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Articles 151 - 180 of 440
Full-Text Articles in Mathematics
Convergence Analysis And Error Estimates For A Second Order Accurate Finite Element Method For The Cahn–Hilliard–Navier–Stokes System, Amanda E. Diegel, Cheng Wang, Xiaoming Wang, Steven M. Wise
Convergence Analysis And Error Estimates For A Second Order Accurate Finite Element Method For The Cahn–Hilliard–Navier–Stokes System, Amanda E. Diegel, Cheng Wang, Xiaoming Wang, Steven M. Wise
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we present a novel second order in time mixed finite element scheme for the Cahn–Hilliard–Navier–Stokes equations with matched densities. the scheme combines a standard second order Crank–Nicolson method for the Navier–Stokes equations and a modification to the Crank–Nicolson method for the Cahn–Hilliard equation. in particular, a second order Adams-Bashforth extrapolation and a trapezoidal rule are included to help preserve the energy stability natural to the Cahn–Hilliard equation. We show that our scheme is unconditionally energy stable with respect to a modification of the continuous free energy of the PDE system. Specifically, the discrete phase variable is shown …
Magnetic Control Of Lateral Migration Of Ellipsoidal Microparticles In Microscale Flows, R. Zhou, C. A. Sobecki, J. Zhang, Yanzhi Zhang, Cheng Wang
Magnetic Control Of Lateral Migration Of Ellipsoidal Microparticles In Microscale Flows, R. Zhou, C. A. Sobecki, J. Zhang, Yanzhi Zhang, Cheng Wang
Mathematics and Statistics Faculty Research & Creative Works
No abstract provided.
Hypoelliptic Multiscale Langevin Diffusions: Large Deviations, Invariant Measures And Small Mass Asymptotics, Wenqing Hu, Konstantinos Spiliopoulosï
Hypoelliptic Multiscale Langevin Diffusions: Large Deviations, Invariant Measures And Small Mass Asymptotics, Wenqing Hu, Konstantinos Spiliopoulosï
Mathematics and Statistics Faculty Research & Creative Works
We consider a general class of hypoelliptic Langevin diffusions and study two related questions. The first question is large deviations for hypoelliptic multiscale diffusions as the noise and the scale separation parameter go to zero. The second question is small mass asymptotics of (a) the invariant measure corresponding to the hypoelliptic Langevin operator and of (b) related hypoelliptic Poisson equations. The invariant measure corresponding to the hypoelliptic problem and appropriate hypoelliptic Poisson equations enter the large deviations rate function due to the multiscale effects. Based on the small mass asymptotics we derive that the large deviations behavior of the multiscale …
Oscillation Criteria For Third-Order Nonlinear Functional Difference Equations With Damping, Martin Bohner, C. Dharuman, R. Srinivasan, Ethiraju Thandapani
Oscillation Criteria For Third-Order Nonlinear Functional Difference Equations With Damping, Martin Bohner, C. Dharuman, R. Srinivasan, Ethiraju Thandapani
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we obtain some new criteria for the oscillation of certain third-order difference equations using comparison principles with a suitable couple of first-order difference equations. The presented results improve and extend the earlier ones. Examples are provided to illustrate the main results.
Stationary Acceleration Of Frenet Curves, Nemat Abazari, Martin Bohner, Ilgin Sager, Yusuf Yayli
Stationary Acceleration Of Frenet Curves, Nemat Abazari, Martin Bohner, Ilgin Sager, Yusuf Yayli
Mathematics and Statistics Faculty Research & Creative Works
In this paper, the stationary acceleration of the spherical general helix in a 3-dimensional Lie group is studied by using a bi-invariant metric. The relationship between the Frenet elements of the stationary acceleration curve in 4-dimensional Euclidean space and the intrinsic Frenet elements of the Lie group is outlined. As a consequence, the corresponding curvature and torsion of these curves are computed. In Minkowski space, for the curves on a timelike surface to have a stationary acceleration, a necessary and sufficient condition is refined.
Itô'S Formula, The Stochastic Exponential, And Change Of Measure On General Time Scales, Wenqing Hu
Itô'S Formula, The Stochastic Exponential, And Change Of Measure On General Time Scales, Wenqing Hu
Mathematics and Statistics Faculty Research & Creative Works
We provide an Itô formula for stochastic dynamical equation on general time scales. Based on this Itô's formula we give a closed-form expression for stochastic exponential on general time scales. We then demonstrate Girsanov's change of measure formula in the case of general time scales. Our result is being applied to a Brownian motion on the quantum time scale (𝑞-time scale).
Founders, Feminists, And A Fascist -- Some Notable Women In The Missouri Section Of The Maa, Leon M. Hall
Founders, Feminists, And A Fascist -- Some Notable Women In The Missouri Section Of The Maa, Leon M. Hall
Mathematics and Statistics Faculty Research & Creative Works
In the history of the Missouri Section of the MAA, some of the more interesting people who influenced the growth and development of the section through the years were and are women. In this chapter, we discuss the contributions of a few (certainly not all) of these women to the Missouri Section and mathematics as a whole, including Emily Kathryn Wyant (founder of KME), Margaret F. Willerding (who dealt with sexism in the 1940s), Maria Castellani (an official in Mussolini’s Italy before coming to America), and T. Christine Stevens (co-founder of Project NExT). Without them, and others like them, both …
Chain Transitive Homeomorphisms On A Space: All Or None, Ethan Akin, Juho Rautio
Chain Transitive Homeomorphisms On A Space: All Or None, Ethan Akin, Juho Rautio
Mathematics and Statistics Faculty Research & Creative Works
Extending earlier work, we consider when a compact metric space can be realized as the omega limit set of a discrete time dynamical system. This is equivalent to asking when the space admits a chain transitive homeomorphism. We approach this problem in terms of various conditions on the connected components of the space. We also construct spaces where all homeomorphisms are chain transitive.
Asymptotic Behavior Of Even-Order Damped Differential Equations With P-Laplacian Like Operators And Deviating Arguments, Qingmin Liu, Martin Bohner, Said R. Grace, Tongxing Li
Asymptotic Behavior Of Even-Order Damped Differential Equations With P-Laplacian Like Operators And Deviating Arguments, Qingmin Liu, Martin Bohner, Said R. Grace, Tongxing Li
Mathematics and Statistics Faculty Research & Creative Works
We study the asymptotic properties of the solutions of a class of even-order damped differential equations with p-Laplacian like operators, delayed and advanced arguments. We present new theorems that improve and complement related contributions reported in the literature. Several examples are provided to illustrate the practicability, maneuverability, and efficiency of the results obtained. An open problem is proposed.
An Efficient And Long-Time Accurate Third-Order Algorithm For The Stokes–Darcy System, Wenbin Chen, Max Gunzburger, Dong Sun, Xiaoming Wang
An Efficient And Long-Time Accurate Third-Order Algorithm For The Stokes–Darcy System, Wenbin Chen, Max Gunzburger, Dong Sun, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
A third order in time numerical IMEX-type algorithm for the Stokes–Darcy system for flows in fluid saturated karst aquifers is proposed and analyzed. a novel third-order Adams–Moulton scheme is used for the discretization of the dissipative term whereas a third-order explicit Adams–Bashforth scheme is used for the time discretization of the interface term that couples the Stokes and Darcy components. the scheme is efficient in the sense that one needs to solve, at each time step, decoupled Stokes and Darcy problems. Therefore, legacy Stokes and Darcy solvers can be applied in parallel. the scheme is also unconditionally stable and, with …
Birth Mass Is The Key To Understanding The Negative Correlation Between Lifespan And Body Size In Dogs, Rong Fan, Gayla R. Olbricht, Xavior Baker, Chen Hou
Birth Mass Is The Key To Understanding The Negative Correlation Between Lifespan And Body Size In Dogs, Rong Fan, Gayla R. Olbricht, Xavior Baker, Chen Hou
Mathematics and Statistics Faculty Research & Creative Works
Larger dog breeds live shorter than the smaller ones, opposite of the mass-lifespan relationship observed across mammalian species. Here we use data from 90 dog breeds and a theoretical model based on the first principles of energy conservation and life history tradeoffs to explain the negative correlation between longevity and body size in dogs. We found that the birth/adult mass ratio of dogs scales negatively with adult size, which is different than the weak interspecific scaling in mammals. Using the model, we show that this ratio, as an index of energy required for growth, is the key to understanding why …
Qualitative Theory Of Differential Equations, Difference Equations, And Dynamic Equations On Time Scales, Tongxing Li, Martin Bohner, Tuncay Candan, Yuriy V. Rogovchenko, Qi-Ru Wang
Qualitative Theory Of Differential Equations, Difference Equations, And Dynamic Equations On Time Scales, Tongxing Li, Martin Bohner, Tuncay Candan, Yuriy V. Rogovchenko, Qi-Ru Wang
Mathematics and Statistics Faculty Research & Creative Works
This issue on qualitative analysis on differential, fractional differential, and dynamic equations and related topics aims at an all-around research and the state-of-the-art theoretical, numerical, and practical achievements that contribute to this field.
A Dual-Porosity-Stokes Model And Finite Element Method For Coupling Dual-Porosity Flow And Free Flow, Jiangyong Hou, Meilan Qiu, Xiaoming He, Chaohua Guo, Mingzhen Wei, Baojun Bai
A Dual-Porosity-Stokes Model And Finite Element Method For Coupling Dual-Porosity Flow And Free Flow, Jiangyong Hou, Meilan Qiu, Xiaoming He, Chaohua Guo, Mingzhen Wei, Baojun Bai
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we propose and numerically solve a new model considering confined flow in dual-porosity media coupled with free flow in embedded macrofractures and conduits. Such situation arises, for example, for fluid flows in hydraulic fractured tight/shale oil/gas reservoirs. The flow in dual-porosity media, which consists of both matrix and microfractures, is described by a dual-porosity model. And the flow in the macrofractures and conduits is governed by the Stokes equation. Then the two models are coupled through four physically valid interface conditions on the interface between dual-porosity media and macrofractures/conduits, which play a key role in a physically …
Oscillation Criteria For Third-Order Functional Differential Equations With Damping, Martin Bohner, Said R. Grace, Irena Jadlovska
Oscillation Criteria For Third-Order Functional Differential Equations With Damping, Martin Bohner, Said R. Grace, Irena Jadlovska
Mathematics and Statistics Faculty Research & Creative Works
This paper is a continuation of the recent study by Bohner et al [9] on oscillation properties of nonlinear third order functional differential equation under the assumption that the second order differential equation is nonoscillatory. We consider both the delayed and advanced case of the studied equation. The presented results correct and extend earlier ones. Several illustrative examples are included.
Is There A Symmetric Version Of Hindman's Theorem?, Ethan Akin, Eli Glasner
Is There A Symmetric Version Of Hindman's Theorem?, Ethan Akin, Eli Glasner
Mathematics and Statistics Faculty Research & Creative Works
We show that there does not exist a symmetric version of Hindman's Theorem, or more explicitly, that the property of containing a symmetric IP-set is not divisible. We consider several related dynamics questions.
Missouri Section Of The Mathematical Association Of America: Centennial History 1915-2015, Leon M. Hall
Missouri Section Of The Mathematical Association Of America: Centennial History 1915-2015, Leon M. Hall
Mathematics and Statistics Faculty Research & Creative Works
"Compiling and writing the history of the Missouri MAA Section has been time-consuming, but it has mainly been rewarding and a wonderful learning experience. Both the Monthly and the MAA began with strong Midwestern and Missouri influences, something which our section can look back on with well-deserved pride. Missouri MAA members have consistently advanced collegiate mathematics, mathematics education, mathematics research and scholarship, and public appreciation for and understanding of mathematics in both Missouri and the nation. Looking to the future, the MAA and the Missouri Section can continue to be a great source of opportunities for leadership and service for …
Asymptotic Behavior Of Certain Integrodifferential Equations, Said R. Grace, Elvan Akin
Asymptotic Behavior Of Certain Integrodifferential Equations, Said R. Grace, Elvan Akin
Mathematics and Statistics Faculty Research & Creative Works
This paper deals with asymptotic behavior of nonoscillatory solutions of certain forced integrodifferential equations of the form: (a(t)x'(t))' = e (t) + ∫ tc (t - s)α - 1k(t,s)ƒ(s,x(s))ds, c > 1, 0 < α < 1. From the obtained results, we derive a technique which can be applied to some related integrodifferential as well as integral equations.
Nonoscillation Criteria For Two-Dimensional Time-Scale Systems, Ozkan Ozturk, Elvan Akin
Nonoscillation Criteria For Two-Dimensional Time-Scale Systems, Ozkan Ozturk, Elvan Akin
Mathematics and Statistics Faculty Research & Creative Works
We study the existence and nonexistence of nonoscillatory solutions of a two-dimensional system of first-order dynamic equations on time scales. Our approach is based on the Knaster and Schauder fixed point theorems and some certain integral conditions. Examples are given to illustrate some of our main results.
Qualitative Analysis On Differential, Fractional Differential, And Dynamic Equations And Related Topics, Said R. Grace, Taher S. Hassan, Shurong Sun, Elvan Akin
Qualitative Analysis On Differential, Fractional Differential, And Dynamic Equations And Related Topics, Said R. Grace, Taher S. Hassan, Shurong Sun, Elvan Akin
Mathematics and Statistics Faculty Research & Creative Works
This issue on qualitative analysis on differential, fractional differential, and dynamic equations and related topics aims at an all-around research and the state-of-the-art theoretical, numerical, and practical achievements that contribute to this field.
Sneak-Out Principle On Time Scales, Martin Bohner, Samir H. Saker
Sneak-Out Principle On Time Scales, Martin Bohner, Samir H. Saker
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we show that the so-called "sneak-out principle" for discrete inequalities is valid also on a general time scale. In particular, we prove some new dynamic inequalities on time scales which as special cases contain discrete inequalities obtained by Bennett and Grosse-Erdmann. The main results also are used to formulate the corresponding continuous integral inequalities, and these are essentially new. The techniques employed in this paper are elementary and rely mainly on the time scales integration by parts rule, the time scales chain rule, the time scales Hölder inequality, and the time scales Minkowski inequality.
Oscillation Criteria For Fourth Order Nonlinear Positive Delay Differential Equations With A Middle Term, Said R. Grace, Elvan Akin
Oscillation Criteria For Fourth Order Nonlinear Positive Delay Differential Equations With A Middle Term, Said R. Grace, Elvan Akin
Mathematics and Statistics Faculty Research & Creative Works
In this article, we establish some new criteria for the oscillation of fourth order nonlinear delay differential equations of the form (Equation presented) provided that the second order equation (Equation presented) is nonoscillatiory or oscillatory. This equation with g(t) = t is considered in [8] and some oscillation criteria for this equation via certain energy functions are established. Here, we continue the study on the oscillatory behavior of this equation via some inequalities.
Discrete Grüss Type Inequality On Fractional Calculus, Elvan Akin, Serkan Asliyuce, Ayse Feza Guvenilir, Billur Kaymakcalan
Discrete Grüss Type Inequality On Fractional Calculus, Elvan Akin, Serkan Asliyuce, Ayse Feza Guvenilir, Billur Kaymakcalan
Mathematics and Statistics Faculty Research & Creative Works
We give a discrete Grüss type inequality on fractional calculus.
Subexponential Solutions Of Linear Volterra Difference Equations, Martin Bohner, Nasrin Sultana
Subexponential Solutions Of Linear Volterra Difference Equations, Martin Bohner, Nasrin Sultana
Mathematics and Statistics Faculty Research & Creative Works
We study the asymptotic behavior of the solutions of a scalar convolution sum-difference equation. The rate of convergence of the solution is found by determining the asymptotic behavior of the solution of the transient renewal equation.
Hartogs-Type Extension For Tube-Like Domains In C², Al Boggess, Roman Dwilewicz, Zbigniew Slodkowski
Hartogs-Type Extension For Tube-Like Domains In C², Al Boggess, Roman Dwilewicz, Zbigniew Slodkowski
Mathematics and Statistics Faculty Research & Creative Works
In this paper we consider the Hartogs-type extension problem for unbounded domains in C2. An easy necessary condition for a domain to be of Hartogs-type is that there is not a closed (in C2) complex variety of codimension one in the domain which is given by a holomorphic function smooth up to the boundary. The question is, how far this necessary condition is from the sufficient one? To show how complicated this question is, we give a class of tube-like domains which contain a complex line in the boundary which are either of Hartogs-type or not, …
Long-Time Dynamics Of 2d Double-Diffusive Convection: Analysis And/Of Numerics, Florentina Tone, Xiaoming Wang, Djoko Wirosoetisno
Long-Time Dynamics Of 2d Double-Diffusive Convection: Analysis And/Of Numerics, Florentina Tone, Xiaoming Wang, Djoko Wirosoetisno
Mathematics and Statistics Faculty Research & Creative Works
We consider a two-dimensional model of double-diffusive convection and its time discretisation using a second-order scheme (based on backward differentiation formula for the time derivative) which treats the non-linear term explicitly. Uniform bounds on the solutions of both the continuous and discrete models are derived (under a timestep restriction for the discrete model), proving the existence of attractors and invariant measures supported on them. as a consequence, the convergence of the attractors and longtime statistical properties of the discrete model to those of the continuous one in the limit of vanishing timestep can be obtained following established methods.
What You Gotta Know To Play Good In The Iterated Prisoner’S Dilemma, Ethan Akin
What You Gotta Know To Play Good In The Iterated Prisoner’S Dilemma, Ethan Akin
Mathematics and Statistics Faculty Research & Creative Works
For the iterated Prisoner's Dilemma there exist good strategies which solve the problem when we restrict attention to the long-term average payoff. When used by both players, these assure the cooperative payoff for each of them. Neither player can benefit by moving unilaterally to any other strategy, i.e., these provide Nash equilibria. In addition, if a player uses instead an alternative which decreases the opponent's payoff below the cooperative level, then his own payoff is decreased as well. Thus, if we limit attention to the long-term payoff, these strategies effectively stabilize cooperative behavior. The existence of such strategies follows from …
Global Attractor Of Solutions Of A Rational System In The Plane, Miron B. Bekker, Martin Bohner, Hristo D. Voulov
Global Attractor Of Solutions Of A Rational System In The Plane, Miron B. Bekker, Martin Bohner, Hristo D. Voulov
Mathematics and Statistics Faculty Research & Creative Works
We consider a two-dimensional autonomous system of rational difference equations with three positive parameters. It was conjectured that every positive solution of this system converges to a finite limit. Here we confirm this conjecture, subject to an additional assumption.
A Domain Decomposition Method For The Steady-State Navier-Stokes-Darcy Model With Beavers-Joseph Interface Condition, Xiaoming He, Jian Li, Yanping Lin, Ju Ming
A Domain Decomposition Method For The Steady-State Navier-Stokes-Darcy Model With Beavers-Joseph Interface Condition, Xiaoming He, Jian Li, Yanping Lin, Ju Ming
Mathematics and Statistics Faculty Research & Creative Works
This paper proposes and analyzes a Robin-type multiphysics domain decomposition method (DDM) for the steady-state Navier-Stokes-Darcy model with three interface conditions. In addition to the two regular interface conditions for the mass conservation and the force balance, the Beavers-Joseph condition is used as the interface condition in the tangential direction. The major mathematical difficulty in adopting the Beavers-Joseph condition is that it creates an indefinite leading order contribution to the total energy budget of the system [Y. Cao et al., Comm. Math. Sci., 8 (2010), pp. 1-25; Y. Cao et al., SIAM J. Numer. Anal., 47 (2010), pp. 4239-4256]. In …
Oscillation Of Second-Order Emden–Fowler Neutral Delay Differential Equations, Ravi P. Agarwal, Martin Bohner, Tongxing Li, Chenghui Zhang
Oscillation Of Second-Order Emden–Fowler Neutral Delay Differential Equations, Ravi P. Agarwal, Martin Bohner, Tongxing Li, Chenghui Zhang
Mathematics and Statistics Faculty Research & Creative Works
We establish some new criteria for the oscillation of second-order Emden–Fowler neutral delay differential equations. We study the case of super linear and the case of sublinear equations subject to various conditions. The results obtained show that the presence of a neutral term in a differential equation can cause or destroy oscillatory properties. Several examples are provided to illustrate the relevance of new theorems.
Planarity Of Whitney Levels, Jorbe Bustamante, W. J. Charatonik, Raul Escobedo
Planarity Of Whitney Levels, Jorbe Bustamante, W. J. Charatonik, Raul Escobedo
Mathematics and Statistics Faculty Research & Creative Works
First, we characterize all locally connected continua whose all Whitney levels are planar. Second, we show by example that planarity is not a (strong) Whitney reversible property. This answers a question from Illanes-Nadler book [2].