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Articles 271 - 300 of 434
Full-Text Articles in Statistics and Probability
On A Theorem Of Shchepin And Repovš Concerning The Smoothness Of Compacta, Ethan Akin, William Ott
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.
Discrete Kato-Type Theorem On Inviscid Limit Of Navier-Stokes Flows, Wenfang Cheng, Xiaoming Wang
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 …
Note On The Emergence Of Large Scale Coherent Structure Under Small Scale Random Bombardments: The Discrete Case, Andrew Majda, Xiaoming Wang
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.
Balanced Proper Orthogonal Decomposition For Model Reduction Of Infinite Dimensional Linear Systems, John R. Singler, Belinda A. Batten
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.
Periodic Solutions Of Functional Dynamic Equations With Infinite Delay, Li Bi, Meng Fan, Martin Bohner
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 …
The Convolution On Time Scales, Gusein Sh. Guseinov, Martin Bohner
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. …
Trench's Perturbation Theorem For Dynamic Equations, Stevo Stevic, Martin Bohner
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.
Oscillation And Nonoscillation Of Forced Second Order Dynamic Equations, Christopher C. Tisdell, Martin Bohner
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. …
The Dynamics And Interaction Of Quantized Vortices In The Ginzburg-Landau-Schrödinger Equation, Yanzhi Zhang, Weizhu Bao, Qiang Du
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 …
On A Sub-Supersolution Method For The Prescribed Mean Curvature Problem, Vy Khoi Le
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.
Differentiability With Respect To Parameters Of Weak Solutions Of Linear Parabolic Equations, John R. Singler
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.
Oscillation Criteria For A Certain Class Of Second Order Emden-Fowler Dynamic Equations, Elvan Akin, S. H. Saker, Martin Bohner
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.
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
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.
On Self-Adjoint And J-Self-Adjoint Dirac-Type Operators: A Case Study, Stephen L. Clark, Fritz Gesztesy
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 …
Multiple Lebesgue Integration On Time Scales, Gusein Sh. Guseinov, Martin Bohner
Multiple Lebesgue Integration On Time Scales, Gusein Sh. Guseinov, Martin Bohner
Mathematics and Statistics Faculty Research & Creative Works
We study the process of multiple Lebesgue integration on time scales. The relationship of the Riemann and the Lebesgue multiple integrals is investigated.
Singular Second-Order Multipoint Dynamic Boundary Value Problems With Mixed Derivatives, Hua Luo, Martin Bohner
Singular Second-Order Multipoint Dynamic Boundary Value Problems With Mixed Derivatives, Hua Luo, Martin Bohner
Mathematics and Statistics Faculty Research & Creative Works
We study a certain singular second-order m-point boundary value problem on a time scale and establish the existence of a solution. The proof of our main result is based upon the Leray-Schauder continuation theorem.
Modeling Of Bioinspired Sensors For Flow Separation Detection For Micro Air Vehicles, Belinda A. Batten, John R. Singler, Benjamin T. Dickinson
Modeling Of Bioinspired Sensors For Flow Separation Detection For Micro Air Vehicles, Belinda A. Batten, John R. Singler, Benjamin T. Dickinson
Mathematics and Statistics Faculty Research & Creative Works
Autonomous micro air vehicle (MAV) flight faces inherent stability challenges. One challenge is controlling flow separation over the airfoil and an autonomous control system for MAV flight may be enhanced with closed loop separation control. In this work, we focus on modeling biologically inspired hair cell sensors for future flow control applications. We model the sensor output and present examples and numerical results.
Feedback Control Of Low Dimensional Models Of Transition To Turbulence, John A. Burns, John R. Singler
Feedback Control Of Low Dimensional Models Of Transition To Turbulence, John A. Burns, John R. Singler
Mathematics and Statistics Faculty Research & Creative Works
The problem of controlling or delaying transition to turbulence in shear flows has been the subject of numerous papers over the past twenty years. This period has seen the development of several low dimensional models for parallel shear flows in an attempt to explain the failure of classical linear hydrodynamic stability theory to correctly predict transition. In recent years, ideas from robust control theory have been employed to attack this problem. In this paper we use these models to develop a scenario for transition that employs both classical bifurcation theory and robust control theory. In addition, we present numerical results …
The Poweratlas: A Power And Sample Size Atlas For Microarray Experimental Design And Research, Grier P. Page, Jode W. Edwards, Gary L. Gadbury, Prashanth Yelisetti, Jelai Wang, Prinal Trivedi, David B. Allison
The Poweratlas: A Power And Sample Size Atlas For Microarray Experimental Design And Research, Grier P. Page, Jode W. Edwards, Gary L. Gadbury, Prashanth Yelisetti, Jelai Wang, Prinal Trivedi, David B. Allison
Mathematics and Statistics Faculty Research & Creative Works
Microarrays permit biologists to simultaneously measure the mRNA abundance of thousands of genes. An important issue facing investigators planning microarray experiments is how to estimate the sample size required for good statistical power. What is the projected sample size or number of replicate chips needed to address the multiple hypotheses with acceptable accuracy? Statistical methods exist for calculating power based upon a single hypothesis, using estimates of the variability in data from pilot studies. There is, however, a need for methods to estimate power and/or required sample sizes in situations where multiple hypotheses are being tested, such as in microarray …
The Emergence Of Large-Scale Coherent Structure Under Small-Scale Random Bombardments, Andrew Majda, Xiaoming Wang
The Emergence Of Large-Scale Coherent Structure Under Small-Scale Random Bombardments, Andrew Majda, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
We provide mathematical justification of the emergence of large-scale coherent structure in a two-dimensional fluid system under small-scale random bombardments with small forcing and appropriate scaling assumptions. the analysis shows that the large-scale structure emerging out of the small-scale random forcing is not the one predicted by equilibrium statistical mechanics. But the error is very small, which explains earlier successful prediction of the large-scale structure based on equilibrium statistical mechanics. © 2005 Wiley Periodicals, Inc.
Dynamics Of Rotating Bose-Einstein Condensates And Its Efficient And Accurate Numerical Computation, Weizhu Bao, Qiang Du, Yanzhi Zhang
Dynamics Of Rotating Bose-Einstein Condensates And Its Efficient And Accurate Numerical Computation, Weizhu Bao, Qiang Du, Yanzhi Zhang
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we study the dynamics of rotating Bose--Einstein condensates (BEC) based on the Gross--Pitaevskii equation (GPE) with an angular momentum rotation term and present an efficient and accurate algorithm for numerical simulations. We examine the conservation of the angular momentum expectation and the condensate width and analyze the dynamics of a stationary state with a shift in its center. By formulating the equation in either the two-dimensional polar coordinate system or the three-dimensional cylindrical coordinate system, the angular momentum rotation term becomes a term with constant coefficients. This allows us to develop an efficient time-splitting method which is …
The Hurwitz Zeta Function As A Convergent Series, Roman Dwilewicz, Jan Minac
The Hurwitz Zeta Function As A Convergent Series, Roman Dwilewicz, Jan Minac
Mathematics and Statistics Faculty Research & Creative Works
New series for the Hurwitz zeta function which converge on the whole plane, except s = 1, are developed. This is applied to obtain a remarkably simple evaluation of some special values of the function.
A Peano-Akô Type Theorem For Variational Inequalities, Vy Khoi Le
A Peano-Akô Type Theorem For Variational Inequalities, Vy Khoi Le
Mathematics and Statistics Faculty Research & Creative Works
We consider in this paper a Peano-Akô property of solution sets in some quasilinear elliptic variational inequalities. As consequences, variants of that property and a partial Hukuhara-Kneser theorem for inequalities are derived.
Boundedness In Functional Dynamic Equations On Time Scales, Elvan Akin, Youssef N. Raffoul
Boundedness In Functional Dynamic Equations On Time Scales, Elvan Akin, Youssef N. Raffoul
Mathematics and Statistics Faculty Research & Creative Works
Using nonnegative definite Lyapunov functionals, we prove general theorems for the boundedness of all solutions of a functional dynamic equation on time scales. We apply our obtained results to linear and nonlinear Volterra integro-dynamic equations on time scales by displaying suitable Lyapunov functionals.
Good Measures On Cantor Space, Ethan Akin
Good Measures On Cantor Space, Ethan Akin
Mathematics and Statistics Faculty Research & Creative Works
While there is, up to homeomorphism, only one Cantor space, i.e. one zero-dimensional, perfect, compact, nonempty metric space, there are many measures on Cantor space which are not topologically equivalent. The clopen values set for a full, nonatomic measure μ is the countable dense subset {μ(U): U is clopen} of the unit interval. It is a topological invariant for the measure. For the class of good measures, it is a complete invariant. A full, nonatomic measure μ is good if whenever U, V are clopen sets with μ(U) < μ(V), there exists W a clopen subset of V such that μ(W) = μ(U). These measures have interesting dynamical properties. They are exactly the measures which arise from uniquely ergodic minimal systems on Cantor space. For some of them there is a unique generic measure-preserving homeomorphism. That is, within the Polish group of such homeomorphisms there is a dense, G δ conjugacy class. ©2004 American Mathematical Society.
A Platform-Independent Software Suite For Statistical Analysis Of High Dimensional Biology Data, David B. Allison, Jacob P. L. Brand, Jode W. Edwards, Gary L. Gadbury, Kyoungmi Kim, Tapan Mehta, Grier P. Page, Amit Patki, Vinodh Srinivasasainagendra, Prinal Trivedi, Jelai Wang, Stanislav O. Zakharkin
A Platform-Independent Software Suite For Statistical Analysis Of High Dimensional Biology Data, David B. Allison, Jacob P. L. Brand, Jode W. Edwards, Gary L. Gadbury, Kyoungmi Kim, Tapan Mehta, Grier P. Page, Amit Patki, Vinodh Srinivasasainagendra, Prinal Trivedi, Jelai Wang, Stanislav O. Zakharkin
Mathematics and Statistics Faculty Research & Creative Works
Many efforts in microarray data analysis are focused on providing tools and methods for the qualitative analysis of microarray data. HDBStat! (High-Dimensional Biology-Statistics) is a software package designed for analysis of high dimensional biology data such as microarray data. It was initially developed for the analysis of microarray gene expression data, but it can also be used for some applications in proteomics and other aspects of genomics. HDBStat! provides statisticians and biologists a flexible and easy-to-use interface to analyze complex microarray data using a variety of methods for data preprocessing, quality control analysis and hypothesis testing.
Maximal Regular Boundary Value Problems In Banach-Valued Weighted Space, Ravi P. Agarwal, Veli B. Shakhmurov, Martin Bohner
Maximal Regular Boundary Value Problems In Banach-Valued Weighted Space, Ravi P. Agarwal, Veli B. Shakhmurov, Martin Bohner
Mathematics and Statistics Faculty Research & Creative Works
This study focuses on nonlocal boundary value problems for elliptic ordinary and partial differential-operator equations of arbitrary order, defined in Banach-valued function spaces. The region considered here has a varying bound and depends on a certain parameter. Several conditions are obtained that guarantee the maximal regularity and Fredholmness, estimates for the resolvent, and the completeness of the root elements of differential operators generated by the corresponding boundary value problems in Banach-valued weighted Lp spaces. These results are applied to nonlocal boundary value problems for regular elliptic partial differential equations and systems of anisotropic partial differential equations on cylindrical domain to …
Second Order Dynamic Inclusions, Christopher C. Tisdell, Martin Bohner
Second Order Dynamic Inclusions, Christopher C. Tisdell, Martin Bohner
Mathematics and Statistics Faculty Research & Creative Works
The theory of dynamic inclusions on a time scale is introduced, hence accommodating the special cases of differential inclusions and difference inclusions. Fixed point theory for set-valued upper semicontinuous maps, Green's functions, and upper and lower solutions are used to establish existence results for solutions of second order dynamic inclusions.
Existence And Comparison Principles For General Quasilinear Variational-Hemivariational Inequalities, Siegfried Carl, Vy Khoi Le, Dumitru Motreanu
Existence And Comparison Principles For General Quasilinear Variational-Hemivariational Inequalities, Siegfried Carl, Vy Khoi Le, Dumitru Motreanu
Mathematics and Statistics Faculty Research & Creative Works
We consider quasilinear elliptic variational-hemivariational inequalities involving convex, lower semicontinuous and locally Lipschitz functionals. We provide a generalization of the fundamental notion of sub- and supersolutions on the basis of which we then develop the sub-supersolution method for variational-hemivariational inequalities, including existence, comparison, compactness and extremality results.
Existence, Comparison, And Compactness Results For Quasilinear Variational-Hemivariational Inequalities, Vy Khoi Le, Dumitru Motreanu, Siegfried Carl
Existence, Comparison, And Compactness Results For Quasilinear Variational-Hemivariational Inequalities, Vy Khoi Le, Dumitru Motreanu, Siegfried Carl
Mathematics and Statistics Faculty Research & Creative Works
We consider quasilinear elliptic variational-hemivariational inequalities involving the indicator function of some closed convex set and a locally Lipschitz functional. We provide a generalization of the fundamental notion of sub- and supersolutions, on the basis of which we then develop the sub-supersolution method for variational-hemivariational inequalities, including existence, comparison, compactness, and extremality results.