Mathematics Commons^™

Berry-Esseen-Type Bounds For Signed Linear Rank Statistics With A Broad Range Of Scores, Munsup Seoh

Mathematics and Statistics Faculty Publications

The Berry-Esseen-type bounds of order N^−1/2 for the rate of convergence to normality are derived for the signed linear rank statistics under the hypothesis of symmetry. The results are obtained with a broad range of regression constants and scores (allowed to be generated by discontinuous score generating functions, but not necessarily) restricted by only mild conditions, while almost all previous results are obtained with continuously differentiable score generating functions. Furthermore, the proof is very short and elementary, based on the conditioning argument.

Notions Of Relative Ubiquity For Invariant Sets Of Relational Structures, Paul Bankston, Wim Ruitenburg

Mathematics, Statistics and Computer Science Faculty Research and Publications

Given a finite lexicon L of relational symbols and equality, one may view the collection of all L-structures on the set of natural numbers w as a space in several different ways. We consider it as: (i) the space of outcomes of certain infinite two-person games; (ii) a compact metric space; and (iii) a probability measure space. For each of these viewpoints, we can give a notion of relative ubiquity, or largeness, for invariant sets of structures on w. For example, in every sense of relative ubiquity considered here, the set of dense linear orderings on w is …

Oscillations In Lotka-Volterra Systems Of Chemical Reactions, Roger H. Hering

Mathematics and Statistics Faculty Research & Creative Works

For a chemical reaction system modeled by x =k₁Ax -k₂x² -k₃xy +k₄y², y =k₃xy -k₄y² -k₅y +k₆B, it is shown that for each positive choice of parameters k₁A, B there exists a unique stationary state which is globally asymptotically stable in the positive quadrant. A criterion for the non-existence of periodic solutions is given for the generalized Lotka-Volterra system:x = f(x)h(x, y), y. © 1990 J.C. Baltzer AG, Scientific Publishing Company.

Taxonomies Of Model-Theoretically Defined Topological Properties, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

A topological classification scheme consists of two ingredients: (1) an abstract class K of topological spaces; and (2) a "taxonomy", i.e. a list of first order sentences, together with a way of assigning an abstract class of spaces to each sentence of the list so that logically equivalent sentences are assigned the same class.K, is then endowed with an equivalence relation, two spaces belonging to the same equivalence class if and only if they lie in the same classes prescribed by the taxonomy. A space X in K is characterized within the classification scheme if whenever Y _{E …}

Bimodules Over Cartan Subalgebras, Richard Mercer

Mathematics and Statistics Faculty Publications

Given a Cartan subalgebra A of a non Neumann algebra M, the techniques of Feldman and Moore are used to analyze the partial isometries v in M such that v* Av is contained in A. Orthonormal bases for M consisting of such partial isometries are discussed, and convergence of the resulting generalized fourier series is shown to take place in the Bures A-topology. The Bures A-topology is shown to be equivalent to the strong topology on the unit ball of M. These ideas are applied to A-bimodules and to give a simplified and intuitive proof of the Spectral Theorem …

On The Equivalence Of The Operator Equations Xa + Bx = C And X - P(-B)Xp(A)(-1) = W In A Hilbert-Space, P A Polynomial, Tapas Mazumdar, David Miller

Mathematics and Statistics Faculty Publications

We consider the solution of (*) XA+BX = C for bounded operators A,B,C and X on a Hilbert space, A normal. We establish the existence of a polynomial p and a bounded operator W with the property that the unique solution X of (*) also solves X − p(−B)Xp(A)⁻¹ = W uniquely. A known iterative algorithm can be applied to the latter equation to solve (*).

A Statistical Theory Of Digital Circuit Testability, Sharad C. Seth, Vishwani D. Agrawal, Hassan Farhat

Mathematics Faculty Publications

When test vectors are applied to a circuit, the fault coverage increases. The rate of increase, however, could be circuit dependent. A relation between the average fault coverage and circuit testability is developed in this paper. The statistical formulation allows computation of coverage for deterministic and random vectors. We discuss the following applications of this analysis: determination of circuit testability from fault simulation, coverage prediction from testability analysis, prediction of test length, and test generation by fault sampling.

Spatial Critical Points Of Solutions Of A One-Dimensional Nonlinear Parabolic Problem, Larry Turyn

Mathematics and Statistics Faculty Publications

The number of spatial critical points is nonincreasing in time, for positive, analytic solutions of a scalar, nonlinear, parabolic partial differential equation in one space dimension. While proving this, we answer the question: What happens to a critical point which loses simplicity?

Robustness & Precision Of Parametric & Distribution-Free Tolerance Limits For Two Lifetime Distributions, Wei Kei Shiue, Lee J. Bain

Mathematics and Statistics Faculty Research & Creative Works

Exact parametric tolerance limits or confidence limits on reliability are not available for the gamma distribution, and it is, difficult to determine approximate methods which are accurate for all parameter values. The precision lost by using the distribution-free tolerance-limit method based on the first order statistic, compared to using an approximate gamma tolerance limit method is studied. The robustness of the approximate gamma tolerance limit when the true model is Weibull and the robustness of a Weibull tolerance limit when the true model is gamma are also studied. The efficiency of the distribution-free method ranges from about 0.60 to 0.90 …

Periodic Points For Homeomorphisms Of Hereditarily Decomposable Chainable Continua, W. T. Ingram

Mathematics and Statistics Faculty Research & Creative Works

In this paper it is shown that homeomorphisms of hereditarily decomposable chainable continua cannot have periodic points whose periods are not powers of two. Examples show that for each power of two there is a hereditarily decomposable chainable continuum and a homeomorphism of it which has a periodic point of period that power of two. © 1989 American Mathematical Society.

Sharp Lower Bounds For A Generalized Jensen Inequality, A. K. Rigler, S. Y. Trimble, R. S. Varga

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

A Theory Of Testability With Application To Fault Coverage Analysis, Sharad Seth, Vishwani Agrawal, Hassan Farhat

Mathematics Faculty Publications

When test vectors are applied to a circuit, the fault coverage increases. The rate of increase, however, could be circuit-dependent. In fact, the actual rise of fault coverage depends on the characteristics of vectors, as well as, on the circuit. The paper shows that the average fault coverage can be computed from circuit testability. A relationship between fault coverage and circuit testability is derived. The mathematical formulation allows computation of coverage for deterministic and random vectors. Applications of this analysis include: determination of circuit testability from fault simulation, coverage prediction from testability analysis, prediction of test length, and test generation …

Pixley-Roy Hyperspaces Of Ω-Graphs, Joe Mashburn

Mathematics Faculty Publications

The techniques developed by Wage and Norden are used to show that the Pixley-Roy hyperspaces of any two ω-graphs are homeomorphic. The Pixley-Roy hyperspaces of several subsets of Rⁿ are also shown to be homeomorphic.

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.

Impedance Controlled Connector Interface, Stephen L. Clark

Mathematics and Statistics Faculty Research & Creative Works

A connector interface for electrically mating a multi-row connector with a printed circuit board is defined by a flex circuit in the form of laminated polyimide layers having conductive traces for each interconnect pair with connection fields at the opposite ends of the traces for electrical connection to the terminal pins on the connector and the conductive pads or pins on the circuit board. The conductive traces are all of equal length to provide equal resistance and impedance paths for each of the circuit interconnects.

Concerning Periodic Points In Mappings Of Continua, W. (William) T. (Thomas) Ingram

Mathematics and Statistics Faculty Research & Creative Works

In this paper we present some conditions which are sufficient for a mapping to have periodic points. © 1988 American Mathematical Society.

Computer Science—A Mathematical Science And Accreditation, Frank Garnett Walters

Mathematics and Statistics Faculty Research & Creative Works

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.

Recruiting More Computer Science Students - What To Do After The "Glamour" Has Gone Away?, William E. Mcbride, James Calhoun, James Richards, Harriet Taylor, Frank Garnett Walters

Mathematics and Statistics Faculty Research & Creative Works

The moderator will first focus on the question: "Are enrollments actually declining in computer science programs across this country?" He will report the results of his surveys which indicate there has been a definite downturn in enrollment over the past two years. The panelists will then discuss what is being done at their schools to recruit students and to meet this new challenge of declining enrollments.

Recruiting More Computer Science Students—What To Do After The “Glamour” Has Gone Away?, William E. Mcbride, James Calhoun, James L. Richards, Harriet G. Taylor, Frank Garnett Walters

Mathematics and Statistics Faculty Research & Creative Works

The moderator will first focus on the question: "Are enrollments actually declining in computer science programs across this country?" He will report the results of his surveys which indicate there has been a definite downturn in enrollment over the past two years. The panelists will then discuss what is being done at their schools to recruit students and to meet this new challenge of declining enrollments. © 1988, ACM. All rights reserved.

Structure Of Fourier And Fourier-Stieltjes Coefficients Of Series With Slowly Varying Convergence Moduli, Časlav V. Stanojević

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

A Fixed Point Theorem Revisited, Alberta Bollenbacher, Troy L. Hicks

Mathematics and Statistics Faculty Research & Creative Works

A version of a theorem commonly referred to as Caristi's Theorem is given. It has an elementary constructive proof, and it includes many generalizations of Banach's fixed point theorem. Several examples illustrate the diversity that can occur. © 1988 American Mathematical Society.

Generalized Homogeneity Of Finite And Of Countable Topological Spaces, J. J. Charatonik, W. J. Charatonik

Mathematics and Statistics Faculty Research & Creative Works

Finite and countable topological spaces are investigated which are homogeneous, homogeneous with respect to open mappings or with respect to continuous ones. It is shown that for finite spaces all three concepts of homogeneity coincide, while for countable or for uncountable ones they are distinct. Some characterization of countable spaces that are homogeneous in either sense are found for the metric setting.

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

Mathematics and Statistics Faculty Publications

No abstract provided.

Periodic Solutions Of Volterra Integral Equations, Muhammad Islam

Mathematics Faculty Publications

Consider the system of equations

x(t)=f(t)+∫−∞tk(t,s)x(s)ds,           (1)

and

x(t)=f(t)+∫−∞tk(t,s)g(s,x(s))ds.        (2)

Existence of continuous periodic solutions of (1) is shown using the resolvent function of the kernel k. Some important properties of the resolvent function including its uniqueness are obtained in the process. In obtaining periodic solutions of (1) it is necessary that the resolvent of k is integrable in some sense. For a scalar convolution kernel k some explicit conditions are derived to determine whether or not the resolvent of k is integrable. Finally, the existence and uniqueness of continuous periodic solutions of (1) and (2) are obtained using the …

A Proposed C Language Binding For The Graphical Kernel System 3-D, M. G. Bolten, C. Y. Ho

Computer Science Technical Reports

This thesis introduces a proposed C language binding definition for the International standards Organization's draft international standard of the Graphical Kernel System-JD. This work augments the earlier C language binding of the two-dimensional version of the Graphical Kernel System commonly known as GKS. The proposed function interface will provide a basis for, if not a final, C language binding for the three-dimensional version of the Graphical Kernel System.

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.

Reduced Coproducts Of Compact Hausdorff Spaces, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

By analyzing how one obtains the Stone space of the reduced product of an indexed collection of Boolean algebras from the Stone spaces of those algebras, we derive a topological construction, the "reduced coproduct", which makes sense for indexed collections of arbitrary Tichonov spaces. When the filter in question is an ultrafilter, we show how the "ultracoproduct" can be obtained from the usual topological ultraproduct via a compactification process in the style of Wallman and Frink. We prove theorems dealing with the topological structure of reduced coproducts (especially ultracoproducts) and show in addition how one may use this construction to …

A Logic Programming Model Of The Game Of Sprouts, Ralph M. Butler, Selden Y. Trimble, Ralph W. Wilkerson

Computer Science Faculty Research & Creative Works

The Game of Sprouts Has Intrigued Mathematicians for Nearly Twenty Years. This Paper Describes a Representation Scheme Which Simplifies Much of the Geometry of the Game. using This Representation, We Develop a Prolog Program Which Will Play Sprouts. It is Hoped that the Program Will Prove to Be a Useful Research Tool in Finding the Key to a Winning Strategy for Sprouts and that the Representation Will Serve as a Useful Model for Studying Planar Graphs.