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Articles 121 - 150 of 440
Full-Text Articles in Mathematics
Parameter Identification For Gompertz And Logistic Dynamic Equations, Elvan Akin, Neslihan Nesliye Pelen, Ismail Ugur Tiryaki, Fusun Yalcin
Parameter Identification For Gompertz And Logistic Dynamic Equations, Elvan Akin, Neslihan Nesliye Pelen, Ismail Ugur Tiryaki, Fusun Yalcin
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we generalize and compare Gompertz and Logistic dynamic equations in order to describe the growth patterns of bacteria and tumor. First of all, we introduce two types of Gompertz equations, where the first type 4-paramater and 3-parameter Gompertz curves do not include the logarithm of the number of individuals, and then we derive 4-parameter and 3-parameter Logistic equations. We notice that Logistic curves are better in modeling bacteria whereas the growth pattern of tumor is described better by Gompertz curves. Increasing the number of parameters of Logistic curves give favorable results for bacteria while decreasing the number …
Binary Metrics, Samer Assaf, Tom Cuchta, Matt Insall
Binary Metrics, Samer Assaf, Tom Cuchta, Matt Insall
Mathematics and Statistics Faculty Research & Creative Works
We define a binary metric as a symmetric, distributive lattice ordered magma-valued function of two variables, satisfying a “triangle inequality". Using the notion of a Kuratowski topology, in which topologies are specified by closed sets rather than open sets, we prove that every topology is induced by a binary metric. We conclude with a discussion on the relation between binary metrics and some separation axioms.
Gehring Inequalities On Time Scales, Martin Bohner, S. H. Saker
Gehring Inequalities On Time Scales, Martin Bohner, S. H. Saker
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we first prove a new dynamic inequality based on an application of the time scales version of a Hardy-type inequality. Second, by employing the obtained inequality, we prove several Gehring-type inequalities on time scales. As an application of our Gehring-type inequalities, we present some interpolation and higher integrability theorems on time scales. The results as special cases, when the time scale is equal to the set of all real numbers, contain some known results, and when the time scale is equal to the set of all integers, the results are essentially new.
Existence And Multiplicity Of Weak Solutions For A Neumann Elliptic Problem With -Laplacian, Martin Bohner, Giuseppe Caristi, Fariba Gharehgazlouei, Shapour Heidarkhani
Existence And Multiplicity Of Weak Solutions For A Neumann Elliptic Problem With -Laplacian, Martin Bohner, Giuseppe Caristi, Fariba Gharehgazlouei, Shapour Heidarkhani
Mathematics and Statistics Faculty Research & Creative Works
We are interested in the existence of multiple weak solutions for the Neumann elliptic problem involving the anisotropic -Laplacian operator, on a bounded domain with smooth boundary. We work on the anisotropic variable exponent Sobolev space, and by using a consequence of the local minimum theorem due to Bonanno, we establish existence of at least one weak solution under algebraic conditions on the nonlinear term. Also, we discuss existence of at least two weak solutions for the problem, under algebraic conditions including the classical Ambrosetti-Rabinowitz condition on the nonlinear term. Furthermore, by employing a three critical point theorem due to …
Efficient Smooth Non-Convex Stochastic Compositional Optimization Via Stochastic Recursive Gradient Descent, Wenqing Hu, Chris Junchi Li, Xiangru Lian, Ji Liu, Huizhuo Yuan
Efficient Smooth Non-Convex Stochastic Compositional Optimization Via Stochastic Recursive Gradient Descent, Wenqing Hu, Chris Junchi Li, Xiangru Lian, Ji Liu, Huizhuo Yuan
Mathematics and Statistics Faculty Research & Creative Works
Stochastic compositional optimization arises in many important machine learning applications. The objective function is the composition of two expectations of stochastic functions, and is more challenging to optimize than vanilla stochastic optimization problems. In this paper, we investigate the stochastic compositional optimization in the general smooth non-convex setting. We employ a recently developed idea of Stochastic Recursive Gradient Descent to design a novel algorithm named SARAH-Compositional, and prove a sharp Incremental First-order Oracle (IFO) complexity upper bound for stochastic compositional optimization: 𝒪((n + m)1/2ε-2) in the finite-sum case and 𝒪(ε-3) in the online case. …
Approximation Dynamics, Ethan Akin
Approximation Dynamics, Ethan Akin
Mathematics and Statistics Faculty Research & Creative Works
We describe the approximation of a continuous dynamical system on a p.l. manifold or Cantor set by a tractable system. A system is tractable when it has a finite number of chain components and, with respect to a given full background measure, almost every point is generic for one of a finite number of ergodic invariant measures. The approximations we use are non-degenerate simplicial dynamical systems for p.l. manifolds and shift-like dynamical systems for Cantor Sets.
A Multi-Step Approach To Modeling The 24-Hour Daily Profiles Of Electricity Load Using Daily Splines, Abdelmonaem Jornaz, V. A. Samaranayake
A Multi-Step Approach To Modeling The 24-Hour Daily Profiles Of Electricity Load Using Daily Splines, Abdelmonaem Jornaz, V. A. Samaranayake
Mathematics and Statistics Faculty Research & Creative Works
Forecasting of real-time electricity load has been an important research topic over many years. Electricity load is driven by many factors, including economic conditions and weather. Furthermore, the demand for electricity varies with time, with different hours of the day and different days of the week having an effect on the load. This paper proposes a hybrid load-forecasting method that combines classical time series formulations with cubic splines to model electricity load. It is shown that this approach produces a model capable of making short-term forecasts with reasonable accuracy. In contrast to forecasting models that utilize a multitude of regressor …
An Optimal Edg Method For Distributed Control Of Convection Diffusion Pdes, X. Zhang, Y. Zhang, John R. Singler
An Optimal Edg Method For Distributed Control Of Convection Diffusion Pdes, X. Zhang, Y. Zhang, John R. Singler
Mathematics and Statistics Faculty Research & Creative Works
We propose an embedded discontinuous Galerkin (EDG) method to approximate the solution of a distributed control problem governed by convection diffusion PDEs, and obtain optimal a priori error estimates for the state, dual state, their uxes, and the control. Moreover, we prove the optimize-then-discretize (OD) and discrtize-then-optimize (DO) approaches coincide. Numerical results confirm our theoretical results.
Three-Dimensional Rotation Of Paramagnetic And Ferromagnetic Prolate Spheroids In Simple Shear And Uniform Magnetic Field, Christopher A. Sobecki, Yanzhi Zhang, Cheng Wang
Three-Dimensional Rotation Of Paramagnetic And Ferromagnetic Prolate Spheroids In Simple Shear And Uniform Magnetic Field, Christopher A. Sobecki, Yanzhi Zhang, Cheng Wang
Mathematics and Statistics Faculty Research & Creative Works
We examine a time-dependent, three-dimensional rotation of magnetic ellipsoidal particles in a two-dimensional, simple shear flow and a uniform magnetic field. We consider that the particles have paramagnetic and ferromagnetic properties, and we compare their rotational dynamics due to the strengths and directions of the applied uniform magnetic field. We determine the critical magnetic field strength that can pin the particles' rotations. Above the critical field strength, the particles' stable steady angles were determined. In a weak magnetic regime (below the critical field strength), a paramagnetic particle's polar angle will oscillate toward the magnetic field plane while its azimuthal angle …
On Nonoscillatory Solutions Of Three Dimensional Time-Scale Systems, Elvan Akin, Taher Hassan, Ozkan Ozturk, Ismail U. Tiryaki
On Nonoscillatory Solutions Of Three Dimensional Time-Scale Systems, Elvan Akin, Taher Hassan, Ozkan Ozturk, Ismail U. Tiryaki
Mathematics and Statistics Faculty Research & Creative Works
In this article, we classify nonoscillatory solutions of a system of three-dimensional time scale systems. We use the method of considering the sign of components of such solutions. Examples are given to highlight some of our results. Moreover, the existence of such solutions is obtained by Knaster's fixed point theorem.
An Hdg Method For Dirichlet Boundary Control Of Convection Dominated Diffusion Pdes, Gang Chen, John R. Singler, Yangwen Zhang
An Hdg Method For Dirichlet Boundary Control Of Convection Dominated Diffusion Pdes, Gang Chen, John R. Singler, Yangwen Zhang
Mathematics and Statistics Faculty Research & Creative Works
We first propose a hybridizable discontinuous Galerkin (HDG) method to approximate the solution of a convection dominated Dirichlet boundary control problem without constraints. Dirichlet boundary control problems and convection dominated problems are each very challenging numerically due to solutions with low regularity and sharp layers, respectively. Although there are some numerical analysis works in the literature on diffusion dominated convection diffusion Dirichlet boundary control problems, we are not aware of any existing numerical analysis works for convection dominated boundary control problems. Moreover, the existing numerical analysis techniques for convection dominated PDEs are not directly applicable for the Dirichlet boundary control …
Joint Manufacturing And Onsite Microgrid System Control Using Markov Decision Process And Neural Network Integrated Reinforcement Learning, Wenqing Hu, Zeyi Sun, Y. Zhang, Y. Li
Joint Manufacturing And Onsite Microgrid System Control Using Markov Decision Process And Neural Network Integrated Reinforcement Learning, Wenqing Hu, Zeyi Sun, Y. Zhang, Y. Li
Mathematics and Statistics Faculty Research & Creative Works
Onsite microgrid generation systems with renewable sources are considered a promising complementary energy supply system for manufacturing plant, especially when outage occurs during which the energy supplied from the grid is not available. Compared to the widely recognized benefits in terms of the resilience improvement when it is used as a backup energy system, the operation along with the electricity grid to support the manufacturing operations in non-emergent mode has been less investigated. In this paper, we propose a joint dynamic decision-making model for the optimal control for both manufacturing system and onsite generation system. Markov Decision Process (MDP) is …
On The Instabilities And Transitions Of The Western Boundary Current, Daozhi Han, Marco Hernandez, Quan Wang
On The Instabilities And Transitions Of The Western Boundary Current, Daozhi Han, Marco Hernandez, Quan Wang
Mathematics and Statistics Faculty Research & Creative Works
We study the stability and dynamic transitions of the western boundary currents in a rectangular closed basin. By reducing the infinite dynamical system to a finite dimensional one via center manifold reduction, we derive a non-dimensional transition number that determines the types of dynamical transition. We show by careful numerical evaluation of the transition number that both continuous transitions (supercritical Hopf bifurcation) and catastrophic transitions (subcritical Hopf bifurcation) can happen at the critical Reynolds number, depending on the aspect ratio and stratification. The regions separating the continuous and catastrophic transitions are delineated on the parameter plane.
Positivity-Preserving, Energy Stable Numerical Schemes For The Cahn-Hilliard Equation With Logarithmic Potential, Wenbin Chen, Cheng Wang, Xiaoming Wang, Steven M. Wise
Positivity-Preserving, Energy Stable Numerical Schemes For The Cahn-Hilliard Equation With Logarithmic Potential, Wenbin Chen, Cheng Wang, Xiaoming Wang, Steven M. Wise
Mathematics and Statistics Faculty Research & Creative Works
In this paper we present and analyze finite difference numerical schemes for the Cahn-Hilliard equation with a logarithmic Flory Huggins energy potential. Both first and second order accurate temporal algorithms are considered. in the first order scheme, we treat the nonlinear logarithmic terms and the surface diffusion term implicitly and update the linear expansive term and the mobility explicitly. We provide a theoretical justification that this numerical algorithm has a unique solution, such that the positivity is always preserved for the logarithmic arguments, i.e., the phase variable is always between −1 and 1, at a point-wise level. in particular, our …
Smale Strategies For The $N$-Person Iterated Prisoner's Dilemma, Ethan Akin, Sławomir Plaskacz, Joanna Zwierzchowska
Smale Strategies For The $N$-Person Iterated Prisoner's Dilemma, Ethan Akin, Sławomir Plaskacz, Joanna Zwierzchowska
Mathematics and Statistics Faculty Research & Creative Works
Adapting methods introduced by Steven Smale, we describe good strategies for a symmetric version of the Iterated Prisoner's Dilemma with n players.
Extensions Of Schauder's And Darbo's Fixed Point Theorems, Zhaocai Hao, Martin Bohner, Junjun Wang
Extensions Of Schauder's And Darbo's Fixed Point Theorems, Zhaocai Hao, Martin Bohner, Junjun Wang
Mathematics and Statistics Faculty Research & Creative Works
In this paper, some new extensions of Schauder's and Darbo's fixed point theorems are given. As applications of the main results, the existence of global solutions for first-order nonlinear integro-differential equations of mixed type in a real Banach space is investigated.
A Second Order Bdf Numerical Scheme With Variable Steps For The Cahn-Hilliard Equation, Wenbin Chen, Xiaoming Wang, Yue Yan, Zhuying Zhang
A Second Order Bdf Numerical Scheme With Variable Steps For The Cahn-Hilliard Equation, Wenbin Chen, Xiaoming Wang, Yue Yan, Zhuying Zhang
Mathematics and Statistics Faculty Research & Creative Works
We present and analyze a second order in time variable step BDF2 numerical scheme for the Cahn-Hilliard equation. the construction relies on a second order backward difference, convex-splitting technique and viscous regularizing at the discrete level. We show that the scheme is unconditionally stable and uniquely solvable. in addition, under mild restriction on the ratio of adjacent time-steps, an optimal second order in time convergence rate is established. the proof involves a novel generalized discrete Gronwall-type inequality. as far as we know, this is the first rigorous proof of second order convergence for a variable step BDF2 scheme, even in …
Almost Periodic Functions In Quantum Calculus, Martin Bohner, Jaqueline Godoy Mesquita
Almost Periodic Functions In Quantum Calculus, Martin Bohner, Jaqueline Godoy Mesquita
Mathematics and Statistics Faculty Research & Creative Works
In this article, we introduce the concepts of Bochner and Bohr almost periodic functions in quantum calculus and show that both concepts are equivalent. Also, we present a correspondence between almost periodic functions defined in quantum calculus and N0, proving several important properties for this class of functions. We investigate the existence of almost periodic solutions of linear and nonlinear q-difference equations. Finally, we provide some examples of almost periodic functions in quantum calculus.
Modeling And An Immersed Finite Element Method For An Interface Wave Equation, Jinwei Bai, Yong Cao, Xiaoming He, Hongyan Liu, Xiaofeng Yang
Modeling And An Immersed Finite Element Method For An Interface Wave Equation, Jinwei Bai, Yong Cao, Xiaoming He, Hongyan Liu, Xiaofeng Yang
Mathematics and Statistics Faculty Research & Creative Works
The electromagnetic field, which is governed by Maxwell's equation, plays a key role in plasma simulation. In this article, we first derive the interface conditions when we rewrite the interface Maxwell's equation, whose problem domain involves complex media such as objects of different materials, into a parabolic–hyperbolic type of interface model, which is a modified wave equation by adding a first order time derivative term due to the lossy medium. Based on the interface conditions and the existing bilinear immersed finite element space for the interface Poisson equation, we propose an immersed finite element method for the spatial discretization of …
A Further Extension Of The Extended Riemann-Liouville Fractional Derivative Operator, Martin Bohner, Gauhar Rahman, Shahid Mubeen, Kottakkaran Sooppy Nisar
A Further Extension Of The Extended Riemann-Liouville Fractional Derivative Operator, Martin Bohner, Gauhar Rahman, Shahid Mubeen, Kottakkaran Sooppy Nisar
Mathematics and Statistics Faculty Research & Creative Works
The main objective of this paper is to establish the extension of an extended fractional derivative operator by using an extended beta function recently defined by Parmar et al. by considering the Bessel functions in its kernel. We also give some results related to the newly defined fractional operator, such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.
Dynamics Of Paramagnetic And Ferromagnetic Ellipsoidal Particles In Shear Flow Under A Uniform Magnetic Field, Christopher A. Sobecki, Jie Zhang, Yanzhi Zhang, Cheng Wang
Dynamics Of Paramagnetic And Ferromagnetic Ellipsoidal Particles In Shear Flow Under A Uniform Magnetic Field, Christopher A. Sobecki, Jie Zhang, Yanzhi Zhang, Cheng Wang
Mathematics and Statistics Faculty Research & Creative Works
We investigate the two-dimensional dynamic motion of magnetic particles of ellipsoidal shapes in shear flow under the influence of a uniform magnetic field. In the first part, we present a theoretical analysis of the rotational dynamics of the particles in simple shear flow. By considering paramagnetic and ferromagnetic particles, we study the effects of the direction and strength of the magnetic field on the particle rotation. The critical magnetic-field strength, at which particle rotation is impeded, is determined. In a weak-field regime (i.e., below the critical strength) where the particles execute complete rotations, the symmetry property of the rotational velocity …
A Multi-Step Nonlinear Dimension-Reduction Approach With Applications To Bigdata, R. Krishnan, V. A. Samaranayake, Jagannathan Sarangapani
A Multi-Step Nonlinear Dimension-Reduction Approach With Applications To Bigdata, R. Krishnan, V. A. Samaranayake, Jagannathan Sarangapani
Mathematics and Statistics Faculty Research & Creative Works
In this paper, a multi-step dimension-reduction approach is proposed for addressing nonlinear relationships within attributes. In this work, the attributes in the data are first organized into groups. In each group, the dimensions are reduced via a parametric mapping that takes into account nonlinear relationships. Mapping parameters are estimated using a low rank singular value decomposition (SVD) of distance covariance. Subsequently, the attributes are reorganized into groups based on the magnitude of their respective singular values. The group-wise organization and the subsequent reduction process is performed for multiple steps until a singular value-based user-defined criterion is satisfied. Simulation analysis is …
Preface Of 2nd Annual Meeting Of Siam Central States Section, Xiaoming He, Stephen Pankavich, Erik Van Vleck, Zhu Wang, Xiu Ye
Preface Of 2nd Annual Meeting Of Siam Central States Section, Xiaoming He, Stephen Pankavich, Erik Van Vleck, Zhu Wang, Xiu Ye
Mathematics and Statistics Faculty Research & Creative Works
No abstract provided.
Approximation Degree Of Durrmeyer-Bézier Type Operators, Purshottam N. Agrawal, Serkan Araci, Martin Bohner, Kumari Lipi
Approximation Degree Of Durrmeyer-Bézier Type Operators, Purshottam N. Agrawal, Serkan Araci, Martin Bohner, Kumari Lipi
Mathematics and Statistics Faculty Research & Creative Works
Recently, a mixed hybrid operator, generalizing the well-known Phillips operators and Baskakov-Szász type operators, was introduced. In this paper, we study Bézier variant of these new operators. We investigate the degree of approximation of these operators by means of the Lipschitz class function, the modulus of continuity, and a weighted space. We study a direct approximation theorem by means of the unified Ditzian-Totik modulus of smoothness. Furthermore, the rate of convergence for functions having derivatives of bounded variation is discussed.
Phytoforensics: Trees As Bioindicators Of Potential Indoor Exposure Via Vapor Intrusion, Jordan L. Wilson, V. A. Samaranayake, Matt A. Limmer, Joel Gerard Burken
Phytoforensics: Trees As Bioindicators Of Potential Indoor Exposure Via Vapor Intrusion, Jordan L. Wilson, V. A. Samaranayake, Matt A. Limmer, Joel Gerard Burken
Mathematics and Statistics Faculty Research & Creative Works
Human exposure to volatile organic compounds (VOCs) via vapor intrusion (VI) is an emerging public health concern with notable detrimental impacts on public health. Phytoforensics, plant sampling to semi-quantitatively delineate subsurface contamination, provides a potential non-invasive screening approach to detect VI potential, and plant sampling is effective and also time- and cost-efficient. Existing VI assessment methods are time- and resource-intensive, invasive, and require access into residential and commercial buildings to drill holes through basement slabs to install sampling ports or require substantial equipment to install groundwater or soil vapor sampling outside the home. Tree-core samples collected in 2 days at …
Mini Review: A Note On Nonoscillatory Solutions For Higher Dimensional Time Scale Systems, Elvan Akin, Ozkan Ozturk, Ismail Ugur Tiryaki, Gulsah Yeni
Mini Review: A Note On Nonoscillatory Solutions For Higher Dimensional Time Scale Systems, Elvan Akin, Ozkan Ozturk, Ismail Ugur Tiryaki, Gulsah Yeni
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we focus on nonoscillatory solutions of two (2D) and three (3D) dimensional time scale systems and discuss nonexistence of such solutions.
The Generalized Hypergeometric Difference Equation, Martin Bohner, Tom Cuchta
The Generalized Hypergeometric Difference Equation, Martin Bohner, Tom Cuchta
Mathematics and Statistics Faculty Research & Creative Works
A difference equation analogue of the generalized hypergeometric differential equation is defined, its contiguous relations are developed, and its relation to numerous well-known classical special functions are demonstrated.
A Higher-Order Ensemble/Proper Orthogonal Decomposition Method For The Nonstationary Navier-Stokes Equations, Max Gunzburger, Nan Jiang, Michael Schneier
A Higher-Order Ensemble/Proper Orthogonal Decomposition Method For The Nonstationary Navier-Stokes Equations, Max Gunzburger, Nan Jiang, Michael Schneier
Mathematics and Statistics Faculty Research & Creative Works
Partial differential equations (PDE) often involve parameters, such as viscosity or density. An analysis of the PDE may involve considering a large range of parameter values, as occurs in uncertainty quantification, control and optimization, inference, and several statistical techniques. The solution for even a single case may be quite expensive; whereas parallel computing may be applied, this reduces the total elapsed time but not the total computational effort. In the case of flows governed by the Navier-Stokes equations, a method has been devised for computing an ensemble of solutions. Recently, a reduced-order model derived from a proper orthogonal decomposition (POD) …
Parametrization Of Scale-Invariant Self-Adjoint Extensions Of Scale-Invariant Symmetric Operators, Miron B. Bekker, Martin Bohner, Alexander P. Ugol'nikov, Hristo Voulov
Parametrization Of Scale-Invariant Self-Adjoint Extensions Of Scale-Invariant Symmetric Operators, Miron B. Bekker, Martin Bohner, Alexander P. Ugol'nikov, Hristo Voulov
Mathematics and Statistics Faculty Research & Creative Works
On a Hilbert space H, we consider a symmetric scale-invariant operator with equal defect numbers. It is assumed that the operator has at least one scale invariant self-adjoint extension in H. We prove that there is a one-to-one correspondence between (generalized) resolvents of scale-invariant extensions and solutions of some functional equation. Two examples of Dirac-type operators are considered.
Decoupled, Linear, And Energy Stable Finite Element Method For The Cahn-Hilliard-Navier-Stokes-Darcy Phase Field Model, Yali Gao, Xiaoming He, Liquan Mei, Xiaofeng Yang
Decoupled, Linear, And Energy Stable Finite Element Method For The Cahn-Hilliard-Navier-Stokes-Darcy Phase Field Model, Yali Gao, Xiaoming He, Liquan Mei, Xiaofeng Yang
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we consider the numerical approximation for a phase field model of the coupled two-phase free flow and two-phase porous media flow. This model consists of Cahn—Hilliard—Navier—Stokes equations in the free flow region and Cahn—Hilliard—Darcy equations in the porous media region that are coupled by seven interface conditions. The coupled system is decoupled based on the interface conditions and the solution values on the interface from the previous time step. A fully discretized scheme with finite elements for the spatial discretization is developed to solve the decoupled system. In order to deal with the difficulties arising from the …