Digital Commons Network^™

Prediction Intervals Based On Partial Observations For Some Discrete Distributions, Lee J. Bain, Jagdish K. Patel

Mathematics and Statistics Faculty Research & Creative Works

Prediction limits of the following type are considered for the binomial, hypergeometric, and negative-binomial distributions. For the binomial distribution, suppose Xr successes have occurred in the first r trials, and based on this partial information it is desired to predict the total number of successes Xs (r < s), which will have occurred by trial s. Similar results are considered for the Poisson and negative-binomial distributions. The results are expressed in terms of well-known distributions which have been tabulated, but it is quite tedious to carry out the procedures based on available tables. Normal (Gaussian) approximations are provided which makes these methods convenient to apply. © 1993 IEEE

Prime Decomposition Of Knots In Lorenz-Like Templates, Michael C. Sullivan

Articles and Preprints

In [8] R.F. Williams showed that all knots in the Lorenz template are prime. His proof included the cases where any number of positive twists were added to one of the template’s branches. However [8] does give an example of a composite knot in a template with a single negative twist. Below we will show that in all the negative cases composite knots do exist, and give a mechanism for producing many examples. This problem was cited in a list of problems in dynamics in [1, problem 4.2].

Beauty Bare, Thomas Q. Sibley

Mathematics Faculty Publications

No abstract provided.

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.

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 …

Georg Cantor And The Battle For Transfinite Set Theory, Joseph Dauben

ACMS Journal 2004

Georg Cantor is well known as the founder of transfinite set theory. Equally celebrated, however, are the obstacles he faced in trying to win acceptance for his seemingly unorthodox views, his acrimonious differences with Leopold Kronecker and his unfortunate but progressively debilitating nervous breakdowns that some authors have linked directly to his many problems with set theory. Above all, Cantor's justification of set theory was all the more urgent because of Kronecker's critical denunciation of Cantor's mathematics. In tracing the evolution of Cantorian set theory, it is necessary to examine the opposition it met, and evaluate the technical, philosophical, psychological, …

Generalized Lame-Clapeyron Solution For A One-Phase Source Stefan Problem, José Luis Menaldi, Domingo Alberto Tarzia

Mathematics Faculty Research Publications

In this paper we obtain a generalized Lamé-Clapeyron solution for a one-phase Stefan problem with a particular type of sources. Necessary and sufficient conditions are given in order to characterize the source term which provides a unique solution. Some estimates on the free boundary and the temperature are presented. In particular, asymptotic expansions are given for small Stefan number and source.

Regularizing Effect For Integro-Differential Parabolic Equations, Maria Giovanna Garroni, José Luis Menaldi

Mathematics Faculty Research Publications

No abstract provided.

On Extremal Nonsupereulerian Graphs With Clique Number M, Zhi-Hong Chen

Scholarship and Professional Work - LAS

No abstract provided.

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.

Particle Simulation Of Large Carbon Dioxide Bubbles In Water, Donald Greenspan

Mathematics Technical Papers - Archive

A method which can be applied to simulate the motion of fluid drops within fluids is described through a detailed study of a prototype problem, that is, the motion of carbon dioxide bubbles in water. The mathematical formulation uses classical molecular type formulas and results in an n-body problem which is solved numerically. The rise of the bubbles is described, as is the motion of the water near the bubbles. For variety, both H2O water and D20 heavy water are considered. Only workstation computer capabilities are required.

The Sharp Lipschitz-Constants For Feasible And Optimal-Solutions Of A Perturbed Linear Program, Wu Li

Mathematics & Statistics Faculty Publications

The purpose of this paper is to derive the sharp Lipschitz constants for the feasible solutions and optimal solutions of a linear program with respect to right-hand-side perturbations. The Lipschitz constants are given in terms of pseudoinverses of submatrices of the matrices involved and are proven to be sharp.

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 …

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 Semiclassical, Dynamical Model Of Methane, Donald Greenspan

Mathematics Technical Papers - Archive

In this paper we present a semiclassical, dynamical model of the ground state methane molecule. The resulting 13-body problem is solved numerically using energy conserving methodology. The bond length and bond angle results are in complete agreement with experimental results.

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

Mathematics Technical Papers - Archive

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.

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

Mathematics Technical Papers - Archive

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.

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

Mathematics Technical Papers - Archive

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 - Archive

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.

On Matching Ann Structure To Problem Domain Structure, George G. Lendaris, Martin Zwick, Karl Mathia

Complex Systems Faculty Publications and Presentations

To achieve reduced training time and improved generalization with artificial neural networks (ANN, or NN), it is important to use a reduced complexity NN structure. A "problem" is defined by constraints among the variables describing it. If knowledge about these constraints could be obtained a priori, this could be used to reduce the complexity of the ANN before training it. Systems theory literature contains methods for determining and representing structural aspects of constrained data (these methods are herein called GSM, general systems method). The suggestion here is to use the GSM model of the given data as a pattern for …

Mathtype Version 3.0 A Software Review, David W. Clay

Mathematics and System Engineering Faculty Publications

Math Type is a mathematical equation editor in the Windows 3.1 environment. It lets you build up any kind of mathematical expression by using simple point-and-click techniques and then insert them into any Windows 3.1 compatible word processor; for instance, Word Perfect 5.1/5.2 for Windows, Word 2.0 for Windows, and AMI Pro 3.0 for Windows. An expression designed by Math Type can be transferred into a word processor by using standard Cut and Paste commands or by using Object Linking and Embedding techniques.

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.

Orbifolds Of Maximal Diameter, Joseph Borzellino

Mathematics

In this paper the Maximal Diameter Theorem of Riemannian geometry is proven for Riemannian orbifolds. In particular, it is shown that a complete Riemannian orbifold with Ricci curvature bounded below by (n−1) and diameter = π, must have constant sectional curvature 1, and must be a quotient of the sphere (Sn, can) of constant sectional curvature 1 by a subgroup of the orthogonal group O(n+1) acting discontinuously and isometrically on Sn. It is also shown that the singular locus of the orbifold forms a geometric barrier to the length minimization property of geodesics. We also extend the Bishop relative volume …

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 …

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.

The Proportion Of Fixed-Point-Free Elements Of A Transitive Permutation Group, Nigel Boston, Walter Dabrowski, Tuval Foguel, Paul J. Gies, Judy Leavitt Walker, David T. Ose, David A. Jackson

Department of Mathematics: Faculty Publications

In 1990 Hendrik W. Lenstra, Jr. asked the following question: if G is a transitive permutation group of degree n and A is the set of elements of G that move every letter, then can one find a lower bound (in terms of n) for f(G) = |A|/|G|? Shortly thereafter, Arjeh Cohen showed that 1/n is such a bound.

Lenstra’s problem arose from his work on the number field sieve. A simple example of how f(G) arises in number theory is the following: if h is an irreducible polynomial …

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 …

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 …

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 …