Statistics and Probability Commons^™

Network Key Management In A Large Distributed Environment, J. J. Stapleton, D. C. St. Clair

Computer Science Technical Reports

The technique of using encryption for protecting information in a network environment involves managing encryption keys within that same network. In large distributed networks the goal of achieving a secure environment requires a secure method of performing network key management. Network security, system security, and application security by means of data encryption rely on encryption keys remaining secret.

Both international and domestic standards organizations such as the International Organization for Standardization (ISO), the American National Standards Institute (ANSI), and the National Institute of Standards and Technology (NIST) address the issues of encryption through various standards. However, these standards discuss methods …

Optimization In Chemical Kinetics, Arthur T. Benjamin, Gordon J. Hogenson '92

All HMC Faculty Publications and Research

No abstract provided in this article.

Boundedness And Periodic Solutions In Infinite Delay Systems, Roger H. Hering

Mathematics and Statistics Faculty Research & Creative Works

Liapunov methods are used to give conditions ensuring that solutions of infinite delay equations are uniformly bounded and uniformly ultimately bounded with respect to unbounded (Cg) initial function spaces; and the connection to proving existence of periodic solutions is examined. Several examples illustrate the application of these results, especially to integrodifferential equations. © 1992.

Fixed Point Theorems For D-Complete Topological Spaces I, Troy L. Hicks

Mathematics and Statistics Faculty Research & Creative Works

Generalizations of Banach's fixed point theorem are proved for a large class of non-metric spaces. These include d-complete symmetric (semi-metric) spaces and complete quasi-metric spaces. The distance function used need not be symmetric and need not satisfy the triangular inequality. © 1992, Hindawi Publishing Corporation. All rights reserved.

Prediction Intervals, Based On Ranges And Waiting Times, For An Exponential Distribution, Laura Colangelo, Jagdish K. Patel

Mathematics and Statistics Faculty Research & Creative Works

This article contains two prediction intervals applicable to a 2-parameter as well as a 1-parameter exponential distribution. One can be used to predict a future sample range on the basis of an observed sample range. Appropriate prediction factors are tabulated. The other can be used to predict a waiting time between two future successive failures on the basis of an observed waiting time between two previous successive failures. © 1992 IEEE

Formation Of Clusters And Resolution Of Ordinal Attributes In Id3 Classification Trees, Chaman Sabharwal, Keith R. Hacke, Daniel C. St. Clair

Computer Science Faculty Research & Creative Works

Many learning systems have been designed to construct classification trees from a set of training examples. One of the most widely used approaches for constructing decision trees is the ID3 algorithm [Quinlan 1986]. Decision trees are ill-suited to handle attributes with ordinal values. Problems arise when a node representing an ordinal attribute has a branch for each value of the ordinal attribute in the training set. This is generally infeasible when the set of ordinal values is very large. Past approaches have sought to cluster large sets of ordinal values before the classification tree is constructed [Quinlan 1986; Lebowitz 1985; …

On The Asymptotic Behavior And Radial Symmetry Of Positive Solutions Of Semilinear Elliptic Equations In Rn. I. Asymptotic Behavior, Yi Li, Wei-Ming Ni

Mathematics and Statistics Faculty Publications

No abstract provided.

The Statistics Of Lotteries, Matthew Thomas Bremer

Honors Theses, 1963-2015

This project begins with the analysis of several existing lotteries in the state of Minnesota. The raw data of these lotteries are used to calculate the expected values of certain random variables in an effort to describe and compare the lotteries mathematically. Next, the different criteria that contribute to a successful lottery are described and brought together. Finally, via mathematical modeling and computer simulation, a new lottery proposal is presented with the claim that it is superior to existing lotteries from an administrative standpoint.

Boundary Velocity Control Of Incompressible-Flow With An Application To Viscous Drag Reduction, Max D. Gunzberger, Lisheng Hou, Tom Svobodny

Mathematics and Statistics Faculty Publications

An optimal boundary control problem for the Navier-Stokes equations is presented. The control is the velocity on the boundary, which is constrained to lie in a closed, convex subset of H^1/2 of the boundary. A necessary condition for optimality is derived. Computations are done when the control set is actually finite-dimensional, resulting in all application to viscous drag reduction.

Uniqueness Of Radial Solutions Of Semilinear Elliptic Equations, Man Kam Kwong, Yi Li

Mathematics and Statistics Faculty Publications

E. Yanagida recently proved that the classical Matukuma equation with a given exponent has only one finite mass solution. We show how similar ideas can be exploited to obtain uniqueness results for other classes of equations as well as Matukuma equations with more general coefficients.

On The Asymptotic Behavior And Radial Symmetry Of Positive Solutions Of Semilinear Elliptic Equations In R N Ii. Radial Symmetry, Yi Li, Wei-Ming Ni

Mathematics and Statistics Faculty Publications

The main purpose of this paper is to prove Theorems 1 and 2 of the preceding paper, Part I, together with their extensions and related symmetry results. To make this part essentially self-contained, we shall apply the method developed in Section 2 to equations with radial symmetry. Combining the asymptotic behavior and the "moving plane" technique, we are then able to obtain the desired results.

A Mathematical Model For Outgassing And Contamination, Weifu Fang, Meir Shillor, E. Stahel, E. Epstein, C. Ly, J. Mcniel, E. Zaron

Mathematics and Statistics Faculty Publications

A model for the mathematical description of the processes of outgassing and contamination in a vacuum system is proposed. The underlying assumptions are diffusion in the source, convection and diffusion in the cavity, mass transfer across the source-cavity interface, and a generalization of the Langmuir isotherm for the sorption kinetics on the target. Three approximations are considered where the asymptotic behavior of the model for large time is shown as well as the dependence and sensitivity of the model on some of the parameters. Some numerical examples of the full model are then presented together with a proof of the …

Boundary C1, Α Regularity For Variational Inequalities, Fang-Hua Lin, Yi Li

Mathematics and Statistics Faculty Publications

No abstract provided.

Analysis And Finite-Element Approximation Of Optimal-Control Problems For The Stationary Navier-Stokes Equations With Distributed And Neumann Controls, Max D. Gunzburger, L. Hou, Tom Svobodny

Mathematics and Statistics Faculty Publications

We examine certain analytic and numerical aspects of optimal control problems for the stationary Navier-Stokes equations. The controls considered may be of either the distributed or Neumann type; the functionals minimized are either the viscous dissipation or the L⁴-distance of candidate flows to some desired flow. We show the existence of optimal solutions and justify the use of Lagrange multiplier techniques to derive a system of partial differential equations from which optimal solutions may be deduced. We study the regularity of solutions of this system. Then, we consider the approximation, by finite element methods, of solutions of the …

Corrigendum To "Taxonomies Of Model-Theoretically Defined Topological Properties", Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

An error has been found in the cited paper; namely, Theorem 3.1 is false.

Linear Operators Strongly Preserving Polynomial Equations Over Antinegative Semirings, Sang-Gu Lee

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

We characterized the group of linear operators that strongly preserve r-potent matrices over the binary Boolean semiring, nonbinary Boolean semirings, and zero-divisor free antinegative semirings. We extended these results to show that linear operators that strongly preserve r-potent matrices are equivalent to those linear operators that strongly preserve the matrix polynomial equation p(X) = X. where p(X) = X^r₁ + X^r₂ + ... + X^r_t and r₁>r₂>...>r_t≥2.

In addition, we characterized the group of linear operators that strongly preserve r-cyclic matrices over the same semirings. We …

Incremental Learning Of Numeric Clusters In Classifier Systems, K. R. Hacke, D. C. St. Clair

Computer Science Technical Reports

Classifier systems are knowledge-based learning algorithms which take training instances as input and produce a set of rules as output Many classifier systems represent the knowledge they learn in the form of one or more decision trees. Accurate knowledgebase systems for a variety of domains have been constructed by generating decision trees using J. R. Quinlan's (1986) inductive algorithm ID3 and P. E. Utgoffs (1988) IDS. IDS is an incremental version of ID3.

Unfortunately, all these algorithms suffer from the inability to easily and effectively handle domains with numeric-valued attributes. Numeric attributes are those whose values are taken from a …

Modeling The Software Design Project, C. C. Dziedzic, D. C. St. Clair

Computer Science Technical Reports

The information content of the software design product as needed by various user communities is identified. Definitions of design in classical engineering disciplines are investigated and then applied specifically to the area of software design. The Entity-Relationship model is used to describe the information content of the software design product. All the relationship types and entity types that compose the design product are described in detail. The Military Standard: Defense System Software Development, DOD-STD-2167A, is analyzed to determine how it meets the relationship type requirements.

Incremental Learning Of Numeric Clusters In Classifier Systems, K. R. Hacke, D. C. St. Clair

Computer Science Technical Reports

Classifier systems are knowledge-based learning algorithms which take training instances as input and produce a set of rules as output Many classifier systems represent the knowledge they learn in the form of one or more decision trees. Accurate knowledgebase systems for a variety of domains have been constructed by generating decision trees using J. R. Quinlan's (1986) inductive algorithm ID3 and P. E. Utgoffs (1988) IDS. IDS is an incremental version of ID3.

Unfortunately, all these algorithms suffer from the inability to easily and effectively handle domains with numeric-valued attributes. Numeric attributes are those whose values are taken from a …

Modeling The Software Design Project, C. C. Dziedzic, D. C. St. Clair

Computer Science Technical Reports

The information content of the software design product as needed by various user communities is identified. Definitions of design in classical engineering disciplines are investigated and then applied specifically to the area of software design. The Entity-Relationship model is used to describe the information content of the software design product. All the relationship types and entity types that compose the design product are described in detail. The Military Standard: Defense System Software Development, DOD-STD-2167A, is analyzed to determine how it meets the relationship type requirements.

Estimation In A Marked Poisson Error Recapture Model Of Software Reliability, Rajan Gupta

Mathematics & Statistics Theses & Dissertations

Nayak's (1988) model for the detection, removal, and recapture of the errors in a computer program is extended to a larger family of models in which the probabilities that the successive programs produce errors are described by the tail probabilities of discrete distribution on the positive integers. Confidence limits are derived for the probability that the final program produces errors. A comparison of the asymptotic variances of parameter estimates given by the error recapture and by the repetitive-run procedure of Nagel, Scholz, and Skrivan (1982) is made to determine which of these procedures efficiently uses the test time.

Shadow Casting Phenomena At Newgrange, Frank Prendergast

Articles

A digital model of the Newgrange passage tomb and surrounding ring of monoliths known as the Great Circle is used to investigate sunrise shadow casting phenomena at the monument. Diurnal variation in shadow directions and lengths are analysed for their potential use in the Bronze Age to indicate the passage of seasonal time. Computer-aided simulations are developed from a photogrammetric survey to accurately show how three of the largest monoliths, located closest to the tomb entrance and archaeologically coded GC1, GC-1 and GC-2, cast their shadows onto the vertical face of the entrance kerbstone, coded K1. The phenomena occur at …

Analysis And Finite Element Approximation Of Optimal Control Problems For The Stationary Navier-Stokes Equations With Dirichlet Controls, M. D. Gunzburger, L. S. Hou, Tom Svobodny

Mathematics and Statistics Faculty Publications

Optimal control problems for the stationary Navier-Stokes equations are examined from analytical and numerical points of view. The controls considered are of Dirichlet type, that is, control is effected through the velocity field on (or the mass flux through) the boundary; the functionals minimized are either the viscous dissipation or the L4-distance of candidate flows to some desired flow. We show that optimal solutions exist and justify the use of Lagrange multiplier techniques to derive a system of partial differential equations from which optimal solutions may be deduced. We study the regularity of solutions of this system. The n, finite …

Sets Of Typical Subsamples, Joel Atkins, G.J Sherman

Mathematical Sciences Technical Reports (MSTR)

A group theoretic condition on a set of subsamples of a random sample from a continuous random variable symmetric about 0 is shown to be sufficient to provide typical values for 0.

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 (*).