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Articles 1 - 12 of 12
Full-Text Articles in Statistics and Probability
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.
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.
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.