In this paper, we first establish that every operator $ T \in B_{n}(\Omega)$ is frequently hypercyclic. Second, we show that the inverse $T^{-1}$ of such operators is also frequently hypercyclic when $T$ satisfies mild spectral conditions (e.g., its spectrum excludes the origin). Third, we characterize the frequent hypercyclicity of operators in the commutant of $T \in B_{n}(\Omega)$ different from $\lambda I$. This work advances the theory of frequent hypercyclicity by establishing a unified framework for operators in $B_{n}(\Omega)$, their inverses, and their multiples, thus complementing the incomplete studies in literature.
Introduction: Although Burundi and Rwanda have similarities in socio-cultural terms, the countries show different paths in terms of family planning and fertility reduction. Objective: The present study aims to compare the determinants of the use of modern contraceptive methods among women in union in these two countries. Methodology: To this end, the researchers used data from the Demographic and Health Surveys (DHS) which have already been carried out in the two countries. The analysis was carried out using stepwise binary logistic regression, and enabled the researchers to identify and prioritize the determinants of the use of modern contraceptive methods for both countries. Results: The results show that age, number of living children, ideal number of children, place of residence, region of residence, religion, woman's level of education and employment sector are common determinants for both countries. However, it should be noted that, unlike in Burundi, the number of living children, place of residence and religion are no longer determining factors in Rwanda. Conclusion: To enable Burundi to progress with its family planning policy, it is important to raise awareness of the advantages of a smaller family, promote education for all and facilitate women's access to employment.
In this paper, we prove that for a continuous periodic function $f$ from $\mathbb{R}^{n}$ to ${\mathbb{R}}$, the generalized bounded distribution solution $u$ of the Poisson equation $\Delta u=f$ is also periodic. Furthermore, $u$ is continuously differentiable and $u'$ is also periodic. While high-dimensional primitive function problems for recurrent functions, including almost periodic and almost automorphic functions, have been studied in recent years, this paper presents the first results concerning high-dimensional primitive function problems of periodic functions.
In this paper, we consider the following chemotaxis system \begin{equation*} \left\{ \begin{split} &n_{t}=\nabla\cdot((n+1)^{m-1}\nabla n)-\nabla\cdot\left(\frac{n\nabla v}{(1+n)^\alpha}\right),&&x\in \Omega ,t> 0,\\ &0=\Delta v-v+n^\gamma,&&x\in \Omega ,t> 0\\ \end{split} \right. \end{equation*} in a bounded domain $\Omega\subset\mathbb{R}^N, N\geq2$ with smooth boundary. It is shown that for all reasonably regular initial data, if $\alpha>max\left\{0,\gamma-m-\frac{2}{N}+1\right\}$, $\gamma>0$ and $m\geq1$, then the problem possesses a unique global bounded classical solution.
In this paper, we study the dynamical properties of a discrete linear harvesting metapopulation with diffusion. By using Euler iteration algorithm to discretize the space, we obtain the two-dimensional discrete-time model with diffusion. We survey the existence conditions and stability of the fixed points, the analysis of transcritical, pitchfork, and flip bifurcations of nonhyperbolic fixed pointsis provided by using the center manifold theorem. Numerical simulations and biological explanation analyzes are made to demonstrate the effective of the theoretical analyzes and to present the relations between these bifurcations.
This research article investigates the compression of attractors generated by Iterated Function Systems (IFS). By analyzing the affine contraction mappings and their fixed points, we explore the efficiency of fractal-based compression methods. We demonstrate the potential of IFS attractors to achieve high compression ratios with minimal loss in image quality.
This paper presents a systematic truncation method for constructing Lax pairs and B\"acklund transformations of integrable nonlinear differential equations. By combining the mirror method and the WTC approach, we establish connections between Painlev\'e analysis, Riccati linearization, and Lax integrability. Our framework enables the derivation of symmetric auto-B\"acklund transformations and Schlesinger transformations, offering a unified approach to understanding these systems. This approach yields a constructive algorithm that links geometric, algebraic, and analytical perspectives of integrability with significant implications for physical applications.
We make the following conjecture: the marginal stability of the characteristic polynomial of a discrete-time system of difference equations implies the asymptotic stability of a class of associated perturbed polynomials. We support our claim by a random list of examples.
This paper is concerned with the Abels-Garcke-Grün (AGG) model for two-phase flows of two viscous incompressible system with different densities. The AGG model consists of a Navier-Stokes-Cahn-Hilliard system characterized by a mixture density depending on a volume fraction and an additional flux term due to interface diffusion. We establish the global existence of weak solutions to the initial boundary value problem with the mixed boundary conditions, including the velocity, pressure and Navier-slip conditions for fluid, and the Dirichlet and Neumann conditions for volume fraction and chemical potential, together, in a cubic domain of $\mathbb{R}^3$.
Recognizing the crucial roles of media-driven awareness in shaping public responses to precautionary measures, we propose and analyse an SEIRM epidemic model with infectious force in incubation period affected by the intensity of the disease awareness through a novel media function. We discuss the existence and stability of disease free and endemic equilibrium, and establish conditions for periodic oscillations. When awareness growth surpasses a critical threshold, Hopf bifurcation induces limit cycles with amplitude increasing as awareness intensifies.
Let $C^{\mathbb B}[a,b]$ denote an analogue of Wiener space over paths in abstract Wiener space $\mathbb B$, the space of $\mathbb B$-valued continuous functions on $[a,b]$. In this paper, we introduce a positive finite measure on $C^{\mathbb B}[a,b]$ with a scale and arbitrary variance function. We then introduce a generalized analytic Feynman integral for the functions on $C^{\mathbb B}[a,b]$. With regards to the definition, we establish the generalized analytic Feynman integral of the product of the cylinder functions and the functions in a Banach algebra corresponding to the Fresnel class. We note that the established analytic Feynman integrals are of interest in quantum mechanics, especially in Feynman integration theory.
Let E be a uniformly smooth and uniformly convex real Banach space and $E^*$ be its dual space. Let $A : E \rightarrow E^*$ be a bounded maximal monotone mappping such that $A^{-1}(0) \ne 0$. Define the algorithm $\{x_n\}$ as follows: for given $x_1 \in E$,\;\; $x_{n+1}= J^{-1}\big(Jx_n-\lambda_nAx_n-\lambda_n\theta_n (Jx_n-Jx_1)\big)$ where $J$ is the normalized duality mapping from $E$ into $E^*$ and $ \{\lambda_n \}$ and $ \theta_n $ are positive real numbers in $(0, 1)$ satisfying suitable conditions. It is proved that $x_n$ converges strongly to some $x^*\in A^{-1}(0)$. The results extend our recent works \cite{mendy-et-al} to larger class of Banach spaces with numerical simulations.
Three comparison criteria are obtained for second order Riccati equations. On the basis of these criteria some global existence theorems are proved mentioned equations. The results obtained are used to derive a non oscillation criterion for three dimensional linear systems of ordinary differential equations.
Some properties of global solution of scalar Riccati equation are studied. On the basis of these properties using the Whiburn's and Leighton - Nehary's theorems some oscillatory and criteria are proved for second order linear systems of ordinary differential equations.
Solutions of the Navier-Stokes and Euler equations with initial conditions for 2D and 3D cases were obtained in the form of converging series, by an analytical iterative method using Fourier and Laplace transforms in [28, 29]. There the solutions are infinitely differentiable functions, and for several combinations of parameters numerical results are presented. This article provides a detailed proof of the existence, uniqueness and smoothness of the solution of the Cauchy problem for the 3D Navier-Stokes equations with any smooth initial velocity. When the viscosity tends to zero, this proof applies also to the Euler equations.
This paper focuses on a parabolic-elliptic chemotaxis model with nonlinear signal production and nonlocal term.
This paper presents a novel numerical approach for solving Volterra-renewal integral equations, which arise in various fields, including biology, engineering, and economics. Traditional treatment of the Volterra-renewal integral equations systems of this type utilises computationally large iterative algorithms. In order to tackle these limitations, we propose a hybrid method that is numerical in nature whereby an analytic and discretisation techniques are used to obtain accurate and efficient solutions. Several test problems have been solved and the peculiarities of this method demonstrated, its possibility to solve a wide class of renewal-type problems is also presented. We have addressed a number of obstacles, such as managing nonlinearities and memory effects over extended periods of time, by using the Picard approach to provide a more accurate numerical approximation. We illustrate the benefits of the proposed methods over closed-form solutions using numerical examples.
