Physical Sciences and Mathematics Commons^™

A Bulk Queueing System Under N-Policy With Bilevel Service Delay Discipline And Start-Up Time, David C.R. Muh

Mathematics and System Engineering Faculty Publications

The author studies the queueing process in a single-server, bulk arrival and batch service queueing system with a compound Poisson input, bilevel service delay discipline, start-up time, and a fixed accumulation level with control operating policy. It is assumed that when the queue length falls below a predefined level r (≥ 1), the system, with server capacity Λ, immediately stops service until the queue length reaches or exceeds the second predefined accumulation level N(≥ r). Two cases, with N ≦ R and N ≥ R, are studied. The author finds explicitly the probability generating function of the stationary distribution of …

Beauty Bare, Thomas Q. Sibley

Mathematics Faculty Publications

No abstract provided.

On Infinite Delay Integral Equations Having Nonlinear Perturbations, Muhammad Islam

Mathematics Faculty Publications

The existence of bounded solutions and periodic solutions is studied for a system of infinite delay integral equations having nonlinear perturbations. An equivalent system of equations is obtained in terms of the resolvent kernel. Then the existence results are shown for the equivalent equations. Contraction principle, Schauder’s fixed point theorem, and monotone method are used in the study.

On The Positive Solutions Of The Matukuma Equation, Yi Li

Mathematics and Statistics Faculty Publications

No abstract provided.

Radial Symmetry Of Positive Solutions Of Nonlinear Elliptic Equations In Rn, Yi Li, Wei-Ming Ni

Mathematics and Statistics Faculty Publications

No abstract provided.

On Applications Of Little's Formula, Jewgeni H. Dshalalow

Mathematics and System Engineering Faculty Publications

In classical Little's formula L=λW used in queueing, the parameter λ serves as the intensity of the input process. In various applications this parameter may not be known. The author discusses important classes of modulated input processes, where this parameter can be found.

Converge, Version 3.0 Software For Algebra Through Calculus A Software Review, Lotfi Tadj

Mathematics and System Engineering Faculty Publications

Although intended for college teachers/students, Converge presents a feature that may interest all scientists: it allows an easy export of graphic files to most known word processors, specifically to the EXP, Version 2.1, a powerful WYSIWYG mathematical word processor.

Partitioning Inequalities In Probability And Statistics, Theodore P. Hill

Research Scholars in Residence

This article surveys fair-division or cake-cutting inequalities in probability statistics, including bisection inequalities, basic fairness inequalities, convexity tools, superfairness inequalities, and partitioning inequalities hypotheses testing and optimal stopping theory. The emphasis is measure theoretic, as opposed to game theoretic or economic, and a number of open problems in the area are mentioned.

Dynamics Of Population Growth, Jennifer Fess

Honors Theses, 1963-2015

The objective of this project was to examine the dynamics of population size based on age-specific life history parameters, as well as on genetic information. Two basic models were developed and exercised based upon the Leslie Matrix. the first model examined different life history patterns and their impact on the resulting dynamics of population growth. The second model expanded the first to include different genotypes. The life history parameters, fecundity and survivorship, were the same for both models. Four fecundity patterns represented age-specific fecundity that is monotonically increasing, monotonically decreasing, constant, and peaking at an intermediate age; three survivorship patterns …

On Quasi-Permutation Representations Of Finite Groups, J. M. Burns, Brendan Goldsmith, B. Hartley, R. Sandling

Articles

In [6], Wong defined a quasi-permutation group of degree n to be a finite group G of automorphisms of an n-dimensional complex vector space such that every element of G has non-negative integral trace. The terminology derives from the fact that if G is a finite group of permutations of a set ω of size n, and we think of G as acting on the complex vector space with basis ω, then the trace of an element g ∈ G is equal to the number of points of ω fixed by g. In [6] and [7], Wong studied the extent …

Bochner Integrals And Vector Measures, Ivaylo D. Dinov

Dissertations, Master's Theses and Master's Reports

This project extends known theorems for scalar valued functions to the context of Banach space valued functions. In particular, it contains generalizations of the classical theory of Lebesgue Integrals, complex measures, Radon-Nikodym theorem and Riesz Representation theorem. We explore some properties of functions whose domains are abstract Banach spaces, where the usual derivatives are replaced by Radon-Nikodym derivatives.

The first two Chapters are devoted to infinite dimensional measurable functions and the problem of integrating them. Most of the basic properties of Bochner integration are forced on it by the classical Lebesgue integration and the usual definition of measurability.

The Radon-Nikodym …

Variate Generation For Nonhomogeneous Poisson Processes With Time Dependent Covariates, Li-Hsing Shih, Lawrence Leemis

Arts & Sciences Articles

Algorithms are developed for generating a sequence of event times from a nonhomogeneous Poisson process that is influenced by the values of covariates that vary with time. Closed form expressions for random variate generation are shown for several baseline intensity and link functions. Two specific models linking the baseline process to the general model are considered: the accelerated time model and the proportional intensity model. In the accelerated time model, the cumulative intensity function of a nonhomogeneous Poisson process under covariate effects is [formula], where z is a covariate vector, ⋀0(t) is the baseline cumulative intensity function and …

Only Problems, Not Solutions! (Fourth Edition), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

An Elementary Approach To Some Analytic Asymptotics, Nicholas Pippenger

All HMC Faculty Publications and Research

Fredman and Knuth have treated certain recurrences, such as $M(0) = 1$ and\[M(n + 1) = \mathop {\min }\limits_{0 \leqslant k \leqslant n} (\alpha M(k) + \beta M(n - k)),\] where $\min (\alpha ,\beta ) > 1$, by means of auxiliary recurrences such as \[h(x) = \left\{ {\begin{array}{*{20}c} {0\qquad {\text{if}}0 \leqslant x < 1,} \\ {1 + h({x / \alpha }) + h({x / \beta }){\text{ if}}1 \leq x < \infty .} \\ \end{array} } \right.\] The asymptotic behavior of $h(x)$ as $x \to \infty $ with $\alpha $ and $\beta $ fixed depends on whether ${{\log \alpha } / {\log \alpha }}$ is rational or irrational.

The solution of Fredman and Knuth used analytic methods in both cases, and used in particular the Wiener–Ikehara Tauberian theorem in the irrational case. The author shows that a more explicit solution to these recurrences can be obtained by entirely elementary methods, based on a geometric interpretation of $h(x)$ …

A Bifurcation Theorem And Applications, Alfonso Castro, Jorge Cossio

All HMC Faculty Publications and Research

In this paper we give a sufficient condition on the nonlinear operator N for a point (λ, u) to be a local bifurcation point of equations of the form u + λL^-1(N(u)) = 0, where L is a linear operator in a real Hilbert space, L has compact inverse, and λ ∈ R is a parameter. Our result does not depend on the variational structure of the equation or the multiplicity of the eigenvalue of the linear operator L. Applications are made to systems of differential equations and to the existence of periodic solutions of nonlinear second order …

Topologies And Cotopologies Generated By Sets Of Functions, Alan Dow, Melvin Henriksen, Ralph Kopperman, R. G. Woods

All HMC Faculty Publications and Research

Let L be either [0, 1] or {0, 1} with the usual order. We study topologies on a set X for which the cozero-sets of certain subfamilies H of L^x form a base, and the properties imposed on such topologies by hypothesizing various order-theoretic conditions on H. We thereby obtain useful generalizations of extremely disconnected spaces, basically disconnected spaces, and F-spaces. In particular we use these tools to study the space of minimal prime ideals of certain commutative rings.

Projection Solutions Of Frobenius-Perron Operator Equations, Jiu Ding, Tien Tien Li

Faculty Publications

We construct in this paper the first order and second order piecewise polynomial finite approximation schemes for the computation of invariant measures of a class of nonsingular measurable transformations on the unit interval of the real axis. These schemes are based on the Galerkin’s projection method for L¹-spaces and are proved to be convergent for the class of Frobenius-Perron operators.

Analysis Of Factors Contributing To Environmental Activism: A Case Study Of Beach Clean-Up Participants, Elizabeth Ann Fuller

Marine Affairs Theses and Major Papers

This study was initiated to investigate factors which contribute to environmental activism. Towards this end, three hypotheses were investigated. First, it was hypothesized that beach clean-up participants would harbor pro-environmental attitudes. Second, it was hypothesized that participants would be relatively young, politically liberal, well-educated, and wealthy. Finally, it was hypothesized that particular types of social structure would influence a person's decision to participate in a beach clean-up. Specifically, it was hypothesized that participants at each clean-up location would be clique members and/or would be structurally equivalent. Surprising, it was revealed that there was virtually no difference in attitude between the …

Electron Attraction As A Mechanism For The Chemical Bond Of Ground State H2, Donald Greenspan

Mathematics Technical Papers

Previously, electron attraction, incorporated into classical models of the chemical bond, yielded correct bond lengths and vibrational frequencies for all the diatomic molecules through 02. In each case, maximally symmetric electron-nuclei configurations were utilized. In this paper, which concentrates only on ground state H2, it is shown that maximal symmetry is not necessary for the attainment of correct results.

A Temperature-Adjusted Ozone Attainment Criterion Based On Extreme Value Regression Analysis, D. L. Hawkins

Mathematics Technical Papers

We propose a new statistical methodology to adjust observed peak ozone levels to "normal" meteorology (say, temperatures) across the year for a given site. The adjusted ozone levels can be used to establish a yearly ozone attainment criterion without undue influence of meteorology. They can also be used to estimate ozone trends resistant to meteorological influences. The adjustment process is based on an extreme value regression model of the relationship between peak ozone, temperature and various precursors of ozone. The proposed temperature-adjustment criterion is applied to data for seven sites in Los Angeles County for each of the years 1989-1993, …

Particle Modelling Of A Jiggling Gel, Donald Greenspan

Mathematics Technical Papers

Computer generated conical gels are constructed using classical molecular type formulas. Gravity is included in the modeling. Illustrative examples of gel jiggling are described and discussed. Only workstation capabilities are required.

Beam Collapse As An Explanation Foranomalous Ocular Damage, James A. Powell, J. V. Moloney, A. C. Newell, R. A. Albanese

James A. Powell

The basic mathematical phenomena relevant to ocular damage caused by ultrashort laser pulses are discussed with the use of mathematical results and numerical modeling. The primary effects of nonlinear self-focusing and beam collapse are examined in the ocular safety context. Finite-time material response and group-velocity dispersion are discussed as possible mitigating factors. An argument is presented that indicates that the initial stages of beam collapse are essentially two-dimensional. Experiments are suggested that might help distinguish the most important contributing factors in the damage regime. The numerical methodology is detailed in an appendix.

An Efficient Presentation Of Pgl(2,P), Theresa Marie Hert

Theses Digitization Project

No abstract provided.

Weak-Star Limits On Polynomials And Their Derivatives, William T. Ross, Joseph A. Ball

Department of Math & Statistics Faculty Publications

Let μ and v be regular finite Borel measures with compact support in the real line ℝ and define the differential operator D :L ∞(μ) → L ∞(v) with domain equal to the polynomials P by Dp = p′. In this paper we will characterize the weak-star closure of the graph of D in ∞(μ) ⊕ ∞(y). As a consequence we will characterize when D is closable (i.e. the weak-star closure of G contains no non-zero elements of the form o ⊕ g) and when g is weak-star dense in L∞(μ) ⊕ …

Computational Problems With Binomial Failure Rate Model And Incomplete Common Cause Failure Reliability Data, Paul H. Kvam

Department of Math & Statistics Faculty Publications

In estimating the reliability of a system of components, it is ordinarily assumed that the component lifetimes are independently distributed. This assumption usually alleviates the difficulty of analyzing complex systems, but it is seldom true that the failure of one component in an interactive system has no effect on the lifetimes of the other components. Often, two or more components will fail simultaneously due to a common cause event. Such an incident is called a common cause failure (CCF), and is now recognized as an important contribution to system failure in various applications of reliability. We examine current methods for …

The Commutant Of A Certain Compression, William T. Ross

Department of Math & Statistics Faculty Publications

Let G be any bounded region in the complex plane and K Ϲ G be a simple compact arc of class C¹. Let A²(G\K) (resp. A²(G)) be the Bergman space on G\K (resp. G). Let S be the operator multiplication by z on A²(G\K) and C = P_N S│_N be the compression of S to the semi-invariant subspace N = A²(G\K) Ɵ A²(G). We show that the commutant of C* is the set of all operators …

A Summary Of Menon Difference Sets, James A. Davis, Jonathan Jedwab

Department of Math & Statistics Faculty Publications

A (v, k, λ) difference set is a k-element subset D of a group G of order v for which the multiset {d₁d₂^-1 : d_1,d₂ ∈ D, d₁ ≠ d₂} contains each nonidentity element of G exactly λ times. A difference set is called abelian, nonabelian or cyclic if the underlying group is. Difference sets a.re important in design theory because they a.re equivalent to symmetric (v, k, λ) designs with a regular automorphism group. Abelian difference sets arise naturally in …

On The Edge Arboricity Of A Random Graph, P. A. Catlin, Zhi-Hong Chen, E. M. Palmer

Scholarship and Professional Work - LAS

No abstract provided.

Computer Studies Of A Semiclassical Model Of The Water Molecule, Donald Greenspan

Mathematics Technical Papers

A semiclassical model of the water molecule is formulated in ground state as an eleven-body problem. The stiff system of dynamical, nonlinear, ordinary differential equations is solved numerically on a CRAY YMP supercomputer. An energy conservative, implicit numerical method is used in order to assure invariance of the ground state energy. From selected initial data, the results of three examples, each run for 12 billion time steps, are shown to be entirely consistent with experimental bond angle measurements.

Pseudobases In Direct Powers Of An Algebra, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

A subset P of an abstract algebra A is a pseudobasis if every function from P into A extends uniquely to an endomorphism on A. A is called K-free has a pseudobasis of cardinality K; A is minimally free if A has a pseudobasis. (The 0-free algebras are "rigid" in the strong sense; the 1-free groups are always abelian, and are precisely the additive groups of E-rings.) Our interest here is in the existence of pseudobases in direct powers A^I of an algebra A. On the positive side, if A is a rigid …