Digital Commons Network^™

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

Theses Digitization Project

No abstract provided.

Riemannian Geometry Of Orbifolds, Joseph Ernest Borzellino

Mathematics

We investigate generalizations of many theorems of Riemannian geometry to Riemannian orbifolds. Basic definitions and many examples are given. It is shown that Riemannian orbifolds inherit a natural stratified length space structure. A version of Toponogov's triangle comparison theorem for Riemannian orbifolds is proven. A structure theorem for minimizing curves shows that such curves cannot pass through the singular set. A generalization of the Bishop relative volume comparison theorem is presented. The maximal diameter theorem of Cheng is generalized. A finiteness result and convergence result is proven for good Riemannian orbifolds, and the existence of a closed geodesic is shown …

A P-Adic Cohomological Method For The Weierstrass Family And Its Zeta Invariants, Goro Kato

Mathematics

After a survey of the Weierstrass family and cohomology, we compute the lifted homology of the Weierstrass family with compact supports so that explicit formulae for the zeta function of each fibre of the Weierstrass family may be obtained. The (co-)homology theory that we use is found in [L₁], [L₂] and [L₃]. Therefore, this article can be regarded as an application of Lubkin's p-adic theory of cohomologies to an algebraic family called the Weierstrass scheme over the ring (Z/pZ)[g₂,g₃). The cohomological background for the computation will be rather carefully exploited.

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.

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.

On Hamiltonian Line Graphs, Zhi-Hong Chen

Scholarship and Professional Work - LAS

No abstract provided.

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

Mathematics Technical Papers - Archive

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.

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.

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

Mathematics Technical Papers - Archive

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.

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 …

A Queueing System With A Fixed Accumulation Level, Random Server Capacity And Capacity Dependent Service Time, Jewgeni H. Dshalalow, Lotfi Tadj

Mathematics and System Engineering Faculty Publications

This paper introduces a bulk queueing system with a single server processing groups of customers of a variable size. If upon completion of service the queueing level is at least r the server takes a batch of size r and processes it a random time arbitrarily distributed. If the queueing level is less than r the server idles until the queue accumulates r customers in total. Then the server capacity is generated by a random number equals the batch size taken for service which lasts an arbitrarily distributed time dependent on the batch size. The objective of the paper is …

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.

A Binary Tree Decomposition Space Of Permutation Statistics, Don Rawlings

Mathematics

Based on the binary tree decomposition of a permutation, a natural vector space of permutation statistics is defined. Besides containing many well known permutation statistics, this space provides the general context for an archetypal recurrence relationship that contains most of the classic combinatorial sequences and some of their known generalizations.

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.

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.

Sound And Mathematics, Nancy Jean Parham

Theses Digitization Project

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

A Survey Of Prophet Inequalities In Optimal Stopping Theory, Theodore P. Hill, Robert P. Kertz

Research Scholars in Residence

This paper surveys the origin and development of what has come to be known as "prophet inequalities" in optimal stopping theory. Included is a review of all published work to date on these problems, including extensions and variations, descriptions and examples of the main proof techniques, and a list of a number of basic open problems.

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.

[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.

Splitting Of The Identity Component In Locally Compact Abelian Groups, Peter Loth

Mathematics Faculty Publications

In this paper we are concerned with the splitting of the identity component G₀ in an LCA group G. As Pontrjagin duality shows, this splitting is to the splitting of the torsion part tA in a discrete abelian group A, if G is assumed to be compact.

One-Sided Refinements Of The Strong Law Of Large Numbers And The Glivenko-Cantelli Theorem, David Gilat, Theodore P. Hill

Research Scholars in Residence

A one-sided refinement of the strong law of large numbers is found for which the partial weighted sums not only converge almost surely to the expected value, but also the convergence is such that eventually the partial sums all exceed the expected value. The new weights are distribution-free, depending only on the relative ranks of the observations. A similar refinement of the Glivenko-Cantelli theorem is obtained, in which a new empirical distribution function not only has the usual uniformly almost-sure convergence property of the classical empirical distribution function, but also has the property that all its quantiles converge almost surely. …

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 …

A Theorem On Reproducing Kernel Hilbert Spaces Of Pairs, Daniel Alpay

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we study reproducing kernel Hilbert and Banach spaces of pairs. These are a generalization of reproducing kernel Krein spaces and, roughly speaking, consist of pairs of Hilbert (or Banach) spaces of functions in duality with respect to a sesquilinear form and admitting a left and right reproducing kernel. We first investigate some properties of these spaces of pairs. It is then proved that to every function K(z, ω) analytic in z and ω* there is a neighborhood of the origin that can be associated with a reproducing kernel Hilbert space of pairs with left reproducing kernel K(z, …

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 …

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.

Proof In Law And Science, David H. Kaye

Faculty Scholarship

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 …

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?

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.