Mathematical Methods in the Applied Sciences最新文献

{"title":"Mathematical Formulation and Numerical Study of Parameter-Performance Relationships for Thermal Protective Clothing Under Windy Conditions","authors":"Anna Miao,&nbsp;Dinghua Xu","doi":"10.1002/mma.70851","DOIUrl":"https://doi.org/10.1002/mma.70851","url":null,"abstract":"<div>\u0000 \u0000 <p>This study focuses on developing a coupled heat transfer model in the Environment-Clothing-Human body system under realistic firefighting conditions, which shows how ambient temperature, wind velocity, and perspiration rate influence skin-burn injury. The model, consisting of a three-layer fabric, a single air gap and a double-layer skin structure, is derived based on Darcy's law and the Bernoulli equation for airflow. The existence of weak solutions to the resulting nonlinear PDE system is mathematically proved via the Galerkin approximation, energy estimates, and compactness arguments. Uniqueness is established using the classical energy method combined with Grönwall's inequality. Numerical simulations are performed with a mixed explicit-implicit finite difference scheme, and Henriques' burn integral is employed to evaluate skin burn injury and predict the longest safe working time. The numerical simulation results indicate that burn injury increases with higher wind velocities and meanwhile decreases with greater perspiration rates when the parameters are chosen from engineering applications. These results provide a scientific basis for the design of firefighting protective clothing and enhance the interpretability of the model.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 14","pages":"15839-15874"},"PeriodicalIF":2.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148754210","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Practical Exponential Stability and Applications of Switched Impulsive Homogeneous Positive Nonlinear Systems With Stable and Unstable Subsystems","authors":"Yanchao He,&nbsp;Yuzhen Bai,&nbsp;Dongpo Hu","doi":"10.1002/mma.70853","DOIUrl":"https://doi.org/10.1002/mma.70853","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper studies the practical exponential stability of switched impulsive homogeneous positive nonlinear systems composed of both stable and unstable subsystems, including continuous-time and discrete-time systems. Specifically, we introduce a class of nonnegative impulses that are consistent with the switching behavior of the systems. It should be emphasized that a special switching sequence and switching-impulsive signals are designed for the systems. First, by using the max-separable Lyapunov function method and introducing an impulse strength parameter, we establish several new sufficient stability criteria. Second, we derive a new relation between the average dwell-time parameter and the impulse strength parameter, and analyze the case of different impulse strength parameters. Then, based on the comparison principle, we apply the obtained stability criteria to time-varying switched impulsive homogeneous nonlinear systems, which are not restricted to being positive, and this holds for both the main systems and the subsystems. Finally, four examples and a specific algorithm verification procedure are provided to illustrate the effectiveness of the obtained results.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 14","pages":"15875-15898"},"PeriodicalIF":2.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Development of Chelyshkov Wavelets Neural Network Method for Solving Nonlinear Fractal–Fractional Optimal Control Problems","authors":"Parisa Rahimkhani,&nbsp;Seydi Battal Gazi Karakoc,&nbsp;Thabet Abdeljawad","doi":"10.1002/mma.70839","DOIUrl":"https://doi.org/10.1002/mma.70839","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper employs Chelyshkov wavelets neural network method for solving nonlinear fractal–fractional optimal control problems (FFOCPs) in the Atangana–Riemann–Liouville sense. The described neural network is comprised of three layers: the input layer, the hidden layer, and the output layer. This three-layer structure allows the neural network to learn complex relationships between input and output by applying Chelyshkov wavelets in the hidden layer and nonlinear scaling in the output layer. Initially, the problem under investigation is transformed into an equivalent variational problem by applying the definition of the fractal–fractional integral. Subsequently, by utilizing the Chelyshkov wavelets, the neural network method, and the Gauss–Legendre integration, the problem is reformulated as a system of algebraic equations. Finally, this system is solved using Newton's iterative method. Additionally, we show the convergence of the proposed approach within the Hilbert space framework. To assess the applicability and efficacy of the proposed scheme, four examples are given.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 14","pages":"15517-15533"},"PeriodicalIF":2.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global Stability of a Diffusive Leslie-Gower Type Model With Intraspecific Competition","authors":"Norberto Aníbal Maidana","doi":"10.1002/mma.70832","DOIUrl":"https://doi.org/10.1002/mma.70832","url":null,"abstract":"<div>\u0000 \u0000 <p>The aim of this work is to improve the global stability results for reaction-diffusion Leslie-Gower type models in a bounded domain <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ω</mi>\u0000 <mo>∈</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ Omega in {mathbb{R}}^n $$</annotation>\u0000 </semantics></math>, with no-flux boundary conditions. Our approach involves constructing a novel Lyapunov function by modifying a previously known one. This approach can also be applied to other reaction-diffusion models.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 14","pages":"15473-15494"},"PeriodicalIF":2.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global Dynamics of a CTL Immune Response Delayed Virus Infection Model With Lytic and Nonlytic Effector Mechanisms","authors":"Zhipeng Xu,&nbsp;Wanbiao Ma","doi":"10.1002/mma.70843","DOIUrl":"https://doi.org/10.1002/mma.70843","url":null,"abstract":"<div>\u0000 \u0000 <p>This study investigates a class of delayed virus infection model that incorporates CTL immune responses with both lytic and nonlytic effector mechanisms. The model incorporates two delays: an intracellular delay <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>τ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {tau}_1 $$</annotation>\u0000 </semantics></math> and a CTL immune response delay <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>τ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {tau}_2 $$</annotation>\u0000 </semantics></math>. By fully leveraging the expressions of the model's two threshold parameters <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {R}_0 $$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {R}_1 $$</annotation>\u0000 </semantics></math>, constructing appropriate Lyapunov functionals, and employing sophisticated inequality analysis techniques, we establish the following results: (i) the global asymptotic stability (GAS) of the infection-free equilibrium is completely obtained; (ii) the sufficient conditions for the GAS of the immune-free equilibrium are derived; (iii) under specific parameter constraints, the sufficient conditions for the GAS of the immune activation equilibrium are obtained. The results in this paper further extend the conclusions in the existing literature. Meanwhile, the model is applied to experimental data from humanized mice infected with HIV-1, demonstrating the effectiveness of the model in predicting empirical data.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 14","pages":"15730-15752"},"PeriodicalIF":2.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148754184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Energy Shaping of Distributed Port-Hamiltonian Systems Based on Finite Volume Approximation","authors":"Fu Zheng,&nbsp;Ziwei Zhang,&nbsp;Sizhe Wang","doi":"10.1002/mma.70835","DOIUrl":"https://doi.org/10.1002/mma.70835","url":null,"abstract":"<div>\u0000 \u0000 <p>This work introduces a semi-discrete formulation for a class of infinite-dimensional port-Hamiltonian systems (PHS) through a finite volume approach. After spatial discretization, the resulting models maintain the core structural properties of PHS, including the underlying Dirac structure, which is preserved in the absence of external interconnections. A key aspect of this approach involves the integration of a finite-dimensional controller with the infinite-dimensional system through a power-conserving interconnection. Furthermore, we establish a criterion for the existence of discrete analogs of Casimir functions in the discretized framework. The methodology is illustrated through its application to the Timoshenko beam model, where a discrete Casimir function is effectively constructed, reflecting the essential features of the continuous case.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 14","pages":"15552-15573"},"PeriodicalIF":2.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Finite-Time Synchronization of Multi-Weighted Fractional-Order Complex Neural Networks","authors":"Muhammad Shakeel,&nbsp;Xinge Liu,&nbsp;Meilan Tang,&nbsp;Shuailei Zhang,&nbsp;Nadeem Khan","doi":"10.1002/mma.70847","DOIUrl":"https://doi.org/10.1002/mma.70847","url":null,"abstract":"<div>\u0000 \u0000 <p>This article explores the finite-time synchronization (FTS) of multi-weighted fractional-order complex neural networks (MWFOCNNs) with time-varying delays. By employing Lyapunov stability theory and fractional-order inequalities, several sufficient conditions are derived to ensure the FTS of multi-weighted fractional-order complex neural networks (MWFOCNNs) with time-varying delay. The proposed approach incorporates Lyapunov direct method and the Razumikhin condition to handle the time-varying delays. Finally, two numerical examples are presented to validate the effectiveness and accuracy of the proposed technique in achieving finite-time synchronization.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 14","pages":"15778-15795"},"PeriodicalIF":2.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753707","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Robust Analytical Framework for Solving Nonlinear Differential Equations Arising in Physical Sciences","authors":"Saurabh Tomar","doi":"10.1002/mma.70844","DOIUrl":"https://doi.org/10.1002/mma.70844","url":null,"abstract":"<div>\u0000 \u0000 <p>In this study, we propose an effective analytical framework for solving nonlinear differential equations, termed the quasi-linearized Picard iteration method (QPIM). This method combines Newton's quasilinearization technique, which is known for its quadratic convergence, with the Picard iteration method, which offers a straightforward iterative framework. The proposed approach converts nonlinear differential equations into a sequence of linear problems via quasilinearization, which are then solved analytically using Picard iterations. A detailed convergence analysis confirms the quadratic rate of convergence under suitable conditions. Several examples are provided to illustrate the applicability and accuracy of the QPIM. Numerical comparisons revealed that QPIM achieved higher accuracy with fewer iterations. Furthermore, the QPIM provides monotonic sequences of approximations, enabling pointwise upper and lower bounds for solutions, which is especially useful for problems with unique solutions. These advantages establish the QPIM as a reliable tool for solving a broad class of nonlinear differential equations.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 14","pages":"15796-15821"},"PeriodicalIF":2.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148754208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Iterations of Endomorphisms for 4-Torsion Subgroups of Elliptic Curve","authors":"Yutong Fan,&nbsp;Chi Young Ahn,&nbsp;Daeyeoul Kim","doi":"10.1002/mma.70836","DOIUrl":"https://doi.org/10.1002/mma.70836","url":null,"abstract":"<div>\u0000 \u0000 <p>In this article, we consider sequences generated by iterated matrix multiplication, and introduce a classification of stable, amicable pair, and sociable matrix sequences. Based on these classifications, we analyze the behavior of subgroup sequences obtained through iterated endomorphism on the 4-torsion subgroups of elliptic curves. In addition, we present visual interpretations of these iterations, including symmetric patterns such as four-leaf clovers.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 14","pages":"15696-15729"},"PeriodicalIF":2.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148754185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Prüfer Angle Approach to Dependence of Eigenvalue for Sturm-Liouville Problem With Distributional Potentials","authors":"Gaofeng Du,&nbsp;Chenghua Gao","doi":"10.1002/mma.70787","DOIUrl":"https://doi.org/10.1002/mma.70787","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we apply the Prüfer transformation to investigate the dependence of eigenvalues for the Sturm–Liouville problem with distributional potentials. Based on several important properties of Prüfer angle established herein, the precise oscillation theorems for the problem are obtained. Moreover, it is proved that the eigenvalue functionals are not only completely continuous but also continuously differentiable in potentials. Meanwhile, we derive the precise Fréchet derivative formula of eigenvalue in potentials.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 13","pages":"14355-14362"},"PeriodicalIF":2.0,"publicationDate":"2026-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148695777","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}