Open Access. Powered by Scholars. Published by Universities.®

Applied Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

Statistics and Probability

Institution
Keyword
Publication Year
Publication
Publication Type
File Type

Articles 811 - 840 of 992

Full-Text Articles in Applied Mathematics

Oif Spaces, Zoltan Balogh, Harold Bennett, Dennis Burke, Gary Gruenhage, David Lutzer, Joe D. Mashburn Jan 2000

Oif Spaces, Zoltan Balogh, Harold Bennett, Dennis Burke, Gary Gruenhage, David Lutzer, Joe D. Mashburn

Mathematics Faculty Publications

A base β of a space X is called an OIF base when every element of B is a subset of only a finite number of other elements of β. We will explore the fundamental properties of spaces having such bases. In particular, we will show that in T2 spaces, strong OIF bases are the same as uniform bases, and that in T3 spaces where all subspaces have OIF bases, compactness, countable compactness, or local compactness will give metrizability.

Go to article

Separation Property Of Solutions For A Semilinear Elliptic Equation, Yi Liu, Yi Li, Yinbin Deng Jan 2000

Separation Property Of Solutions For A Semilinear Elliptic Equation, Yi Liu, Yi Li, Yinbin Deng

Mathematics and Statistics Faculty Publications

In this paper, we study the following elliptic problem[formula]where K(x) is a given function in Cα(n\0) for some fixed α∈(0, 1), p>1 is a constant. Some existence, monotonicity and asymptotic expansion at infinity of solutions of (*) are discussed.

Go to article

Self-Consistency Algorithms, Thaddeus Tarpey Dec 1999

Self-Consistency Algorithms, Thaddeus Tarpey

Mathematics and Statistics Faculty Publications

The k-means algorithm and the principal curve algorithm are special cases of a self-consistency algorithm. A general self-consistency algorithm is described and results are provided describing the behavior of the algorithm for theoretical distributions, in particular elliptical distributions. The results are used to contrast the behavior of the algorithms when applied to a theoretical model and when applied to finite datasets from the model. The algorithm is also used to determine principal loops for the bivariate normal distribution.

Go to article

Hopf Bifurcation In Models For Pertussis Epidemiology, Herbert W. Hethcote, Yi Li, Zhujun Jing Dec 1999

Hopf Bifurcation In Models For Pertussis Epidemiology, Herbert W. Hethcote, Yi Li, Zhujun Jing

Mathematics and Statistics Faculty Publications

Pertussis (whooping cough) incidence in the United States has oscillated with a period of about four years since data was first collected in 1922. An infection with pertussis confers immunity for several years, but then the immunity wanes, so that reinfection is possible. A pertussis reinfection is mild after partial loss of immunity, but the reinfection can be severe after complete loss of immunity. Three pertussis transmission models with waning of immunity are examined for periodic solutions. Equilibria and their stability are determined. Hopf bifurcation of periodic solutions around the endemic equilibrium can occur for some parameter values in two …

Go to article

Generalized Averages For Solutions Of Two-Point Dirichlet Problems, Philip Korman, Yi Li Nov 1999

Generalized Averages For Solutions Of Two-Point Dirichlet Problems, Philip Korman, Yi Li

Mathematics and Statistics Faculty Publications

For very general two-point boundary value problems we show that any positive solution satisfies a certain integral relation. As a consequence we obtain some new uniqueness and multiplicity results.

Go to article

Random Fluctuations Of Convex Domains And Lattice Points, Alex Iosevich, Kimberly Kinateder Oct 1999

Random Fluctuations Of Convex Domains And Lattice Points, Alex Iosevich, Kimberly Kinateder

Mathematics and Statistics Faculty Publications

In this paper, we examine a random version of the lattice point problem.

Go to article

Axiomatic Approach For Quantification Of Image Resolution, Ge Wang, Yi Li Oct 1999

Axiomatic Approach For Quantification Of Image Resolution, Ge Wang, Yi Li

Mathematics and Statistics Faculty Publications

Image resolution is the primary parameter for performance characterization of any imaging system. In this work, we present an axiomatic approach for quantification of image resolution, and demonstrate that a good image resolution measure should be proportional to the standard deviation of the point spread function of an imaging system.

Go to article

Variational Principles For Average Exit Time Moments For Diffusions In Euclidean Space, Kimberly Kinateder, Patrick Mcdonald Sep 1999

Variational Principles For Average Exit Time Moments For Diffusions In Euclidean Space, Kimberly Kinateder, Patrick Mcdonald

Mathematics and Statistics Faculty Publications

Let D be a smoothly bounded domain in Euclidean space and let Xt be a diffusion in Euclidean space. For a class of diffusions, we develop variational principles which characterize the average of the moments of the exit time from D of a particle driven by Xt, where the average is taken overall starting points in D.

Go to article

Positive Solutions To Semilinear Problems With Coefficient That Changes Sign, Nguyen Phuong Cac, Juan A. Gatica, Yi Li Aug 1999

Positive Solutions To Semilinear Problems With Coefficient That Changes Sign, Nguyen Phuong Cac, Juan A. Gatica, Yi Li

Mathematics and Statistics Faculty Publications

No abstract provided.

Go to article

Solutions To A Nonlinear Drift-Diffusion Model Of Semiconductors, Weifu Fang, Kazufumi Ito May 1999

Solutions To A Nonlinear Drift-Diffusion Model Of Semiconductors, Weifu Fang, Kazufumi Ito

Mathematics and Statistics Faculty Publications

A nonlinear drift-diffusion model for semiconductors is analyzed to show the existence of non-vacuum global solutions and stationary solutions. The long time behavior of the solutions is studied by establishing the existence of an absorbing set and a compact attractor of the dynamical system. Parallel results on vacuum solutions are also obtained under weaker conditions on model parameters.

Go to article

Anticommuting Derivations, Steen Pedersen Apr 1999

Anticommuting Derivations, Steen Pedersen

Mathematics and Statistics Faculty Publications

We show that the re are no non-trivial closable derivations of a C*-algebra anticommuting with an ergodic action of a compact group, supposing that the set of squares is dense in the group. We also show that the re are no non-trivial closable densely defined rank one derivations on any C*-algebra.

Go to article

Invariant Measure For Diffusions With Jumps, Jose-Luis Menaldi, Maurice Robin Feb 1999

Invariant Measure For Diffusions With Jumps, Jose-Luis Menaldi, Maurice Robin

Mathematics Faculty Research Publications

Our purpose is to study an ergodic linear equation associated to diffusion processes with jumps in the whole space. This integro-differential equation plays a fundamental role in ergodic control problems of second order Markov processes. The key result is to prove the existence and uniqueness of an invariant density function for a jump diffusion, whose lower order coefficients are only Borel measurable. Based on this invariant probability, existence and uniqueness (up to an additive constant) of solutions to the ergodic linear equation are established.

Go to article

Stability Of A Semilinear Cauchy Problem, Yi Liu, Yi Li, Yinbin Deng Jan 1999

Stability Of A Semilinear Cauchy Problem, Yi Liu, Yi Li, Yinbin Deng

Mathematics and Statistics Faculty Publications

A report of progress in linear and nonlinear partial differential equations, microlocal analysis, singular partial differential operators, spectral analysis and hyperfunction theory. The papers aretaken from a conference on partial differential equations and their applications, held in Wuhan.

Go to article

On The Decomposition Of Order-Separable Posets Of Countable Width Into Chains, Gary Gruenhage, Joe Mashburn Jan 1999

On The Decomposition Of Order-Separable Posets Of Countable Width Into Chains, Gary Gruenhage, Joe Mashburn

Mathematics Faculty Publications

partially ordered set X has countable width if and only if every collection of pairwise incomparable elements of X is countable. It is order-separable if and only if there is a countable subset D of X such that whenever p, q ∈ X and p < q, there is r ∈ D such that p ≤ r ≤ q. Can every order-separable poset of countable width be written as the union of a countable number of chains? We show that the answer to this question is "no" if there is a 2-entangled subset of IR, and "yes" under the Open Coloring Axiom.

Go to article

On The Exactness Of An S-Shaped Bifurcation Curve, Philip Korman, Yi Li Jan 1999

On The Exactness Of An S-Shaped Bifurcation Curve, Philip Korman, Yi Li

Mathematics and Statistics Faculty Publications

For a class of two-point boundary value problems we prove exactness of an S-shaped bifurcation curve. Our result applies to a problem from combustion theory, which involves nonlinearities like for .

Go to article

A Structural Result Of Irreducible Inclusions Of Type Iii Lambda Factors, Lambda Is An Element Of (0,1), Phan Loi Sep 1998

A Structural Result Of Irreducible Inclusions Of Type Iii Lambda Factors, Lambda Is An Element Of (0,1), Phan Loi

Mathematics and Statistics Faculty Publications

Given an irreducible inclusion of factors with finite index N ⊂ M, where M is of type IIIλ1/m, N of type IIIλ1/n, 0 < λ < 1, and m,n are relatively prime positive integers, we will prove that if N ⊂ M satisfies a commuting square condition, then its structure can be characterized by using fixed point algebras and crossed products of automorphisms acting on the middle inclusion of factors associated with N ⊂ M. Relations between N ⊂ M and a certain G-kernel on subfactors are also discussed.

Go to article

Evolution Of Mixed-State Regions In Type-Ii Superconductors, Chaocheng Huang, Tom Svobodny Jul 1998

Evolution Of Mixed-State Regions In Type-Ii Superconductors, Chaocheng Huang, Tom Svobodny

Mathematics and Statistics Faculty Publications

A mean-field model for dynamics of superconducting vortices is studied. The model, consisting of an elliptic equation coupled with a hyperbolic equation with discontinuous initial data, is formulated as a system of nonlocal integrodifferential equations. We show that there exists a unique classical solution in C1+α(Ω0) for all t > Ω, where Ω0 is the initial vortex region that is assumed to be in C1+α. Consequently, for any time t, the vortex region Ωt is of C1+α, and the vorticity is in Cα(Ωt).

Go to article

Perturbed Hamiltonian System Of Two Parameters With Several Turning Points, Myeong Joon Ann Jun 1998

Perturbed Hamiltonian System Of Two Parameters With Several Turning Points, Myeong Joon Ann

Dissertations

No abstract provided.

Go to article

Orthogonal Harmonic Analysis Of Fractal Measures, Palle Jorgensen, Steen Pedersen Jan 1998

Orthogonal Harmonic Analysis Of Fractal Measures, Palle Jorgensen, Steen Pedersen

Mathematics and Statistics Faculty Publications

We show that certain iteration systems lead to fractal measures admitting an exact orthogonal harmonic analysis.

Go to article

Averaged Motion Of Charged Particles In A Curved Strip, Avner Friedman, Chaocheng Huang Dec 1997

Averaged Motion Of Charged Particles In A Curved Strip, Avner Friedman, Chaocheng Huang

Mathematics and Statistics Faculty Publications

This paper is concerned with the motion of electrically charged particles in a "curved" infinite strip.

Go to article

On The Product Of Two Generalized Derivations, Mohamed Barraa, Steen Pedersen Sep 1997

On The Product Of Two Generalized Derivations, Mohamed Barraa, Steen Pedersen

Mathematics and Statistics Faculty Publications

Two elements A and B in a ring R determine a generalized derivation deltaA,B on R by setting δA,B(X) = AX - XA for any X in R. We characterize when the product δC,DδA,B is a generalized derivation in the cases when the ring R is the algebra of all bounded operators on a Banach space epsilon, and when R is a C*-algebra U. We use the se characterizations to compute the commutant of the range of δA,B.

Go to article

Hypersurfaces In R-D And The Variance Of Exit Times For Brownian Motion, Kimberly Kinateder, Patrick Mcdonald Aug 1997

Hypersurfaces In R-D And The Variance Of Exit Times For Brownian Motion, Kimberly Kinateder, Patrick Mcdonald

Mathematics and Statistics Faculty Publications

Using the first exit time for Brownian motion from a smoothly bounded domain in Euclidean space, we define two natural functionals on the space of embedded, compact, oriented, unparametrized hypersurfaces in Euclidean space. We develop explicit formulas for the first variation of each of the functionals and characterize the critical points.

Go to article

Ergodic Control Of Reflected Diffusions With Jumps, Jose-Luis Menaldi, Maurice Robin Mar 1997

Ergodic Control Of Reflected Diffusions With Jumps, Jose-Luis Menaldi, Maurice Robin

Mathematics Faculty Research Publications

No abstract provided.

Go to article

Lyapunov Exponents Of Linear Stochastic Functional-Differential Equations. Ii. Examples And Case Studies, Salah-Eldin A. Mohammed, Michael K. R. Scheutzow Jan 1997

Lyapunov Exponents Of Linear Stochastic Functional-Differential Equations. Ii. Examples And Case Studies, Salah-Eldin A. Mohammed, Michael K. R. Scheutzow

Articles and Preprints

We give several examples and examine case studies of linear stochastic functional differential equations. The examples fall into two broad classes: regular and singular, according to whether an underlying stochastic semi-flow exists or not. In the singular case, we obtain upper and lower bounds on the maximal exponential growth rate $\overlineλ1$(σ) of the trajectories expressed in terms of the noise variance σ . Roughly speaking we show that for small σ, $\overlineλ1$(σ) behaves like -σ2 /2, while for large σ, it grows like logσ. In the regular case, it is shown that a discrete Oseledec …

Go to article

Travelling Fronts In Cylinders And Their Stability, Jerrold W. Bebernes, Comgming Li, Yi Li Jan 1997

Travelling Fronts In Cylinders And Their Stability, Jerrold W. Bebernes, Comgming Li, Yi Li

Mathematics and Statistics Faculty Publications

No abstract provided.

Go to article

Eigenfunction And Harmonic Function Estimates In Domains With Horns And Cusps, Michael Cranston, Yi Li Jan 1997

Eigenfunction And Harmonic Function Estimates In Domains With Horns And Cusps, Michael Cranston, Yi Li

Mathematics and Statistics Faculty Publications

No abstract provided.

Go to article

Existence And Bifurcation Of The Positive Solutions For A Semilinear Equation With Critical Exponent, Yinbin Deng, Yi Li Sep 1996

Existence And Bifurcation Of The Positive Solutions For A Semilinear Equation With Critical Exponent, Yinbin Deng, Yi Li

Mathematics and Statistics Faculty Publications

In this paper, we consider the semilinear elliptic equation[formula]Forp=2N/(N−2), we show that there exists a positive constantμ*>0 such that (∗)μpossesses at least one solution ifμ∈(0, μ*) and no solutions ifμ>μ*. Furthermore, (∗)μpossesses a unique solution whenμ=μ*, and at least two solutions whenμ∈(0, μ*) and 2<NN⩾6, under some monotonicity conditions onf((1.6)) we show that there exist two constants 0<μ**⩽μ**<μ* such that problem (∗)μ …

Go to article

Self-Consistency: A Fundamental Concept In Statistics, Thaddeus Tarpey, Bernard Flury Aug 1996

Self-Consistency: A Fundamental Concept In Statistics, Thaddeus Tarpey, Bernard Flury

Mathematics and Statistics Faculty Publications

The term ''self-consistency'' was introduced in 1989 by Hastie and Stuetzle to describe the property that each point on a smooth curve or surface is the mean of all points that project orthogonally onto it. We generalize this concept to self-consistent random vectors: a random vector Y is self-consistent for X if E[X|Y] = Y almost surely. This allows us to construct a unified theoretical basis for principal components, principal curves and surfaces, principal points, principal variables, principal modes of variation and other statistical methods. We provide some general results on self-consistent random variables, give …

Go to article

Stability Analysis Of A Model For The Defect Structure Of Yba2cu3ox, Gregory Kozlowski, Tom Svobodny Apr 1996

Stability Analysis Of A Model For The Defect Structure Of Yba2cu3ox, Gregory Kozlowski, Tom Svobodny

Physics Faculty Publications

Unusual microstructures of YBa2Cu3Ox (123) crystals have been observed. These structures have been shown to pass very high transport currents. A model of the solidification of 123 from a melt with Y2BaCuO5 (211) inclusions indicates that the stability of the 123 interface can depend on the sizes of the 211 inclusions. The observed formations are interpreted in the light of this instability.

Go to article

On An Investment-Consumption Model With Transaction Costs, Marianne Akian, José Luis Menaldi, Agnès Sulem Jan 1996

On An Investment-Consumption Model With Transaction Costs, Marianne Akian, José Luis Menaldi, Agnès Sulem

Mathematics Faculty Research Publications

This paper considers the optimal consumption and investment policy for an investor who has available one bank account paying a fixed interest rate and n risky assets whose prices are log-normal diffusions. We suppose that transactions between the assets incur a cost proportional to the size of the transaction. The problem is to maximize the total utility of consumption. Dynamic programming leads to a variational inequality for the value function. Existence and uniqueness of a viscosity solution are proved. The variational inequality is solved by using a numerical algorithm based on policies, iterations, and multigrid methods. Numerical results are displayed …

Go to article

First Prev Next Last