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Mathematics

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1998

Articles 1 - 14 of 14

Full-Text Articles in Statistics and Probability

Complexity Reduction In State-Based Modeling, Martin Zwick Oct 1998

Complexity Reduction In State-Based Modeling, Martin Zwick

Systems Science Faculty Publications and Presentations

For a system described by a relation among qualitative variables (or quantitative variables "binned" into symbolic states), expressed either set-theoretically or as a multivariate joint probability distribution, complexity reduction (compression of representation) is normally achieved by modeling the system with projections of the overall relation. To illustrate, if ABCD is a four variable relation, then models ABC:BCD or AB:BC:CD:DA, specified by two triadic or four dyadic relations, respectively, represent simplifications of the ABCD relation. Simplifications which are lossless are always preferred over the original full relation, while simplifications which lose constraint are still preferred if the reduction of complexity more …

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Attractors For Non-Compact Semigroups Via Energy Equations, Ioana Moise, Ricardo Rosa, Xiaoming Wang Sep 1998

Attractors For Non-Compact Semigroups Via Energy Equations, Ioana Moise, Ricardo Rosa, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

The energy-equation approach used to prove the existence of the global attractor by establishing the so-called asymptotic compactness property of the semigroup is considered, and a general formulation that can handle a number of weakly damped hyperbolic equations and parabolic equations on either bounded or unbounded spatial domains is presented. as examples, three specific and physically relevant problems are considered, namely the flows of a second-grade fluid, the flows of a Newtonian fluid in an infinite channel past an obstacle, and a weakly damped, forced Korteweg-de Vries equation on the whole line.

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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.

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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).

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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.

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Spatial Estimates For Stochastic Flows In Euclidean Space, Salah-Eldin A. Mohammed, Michael K. R. Scheutzow Jan 1998

Spatial Estimates For Stochastic Flows In Euclidean Space, Salah-Eldin A. Mohammed, Michael K. R. Scheutzow

Articles and Preprints

We study the behavior for large |x| of Kunita-type stochastic flows φ(t, ω, x) on Rd, driven by continuous spatial semimartingales. For this class of flows we prove new spatial estimates for large |x|, under very mild regularity conditions on the driving semimartingale random field. It is expected that the results would be of interest for the theory of stochastic flows on noncompact manifolds as well as in the study of nonlinear filtering, stochastic functional and partial differential equations. Some examples and counterexamples are given.

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Further Properties Of An Extremal Set Of Uniqueness, David E. Grow, Matt Insall Jan 1998

Further Properties Of An Extremal Set Of Uniqueness, David E. Grow, Matt Insall

Mathematics and Statistics Faculty Research & Creative Works

Consider the circle group T = R mod 2_ as the interval [0, 1). Then each x 2 T has a binary expansion: x =P1 k=1 xk2−k where each xk is 0 or 1. Let S be the set of x with a binary expansionsuch that the number of 1's does not exceed the number of the leading zeros by more than one. The authors prove that the countable compact set S cannot be expressed as the union of a finite number of Dirichlet sets.

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Attractor Dimension Estimates For Two-Dimensional Shear Flows, Charles R. Doering, Xiaoming Wang Jan 1998

Attractor Dimension Estimates For Two-Dimensional Shear Flows, Charles R. Doering, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We study the large time behavior of boundary and pressure-gradient driven incompressible fluid flows in elongated two-dimensional channels with emphasis on estimates for their degrees of freedom, i.e., the dimension of the attractor for the solutions of the Navier-Stokes equations. for boundary driven shear flows and flux driven channel flows we present upper bounds for the degrees of freedom of the form ca Re3/2 where c is a universal constant, a denotes the aspect ratio of the channel (length/width), and Re is the Reynolds number based on the channel width and the imposed "outer" velocity scale. for fixed pressure …

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Atomoicity Of Mappings, J. J. Charatonik, W. J. Charatonik Jan 1998

Atomoicity Of Mappings, J. J. Charatonik, W. J. Charatonik

Mathematics and Statistics Faculty Research & Creative Works

A mapping f:X→Y between continua X and Y is said to be atomic at a subcontinuumK of the domain X provided that f(K) is nondegenerate and K=f-1(f(K)). The set of subcontinua at which a given mapping is atomic, considered as a subspace of the hyperspace of all subcontinua of X, is studied. The introduced concept is applied to get new characterizations of atomic and monotone mappings. Some related questions are asked.

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Arc Approximation Property And Confluence Of Induced Mappings, W. J. Charatonik Jan 1998

Arc Approximation Property And Confluence Of Induced Mappings, W. J. Charatonik

Mathematics and Statistics Faculty Research & Creative Works

We say that a continuum X has the arc approximation property if every subcontinuum K of X is the limit of a sequence of arcwise connected subcontinua of X all containing a fixed point of K. This property is applied to exhibit a class of continua Y such that confluence of a mapping f : X - Y implies confluence of the induced mappings 2^f : 2^x - @^y and C(f) : C(x) - C(y). The converse implications are studied and similar interrelations are considered for some other classes of mappings, related to confluent ones.

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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.

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Convergence Of Random Walks On The Circle Generated By An Irrational Rotation, Francis E. Su Jan 1998

Convergence Of Random Walks On The Circle Generated By An Irrational Rotation, Francis E. Su

All HMC Faculty Publications and Research

Fix . Consider the random walk on the circle which proceeds by repeatedly rotating points forward or backward, with probability , by an angle . This paper analyzes the rate of convergence of this walk to the uniform distribution under ``discrepancy'' distance. The rate depends on the continued fraction properties of the number . We obtain bounds for rates when is any irrational, and a sharp rate when is a quadratic irrational. In that case the discrepancy falls as (up to constant factors), where is the number of steps in the walk. This is the first example of a sharp …

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Exponential Dichotomy And Mild Solutions Of Nonautonomous Equations In Banach Spaces, Y. Latushkin, Timothy W. Randolph, R. Schnaubelt Jan 1998

Exponential Dichotomy And Mild Solutions Of Nonautonomous Equations In Banach Spaces, Y. Latushkin, Timothy W. Randolph, R. Schnaubelt

Mathematics and Statistics Faculty Research & Creative Works

We prove that the exponential dichotomy of a strongly continuous evolution family on a Banach space is equivalent to the existence and uniqueness of continuous bounded mild solutions of the corresponding inhomogeneous equation. This result addresses nonautonomous abstract Cauchy problems with unbounded coefficients. The technique used involves evolution semigroups. Some applications are given to evolution families on scales of Banach spaces arising in center manifolds theory. © 1998 Plenum Publishing Corporation.

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Some Harmonic N-Slit Mappings, Michael Dorff Jan 1998

Some Harmonic N-Slit Mappings, Michael Dorff

Mathematics and Statistics Faculty Research & Creative Works

The class SH consists of univalent, harmonic, and sense-preserving functions f in the unit disk, Δ, such that f = h+ḡ where h(z) = z + ∑2∞ akzk g(z) = ∑1∞ bkzk. SHO will denote the subclass with b1 = 0. We present a collection of n-slit mappings (n ≥ 2) and prove that the 2-slit mappings are in SH while for n ≥ 3 the mappings are in SHO. Finally, we show that these mappings establish the sharpness of a previous theorem by Clunie and Sheil-Small while disproving a conjecture about the inner mapping radius. ©1998 American Mathematical Society.

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