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Articles 1711 - 1740 of 2035

Full-Text Articles in Statistics and Probability

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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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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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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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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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.

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The Convergence Of The Solutions Of The Navier-Stokes Equations To That Of The Euler Equations, R. Temam, X. Wang Sep 1997

The Convergence Of The Solutions Of The Navier-Stokes Equations To That Of The Euler Equations, R. Temam, X. Wang

Mathematics and Statistics Faculty Research & Creative Works

In this article, we establish partial results concerning the convergence of the solutions of the Navier-Stokes equations to that of the Euler equations. Convergence is proved in space dimension two under a physically reasonable assumption, namely that the gradient of the pressure remains bounded at the boundary as the Reynolds number converges to infinity.

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Attractors For Nonautonomous Nonhomogeneous Navier-Stokes Equations, A. Miranville, X. Wang Sep 1997

Attractors For Nonautonomous Nonhomogeneous Navier-Stokes Equations, A. Miranville, X. Wang

Mathematics and Statistics Faculty Research & Creative Works

In this paper our aim is to derive an upper bound on the dimension of the attractor of the family of processes associated to the Navier-Stokes equations with nonhomogeneous boundary conditions depending on time. We consider two-dimensional flows with prescribed quasiperiodic (in time) tangential velocity at the boundary, and obtain an upper bound which is polynomial with respect to the viscosity.

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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.

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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.

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Infinite-Dimensional Hamilton-Jacobi-Bellman Equations In Gauss-Sobolev Spaces, Pao-Liu Chow, Jose-Luis Menaldi Aug 1997

Infinite-Dimensional Hamilton-Jacobi-Bellman Equations In Gauss-Sobolev Spaces, Pao-Liu Chow, Jose-Luis Menaldi

Mathematics Faculty Research Publications

We consider the strong solution of a semi linear HJB equation associated with a stochastic optimal control in a Hilbert space H: By strong solution we mean a solution in a L2(μ,H)-Sobolev space setting. Within this framework, the present problem can be treated in a similar fashion to that of a finite-dimensional case. Of independent interest, a related linear problem with unbounded coefficient is studied and an application to the stochastic control of a reaction-diffusion equation will be given.

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Elimination Of Supply Harmonics, Stephen L. Clark, P. Famouri, W. L. Cooley Jan 1997

Elimination Of Supply Harmonics, Stephen L. Clark, P. Famouri, W. L. Cooley

Mathematics and Statistics Faculty Research & Creative Works

The price of the extensive use of power electronic devices is becoming clear: increasing harmonic "pollution." The greater amount of harmonics being introduced into power distribution systems is of concern to both power consumers and power companies. First, a brief look is taken at background information which describes harmonic sources, effects, and characteristics. Then the evolution of the harmonics elimination approaches of current compensation and active filtering are discussed to give some insight into the directions that research is taking.

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On The Behavior Of The Solutions Of The Navier-Stokes Equations At Vanishing Viscosity, Roger Temam, Xiaoming Wang Jan 1997

On The Behavior Of The Solutions Of The Navier-Stokes Equations At Vanishing Viscosity, Roger Temam, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

In this article we establish partial results concerning the convergence of the solutions of the Navier-Stokes equations to that of the Euler equations. Namely, we prove convergence on any finite interval of time, in space dimension two, under a physically reasonable assumption. We consider the flow in a channel or the flow in a general bounded domain.

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Time Averaged Energy Dissipation Rate For Shear Driven Flows In ℝⁿ, Xiaoming Wang Jan 1997

Time Averaged Energy Dissipation Rate For Shear Driven Flows In ℝⁿ, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We drive an upper bound of the time averaged energy dissipation rate for boundary driven flows directly from the Navier-Stokes equations in ℝn. the upper bound is independent of the kinematic viscosity in accordance with Kolomogorov's scaling result. Copyright © 1997 Elsevier Science B.V. All rights reserved.

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Disconjugacy And Transformations For Symplectic Systems, Martin Bohner, Ondřej Došlý Jan 1997

Disconjugacy And Transformations For Symplectic Systems, Martin Bohner, Ondřej Došlý

Mathematics and Statistics Faculty Research & Creative Works

We examine transformations and diconjugacy for general symplectic systems which include as special cases linear Hamiltonian difference systems and Sturm-Liouville difference equations of higher order. We give a Reid roundabout theorem for these systems and also for reciprocal symplectic systems. Particularly, we investigate a connection between eventual disconjugacy of linear Hamiltonian difference systems and their reciprocals. Finally, we present a dinsconjugacy-preserving transformation of a Sturm-Liouville equation of higher order which transforms this equation into another one of the same order.

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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 …

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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.

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Eigenvalue And Eigenvector Determination For Damped Gyroscopic Systems, D. P. Malone, Don L. Cronin, Timothy W. Randolph Jan 1997

Eigenvalue And Eigenvector Determination For Damped Gyroscopic Systems, D. P. Malone, Don L. Cronin, Timothy W. Randolph

Mechanical and Aerospace Engineering Faculty Research & Creative Works

No abstract provided.

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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.

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Analysis Of Repeated Measures Data Under Circular Covariance, Andrew Montgomery Hartley Jan 1997

Analysis Of Repeated Measures Data Under Circular Covariance, Andrew Montgomery Hartley

Mathematics & Statistics Theses & Dissertations

Circular covariance is important in modelling phenomena in epidemiological, communications and numerous physical contexts. We introduce and develop a variety of methods which make it a more versatile tool. First, we present two classes of estimators for use in the presence of missing observations. Using simulations, we show that the mean squared errors of the estimators of one of these classes are smaller than those of the Maximum Likelihood (ML) estimators under certain conditions. Next, we propose and discuss a parsimonious, autoregressive type of circular covariance structure which involves only two parameters. We specify ML and other types of estimators …

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Some Global Bifurcation Results For Variational Inequalities, Vy Khoi Le Oct 1996

Some Global Bifurcation Results For Variational Inequalities, Vy Khoi Le

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

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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 …

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Some Applications Of Sophisticated Mathematics To Randomized Computing, Ronald I. Greenberg Aug 1996

Some Applications Of Sophisticated Mathematics To Randomized Computing, Ronald I. Greenberg

Computer Science: Faculty Publications and Other Works

No abstract provided.

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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 …

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Application Of Neural Networks To The Non-Destructive Testing Of Aluminum Cans, B. Balasubramaniam, Daniel .. Clair May 1996

Application Of Neural Networks To The Non-Destructive Testing Of Aluminum Cans, B. Balasubramaniam, Daniel .. Clair

Computer Science Technical Reports

Neural Networks are used to c lassify aluminum beverage containers as acceptable or non acceptable, depending upon their wall thicknesses. For each can, the thickness of the wall of the can at different points is measured using a non-destructive, ultra-sound technique. These measureI\}ents are then applied as inputs to the networks and the classification is provided as the output Three architectures, one unsupervised and two supervised, are tested. Their performances are analyzed and compared and the paradigm best suited to the problem is selected.

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Computer Assisted Control Of Robotic Rock Drilling Equipment Using Rock Face Image Mapping, William Robert Macneil, Peter (C. Y.)(Chung You) Ho May 1996

Computer Assisted Control Of Robotic Rock Drilling Equipment Using Rock Face Image Mapping, William Robert Macneil, Peter (C. Y.)(Chung You) Ho

Computer Science Technical Reports

Use of a totally unmanned mining robot is an ideal solution in removing humans from the dangerous underground mining environment. However, a complete autonomous system is a long way from reality. In the meantime, steps towards that goal can be made and integrated into current mining technology to take away some of the risk and stress from the miner making him more alert and the environment safer for those that do have to be undergroμnd. For our purposes here, the machine will be an automated robotic platform with the intelligence necessary for accurate placement of the drill tip on an …

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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.

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Evolutionary Semigroups And Dichotomy Of Linear Skew-Product Flows On Locally Compact Spaces With Banach Fibers, Y. Latushkin, S. Montgomery-Smith, Timothy W. Randolph Feb 1996

Evolutionary Semigroups And Dichotomy Of Linear Skew-Product Flows On Locally Compact Spaces With Banach Fibers, Y. Latushkin, S. Montgomery-Smith, Timothy W. Randolph

Mathematics and Statistics Faculty Research & Creative Works

We study evolutionary semigroups generated by a strongly continuous semi-cocycle over a locally compact metric space acting on Banach fibers. This setting simultaneously covers evolutionary semigroups arising from non-autonomous abstract Cauchy problems and C0-semigroups, and linear skew-product flows. The spectral mapping theorem for these semigroups is proved. The hyperbolicity of the semigroup is related to the exponential dichotomy of the corresponding linear skew-product flow. To this end a Banach algebra of weighted composition operators is studied. The results are applied in the study of: "roughness" of the dichotomy, dichotomy and solutions of nonhomogeneous equations, Green's function for a linear skew-product …

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Applications Of The Upside-Down Normal Loss Function, David Drain, A. M. Gough Jan 1996

Applications Of The Upside-Down Normal Loss Function, David Drain, A. M. Gough

Mathematics and Statistics Faculty Research & Creative Works

The upside-down normal loss function (UDNLF) is a weighted loss function that has accurately modeled losses in a product engineering context. The function''s scale parameter can be adjusted to account for the actual percentage of material failing to work at specification limits. Use of the function along with process history allows the prediction of expected loss-the average loss one would expect over a long period of stable process operation. Theory has been developed for the multivariate loss function (MUDNLF), which can be applied to optimize a process with many parameters-a situation in which engineering intuition is often ineffective. Computational formulae …

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