Mathematics Commons^™

The Support Of Measure-Valued Branching Processes In A Random Environment, Donald A. Dawson, Yi Li, Carl Mueller

Mathematics and Statistics Faculty Publications

We consider the one-dimensional catalytic branching process intro­duced by Dawson and Fleischmann, which is a modification of the super­ Brownian motion. The catalysts are given by a nonnegative infinitely divisible random measure with independent increments. We give sufficient conditions for the global support of the process to be compact, and sufficient conditions for noncompact global support. Since the catalytic process is related to the heat equation, compact support may be surprising. On the other hand, the super-Brownian motion has compact global support. We find that all nonnegative stable random measures lead to compact global support, and we give an example …

Stability Of Growing Front Of Yba(2)Cu(3)O(X) Superconductor In The Presence Of Pt And Ceo(2) Additions, Gregory Kozlowski, Tom Svobodny

Physics Faculty Publications

Distinctive microstructures of textured YBa₂Cu₃O_x (123) superconductors were examined by scanning electron microscopy and metallurgical microscopy. The samples were synthesized under a residual thermal gradient by using a modified melt textured growth on a Y₂BaCuO₅ (211) substrate. Also, the unidirectional solidification by a zone‐melting method was performed to fabricate 123 superconducting bars up to 12 cm long placed on the 211 substrate in the horizontal arrangement, with a growth rate R=0.5 mm/h and a temperature gradient of G=20 °C/cm (G/R=400 °C h/cm²). A ramping …

Population Genetics: Estimation Of Distributions Through Systems Of Non-Linear Differential Equations, Nacer E. Abrouk, Robert J. Lopez

Mathematical Sciences Technical Reports (MSTR)

In stochastic population genetics, the fundamental quantity used for describing the genetic composition of a Mendelian population is the gene frequency. The process of change in the gene frequency is generally modeled as a stochastic process satisfying a stochastic differential equation. The drift and diffusion coefficients in this equation reflect such mechanisms as mutation, selection, and migration that affect the population. Except in very simple cases, it is difficult to determine the probability law of the stochastic process of change in gene frequency. We present a method for obtaining approximations of this process, enabling us to study models more realistic …

Free-Boundary Problems For Potential And Stokes Flows Via Nonsmooth Analysis, Srdjan Stojanovic, Tom Svobodny

Mathematics and Statistics Faculty Publications

A new approach to some free boundary problems of the type of jets and cavities for potential flows is introduced. Both potential and Stokes flows are considered. The variable domain problems are relaxed so that they become nonsmooth optimization problems on fixed domains for somewhat singular state equations. State equations are considered, and multivalued generalized gradients of the variational functionals are studied. The method is constructive.

Principal Points And Self-Consistent Points Of Elliptical Distributions, Thaddeus Tarpey, Luning Li, Bernard Flury

Mathematics and Statistics Faculty Publications

In this paper we study principal points and self-consistent points of p-variate elliptical distributions. We also discuss implications of our results for the computation and estimation of principal points.

Periodicity And Indecomposability, William Thomas Ingram

Mathematics and Statistics Faculty Research & Creative Works

In this paper we characterize the existence of periodic points of odd period greater than one for unimodal mappings of an interval onto itself. The interesting juxtaposition of this condition with the occurrence in inverse limits of the well-known Brouwer-Janiszewski-Knaster continuum is explored. Also obtained is a characterization of indecomposability of certain inverse limits using a single unimodal bonding map. © 1995 American Mathematical Society.

Point-Valued Mappings Of Sets, Matt Insall

Mathematics and Statistics Faculty Research & Creative Works

Let X be a metric space and let CB(X) denote the closed bounded subsets of X with the Hausdorff metric. Given a complete subspace Y of CB(X), two fixed point theorems, analogues of results in [1], are proved, and examples are given to suggest their applicability in practice.

Brain State In A Convex Body, S. Hui, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

We study a generalization of the brain-state-in-a-box (BSB) model for a class of nonlinear discrete dynamical systems where we allow the states of the system to lie in an arbitrary convex body. The states of the classical BSB model are restricted to lie in a hypercube. Characterizations of equilibrium points of the system are given using the support function of a convex body. Also, sufficient conditions for a point to be a stable equilibrium point are investigated. Finally, we study the system in polytopes. The results in this special case are more precise and have simpler forms than the corresponding …

Asymptotic Analysis Of The Linearized Navier-Stokes Equations In A Channel, Roger Temam, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

In this article we study and derive explicit formulas for the boundary layers occurring in the linearized channel flows in the limit of small viscosity. Our study is based on classical boundary layer techniques combined with a new global treatment of the pressure term. © 1995, Khayyam Publishing.

Stability Properties And Integrability Of The Resolvent Of Linear Volterra Equations, Muhammad Islam, Paul W. Eloe

Mathematics Faculty Publications

Integrability of the resolvent and the stability properties of the zero solution of linear Volterra integrodifferential systems are studied. In particular, it is shown that, the zero solution is uniformly stable if and only if the resolvent is integrable in some sense. It is also shown that, the zero solution is uniformly asymptotically stable if and only if the resolvent is integrable and an additional condition in terms of the resolvent and the kernel is satisfied. Finally, the integrability of the resolvent is obtained under an explicit condition.

Singularity Of Super-Brownian Local Time At A Point Catalyst, Donald A. Dawson, Klaus Fleischmann, Yi Li, Carl Mueller

Mathematics and Statistics Faculty Publications

No abstract provided.

Smooth Densities For Degenerate Stochastic Delay Equations With Hereditary Drift, Denis R. Bell, Salah-Eldin A. Mohammed

Articles and Preprints

We establish the existence of smooth densities for solutions of R^d-valued stochastic hereditary differential systems of the form

dx(t) = H(t,x)dt + g(t, x(t - r))dW(t).

In the above equation, W is an n-dimensional Wiener process, r is a positive time delay, H is a nonanticipating functional defined on the space of paths in R^d and g is an n x d matrix-valued function defined on [0, ∞) x R^d, such that gg^* has …

Right Angle Electrical Connector And Insertion Tool Therefor, Stephen L. Clark, Glenn J. Pontius

Mathematics and Statistics Faculty Research & Creative Works

Disclosed is a multi-row right angle connector and a press block for installing the connector on a mounting substrate without soldering the contact pins. The connector legs comprise "eye of the needle" compliant interfaces that make electrical contact with the interior surfaces of the substrate's plated through holes. The press block is designed for use with a four-row right angle receptacle and locates rows 2, 3, and 4 on respective true grid positions and serves as a means for transmitting force from an external press to the contact pin tails. The contact tails in rows 2, 3, and 4 have …

A Note On Reordering Ordered Topological Spaces And The Existence Of Continuous, Strictly Increasing Functions, Joe Mashburn

Mathematics Faculty Publications

The origin of this paper is in a question that was asked of the author by Michael Wellman, a computer scientist who works in artificial intelligence at Wright Patterson Air Force Base in Dayton, Ohio. He wanted to know if, starting with Rn and its usual topology and product partial order, he could linearly reorder every finite subset and still obtain a continuous function from Rⁿ into R that was strictly increasing with respect to the new order imposed on Rⁿ. It is the purpose of this paper to explore the structural characteristics of ordered topological spaces …

Analysis Of Rule Sets Generated By The Cn2, Id3, And Multiple Convergence Symbolic Learning Methods, Elizabeth M. Boll, Daniel C. St. Clair

Mathematics and Statistics Faculty Research & Creative Works

The ability to learn has long been an area of interest to researchers in artificial intelligence. Symbolic inductive learning algorithms have evolved as a class of algorithms that can be used to learn concepts from training examples. The knowledge acquired is represented in the form of rules. Since symbolic learning methods develop distinctive sets of rules when given identical training data, questions arise as to the quality of the different rule sets produced. The results of this research provide techniques for comparing and analyzing rule sets. Numerous rule sets were generated using three well-known symbolic learning methods; Quinlan's ID3, Clark …

Ensuring The Satisfaction Of A Temporal Specification At Run-Time, Grace Tsai, Matt Insall, Bruce M. Mcmillin

Mathematics and Statistics Faculty Research & Creative Works

A responsive computing system is a hybrid of real-time, distributed and fault-tolerant systems. In such a system, severe consequences can occur if the run-time behavior does not conform to the expected behavior or specifications. In this paper, we present a formal approach to ensure satisfaction of the specifications in the operational environment as follows. First we specify behavior of the systems using Interval Temporal Logic (ITL). Next we give algorithms for trace checking of programs in such systems. Finally, we present a fully distributed run-time evaluation system which causally orders the events of the system during its execution and checks …