Mathematical Methods in the Applied Sciences最新文献

Accurate modeling and examination of nonlinear vibration behavior of multilayer structural elements consisting of nanocomposite (NC) materials before use is of great importance in terms of structural safety and operational security. Considering the complex mechanical properties of such structures, detailed analyses will not only ensure safety but also prevent serious economic losses caused by possible failures. In this study, modeling of mechanical properties of multilayer cylindrical shell structures consisting of homogeneous NC and functionally graded nanocomposite (FG-NC) layers and solution of nonlinear vibration problem are discussed. The shear deformation theory (SDT), originally developed for homogeneous cylindrical shells, has been extended to multilayer structures incorporating FG-NC layers. Within this framework, the dynamic equations and related expressions for cylindrical shells composed of FG-NC layers are derived based on the von Kármán-type nonlinear shell theory. The resulting nonlinear partial differential equations (NL-PDEs) are solved using the Galerkin method and a modified version of the Poincaré–Lindstedt method (P-LM). In the final part of the study, the effects of shear stresses, carbon nanotubes (CNT) distribution patterns, symmetric and antisymmetric layer configurations, and the number of layers on the dimensionless nonlinear natural frequencies (DNLFP) of cylindrical shells with various geometric and structural characteristics are examined in detail and evaluated through numerical analyses. The findings reveal the multifaceted influence of stacking sequence and pattern selection on the DNLFP, particularly highlighting the necessity of considering those effects in the design process under high-temperature and low-stiffness conditions.

In this work, we will introduce a new type of space called the generalized rectangular $��b�$-pseudo metric space, which generalizes the concept of metric space, rectangular metric space, $��b�$-rectangular metric space, and pseudo metric space. Next, we will prove a generalization of the famous alternative fixed point theorem of Diaz and Margolis in such space. As applications of our result, we will study the Ulam-stability of a delay differential equation with multiple variable time delays, and we will prove also the existence and uniqueness of the solution to a Fredholm integral equation.

In this paper, a class of hematopoietic stem cell transplantation model with virus-to-cell HIV infection and ratio-dependent recruitment is proposed to characterize the competitive exclusion and coexistence between the host CD4+T cells and donor CD4+T cells. First, the positivity and boundedness of solutions as well as the basic reproduction number $��ℛ�$ are obtained. Second, criteria on the locally and globally asymptotical stability of all feasible equilibria are established. Furthermore, bifurcation analysis is performed on the mixed chimerism infection equilibrium. Finally, the theoretical results are illustrated by numerical simulation, we find that chimerism is an important indicator of model stability, and AIDS may be cured when chimerism reaches a certain threshold.

This paper examines the impact of an almost Ricci-Bourguignon soliton structure on the base and fiber manifolds of twisted warped product manifolds. We establish necessary and sufficient conditions for the existence of such solitons, providing a foundational framework for their analysis. Specifically, we explore the conditions under which an almost Ricci-Bourguignon soliton transforms a twisted warped product manifold into an Einstein manifold. Additionally, we analyze the behavior of these solitons in twisted warped product manifolds that admit a conformal vector field, offering new insights into their geometric properties. The study is further extended to twisted warped product spacetimes, revealing novel perspectives on their curvature and soliton structures. Our results include the classification of almost Ricci-Bourguignon solitons on twisted warped product manifolds, the characterization of Einstein manifolds within this framework, and the implications of conformal vector fields on the soliton structure. These findings significantly advance the understanding of almost Ricci-Bourguignon solitons in the context of twisted warped product manifolds and their applications in differential geometry and theoretical physics. The paper also provides detailed proofs and conditions under which the base and fiber manifolds inherit the soliton structure, contributing to the broader study of geometric flows and their solutions.

This article explores the solvability and approximate controllability of a new class of neutral impulsive stochastic integro-differential systems. These systems are uniquely characterized by their use of fractional calculus to model real-world behavior, the inclusion of hemivariational inequalities and impulsive terms to capture nonlinearities and sudden changes, and a history-dependent operator to account for memory effects. The research demonstrates solvability through a fixed-point framework that combines stochastic analysis, the generalized Clarke subdifferential, and fractional calculus. A numerical example illustrates the practical application of these findings, incorporating a comprehensive framework that uses fractional finite differences for the Caputo derivative, Monte Carlo sampling for stochastic forcing, and finite difference methods for spatial derivatives. The study highlights the effectiveness of selecting a Gaussian spectral decay function in the Monte Carlo approximation for enhancing numerical stability and accuracy, thereby advancing numerical techniques for these complex stochastic models.

We present a mathematical model that describes the bank balance sheets in Indonesia. This model incorporates the use of the loan-to-deposit-ratio-based reserve requirement macroprudential instrument. Initially, we create a model in the absence of the instrument. We assess the stability of the model and evaluate its performance on Indonesian banking data using spiral optimization. Subsequently, the second model with the instrument is introduced and then evaluated using the data. We evaluate the impact of the instrument's parameters on the variables of the bank's balance sheet with regard to their sensitivity. The stochastic model is examined by including the element of randomness in both withdrawal and nonperforming loans. The findings demonstrate that the model effectively captures the reality of Indonesian banking balance sheets, accurately forecasts the future trajectory of loans and equity growth, and offers valuable insights for regulating the instrument and for its future study.

In this paper, we define the harmonic higher order Gauss Fibonacci numbers, which are the complex counterparts of higher order Gauss Fibonacci numbers and have been previously studied in the literature. Due to the absence of a known closed form for harmonic Fibonacci numbers, we also generalize their complex counterparts with respect to a certain parameter $��s�$. The computational analysis in this case is significantly more complex and intricate. Furthermore, for varying values of $��s�$, we can derive several sequences of harmonic complex Fibonacci-type numbers. Using the difference operator and its properties, we give formulas for these numbers. Given their complexity, we present examples using Maple to verify our results. We define hyperharmonic higher order Gauss Fibonacci numbers, encompassing harmonic higher order Gauss Fibonacci numbers. Lastly, we give generating functions for harmonic and hyperharmonic higher order Gauss Fibonacci numbers via the generalized $��q�$-logarithm function.

We construct second-order structure-preserving two-step linearly implicit exponential integrators for Hamiltonian partial differential equations with linear constant damping combining discrete gradient methods and polarization of the polynomial Hamiltonian function. We also construct an exponential version of the well-known one-step Kahan's method by polarizing the quadratic vector field. These integrators are applied to one-dimensional damped Burger's, Korteweg-de Vries, and nonlinear Schrödinger equations. Preservation of the dissipation rate is demonstrated for linear and quadratic conformal invariants and for the Hamiltonians by numerical experiments.