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Articles 331 - 360 of 537

Full-Text Articles in Statistics and Probability

A Semi-Implicit Scheme For Stationary Statistical Properties Of The Infinite Prandtl Number Model, Wenfang Cheng, Xiaoming Wang Dec 2008

A Semi-Implicit Scheme For Stationary Statistical Properties Of The Infinite Prandtl Number Model, Wenfang Cheng, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We propose a semisecret in time semi-implicit numerical scheme for the infinite Prandtl model for convection. Besides the usual finite time convergence, this scheme enjoys the additional highly desirable feature that the stationary statistical properties of the scheme converge to those of the infinite Prandtl number model at vanishing time stop. One of the key characteristics of the scheme is that it preserves the dissipativity of the infinite Prandtl number model uniformly in terms of the time stop. So far as wo know, this is the first rigorous result on convergence of stationary statistical properties of numerical schemes for infinite …

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Confluent Mappings And Arc Kelley Continua, W. J. Charatonik, Janusz R. Prajs, J. J. Charatonik Jul 2008

Confluent Mappings And Arc Kelley Continua, W. J. Charatonik, Janusz R. Prajs, J. J. Charatonik

Mathematics and Statistics Faculty Research & Creative Works

A Kelley continuum X, also called a continuum with the property of Kelley, such that, for each p X, each subcontinuum K containing p is approximated by arc-wise connected continua containing p, is called an arc Kelley continuum. A continuum homeomorphic to the inverse limit of locally connected continua with confluent bonding maps is said to be confluently LC-representable. The main subject of the paper is a study of deep connections between the arc Kelley continua and confluent mappings. It is shown that if a continuum X admits, for each ε > 0, a confluent ε-mapping onto a(n) (arc) Kelley continuum, …

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Generically There Is But One Self Homeomorphism Of The Cantor Set, Ethan Akin, Eli Glasner, Benjamin Weiss Jul 2008

Generically There Is But One Self Homeomorphism Of The Cantor Set, Ethan Akin, Eli Glasner, Benjamin Weiss

Mathematics and Statistics Faculty Research & Creative Works

We describe a self-homeomorphism R of the Cantor set X and then show that its conjugacy class in the Polish group H(X) of all homeomorphisms of X forms a dense Gδ subset of H(X). We also provide an example of a locally compact, second countable topological group which has a dense conjugacy class. © 2008 American Mathematical Society.

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The Detection Of Unsteady Flow Separation With Bioinspired Hair-Cell Sensors, Benjamin T. Dickinson, John R. Singler, Belinda A. Batten Jun 2008

The Detection Of Unsteady Flow Separation With Bioinspired Hair-Cell Sensors, Benjamin T. Dickinson, John R. Singler, Belinda A. Batten

Mathematics and Statistics Faculty Research & Creative Works

Biologists hypothesize that thousands of micro-scale hairs found on bat wings function as a network of air-flow sensors as part of a biological feedback flow control loop. In this work, we investigate hair-cell sensors as a means of detecting flow features in an unsteady separating flow over a cylinder. Individual hair-cell sensors were modeled using an Euler-Bernoulli beam equation forced by the fluid flow. When multiple sensor simulations are combined into an array of hair-cells, the response is shown to detect the onset and span of flow reversal, the upstream movement of the point of zero wall shear-stress, and the …

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Approximate Low Rank Solutions Of Lyapunov Equations Via Proper Orthogonal Decomposition, John R. Singler Jun 2008

Approximate Low Rank Solutions Of Lyapunov Equations Via Proper Orthogonal Decomposition, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

We present an algorithm to approximate the solution Z of a stable Lyapunov equation AZ + ZA* + BB* = 0 using proper orthogonal decomposition (POD). This algorithm is applicable to large-scale problems and certain infinite dimensional problems as long as the rank of B is relatively small. In the infinite dimensional case, the algorithm does not require matrix approximations of the operators A and B. POD is used in a systematic way to provide convergence theory and simple a priori error bounds.

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Stationary Statistical Properties Of Rayleigh-Bénard Convection At Large Prandtl Number, Xiaoming Wang Jun 2008

Stationary Statistical Properties Of Rayleigh-Bénard Convection At Large Prandtl Number, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

This is the third in a series of our study of Rayleigh-Bénard convection at large Prandtl number. Here we investigate whether stationary statistical properties of the Boussinesq system for Rayleigh-Bénard convection at large Prandtl number are related to those of the infinite Prandtl number model for convection that is formally derived from the Boussinesq system via setting the Prandtl number to infinity. We study asymptotic behavior of stationary statistical solutions, or in-variant measures, to the Boussinesq system for Rayleigh-Bénard convection at large Prandtl number. in particular, we show that the invariant measures of the Boussinesq system for Rayleigh-Bénard convection converge …

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Evaluating Statistical Methods Using Plasmode Data Sets In The Age Of Massive Public Databases: An Illustration Using False Discovery Rates, Gary L. Gadbury, Qinfang Xiang, Lin Yang, Stephen Barnes, Grier P. Page, David B. Allison Jun 2008

Evaluating Statistical Methods Using Plasmode Data Sets In The Age Of Massive Public Databases: An Illustration Using False Discovery Rates, Gary L. Gadbury, Qinfang Xiang, Lin Yang, Stephen Barnes, Grier P. Page, David B. Allison

Mathematics and Statistics Faculty Research & Creative Works

Plasmode is a term coined several years ago to describe data sets that are derived from real data but for which some truth is known. Omic techniques, most especially microarray and genome wide association studies, have catalyzed a new zeitgeist of data sharing that is making data and data sets publicly available on an unprecedented scale. Coupling such data resources with a science of plasmode use would allow statistical methodologists to vet proposed techniques empirically (as opposed to only theoretically) and with data that are by definition realistic and representative. We illustrate the technique of empirical statistics by consideration of …

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Property Of Kelley For The Cartesian Products And Hyperspaces, W. J. Charatonik, J. J. Charatonik Jan 2008

Property Of Kelley For The Cartesian Products And Hyperspaces, W. J. Charatonik, J. J. Charatonik

Mathematics and Statistics Faculty Research & Creative Works

A continuum X having the property of Kelley is constructed such that neither X × [0, 1], nor the hyperspace C(X), nor small Whitney levels in C(X) have the property of Kelley. This answers several questions asked in the literature.

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Iterated Oscillation Criteria For Delay Dynamic Equations Of First Order, B. Karpuz, O. Öcalan, Martin Bohner Jan 2008

Iterated Oscillation Criteria For Delay Dynamic Equations Of First Order, B. Karpuz, O. Öcalan, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

We obtain new sufficient conditions for the oscillation of all solutions of first-order delay dynamic equations on arbitrary time scales, hence combining and extending results for corresponding differential and difference equations. Examples, some of which coincide with well-known results on particular time scales, are provided to illustrate the applicability of our results.

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On The Asymptotic Integration Of Nonlinear Dynamic Equations, Elvan Akin, Smail Djebali, Toufik Moussaoui, Martin Bohner Jan 2008

On The Asymptotic Integration Of Nonlinear Dynamic Equations, Elvan Akin, Smail Djebali, Toufik Moussaoui, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

The purpose of this paper is to study the existence and asymptotic behavior of solutions to a class of second-order nonlinear dynamic equations on unbounded time scales. Four different results are obtained by using the Banach fixed point theorem, the Boyd and Wong fixed point theorem, the Leray-Schauder nonlinear alternative, and the Schauder fixed point theorem. For each theorem, an illustrative example is presented. The results provide unification and some extensions in the time scale setup of the theory of asymptotic integration of nonlinear equations both in the continuous and discrete cases

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Transition To Turbulence, Small Disturbances, And Sensitivity Analysis Ii: The Navier-Stokes Equations, John R. Singler Jan 2008

Transition To Turbulence, Small Disturbances, And Sensitivity Analysis Ii: The Navier-Stokes Equations, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

Recent research has shown that small disturbances in the linearized Navier-Stokes equations cause large energy growth in solutions. Although many researchers believe that this interaction triggers transition to turbulence in flow systems, the role of the nonlinearity in this process has not been thoroughly investigated. This paper is the second of a two part work in which sensitivity analysis is used to study the effects of small disturbances on the transition process. In the first part, sensitivity analysis was used to predict the effects of a small disturbance on solutions of a motivating problem, a highly sensitive one dimensional Burgers' …

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Transition To Turbulence, Small Disturbances, And Sensitivity Analysis I: A Motivating Problem, John R. Singler Jan 2008

Transition To Turbulence, Small Disturbances, And Sensitivity Analysis I: A Motivating Problem, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

For over 100 years, researchers have attempted to predict transition to turbulence in fluid flows by analyzing the spectrum of the linearized Navier-Stokes equations. However, for many simple flows this approach fails to match experimental results. Recently, new scenarios for transition have been proposed that are based on the interaction of the linearized equations of motion with small disturbances to the flow system. These new "mostly linear" theories have increased our understanding of the transition process, but the role of nonlinearity has not been explored in detail. This paper is the first of a two part work in which sensitivity …

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Asymptotic Behavior Of The Global Attractors To The Boussinesq System For Rayleigh-Bénard Convection At Large Prandtl Number, Xiaoming Wang Sep 2007

Asymptotic Behavior Of The Global Attractors To The Boussinesq System For Rayleigh-Bénard Convection At Large Prandtl Number, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We study asymptotic behavior of the global attractors to the Boussinesq system for Rayleigh-Bénard convection at large Prandtl number. in particular, we show that the global attractors to the Boussinesq system for Rayleigh-Bénard convection converge to that of the infinite-Prandtl- number model for convection as the Prandtl number approaches infinity. This offers partial justification of the infinite-Prandtl-number model for convection as a valid simplified model for convection at large Prandtl number even in the long-time regime. © 2006 Wiley Periodicals, Inc.

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Double Integral Calculus Of Variations On Time Scales, Gusein Sh. Guseinov, Martin Bohner Jul 2007

Double Integral Calculus Of Variations On Time Scales, Gusein Sh. Guseinov, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

We consider a version of the double integral calculus of variations on time scales, which includes as special cases the classical two-variable calculus of variations and the discrete two-variable calculus of variations. Necessary and sufficient conditions for a local extremum are established, among them an analogue of the Euler-Lagrange equation.

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On A Theorem Of Shchepin And Repovš Concerning The Smoothness Of Compacta, Ethan Akin, William Ott Jul 2007

On A Theorem Of Shchepin And Repovš Concerning The Smoothness Of Compacta, Ethan Akin, William Ott

Mathematics and Statistics Faculty Research & Creative Works

We show that a theorem of Shchepin and Repovš concerning the smoothness of compacta follows from the theory of semicontinuous relations. © 2007 Elsevier B.V. All rights reserved.

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Discrete Kato-Type Theorem On Inviscid Limit Of Navier-Stokes Flows, Wenfang Cheng, Xiaoming Wang Jun 2007

Discrete Kato-Type Theorem On Inviscid Limit Of Navier-Stokes Flows, Wenfang Cheng, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

The inviscid limit of wall bounded viscous flows is one of the unanswered central questions in theoretical fluid dynamics. Here we present a somewhat surprising result related to numerical approximation of the problem. More precisely, we show that numerical solutions of the incompressible Navier-Stokes equations converge to the exact solution of the Euler equations at vanishing viscosity and vanishing mesh size provided that small scales of the order of U in the directions tangential to the boundary are not resolved in the scheme. Here is the kinematic viscosity of the fluid and U is the typical velocity taken to be …

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Note On The Emergence Of Large Scale Coherent Structure Under Small Scale Random Bombardments: The Discrete Case, Andrew Majda, Xiaoming Wang Jun 2007

Note On The Emergence Of Large Scale Coherent Structure Under Small Scale Random Bombardments: The Discrete Case, Andrew Majda, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We continue our study on mathematical justification of the emergence of large-scale coherent structure in a two-dimensional fluid system under small scale random bombardments. We treat the case of small-scale random bombardments at discrete times which is different from our earlier work [Commun. Pure Appl. Math. 59, 467 (2006)], where we approximated the small-scale random kicks by a continuous in time random process. in the absence of geophysical effects, the large-scale structure emerging out of the small-scale random forcing is the same as the case of continuous in time forcing that we studied before. © 2007 American Institute of Physics.

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Balanced Proper Orthogonal Decomposition For Model Reduction Of Infinite Dimensional Linear Systems, John R. Singler, Belinda A. Batten Jun 2007

Balanced Proper Orthogonal Decomposition For Model Reduction Of Infinite Dimensional Linear Systems, John R. Singler, Belinda A. Batten

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we extend a method for reduced order model derivation for finite dimensional systems developed by Rowley to infinite dimensional systems. The method is related to standard balanced truncation, but includes aspects of the proper orthogonal decomposition in its computational approach. The method is also applicable to nonlinear systems. The method is applied to a convection diffusion equation.

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Periodic Solutions Of Functional Dynamic Equations With Infinite Delay, Li Bi, Meng Fan, Martin Bohner Mar 2007

Periodic Solutions Of Functional Dynamic Equations With Infinite Delay, Li Bi, Meng Fan, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

In this paper, sufficient criteria are established for the existence of periodic solutions of some functional dynamic equations with infinite delays on time scales, which generalize and incorporate as special cases many known results for differential equations and for difference equations when the time scale is the set of the real numbers or the integers, respectively. The approach is mainly based on the Krasnosel'skilatin small letter i with breve fixed point theorem, which has been extensively applied in studying existence problems in differential equations and difference equations but rarely applied in studying dynamic equations on time scales. This study shows …

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The Convolution On Time Scales, Gusein Sh. Guseinov, Martin Bohner Jan 2007

The Convolution On Time Scales, Gusein Sh. Guseinov, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

The main theme in this paper is an initial value problem containing a dynamic version of the transport equation. via this problem, the delay (or shift) of a function defined on a time scale is introduced, and the delay in turn is used to introduce the convolution of two functions defined on the time scale. In this paper, we give some elementary properties of the delay and of the convolution and we also prove the convolution theorem. Our investigation contains a study of the initial value problem under consideration as well as some results about power series on time scales. …

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Trench's Perturbation Theorem For Dynamic Equations, Stevo Stevic, Martin Bohner Jan 2007

Trench's Perturbation Theorem For Dynamic Equations, Stevo Stevic, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

We consider a nonoscillatory second-order linear dynamic equation on a time scale together with a linear perturbation of this equation and give conditions on the perturbation that guarantee that the perturbed equation is also nonoscillatory and has solutions that behave asymptotically like a recessive and dominant solutions of the unperturbed equation. As the theory of time scales unifies continuous and discrete analysis, our results contain as special cases results for corresponding differential and difference equations by William F. Trench.

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Oscillation And Nonoscillation Of Forced Second Order Dynamic Equations, Christopher C. Tisdell, Martin Bohner Jan 2007

Oscillation And Nonoscillation Of Forced Second Order Dynamic Equations, Christopher C. Tisdell, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

Oscillation and nonoscillation properties of second order Sturm-Liouville dynamic equations on time scales — for example, second order self-adjoint differential equations and second order Sturm-Liouville difference equations — have attracted much interest. Here we consider a given homogeneous equation and a corresponding equation with forcing term. We give new conditions implying that the latter equation inherits the oscillatory behavior of the homogeneous equation. We also give new conditions that introduce oscillation of the inhomogeneous equation while the homogeneous equation is nonoscillatory. Finally, we explain a gap in a result given in the literature for the continuous and the discrete case. …

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The Dynamics And Interaction Of Quantized Vortices In The Ginzburg-Landau-Schrödinger Equation, Yanzhi Zhang, Weizhu Bao, Qiang Du Jan 2007

The Dynamics And Interaction Of Quantized Vortices In The Ginzburg-Landau-Schrödinger Equation, Yanzhi Zhang, Weizhu Bao, Qiang Du

Mathematics and Statistics Faculty Research & Creative Works

The dynamic laws of quantized vortex interactions in the Ginzburg-Landau-Schrödinger equation (GLSE) are analytically and numerically studied. A review of the reduced dynamic laws governing the motion of vortex centers in the GLSE is provided. The reduced dynamic laws are solved analytically for some special initial data. By directly simulating the GLSE with an efficient and accurate numerical method proposed recently in [Y. Zhang, W. Bao, and Q. Du, Numerical simulation of vortex dynamics in Ginzburg-Landau-Schrödinger equation, European J. Appl. Math., to appear], we can qualitatively and quantitatively compare quantized vortex interaction patterns of the GLSE with those from the …

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On A Sub-Supersolution Method For The Prescribed Mean Curvature Problem, Vy Khoi Le Jan 2007

On A Sub-Supersolution Method For The Prescribed Mean Curvature Problem, Vy Khoi Le

Mathematics and Statistics Faculty Research & Creative Works

The paper is about a sub-supersolution method for the prescribed mean curvature problem. We formulate the problem as a variational inequality and propose appropriate concepts of sub- and supersolutions for such inequality. Existence and enclosure results for solutions and extremal solutions between sub- and supersolutions are established.

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Differentiability With Respect To Parameters Of Weak Solutions Of Linear Parabolic Equations, John R. Singler Jan 2007

Differentiability With Respect To Parameters Of Weak Solutions Of Linear Parabolic Equations, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

We consider the differentiability of weak solutions of linear parabolic equations with respect to parameters and initial data. under natural assumptions, it is shown that solutions possess as much differentiability with respect to the data as do the terms appearing in the equation. The derivatives are shown to satisfy the appropriate sensitivity equations. The theoretical results are illustrated with an example.

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Oscillation Criteria For A Certain Class Of Second Order Emden-Fowler Dynamic Equations, Elvan Akin, S. H. Saker, Martin Bohner Jan 2007

Oscillation Criteria For A Certain Class Of Second Order Emden-Fowler Dynamic Equations, Elvan Akin, S. H. Saker, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

By means of Riccati transformation techniques we establish some oscillation criteria for the second order Emden-Fowler dynamic equation on a time scale. Such equations contain the classical Emden-Fowler equation as well as their discrete counterparts. The classical oscillation results of Atkinson (in the superlinear case) and Belohorec (in the sublinear case) are extended in this paper to Emden-Fowler dynamic equations on any time scale.

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A Comparison Of Techniques To Forecast Consumer Satisfaction For Vehicle Ride, Elizabeth A. Cudney, David Drain, Kenneth M. Ragsdell, Kioumars Paryani Jan 2007

A Comparison Of Techniques To Forecast Consumer Satisfaction For Vehicle Ride, Elizabeth A. Cudney, David Drain, Kenneth M. Ragsdell, Kioumars Paryani

Engineering Management and Systems Engineering Faculty Research & Creative Works

This paper presents a comparison of methods for the identification of a reduced set of useful variables using a multidimensional system. the Mahalanobis-Taguchi System and a standard statistical technique are used reduce the dimensionality of vehicle ride based on consumer satisfaction ratings. the Mahalanobis-Taguchi System and cluster analysis are applied to vehicle ride. the research considers 67 vehicle data sets for the 6 vehicle ride parameters. This paper applies the Mahalanobis-Taguchi System to forecast consumer satisfaction and provides a comparison of results with those obtained from a standard statistical approach to the problem. Copyright © 2007 SAE International.

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Effective Use Of Process Capability Indices For Supplier Management, Elizabeth A. Cudney, David Drain Jan 2007

Effective Use Of Process Capability Indices For Supplier Management, Elizabeth A. Cudney, David Drain

Engineering Management and Systems Engineering Faculty Research & Creative Works

Process capability indices were originally invented to enable an organization to make economically sound decisions for process management. Process capability is a comparison of the voice of the process with the voice of the customer. Current practice is to use Cp and Cpk regardless of the validity of the underlying assumptions necessary for their use. Even if all necessary assumptions are satisfied, important problems can be missed if these indices are the sole process evaluation examined. Customer-supplier axioms are introduced to motivate more useful process evaluations and foster long-term harmonious relationships. This paper explores the alternative capability indices Cpm, Cpmk, …

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Erratum: The Emergence Of A Large-Scale Coherent Structure Under Small-Scale Random Bombardments (Communications On Pure And Applied Mathematics (2006) 59:4 (467-500)), Andrew Majda, Xiaoming Wang Jul 2006

Erratum: The Emergence Of A Large-Scale Coherent Structure Under Small-Scale Random Bombardments (Communications On Pure And Applied Mathematics (2006) 59:4 (467-500)), Andrew Majda, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

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On Self-Adjoint And J-Self-Adjoint Dirac-Type Operators: A Case Study, Stephen L. Clark, Fritz Gesztesy Jan 2006

On Self-Adjoint And J-Self-Adjoint Dirac-Type Operators: A Case Study, Stephen L. Clark, Fritz Gesztesy

Mathematics and Statistics Faculty Research & Creative Works

We provide a comparative treatment of some aspects of spectral theory for self-adjoint and non-self-adjoint (but J-self-adjoint) Dirac-type operators connected with the defocusing and focusing nonlinear Schrödinger equation, of relevance to nonlinear optics. In addition to a study of Dirac and Hamiltonian systems, we also introduce the concept of Weyl-Titchmarsh half-line m-coefficients (and 2 × 2 matrix-valued M-matrices) in the non-self-adjoint context and derive some of their basic properties. We conclude with an illustrative example showing that crossing spectral arcs in the non-self-adjoint context imply the blowup of the norm of spectral projections in the limit where the crossing point …

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