Mathematics Commons^™

On The Qualitative Analysis Of Volterra Iddes With Infinite Delay, Osman Tunç, Erdal Korkmaz, Özkan Atan

Applications and Applied Mathematics: An International Journal (AAM)

This investigation deals with a nonlinear Volterra integro-differential equation with infinite retardation (IDDE).We will prove three new results on the stability, uniformly stability (US) and square integrability (SI) of solutions of that IDDE. The proofs of theorems rely on the use of an appropriate Lyapunov-Krasovskii functional (LKF). By the outcomes of this paper, we generalize and obtain some former results in mathematical literature under weaker conditions.

Avia 201 Project 1 Windtunnel Lab Form Ver 1.20 20200323, Nihad E. Daidzic

Aviation Department Publications

To introduce aviation/aeronautics/aerospace students to wind tunnel(s) and methods used in experimental identification of various aerodynamic (and stability) coefficients of airfoils (2D), wings (3D) and scale models.

Mathematical Modelling Of The Tuberculosis Epidemiology, Ally Yeketi Ayinla

Student Works (2020-2029)

This project analyses the tuberculosis (TB) epidemic mathematically using compartmental modelling approach. Three models are presented to discuss drug susceptible and multi-drug resistant TB. The first model presented has 4 compartments; susceptible, exposed, infectious and recovered. The relevance of the exposed class in managing TB is analysed and found to be useful in delaying the eventual onset of the infection. Compared to previous researches, our results significantly show that when efforts are made such that no infected individual bypasses the exposed class and progresses directly to the infectious, the TB epidemic is successfully combatted. Also, the model is used to …

Discrete Evolutionary Population Models: A New Approach, K. Mokni, Saber Elaydi, M. Ch-Chaoui, A. Eladdadi

Mathematics Faculty Research

In this paper, we apply a new approach to a special class of discrete time evolution models and establish a solid mathematical foundation to analyse them. We propose new single and multi-species evolutionary competition models using the evolutionary game theory that require a more advanced mathematical theory to handle effectively. A key feature of this new approach is to consider the discrete models as non-autonomous difference equations. Using the powerful tools and results developed in our recent work [E. D'Aniello and S. Elaydi, The structure of ω-limit sets of asymptotically non-autonomous discrete dynamical systems, Discr. Contin. Dyn. Series B. …

Quantitative Analysis Of A Stochastic Seitr Epidemic Model With Multiple Stages Of Infection And Treatment, Olusegun M. Otunuga, Mobolaji O. Ogunsolu

Mathematics Faculty Research

We present a mathematical analysis of the transmission of certain diseases using a stochastic susceptible-exposed-infectious-treated-recovered (SEITR) model with multiple stages of infection and treatment and explore the effects of treatments and external fluctuations in the transmission, treatment and recovery rates. We assume external fluctuations are caused by variability in the number of contacts between infected and susceptible individuals. It is shown that the expected number of secondary infections produced (in the absence of noise) reduces as treatment is introduced into the population. By defining R_T,n and ℛ_T,n as the basic deterministic and stochastic reproduction …

Necessary Conditions For Stability Of Vehicle Formations, Pablo Enrique Baldivieso Blanco

Dissertations and Theses

Necessary conditions for stability of coupled autonomous vehicles in R are established in this thesis. The focus is on linear arrays with decentralized vehicles, where each vehicle interacts with only a few of its neighbors. Decentralized means that there is no central authority governing the motion. Instead, each vehicle registers only velocity and position relative to itself and bases its acceleration only on those data. Explicit expressions are obtained for necessary conditions for asymptotic stability in the cases that a system consists of a periodic arrangement of two or three different types of vehicles, i.e. configurations as follows: ...2-1-2-1 or …

Basic Parameters Of Physical Properties Of The Saline Soils In Roadside Of Highways, A. D. Kayumov Abdubaki Djalilovic, O.Z. Zafarov, N. D. Saidbaxromova

Central Asian Problems of Modern Science and Education

This article provides information about the basic parameters of physical properties of the saline soils in roadside of highways, the key and rational indicators which are determined by the experiments and by calculating respectively in the evaluation of soil physical states, the density of solid particles, the basic parameters of density and moisture of the soil in natural condition

Basic Parameters Of Physical Properties Of The Saline Soils In Roadside Of Highways, A. D. Kayumov Abdubaki Djalilovic, O.Z. Zafarov, N. D. Saidbaxromova

Central Asian Problems of Modern Science and Education

This article provides information about the basic parameters of physical properties of the saline soils in roadside of highways, the key and rational indicators which are determined by the experiments and by calculating respectively in the evaluation of soil physical states, the density of solid particles, the basic parameters of density and moisture of the soil in natural condition

Distributed Lagrange Multiplier/Fictitious Domain Finite Element Method For A Transient Stokes Interface Problem With Jump Coefficients, Andrew Lundberg, Pengtao Sun, Cheng Wang, Chen-Song Zhang

Mathematical Sciences Faculty Research

The distributed Lagrange multiplier/fictitious domain (DLM/FD)-mixed finite element method is developed and analyzed in this paper for a transient Stokes interface problem with jump coefficients. The semi- and fully discrete DLM/FD-mixed finite element scheme are developed for the first time for this problem with a moving interface, where the arbitrary Lagrangian-Eulerian (ALE) technique is employed to deal with the moving and immersed subdomain. Stability and optimal convergence properties are obtained for both schemes. Numerical experiments are carried out for different scenarios of jump coefficients, and all theoretical results are validated.

Exponential Stabilization Of A Neutrally Delayed Viscoelastic Timoshenko Beam, Sebti Kerbal, Nasser Eddine Tatar

Turkish Journal of Mathematics

A Timoshenko type beam subject to a viscoelastic damping in the rotational displacement component is considered. Taking into account a neutral type delay, we prove a fast stability result despite the previously observed destabilizing effect due to delays in such systems. The proof relies on the introduction of nine different functionals with which we modify the energy of the system. These functionals are carefully selected and adapted to cope with both the viscoelasticity and the neutral delay.

Stability Analysis For A Class Of Nabla $(Q,H)$-Fractional Difference Equations, Xiang Liu, Baoguo Jia, Lynn Erbe, Allan Peterson

Turkish Journal of Mathematics

This paper investigates stability of the nabla $(q,h)$-fractional difference equations. Asymptotic stability of the special nabla $(q,h)$-fractional difference equations are discussed. Stability theorems for discrete fractional Lyapunov direct method are proved. Furthermore, we give some new lemmas (including important comparison theorems) related to the nabla $(q,h)$-fractional difference operators that allow proving the stability of the nabla $(q,h)$-fractional difference equations, by means of the discrete fractional Lyapunov direct method, using Lyapunov functions. Some examples are given to illustrate these results.

A Circulant Functional Equation For The Additive Function And Its Stability, Vichian Laohakosol, Watcharapon Pimsert, Kanet Ponpetch

Turkish Journal of Mathematics

A general solution of a matrix functional equation involving circulant matrices of the additive function is determined, and its stability is established.

Approximate Analytical Solutions Of Space-Fractional Telegraph Equations By Sumudu Adomian Decomposition Method, Hasib Khan, Cemil Tunç, Rahmat A. Khan, Akhtyar G. Shirzoi, Aziz Khan

Applications and Applied Mathematics: An International Journal (AAM)

The main goal in this work is to establish a new and efficient analytical scheme for space fractional telegraph equation (FTE) by means of fractional Sumudu decomposition method (SDM). The fractional SDM gives us an approximate convergent series solution. The stability of the analytical scheme is also studied. The approximate solutions obtained by SDM show that the approach is easy to implement and computationally very much attractive. Further, some numerical examples are presented to illustrate the accuracy and stability for linear and nonlinear cases.

Global Stability For A 2n + 1 Dimensional Hiv/Aids Epidemic Model With Treatments, Olusegun Michael Otunuga

Mathematics Faculty Research

In this work, we derive and analyze a 2n + 1-dimensional deterministic differential equation modeling the transmission and treatment of HIV (Human Immunodeficiency Virus) disease. The model is extended to a stochastic differential equation by introducing noise in the transmission rate of the disease. A theoretical treatment strategy of regular HIV testing and immediate treatment with Antiretroviral Therapy (ART) is investigated in the presence and absence of noise. By defining R0, n, Rt, n and Rt,n as the deterministic basic reproduction number in the absence of ART treatments, deterministic basic reproduction number in the presence of …

Genetic Variation Determines Which Feedbacks Drive And Alter Predator–Prey Eco-Evolutionary Cycles, Michael H. Cortez

Mathematics and Statistics Faculty Publications

Evolution can alter the ecological dynamics of communities, but the effects depend on the magnitudes of standing genetic variation in the evolving species. Using an eco‐coevolutionary predator–prey model, I identify how the magnitudes of prey and predator standing genetic variation determine when ecological, evolutionary, and eco‐evolutionary feedbacks influence system stability and the phase lags in predator–prey cycles. Here, feedbacks are defined by subsystems, i.e., the dynamics of a subset of the components of the whole system when the other components are held fixed; ecological (evolutionary) feedbacks involve the direct and indirect effects between population densities (species traits) and eco‐evolutionary feedbacks …

Using An A Priori Estimate For Constructing Difference Schemes For Quasi-Linear Hyperbolic Systems, Rakhmatillo Aloev, Mirzoali Khudayberganov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper we consider a class of quasi-linear hyperbolic systems, which allows the construction of a dissipative energy integrals. In the basis of the design and investigation the stability of difference schemes for the numerical solution of the initial boundary value problems for the above class of quasi-linear hyperbolic systems, we put the existence of a discrete analogue of the dissipative energy integrals.

Using An A Priori Estimate For Constructing Difference Schemes For Quasi-Linear Hyperbolic Systems, Rakhmatillo Aloev, Mirzoali Khudayberganov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper we consider a class of quasi-linear hyperbolic systems, which allows the construction of a dissipative energy integrals. In the basis of the design and investigation the stability of difference schemes for the numerical solution of the initial boundary value problems for the above class of quasi-linear hyperbolic systems, we put the existence of a discrete analogue of the dissipative energy integrals.

Partitioning The Effects Of Eco-Evolutionary Feedbacks On Community Stability, Swati Patel, Michael H. Cortez, Sebastian J. Schreiber

Mathematics and Statistics Faculty Publications

A fundamental challenge in ecology continues to be identifying mechanisms that stabilize community dynamics. By altering the interactions within a community, eco-evolutionary feedbacks may play a role in community stability. Indeed, recent empirical and theoretical studies demonstrate that these feedbacks can stabilize or destabilize communities and, moreover, that this sometimes depends on the relative rate of ecological to evolutionary processes. So far, theory on how eco-evolutionary feedbacks impact stability exists only for a few special cases. In our work, we develop a general theory for determining the effects of eco-evolutionary feedbacks on stability in communities with an arbitrary number of …

Switching Diffusion Systems With Past-Dependent Switching Having A Countable State Space, Hai Dang Nguyen

Wayne State University Dissertations

Emerging and existing applications in wireless communications, queueing networks, biological models, financial engineering, and social networks demand the

mathematical modeling and analysis of hybrid models in which continuous dynamics and discrete events coexist.

Assuming that the systems are in continuous times,

stemming from stochastic-differential-equation-based models and random discrete events,

switching diffusions come into being. In such systems, continuous states and discrete events

(discrete states)

coexist and interact.

A switching diffusion is a two-component process $(X(t),\alpha(t))$, a continuous component and a discrete component taking values in a discrete set (a set consisting of isolated points).

When the discrete component takes a …

Exponential Stability Of Periodic Solutions Of Recurrent Neural Networks With Functional Dependence On Piecewise Constant Argument, Marat Akhmet, Duygu Aruğaslan Çi̇nçi̇n, Nur Cengi̇z

Turkish Journal of Mathematics

In this study, we develop a model of recurrent neural networks with functional dependence on piecewise constant argument of generalized type. Using the theoretical results obtained for functional differential equations with piecewise constant argument, we investigate conditions for existence and uniqueness of solutions, bounded solutions, and exponential stability of periodic solutions. We provide conditions based on the parameters of the model.

An Effective Application Of Differential Quadrature Method Based Onmodified Cubic B-Splines To Numerical Solutions Of The Kdv Equation, Ali̇ Başhan

Turkish Journal of Mathematics

In this study, numerical solutions of the third-order nonlinear Korteweg--de Vries (KdV) equation are obtained via differential quadrature method based on modified cubic B-splines. Five different problems are solved. To show the accuracy of the proposed method, $L_{2}$ and $L_{\infty }$ error norms of the problem, which has an analytical solution, and three lowest invariants are calculated and reported. The obtained solutions are compared with some earlier works. Stability analysis of the present method is also given.

Stability Study On Shear Flow And Vortices In Late Boundary Layer Transition, Jie Tang

Mathematics Dissertations - Archive

Turbulence is still an unsolved scientific problem, it has been regarded as “the most important unsolved problem of classical physics”. Dr. Liu proposed a new mechanism about turbulence generation and sustenance after decades of research on turbulence and transition. His new idea challenged the classical theorem in many aspects. One of them is the flow stability of transition. Dr. Liu believes that inside the flow field, shear (dominant in laminar) is very unstable while rotation (dominant in turbulence) is relative stable. This inherent property of flow creates the trend that non-vertical vorticity must transfer to vertical vorticity, and causes the …

Infinitely Many Stability Switches In A Problem With Sublinear Oscillatory Boundary Conditions, Alfonso Castro, Rosa Pardo

All HMC Faculty Publications and Research

We consider the elliptic equation −u+u = 0 with nonlinear boundary condition ∂u ∂n = λu + g(λ, x, u), where g(λ,x,s) s → 0, as |s|→∞ and g is oscillatory. We provide sufficient conditions on g for the existence of unbounded sequences of stable solutions, unstable solutions, and turning points, even in the absence of resonant solutions.

$\Mathcal{Vw}$-Gorenstein Complexes, Renyu Zhao, Wei Ren

Turkish Journal of Mathematics

Let $\mathcal{V,W}$ be two classes of modules. In this paper, we introduce and study $\mathcal{VW}$-Gorenstein complexes as a common generalization of $\mathcal{W}$-complexes, Gorenstein projective (resp., Gorenstein injective) complexes, and $G_C$-projective (resp., $G_C$-injective) complexes. It is shown that under certain hypotheses a complex $X$ is $\mathcal{VW}$-Gorenstein if and only if each $X^n$ is a $\mathcal{VW}$-Gorenstein module. This result unifies the corresponding results of the aforementioned complexes. As an application, the stability of $\mathcal{VW}$-Gorenstein complexes is explored.

Stability Of Nonmonotone Critical Traveling Waves Forspatially Discrete Reaction-Diffusion Equations With Time Delay, Ge Tian, Guobao Zhang, Zhao-Xing Yang

Turkish Journal of Mathematics

This paper is concerned with the existence and stability of critical traveling waves (waves with minimal speed $c=c_*$) for a nonmonotone spatially discrete reaction-diffusion equation with time delay. We first show the existence of critical traveling waves by a limiting argument. Then, using the technical weighted energy method with some new variations, we prove that the critical traveling waves $\phi(x+c_{*}t)$ (monotone or nonmonotone) are time-asymptotically stable when the initial perturbations are small in a certain weighted Sobolev norm.

Near Optimal Step Size And Momentum In Gradient Descent For Quadratic Functions, Engi̇n Taş, Memmedağa Memmedli̇

Turkish Journal of Mathematics

Many problems in statistical estimation, classification, and regression can be cast as optimization problems. Gradient descent, which is one of the simplest and easy to implement multivariate optimization techniques, lies at the heart of many powerful classes of optimization methods. However, its major disadvantage is the slower rate of convergence with respect to the other more sophisticated algorithms. In order to improve the convergence speed of gradient descent, we simultaneously determine near-optimal scalar step size and momentum factor for gradient descent in a deterministic quadratic bowl from the largest and smallest eigenvalues of the Hessian. The resulting algorithm is demonstrated …

Orbital Stability Results For Soliton Solutions To Nonlinear Schrödinger Equations With External Potentials, Joseph B. Lindgren

Theses and Dissertations--Mathematics

For certain nonlinear Schroedinger equations there exist solutions which are called solitary waves. Addition of a potential $V$ changes the dynamics, but for small enough $||V||_{L^\infty}$ we can still obtain stability (and approximately Newtonian motion of the solitary wave's center of mass) for soliton-like solutions up to a finite time that depends on the size and scale of the potential $V$. Our method is an adaptation of the well-known Lyapunov method.

For the sake of completeness, we also prove long-time stability of traveling solitons in the case $V=0$.

Stability Analysis Of Nonlinear Fractional Differential Order Systems With Caputo And Riemann--Liouville Derivatives, Javad Alidousti, Reza Khoshsiar Ghaziani, Ali Bayati Eshkaftaki

Turkish Journal of Mathematics

In this paper we establish stability theorems for nonlinear fractional orders systems (FDEs) with Caputo and Riemann--Liouville derivatives. In particular, we derive conditions for $ {\bf \cal{F}}$-stability of nonlinear FDEs. By numerical simulations, we verify numerically our theoretical results on a test example.

2d Euler Equation On The Strip: Stability Of A Rectangular Patch, Jennifer Beichman, Sergey Denisov

Mathematics Sciences: Faculty Publications

We consider the 2D Euler equation of incompressible fluids on a strip ℝ×�� and prove the stability of the rectangular stationary state χ_|x|<L for large enough L.

Stabilizing The Lorenz Flows Using A Closed Loop Quotient Controller, James P. Braselton, Yan Wu

Mathematical Sciences: Faculty Publications

In this study, we introduce a closed loop quotient controller into the three-dimensional Lorenz system. We then compute the equilibrium points and analyze their local stability. We use several examples to illustrate how cross-sections of the basins of attraction for the equilibrium points look for various parameter values. We then provided numerical evidence that with the controller, the controlled Lorenz system cannot exhibit chaos if the equilibrium points are locally stable.