Mathematics Commons^™

The Application Of Brzdek's Fixed Point Theorem In The Stability Problem Of The Drygas Functional Equation, Mehdi Dehghanian, Yamin Sayyari

Turkish Journal of Mathematics

Using the Brzdek fixed point theorem, we establish the Hyers?Ulam stability problem of Drygas functional equations \begin{equation} \delta(x+y-z)+\delta(x-y)+\delta(-y-z)+\delta(y)=\delta(x-y-z)+\delta(y-z)+\delta(x+y)+\delta(-y)\nonumber \end{equation} for all $x,y,z\in A$.

Stability Of Cauchy's Equation On Δ+., Holden Wells

Electronic Theses and Dissertations

The most famous functional equation f(x+y)=f(x)+f(y) known as Cauchy's equation due to its appearance in the seminal analysis text Cours d'Analyse (Cauchy 1821), was used to understand fundamental aspects of the real numbers and the importance of regularity assumptions in mathematical analysis. Since then, the equation has been abstracted and examined in many contexts. One such examination, introduced by Stanislaw Ulam and furthered by Donald Hyers, was that of stability. Hyers demonstrated that Cauchy's equation exhibited stability over Banach Spaces in the following sense: functions that approximately satisfy Cauchy's equation are approximated with the same level of error by functions …

Modeling And Analyzing Homogeneous Tumor Growth Under Virotherapy, Chayu Yang, Jin Wang

Department of Mathematics: Faculty Publications

We present a mathematical model based on ordinary differential equations to investigate the spatially homogeneous state of tumor growth under virotherapy. The model emphasizes the interaction among the tumor cells, the oncolytic viruses, and the host immune system that generates both innate and adaptive immune responses. We conduct a rigorous equilibrium analysis and derive threshold conditions that determine the growth or decay of the tumor under various scenarios. Numerical simulation results verify our analytical predictions and provide additional insight into the tumor growth dynamics.

Qualitative Study Of A Second Order Difference Equation, Messaoud Berkal, Juan Francisco Navarro

Turkish Journal of Mathematics

In this paper, we study a second order rational difference equation. We analyze the stability of the unique positive equilibrium of the equation and prove the existence of a Neimark-Sacker bifurcation, validating our theoretical analysis via a numerical exploration of the system.

Definite Condition Of The Evolutionary (P)Over-Right-Arrow(X)-Laplacian Equation, Huashui Zhan, Zhaosheng Feng

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

For the nonlinear degenerate parabolic equations, how to find an appropriate boundary value condition to ensure the well-posedness of weak solution has been an interesting and challenging problem. In this paper, we develop the general characteristic function method to study the stability of weak solutions based on a partial boundary value condition.

Delay Dynamic Equations On Isolated Time Scales And The Relevance Of One-Periodic Coefficients, Martin Bohner, Tom Cuchta, Sabrina Streipert

Mathematics and Statistics Faculty Research & Creative Works

We are motivated by the idea that certain properties of delay differential and difference equations with constant coefficients arise as a consequence of their one-periodic nature. We apply the recently introduced definition of periodicity for arbitrary isolated time scales to linear delay dynamic equations and a class of nonlinear delay dynamic equations. Utilizing a derived identity of higher order delta derivatives and delay terms, we rewrite the considered linear and nonlinear delayed dynamic equations with one-periodic coefficients as a linear autonomous dynamic system with constant matrix. As the simplification of a constant matrix is only obtained for one-periodic coefficients, dynamic …

(R1882) Effects Of Viscosity, Oblateness, And Finite Straight Segment On The Stability Of The Equilibrium Points In The Rr3bp, Bhavneet Kaur, Sumit Kumar, Rajiv Aggarwal

Applications and Applied Mathematics: An International Journal (AAM)

Associating the influences of viscosity and oblateness in the finite straight segment model of the Robe’s problem, the linear stability of the collinear and non-collinear equilibrium points for a small solid sphere m₃ of density \rho₃ are analyzed. This small solid sphere is moving inside the first primary m₁ whose hydrostatic equilibrium figure is an oblate spheroid and it consists of an incompressible homogeneous fluid of density \rho₁. The second primary m₂ is a finite straight segment of length 2l. The existence of the equilibrium points is discussed after deriving the pertinent …

On Uniqueness And Stability For The Boltzmann-Enskog Equation, Martin Friesen, Barbara Ruediger, Padmanabhan Subdar

Faculty Publications

The time-evolution of a moderately dense gas in a vacuum is described in classical mechanics by a particle density function obtained from the Boltzmann-Enskog equation. Based on a McKean-Vlasov equation with jumps, the associated stochastic process was recently constructed by modified Picard iterations with the mean-field interactions, and more generally, by a system of interacting particles. By the introduction of a shifted distance that exactly compensates for the free transport term that accrues in the spatially inhomogeneous setting, we prove in this work an inequality on the Wasserstein distance for any two measure-valued solutions to the Boltzmann-Enskog equation. As a …

Some Convergence, Stability, And Data Dependence Results For $K^{\Ast }$ Iterative Method Of Quasi-Strictly Contractive Mappings, Ruken Çeli̇k, Neci̇p Şi̇mşek

Turkish Journal of Mathematics

In a recent paper, Yu et al. obtained convergence and stability results of the $K^{\ast }$ iterative method for quasi-strictly contractive mappings [An iteration process for a general class of contractive-like operators: Convergence, stability and polynomiography. AIMS Mathematics 2021; 6 (7): 6699-6714.]. To guarantee these convergence and stability results, the authors imposed some strong conditions on parametric control sequences which are used in the $K^{\ast }$ iterative method. The aim of the presented work is twofold: (a) to recapture the aforementioned results without any restrictions imposed on the mentioned parametric control sequences (b) to complete the work of Yu et …

Discrete Dynamics Of Dynamic Neural Fields, Eddy Kwessi

Mathematics Faculty Research

Large and small cortexes of the brain are known to contain vast amounts of neurons that interact with one another. They thus form a continuum of active neural networks whose dynamics are yet to be fully understood. One way to model these activities is to use dynamic neural fields which are mathematical models that approximately describe the behavior of these congregations of neurons. These models have been used in neuroinformatics, neuroscience, robotics, and network analysis to understand not only brain functions or brain diseases, but also learning and brain plasticity. In their theoretical forms, they are given as ordinary or …

Stochastic Delay Differential Equations With Applications In Ecology And Epidemics, Hebatallah Jamil Alsakaji

Dissertations

Mathematical modeling with delay differential equations (DDEs) is widely used for analysis and predictions in various areas of life sciences, such as population dynamics, epidemiology, immunology, physiology, and neural networks. The memory or time-delays, in these models, are related to the duration of certain hidden processes like the stages of the life cycle, the time between infection of a cell and the production of new viruses, the duration of the infectious period, the immune period, and so on. In ordinary differential equations (ODEs), the unknown state and its derivatives are evaluated at the same time instant. In DDEs, however, the …

Efficient Time-Stepping Approaches For The Dispersive Shallow Water Equations, Linwan Feng

Dissertations

This dissertation focuses on developing efficient and stable (high order) time-stepping strategies for the dispersive shallow water equations (DSWE) with variable bathymetry. The DSWE extends the regular shallow water equations to include dispersive effects. Dispersion is physically important and can maintain the shape of a wave that would otherwise form a shock in the shallow water system.

In some cases, the DSWE may be simplified when the bathymetry length scales are small (or large) in relation to other length scales in the shallow water system. These simplified DSWE models, which are related to the full DSWEs, are also considered in …

On The Stability Of Some Non-Stationary Nonlinear Systems, Rustamjon V. Mullajonov, Shakhodathon N. Abdugapparova, Jumagul V. Mirzaahmedova

Scientific Bulletin. Physical and Mathematical Research

The objective of the theory of stability of motion is to establish signs that make it possible to judge whether the motion in question is stable or unstable. Since in reality perturbing factors always inevitably exist, it becomes clear that the problem of stability of movement assumes very important theoretical and practical significance.

Mathematical modeling of processes and phenomena in animate and inanimate nature always involves a certain classification of them in accordance with their complexity. Many processes and phenomena are modeled by large-scale systems (CMS), which consist of separate subsystems, united by communication functions. In many cases, CMS is …

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.

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.

Ill-Posed Boundary Value Problem For Operator-Differential Equation Of Fourth Order, Kudratillo Fayazov, Ikrom Khajiev, Z. Fayazova

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

We prove the correctness of the conditional boundary value problem for an operator differential equation of the fourth order. A priori estimate is get. Uniqueness and conditional stability of solution are proved. The approximate solution is construct and get estimates of the norm of the difference between the exact and approximate solution.

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.