predict a player's expected return from the game. Twenty-One has traditionally been one of the most popular casino games and has attracted much effort to accurately estimate the house's true advantage. Probability theory has been tried, but the thousands of different combinations of cards possible in all hands throughout the entire pack make it practically impossible to apply probability theory without overlooking some possibilities. For this reason, Twenty-One is a perfect candidate for simulation. By blocking several simulations, normal theory can …

Perturbation Of Periodic Boundary-Conditions, Larry Turyn

Mathematics and Statistics Faculty Publications

We consider perturbations of the problem (*) - x'' + bx = lambda ax, x(0) - x(1) = 0 = x'(0) - x'(1) both by changes of the boundary conditions and by addition of nonlinear terms. We assume that at lambda = lambda 0 there are two linearly independent solutions of the unperturbed problem (*) and that a(dot) is bounded away from zero. When only the boundary conditions are perturbed either the Hill’s discriminant or the method of Lyapunov–Schmidt reduces the problem to 0 = det ((lambda - lambda 0)A - epsilon …

Evidence Of Intrinsic Double Acceptor In Gaas, Phil Won Yu, W. C. Mithel, M. G. Mier, S. S. Li, Weizhen Wang

Mathematics and Statistics Faculty Publications

Acceptors present in undoped p‐type conducting GaAs have been studied with photoluminescence, temperature‐dependent Hall measurements, deep level transient spectroscopy, and spark source mass spectrometry. It is shown that p‐type conduction is due to presence of the shallow acceptor C_As and the cation antisite double acceptor Ga_As. The first and second ionization energies determined for Ga_As are 77 and 230 meV from the valence‐band edge.

Quasi-Triangular Matrices, Joanne Dombrowski

Mathematics and Statistics Faculty Publications

It is shown that there exist quasitriangular operators which cannot be represented as quasitriangular matrices.

Positive Perturbations Of Unbounded Operators, Joanne Dombrowski

Mathematics and Statistics Faculty Publications

This work studies the spectral properties of certain unbounded selfadjoint operators by considering positive perturbations of such operators and the unitary equivalence of the perturbed and unperturbed transformations. Conditions are obtained on the unitary operators implementing this equivalence which guarantee that the selfadjoint operators have an absolutely continuous part.

An Evaluation Of Truncated Sequential Test, Ryh-Thinn Chang

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The development of sequential analysis has led to the proposal of tests that are more economical in that the Average Sample Number (A. S. N.) of the sequential test is smaller than the sample size of the fixed sample test. Although these tests usually have a smaller A. S. N. than the equivelent fixed sample procedure, there still remains the possibility that an extremely large sample size will be necessary to make a decision. To remedy this, truncated sequential tests have been developed.

A method of truncation for testing a composite hypotheses is studied. This method is formed by mixing …

The Absolute Continuity Of Phase Operators, Joanne Dombrowski, G. H. Fricke

Mathematics and Statistics Faculty Publications

This paper studies the spectral properties of a class of operators known as phase operators which originated in the study of harmonic oscillator phase. Ifantis conjectured that such operators had no point spectrum. It was later shown that certain phase operators were, in fact, absolutely continuous and that all phase operators at least had an absolutely continuous part. The present work completes the discussion by showing that all phase operators are absolutely continuous.

An Evaluation Of Bartlett's Chi-Square Approximation For The Determinant Of A Matrix Of Sample Zero-Order Correlation Coefficients, Stephen M. Hattori

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The single equation least-squares regression model has been extensively studied by economists and statisticians alike in order to determine the problems which arise when particular assumptions are violated. Much literature is available in terms of the properties and limitations of the model. However, on the multicollinearity problem, there has been little research, and consequently, limited literature is available when the problem is encountered. Farrar & Glauber (1967) present a collection of techniques to use in order to detect or diagnose the occurrence of multicollinearity within a regression analysis. They attempt to define multicollinearity in terms of departures from a hypothesized …

A Monte Carlo Evaluation Of A Nonparametric Technique For Estimating The Hazard Function, Sheng Jia Lin

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

This research is primarily concerned with the estimation of the Hazard functions, the Hazard function is the failure rate at time t, and is defined as -R '(t)/R(t), so it plays an important role in Reliability.

In order to compare and evaluate the estimation methods, it is convenient to select one distribution in this research. Since the Weibull distribution is a useful distribution in Reliability, the Weibull distribution is used in this paper.

Analysis Of Contingency Tables, James Joseph Biundo

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Two methods of analyzing multi-dimensional frequency data are detailed.

The Second Order Exponential (SOE) model is applicable for dichotomous classifications. The distribution has two sets of parameters, ϴ_i's and ϴ_j's. The ϴ_i's are interpreted as the log of the odds of the marginal probabilities if no two factor relationships exist. Or if all ϴ_ij are not zero, then the ϴ_i's are analogous to a main effect in a 2^m factorial analysis, (m = number of factors or classifications). The ϴ_if's may be interpreted as a measure and direction …