Physical Sciences and Mathematics Commons^™

On A Single-Server Queue With Fixed Accumulation Level, State Dependent Service, And Semi-Markov Modulated Input Flow, Gary Russell, Jewgeni H. Dshalalow

Mathematics and System Engineering Faculty Publications

The authors study the queueing process in a single-server queueing system with state dependent service and with the input modulated by a semi-Markov process embedded in the queueing process. It is also assumed that the server capacity is r≥1 and that any service act will not begin until the queue accumulates at least r units. In this model, therefore, idle periods also depend upon the queue length. The authors establish an ergodicity criterion for the queueing process and evaluate explicitly its stationary distribution and other characteristics of the system, such as the mean service cycle, intensity of the system, intensity …

Proof In Law And Science, David H. Kaye

Journal Articles

This article addresses proof in both science and law. Both disciplines utilize proof of facts and proof of theories, but for different purposes and, consequently, in different ways. Some similarities exist, however, in how both disciplines use a series of premises followed by a conclusion to form an argument, and thus constitute a logic. This article analyzes the ways in which legal logic and scientific logic differ. Finding facts in law involves the same logic but quite different procedures than scientific fact-finding. Finding, or rather constructing, the law is also very different from scientific theorizing. But such differences do not …

Positive Solutions And J-Focal Points For Two-Point Boundary Value Problems, Paul W. Eloe, Darrel Hankerson, Johnny Henderson

Mathematics Faculty Publications

Cone theory is applied to a class of two-point boundary value problems for ordinary differential equations. Criteria for the existence of extremal points are obtained. These criteria are in terms of the existence of nontrivial solutions that lie in a cone, and in terms of the spectral radius of an associated compact linear operator.

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.

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.

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.

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.

A First Passage Problem And Its Applications To The Analysis Of A Class Of Stochastic Models, Lev M. Abolnikov, Jewgeni H. Dshalalow

Mathematics and System Engineering Faculty Publications

A problem of the first passage of a cumulative random process with generally distributed discrete or continuous increments over a fixed level is considered in the article as an essential part of the analysis of a class of stochastic models (bulk queueing systems, inventory control and dam models). Using direct probability methods the authors find various characteristics of this problem: the magnitude of the first excess of the process over a fixed level, the shortage before the first excess, the levels of the first and pre-first excesses, the index of the first excess and others. The results obtained are illustrated …

On Solvability Of Mixed Monotone Operator Equations With Applications To Mixed Quasimonotone Differential Systems Involving Discontinuities, Seppo V. Heikkilä, Martti Kumpulainen, V. Lakshmikantham

Mathematics and System Engineering Faculty Publications

In this paper we shall first study solvability of mixed monotone systems of operator equations in an ordered normed space by using a generalized iteration method. The obtained results are then applied to prove existence of coupled extremal quasisolutions of the systems of first and second order mixed quasimonotone differential equations with discontinuous right hand sides. Most of the results deal with systems in a Banach space ordered by a regular order cone.

An Investigation Of Iterated Function Systems And Fractals, David Wuolu

Honors Theses, 1963-2015

This paper explores some of the fascinating ideas involved in the generation of fractals. A linear algebra and strong calculus background is sufficient to understand the main ideas, however many of the proofs require analysis. I examined metric spaces, and in particular, the metric space H(X), which consists of the compact subsets of the space X. The completeness of this space is proven, enabling the construction of fractals as fixed points of contractive transformations on H(X). I use the classical Cantor set and the Sierpinski triangle to illustrate the construction of fractals using iterated function systems (IFS's) which consist of …

Rewriteability In Finite Groups, Judy Leavitt Walker, G. J. Sherman, Mark E. Walker

Department of Mathematics: Faculty Publications

What's the probability that two elements in a finite group commute? A formal answer,

Pr₂(G) = {(x, y) [element of] G² |xy = yx}| / |G|²

begs our next question. How many ordered pairs of elements of a finite group commute?

Sound And Mathematics, Nancy Jean Parham

Theses Digitization Project

Laplacian differential operator -- Vibrations of plucked strings and Hollow cylinders.

Contraction And Fixed Point Behavior Of Certain Linear Fractional Transformations, Haragewen Abraham Kinde

Theses Digitization Project

No abstract provided.

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; …

Introduction To Fractal Geometry: Definition, Concept, And Applications, Mary Bond

Presidential Scholars Theses (1990 – 2006)

It has become evident that fractals are not to be tied down to one compact, Webster-style, paragraph definition. The foremost qualities of fractals include self-similarity and dimensionality. One cannot help but appreciate the aesthetic beauty of computer generated fractal art. Beyond these characteristics, when trying to grasp the idea of fractal geometry, it is helpful to learn about its many applications. Fractal geometry is opening new doors for study and understanding in diverse areas such as science, art, and music. All of these facets of fractal geometry unite to provide an intriguing, and alluring, wardrobe for mathematics to wear, so …

Calculator Use And Incorporation In The Mathematics Classroom, Celia D. Denton

Capstone Research Projects

No abstract provided.

Ghost Circles For Twist Maps, Christophe Golé

Mathematics Sciences: Faculty Publications

Completely ordered invariant circles are found for the gradient of the energy flow in the state space, containing the critical sets corresponding to the Birkhoff orbits of all rotation number. In particular, these ghost circles contain the Aubry-Mather sets and map-invariant circles as completely critical sets when these exist. We give a criterion for a sequence of rational ghost circles to converge to a completely critical one.

Fractal (Reconstructive Analogue) Memory, David J. Stucki, Jordan B. Pollack

Mathematics Faculty Scholarship

This paper proposes a new approach to mental imagery that has the potential for resolving an old debate. We show that the methods by which fractals emerge from dynamical systems provide a natural computational framework for the relationship between the “deep” representations of long-term visual memory and the “surface” representations of the visual array, a distinction which was proposed by (Kosslyn, 1980). The concept of an iterated function system (IFS) as a highly compressed representation for a complex topological set of points in a metric space (Barnsley, 1988) is embedded in a connectionist model for mental imagery tasks. Two advantages …

K Dimension Continued Fractions And K Dimension Golden Ratios, Tascha Gwyn Yoder

Presidential Scholars Theses (1990 – 2006)

The following is an investigation dealing with continued fractions based on research conducted by Professor John C. Longnecker at the University of Northern Iowa.

Inference About The Transition-Point In Nbue-Nwue Or Nwue-Nbue Models, Subhash Kochar, D. L. Hawkins

Mathematics Technical Papers

e(t) < e(0) for [see pdf for notation]. If the inequalities for e(t) are reversed on these time intervals, it is called NWUE-NBUE. Using a characterization of such distributions in terms of the scaled total-time-on-test transform (STTT), we first give tests of exponentiality versus NBUE-NWUE or NWUE-NBUE with to unknown. This extends the work of Klefsjo (1989), who devised tests assuming that [see pdf for notation] is known. Then, assuming that F is either NBUE-NWUE or NWUE-NBUE, we give point estimates and asymptotic confidence intervals for to and [see pdf for notation]. The point estimates are asymptotically normal. We rely heavily on the theory of the empirical STTT process discussed in Csorgo, Csorgo and Horvith (1986). Two examples of real-data applications are provided.

Regression Trees Versus Stepwise Regression, Mary Christine Jacobs

UNF Graduate Theses and Dissertations

Many methods have been developed to determine the "appropriate" subset of independent variables in a multiple variable problem. Some of the methods are application specific while others have a wide range of uses. This study compares two such methods, Regression Trees and Stepwise Regression. A simulation using a known distribution is used for the comparison. In 699 out of 742 cases the Regression Tree method gave better predictors than the Stepwise Regression procedure.

An Exponent Bound For Relative Difference Sets In P-Groups, James A. Davis

Department of Math & Statistics Faculty Publications

An exponent bound is presented for abelian (p^i+j, pⁱ, p^i+j, pⁱ) relative difference sets: this bound can be met for i≤j.

On Hamiltonian Line Graphs, Zhi-Hong Chen

Scholarship and Professional Work - LAS

No abstract provided.

A Family Of Complexes Associated To An Almost Alternating Map, With Applications To Residual Intersections, Andrew R. Kustin, Bernd Ulrich

Faculty Publications

No abstract provided.

[Introduction To] The Vax Book: An Introduction, John R. Hubbard

Bookshelf

This book is an expansion of the book, A Gentle Introduction to the Vax System. The purpose of the book is to guide the novice, step-by-step, through the initial stages of learning to use the Digital Equipment Corporation's Vax computers, running under the VMS operating system (Version 5.0 or later). As a tutorial for beginners, this book assumes no previous experience with computers.

Projective And Non-Projective Systems Of First Order Nonlinear Differential Equations, Riad A. Rejoub

University of the Pacific Theses and Dissertations

It is well established that many physical and chemical phenomena such as those in chemical reaction kinetics, laser cavities, rotating fluids, and in plasmas and in solid state physics are governed by nonlinear differential equations whose solutions are of variable character and even may lack regularities. Such systems are usually first studied qualitatively by examining their temporal behavior near singular points of their phase portrait.

In this work we will be concerned with systems governed by the time evolution equations [see PDF for mathematical formulas]

The x_i may generally be considered to be concentrations of species in a chemical …

Intrinsic Chirality Of Complete Graphs, Erica Flapan, Nikolai Weaver

Pomona Faculty Publications and Research

A graph is said to be intrinsically chiral if no embedding of the graph in 3-space is respected by any ambient orientation-reversing homeomorphism. In this note, we characterize those complete graphs that are intrinsically chiral.

Completion Of Partial Operator Matrices, M.(Mihaly) Bakonyi

Dissertations, Theses, and Masters Projects

This work concerns completion problems for partial operator matrices. A partial matrix is an m-by-n array in which some entries are specified and the remaining are unspecified. We allow the entries to be operators acting between corresponding vector spaces (in general, bounded linear operators between Hilbert spaces). Graphs are associated with partial matrices. Chordal graphs and directed graphs with a perfect edge elimination scheme play a key role in our considerations. A specific choice for the unspecified entries is referred to as a completion of the partial matrix. The completion problems studied here involve properties such as: zero-blocks in certain …

Introduction To The Variational Bicomplex, Ian M. Anderson

Mathematics and Statistics Faculty Publications

The variational bicomplex was first introduced in the mid 1970's as a means of studying the inverse problem of the calculus of variations. This is the problem of characterizing those differential equations which are the Euler-Lagrange equations for a classical, unconstrained variational problem. Since then, the variational bicomplex has emerged as an effective means for studying other formal, differential-geometric aspects of the calculus of variations. Moreover, it has been shown that the basic variational bicomplex constructed to solve the inverse problem can be modified in various ways and that the cohomology groups associated with these modified bicomplexes are relevant to …

Completely Conservative And Covariant Numerical Methodology For N-Body Problems With Distance-Dependent Potentials, Donald Greenspan

Mathematics Technical Papers

We consider a general class of N-body problems for arbitrary, distance-dependent potentials. Completely conservative, covariant numerical methodology is established for their solution and an example is provided in which energy conservation is essential.