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Articles 181 - 210 of 434
Full-Text Articles in Statistics and Probability
Oscillatory Behavior Of Solutions Of Third-Order Delay And Advanced Dynamic Equations, Murat Adivar, Elvan Akin, Raegan Higgins
Oscillatory Behavior Of Solutions Of Third-Order Delay And Advanced Dynamic Equations, Murat Adivar, Elvan Akin, Raegan Higgins
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we consider oscillation criteria for certain third-order delay and advanced dynamic equations on unbounded time scales. A time scale T is a nonempty closed subset of the real numbers. Examples will be given to illustrate some of the results.
A Linear Iteration Algorithm For A Second-Order Energy Stable Scheme For A Thin Film Model Without Slope Selection, Wenbin Chen, Cheng Wang, Xiaoming Wang, Steven M. Wise
A Linear Iteration Algorithm For A Second-Order Energy Stable Scheme For A Thin Film Model Without Slope Selection, Wenbin Chen, Cheng Wang, Xiaoming Wang, Steven M. Wise
Mathematics and Statistics Faculty Research & Creative Works
We present a linear iteration algorithm to implement a second-order energy stable numerical scheme for a model of epitaxial thin film growth without slope selection. the PDE, which is a nonlinear, fourth-order parabolic equation, is the L 2 gradient flow of the energy d x. the energy stability is preserved by a careful choice of the second-order temporal approximation for the nonlinear term, as reported in recent work (Shen et al. in SIAM J Numer Anal 50:105-125, 2012). the resulting scheme is highly nonlinear, and its implementation is non-trivial. in this paper, we propose a linear iteration algorithm to solve …
Oscillation Criteria For Second-Order Dynamic Equations On Time Scales, Ravi P. Agarwal, Martin Bohner, Tongxing Li, Chenghui Zhang
Oscillation Criteria For Second-Order Dynamic Equations On Time Scales, Ravi P. Agarwal, Martin Bohner, Tongxing Li, Chenghui Zhang
Mathematics and Statistics Faculty Research & Creative Works
Erbe's and Hassan's contributions regarding oscillation criteria are interesting in the development of oscillation theory of dynamic equations on time scales. The objective of this paper is to amend these results. © 2014 Elsevier Ltd. All rights reserved.
Oscillation Of Second-Order P-Laplace Dynamic Equations With A Nonpositive Neutral Coefficient, Martin Bohner, Tongxing Li
Oscillation Of Second-Order P-Laplace Dynamic Equations With A Nonpositive Neutral Coefficient, Martin Bohner, Tongxing Li
Mathematics and Statistics Faculty Research & Creative Works
We establish some new oscillation criteria for a class of second-order p-Laplace dynamic equations with a nonpositive neutral coefficient on a time scale. The results obtained supplement and improved those reported in the literature. © 2014 Elsevier Ltd. All rights reserved.
Multi-Valued Parabolic Variational Inequalities And Related Variational-Hemivariational Inequalities, Siegfried Carl, Vy Khoi Le
Multi-Valued Parabolic Variational Inequalities And Related Variational-Hemivariational Inequalities, Siegfried Carl, Vy Khoi Le
Mathematics and Statistics Faculty Research & Creative Works
In this paper we study multi-valued parabolic variational inequalities involving quasilinear parabolic operators, and multi-valued integral terms over the underlying parabolic cylinder as well as over parts of the lateral parabolic boundary, where the multi-valued functions involved are assumed to be upper semicontinuous only. Note, since lower semicontinuous multi-valued functions allow always for a Carathéodory selection, this case can be considered as the trivial case and therefore will be omitted. Our main goal is threefold: First, we provide an analytical framework and an existence theory for the problems under consideration. Unlike in recent publications on multi-valued parabolic variational inequalities, the …
Asymptotic Behavior Of Nonoscillatory Solutions Of Higher-Order Integro-Dynamic Equations, Martin Bohner, Said Grace, Nasrin Sultana
Asymptotic Behavior Of Nonoscillatory Solutions Of Higher-Order Integro-Dynamic Equations, Martin Bohner, Said Grace, Nasrin Sultana
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we establish some new criteria on the asymptotic behavior of Non oscillatory solutions of higher-order integro-dynamic equations on time scales. © AGH University of Science and Technology Press, Krakow 2014.
Some Dynamic Hardy-Type Inequalities With General Kernel, Martin Bohner, Ammara Nosheen, Josip Pečarić, Awais Younus
Some Dynamic Hardy-Type Inequalities With General Kernel, Martin Bohner, Ammara Nosheen, Josip Pečarić, Awais Younus
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we extend some Hardy-type inequalities with certain kernels to arbitrary time scales. Certain classical and some new integral and discrete inequalities are deduced in seek of applications. © Zagreb Paper JMI-08-12.
Safety Effect Of Missouri's Strategic Highway Safety Plan: Missouri's Blueprint For Safer Roadways, Mojtaba A. Mohammadi, V. A. Samaranayake, Ghulam H. Bham
Safety Effect Of Missouri's Strategic Highway Safety Plan: Missouri's Blueprint For Safer Roadways, Mojtaba A. Mohammadi, V. A. Samaranayake, Ghulam H. Bham
Mathematics and Statistics Faculty Research & Creative Works
This study systematically evaluated the changes in motor vehicle crashes that occurred on the Missouri Interstate highway system following the implementation of the Missouri Strategic Highway Safety Plan (MSHSP) between 2004 and 2007. The MSHSP implemented crash injury reduction strategies in enforcement, education, engineering, and public policy. Empirical Bayesian methods were commonly used to evaluate the effects of any change in safety as a result of countermeasures. This paper presents a simple new approach to evaluating the effects of Missouri's safety plans on roadway crashes. For crash data associated with traffic and roadway characteristics, negative binomial regression models were developed …
Efficient And Long-Time Accurate Second-Order Methods For The Stokes-Darcy System, Wenbin Chen, Max Gunzburger, Dong Sun, Xiaoming Wan
Efficient And Long-Time Accurate Second-Order Methods For The Stokes-Darcy System, Wenbin Chen, Max Gunzburger, Dong Sun, Xiaoming Wan
Mathematics and Statistics Faculty Research & Creative Works
We propose and study two second order in time implicit-explicit methods for the coupled Stokes-Darcy system that governs flows in karst aquifers and other subsurface flow systems. the first method is a combination of a second-order backward differentiation formula and the second order Gear's extrapolation approach. the second is a combination of the second-order Adams-Moulton and second-order Adams-Bashforth methods. Both algorithms only require the solution of decoupled Stokes and Darcy problems at each time-step. Hence, these schemes are very efficient and can be easily implemented using legacy codes. We establish the unconditional and uniform in time stability for both schemes. …
Mathematical Engineering And Control With Applications, Mamdouh M. El Kady, Martin Bohner, J. Liang, Mouffak Benchohra
Mathematical Engineering And Control With Applications, Mamdouh M. El Kady, Martin Bohner, J. Liang, Mouffak Benchohra
Mathematics and Statistics Faculty Research & Creative Works
No abstract provided.
The Kalman Filter For Linear Systems On Time Scales, Martin Bohner, Nick Wintz
The Kalman Filter For Linear Systems On Time Scales, Martin Bohner, Nick Wintz
Mathematics and Statistics Faculty Research & Creative Works
We introduce the Kalman filter for linear systems on time scales, which includes the discrete and continuous versions as special cases. When the system is also stochastic, we show that the Kalman filter is an observer that estimates the system when the state is corrupted by noisy measurements. Finally, we show that the duality of the Kalman filter and the Linear Quadratic Regulator (LQR) is preserved in their unification on time scales. A numerical example is provided. © 2013 Elsevier Ltd.
Minkowski And Beckenbach-Dresher Inequalities And Functionals On Time Scales, Rabia Bibi, Martin Bohner, Josip Pečarić, Sanja Varǒsanec
Minkowski And Beckenbach-Dresher Inequalities And Functionals On Time Scales, Rabia Bibi, Martin Bohner, Josip Pečarić, Sanja Varǒsanec
Mathematics and Statistics Faculty Research & Creative Works
We obtain integral forms of the Minkowski inequality and Beckenbach-Dresher inequality on time scales. Also, we investigate a converse of Minkowski's inequality and several functionals arising from the Minkowski inequality and the Beckenbach-Dresher inequality. © ELEMENT, Zagreb.
Decoupling The Stationary Navier-Stokes-Darcy System With The Beavers-Joseph-Saffman Interface Condition, Yong Cao, Yuchuan Chu, Xiaoming He, Mingzhen Wei
Decoupling The Stationary Navier-Stokes-Darcy System With The Beavers-Joseph-Saffman Interface Condition, Yong Cao, Yuchuan Chu, Xiaoming He, Mingzhen Wei
Mathematics and Statistics Faculty Research & Creative Works
This paper proposes a domain decomposition method for the coupled stationary Navier-Stokes and Darcy equations with the Beavers-Joseph-Saffman interface condition in order to improve the efficiency of the finite element method. The physical interface conditions are directly utilized to construct the boundary conditions on the interface and then decouple the Navier-Stokes and Darcy equations. Newton iteration will be used to deal with the nonlinear systems. Numerical results are presented to illustrate the features of the proposed method.
Time Scales Integral Inequalities For Superquadratic Functions, Josipa Barić, Rabia Bibi, Martin Bohner, Josip Pečarić
Time Scales Integral Inequalities For Superquadratic Functions, Josipa Barić, Rabia Bibi, Martin Bohner, Josip Pečarić
Mathematics and Statistics Faculty Research & Creative Works
In this paper, two different methods of proving Jensen's inequality on time scales for superquadratic functions are demonstrated. Some refinements of classical inequalities on time scales are obtained using properties of superquadratic functions and some known results for isotonic linear functionals. © 2013 The Korean Mathematical Society.
Oscillation Of Third-Order Nonlinear Delay Differential Equations, Ravi P. Agarwal, Martin Bohner, Tongxing Li, Chenghui Zhang
Oscillation Of Third-Order Nonlinear Delay Differential Equations, Ravi P. Agarwal, Martin Bohner, Tongxing Li, Chenghui Zhang
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we study the oscillatory behavior of a class of third-order nonlinear delay differential equations (a(t)(b(t)y′(t)) ′) ′+q(t)yγ(τ(t)) =0. Some new oscillation criteria are presented by transforming this equation to the first order delayed and advanced differential equations. Employing suitable comparison theorems, we establish new results on oscillation of the studied equation. Assumptions in our theorems are less restrictive; these criteria improve those in the recent paper [Appl. Math. Comput., 202 (2008), 102-112] and related contributions to the subject. Examples are provided to illustrate new results.
Immersed Finite Element Methods For Parabolic Equations With Moving Interface, Xiaoming He, Tao Lin, Yanping Lin, Xu Zhang
Immersed Finite Element Methods For Parabolic Equations With Moving Interface, Xiaoming He, Tao Lin, Yanping Lin, Xu Zhang
Mathematics and Statistics Faculty Research & Creative Works
This article presents three Crank-Nicolson-type immersed finite element (IFE) methods for solving parabolic equations whose diffusion coefficient is discontinuous across a time dependent interface. These methods can use a fixed mesh because IFEs can handle interface jump conditions without requiring the mesh to be aligned with the interface. These methods will be compared analytically in the sense of accuracy and computational cost. Numerical examples are provided to demonstrate features of these three IFE methods. © 2012 Wiley Periodicals, Inc.
Properties Of Higher-Order Half-Linear Functional Differential Equations With Noncanonical Operators, Chenghui Zhang, Ravi P. Agarwal, Martin Bohner, Tongxing Li
Properties Of Higher-Order Half-Linear Functional Differential Equations With Noncanonical Operators, Chenghui Zhang, Ravi P. Agarwal, Martin Bohner, Tongxing Li
Mathematics and Statistics Faculty Research & Creative Works
Some new results are presented for the oscillatory and asymptotic behavior of higher-order half-linear differential equations with a noncanonical operator. We study the delayed and advanced equations subject to various conditions. © 2013 Zhang et al.
New Results For Oscillatory Behavior Of Even-Order Half-Linear Delay Differential Equations, Chenghui Zhang, Ravi P. Agarwal, Martin Bohner, Tongxing Li
New Results For Oscillatory Behavior Of Even-Order Half-Linear Delay Differential Equations, Chenghui Zhang, Ravi P. Agarwal, Martin Bohner, Tongxing Li
Mathematics and Statistics Faculty Research & Creative Works
Some new oscillation results are presented that improve those reported in [C. Zhang, T. Li, B. Sun, and E. Thandapani, On the oscillation of higher-order half-linear delay differential equations, Appl. Math. Lett. 24 (2011) 1618-1621]. © 2012 Elsevier Ltd. All rights reserved.
Rna Profiles Of Porcine Embryos During Genome Activation Reveal Complex Metabolic Switch Sensitive To In Vitro Conditions, Olga Østrup, Gayla R. Olbricht, Esben Østrup, Poul Hyttel, Philippe Collas, Ryan A. Cabot
Rna Profiles Of Porcine Embryos During Genome Activation Reveal Complex Metabolic Switch Sensitive To In Vitro Conditions, Olga Østrup, Gayla R. Olbricht, Esben Østrup, Poul Hyttel, Philippe Collas, Ryan A. Cabot
Mathematics and Statistics Faculty Research & Creative Works
Fertilization is followed by complex changes in cytoplasmic composition and extensive chromatin reprogramming which results in the abundant activation of totipotent embryonic genome at embryonic genome activation (EGA). While chromatin reprogramming has been widely studied in several species, only a handful of reports characterize changing transcriptome profiles and resulting metabolic changes in cleavage stage embryos. The aims of the current study were to investigate RNA profiles of in vivo developed (ivv) and in vitro produced (ivt) porcine embryos before (2-cell stage) and after (late 4-cell stage) EGA and determine major metabolic changes that regulate totipotency. The period before EGA was …
Modeling, Analysis, And Applications Of Complex Systems, Chuandong Li, Xiaodi Li, Shukai Duan, Yanzhi Zhang
Modeling, Analysis, And Applications Of Complex Systems, Chuandong Li, Xiaodi Li, Shukai Duan, Yanzhi Zhang
Mathematics and Statistics Faculty Research & Creative Works
Recent advances in theory and applications of complex dynamical systems have contributed much to the successful handling of certain problems in biology, physics, economics, engineering, and so forth that until recently were thought too difficult to be analyzed. These complex systems may be characterized by systems with uncertainty, impulse, time delay, stochastic perturbation, hybrid dynamics, distributed dynamics, and chaotic dynamics. The overall aim of this special issue is to bring together the latest or innovative knowledge and advances in mathematics for handling complex systems, which may depend largely on methods from mathematical analysis, artificial intelligence, statistics, and engineering, including nonlinear …
A Bound On The Vertical Transport Of Heat In The 'Ultimate' State Of Slippery Convection At Large Prandtl Numbers, Xiaoming Wang, Jared P. Whitehead
A Bound On The Vertical Transport Of Heat In The 'Ultimate' State Of Slippery Convection At Large Prandtl Numbers, Xiaoming Wang, Jared P. Whitehead
Mathematics and Statistics Faculty Research & Creative Works
An upper bound on the rate of vertical heat transport is established in three dimensions for stress-free velocity boundary conditions on horizontally periodic plates. a variation of the background method is implemented that allows negative values of the quadratic form to yield 'small' (O.1=Pr/) corrections to the subsequent bound. for large (but finite) Prandtl numbers this bound is an improvement over the 'ultimate' Ra1=2 scaling and, in the limit of infinite Pr, agrees with the bound of Ra5=12 recently derived in that limit for stress-free boundaries. © 2013 Cambridge University Press.
Well-Posedness Of The Hele-Shaw-Cahn-Hilliard System, Xiaoming Wang, Zhifei Zhang
Well-Posedness Of The Hele-Shaw-Cahn-Hilliard System, Xiaoming Wang, Zhifei Zhang
Mathematics and Statistics Faculty Research & Creative Works
We study the well-posedness of the Hele-Shaw-Cahn-Hilliard system modeling binary fluid flow in porous media with arbitrary viscosity contrast but matched density between the components. for initial data in Hs, s>d2+1, the existence and uniqueness of solution in C([0,T];Hs) ∪L2(0,T;Hs+2) that is global in time in the two-dimensional case (d=2) and local in time in the three-dimensional case (d=3) are established. Several blow-up criterions in the three-dimensional case are provided as well. One of the tools that we utilized is the Littlewood-Paley theory in order to establish certain key commutator estimates. © 2012 Elsevier Masson SAS.
The Beverton–Holt Q-Difference Equation, Martin Bohner, Rotchana Chieochan
The Beverton–Holt Q-Difference Equation, Martin Bohner, Rotchana Chieochan
Mathematics and Statistics Faculty Research & Creative Works
The Beverton–Holt model is a classical population model which has been considered in the literature for the discrete-time case. Its continuous-time analogue is the well-known logistic model. In this paper, we consider a quantum calculus analogue of the Beverton–Holt equation. We use a recently introduced concept of periodic functions in quantum calculus in order to study the existence of periodic solutions of the Beverton–Holt q-difference equation. Moreover, we present proofs of quantum calculus versions of two so-called Cushing–Henson conjectures. © 2013 The Author(s). Published by Taylor & Francis.
Oscillation Results For Fourth-Order Nonlinear Dynamic Equations, Chenghui Zhang, Tongxing Li, Ravi P. Agarwal, Martin Bohner
Oscillation Results For Fourth-Order Nonlinear Dynamic Equations, Chenghui Zhang, Tongxing Li, Ravi P. Agarwal, Martin Bohner
Mathematics and Statistics Faculty Research & Creative Works
This work is concerned with the oscillation of a certain class of fourth-order nonlinear dynamic equations on time scales. a new oscillation result and an example are included. © 2012 Elsevier Ltd. All rights reserved.
Jensen's Functionals On Time Scales, Matloob Anwar, Rabia Bibi, Martin Bohner, Josip Pečarić
Jensen's Functionals On Time Scales, Matloob Anwar, Rabia Bibi, Martin Bohner, Josip Pečarić
Mathematics and Statistics Faculty Research & Creative Works
We consider Jensen's functionals on time scales and discuss its properties and applications. Further, we define weighted generalized and power means on time scales. by applying the properties of Jensen's functionals on these means, we obtain several refinements and converses of Hölder's inequality on time scales. Copyright © 2012 Matloob Anwar et al.
An Impulsive Delay Differential Inequality And Applications, Xiaodi Li, Martin Bohner
An Impulsive Delay Differential Inequality And Applications, Xiaodi Li, Martin Bohner
Mathematics and Statistics Faculty Research & Creative Works
An impulsive delay differential inequality is formulated in this paper. an estimate of the rate of decay of solutions to this inequality is obtained. It can be applied to the study of dynamical behavior of delay differential equations from the impulsive control point of view. as an application, we consider a class of impulsive control systems with time-varying delays and establish a sufficient condition to guarantee the global exponential stability. It is shown that, via proper impulsive control law, a linear delay differential system can be exponentially stabilized even if it is initially unstable. a numerical example is given to …
An Efficient Second Order In Time Scheme For Approximating Long Time Statistical Properties Of The Two Dimensional Navier-Stokes Equations, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
We investigate the long-time behavior of the following efficient second order in time scheme for the 2D Navier-Stokes equations in a periodic box: The scheme is a combination of a 2nd-order in time backward-differentiation and a particular explicit Adams-Bashforth treatment of the advection term. Therefore, only a linear constant coefficient Poisson solver is needed at each time step. We prove uniform in time bounds on this scheme in L 2, H per1 and H per2 provided that the time-step is sufficiently small. These time uniform estimates further lead to the convergence of long-time statistics (stationary statistical properties) of the scheme …
Oscillation And Spectral Theory For Linear Hamiltonian Systems With Nonlinear Dependence On The Spectral Parameter, Martin Bohner, Werner Kratz, Roman Šimon Hilscher
Oscillation And Spectral Theory For Linear Hamiltonian Systems With Nonlinear Dependence On The Spectral Parameter, Martin Bohner, Werner Kratz, Roman Šimon Hilscher
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we consider linear Hamiltonian differential systems which depend in general nonlinearly on the spectral parameter and with Dirichlet boundary conditions. Our results generalize the known theory of linear Hamiltonian systems in two respects. Namely, we allow nonlinear dependence of the coefficients on the spectral parameter and at the same time we do not impose any controllability and strict normality assumptions. We introduce the notion of a finite eigenvalue and prove the oscillation theorem relating the number of finite eigenvalues which are less than or equal to a given value of the spectral parameter with the number of …
Experimental And Computational Validation And Verification Of The Stokes-Darcy And Continuum Pipe Flow Models For Karst Aquifers With Dual Porosity Structure, Xiaolong Hu, Xiaoming Wang, Max Gunzburger, Fei Hua, Yanzhao Cao
Experimental And Computational Validation And Verification Of The Stokes-Darcy And Continuum Pipe Flow Models For Karst Aquifers With Dual Porosity Structure, Xiaolong Hu, Xiaoming Wang, Max Gunzburger, Fei Hua, Yanzhao Cao
Mathematics and Statistics Faculty Research & Creative Works
In our previous study, we developed the Stokes-Darcy (SD) model was developed for flow in a karst aquifer with a conduit bedded in matrix, and the Beavers-Joseph (BJ) condition was used to describe the matrix-conduit interface. We also studied the mathematical well-posedness of a coupled continuum pipe flow (CCPF) model as well as convergence rates of its finite element approximation. in this study, to compare the SD model with the CCPF model, we used numerical analyses to validate finite element discretisation methods for the two models. using computational experiments, simulation codes implementing the finite element discretisations are then verified. Further …
Second-Order Convex Splitting Schemes For Gradient Flows With Ehrlich-Schwoebel Type Energy: Application To Thin Film Epitaxy, Jie Shen, Cheng Wang, Xiaoming Wang, Steven M. Wise
Second-Order Convex Splitting Schemes For Gradient Flows With Ehrlich-Schwoebel Type Energy: Application To Thin Film Epitaxy, Jie Shen, Cheng Wang, Xiaoming Wang, Steven M. Wise
Mathematics and Statistics Faculty Research & Creative Works
We construct unconditionally stable, unconditionally uniquely solvable, and second order accurate (in time) schemes for gradient flows with energy of the form {equation presented} dx. the construction of the schemes involves the appropriate combination and extension of two classical ideas: (i) appropriate convex-concave decomposition of the energy functional and (ii) the secant method. as an application, we derive schemes for epitaxial growth models with slope selection (F(y) = 1/4 (|y| 2 - 1) 2) or without slope selection (F(y) = -1/2 ln(1 + |y| 2)). Two types of unconditionally stable uniquely solvable second-order schemes are presented. the first type inherits …