Mathematical Methods in the Applied Sciences最新文献

{"title":"Geometric and Topological Properties of Fractal Networks","authors":"J. A. Méndez-Bermúdez,&nbsp;Rosalio Reyes,&nbsp;José M. Rodríguez,&nbsp;José M. Sigarreta","doi":"10.1002/mma.10877","DOIUrl":"https://doi.org/10.1002/mma.10877","url":null,"abstract":"<div>\u0000 \u0000 <p>Fractals have been studied in areas such as mathematics, physics, chemistry, social sciences, computing, economics, and biology. Fractal networks have many interesting properties, such as recursive self-similarity, that are present in many real networks. In this paper, we study the geometrical and topological properties of fractal networks (the Sierpiński triangle, the Sierpiński carpet, and the Koch snowflake). Furthermore, we establish relationships, in the fractal structures studied, between the geometric properties associated with hyperbolicity and the topological indices.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"10175-10188"},"PeriodicalIF":2.1,"publicationDate":"2025-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950076","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 Regret Bound for the AdaMax Algorithm With Image Segmentation Application","authors":"Wachirapong Jirakitpuwapat","doi":"10.1002/mma.10879","DOIUrl":"https://doi.org/10.1002/mma.10879","url":null,"abstract":"<div>\u0000 \u0000 <p>The AdaMax algorithm provides enhanced convergence properties for stochastic optimization problems. In this paper, we present a regret bound for the AdaMax algorithm, offering a tighter and more refined analysis compared to existing bounds. This theoretical advancement provides deeper insights into the optimization landscape of machine learning algorithms. Specifically, the You Only Look Once (YOLO) framework has become well-known as an extremely effective object segmentation tool, mostly because of its extraordinary accuracy in real-time processing, which makes it a preferred option for many computer vision applications. Finally, we used this algorithm for image segmentation.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"10208-10214"},"PeriodicalIF":2.1,"publicationDate":"2025-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950075","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":"Simultaneous Root Approximation: A High-Convergence Iterative Approach","authors":"Sonia Bhalla,&nbsp;Monika Panwar,&nbsp;Ramandeep Behl,&nbsp;Changbum Chun","doi":"10.1002/mma.10782","DOIUrl":"https://doi.org/10.1002/mma.10782","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper introduces a novel and innovative iterative methodology that not only transforms arbitrary iterative schemes into an efficient framework but also redefines the process of simultaneous root approximation for polynomials and nonlinear equations. The proposed methods are distinguished by their exceptional convergence orders, achieving up to \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>+</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$$ p&amp;#x0002B;2 $$</annotation>\u0000 </semantics></math> for polynomial equations and \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 <annotation>$$ 2p $$</annotation>\u0000 </semantics></math> for nonlinear equations, where \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 <annotation>$$ p $$</annotation>\u0000 </semantics></math> is the order of the base iterative scheme. In contrast to existing techniques, these methods incorporate advanced correction mechanisms, such as an arithmetic mean blending Newton's and Ehrlich-Aberth methods, to enhance stability and convergence performance. Comprehensive numerical experiments validate the robustness and efficiency of our approaches, with clear advantages in terms of convergence speed, computational cost, and error minimization. Moreover, we present a detailed analysis of convergence behavior, supported by graphical illustrations of residual errors, shedding new light on the dynamics of iterative methods. These findings not only establish the superiority of the proposed schemes but also open new avenues for applying iterative techniques to complex mathematical and engineering problems.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 8","pages":"9098-9107"},"PeriodicalIF":2.1,"publicationDate":"2025-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143909456","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":"Existence and Asymptotic Behaviors of Traveling Wave Solutions for the FitzHugh–Nagumo System","authors":"Xiaojie Lin,&nbsp;Chen Li,&nbsp;Zengji Du,&nbsp;Ke Wang","doi":"10.1002/mma.10849","DOIUrl":"https://doi.org/10.1002/mma.10849","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we are concerned with the existence of traveling wave solution for FitzHugh–Nagumo system, which is an excitable model for studying nerve impulse propagation. By using traveling wave transformation and time scale transformation, the FitzHugh–Nagumo system is transformed into a singularly perturbed differential system. We construct a locally invariant manifold for the associated traveling wave equation and obtain the existence of traveling wave solution by employing geometric singular perturbation theory and Fredholm orthogonality. Furthermore, we also discuss the asymptotic behaviors of the traveling wave solution by applying the asymptotic theory.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"9866-9876"},"PeriodicalIF":2.1,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950175","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":"Dynamical Analysis of a Simple Tumor-Immune Model With Two-Stage Lymphocytes","authors":"Jianquan Li,&nbsp;Yuming Chen,&nbsp;Jiaojiao Guo,&nbsp;Huihui Wu,&nbsp;Xiaojian Xi,&nbsp;Dian Zhang","doi":"10.1002/mma.10863","DOIUrl":"https://doi.org/10.1002/mma.10863","url":null,"abstract":"<div>\u0000 \u0000 <p>The growth of tumor cells involves complex interactions with the immune response. We propose a simple two-stage model that describes the interaction between tumor cells and lymphocytes, where it is assumed that lymphocytes undergo two stages of development (immature and mature) and that only mature lymphocytes can kill tumor cells. The model incorporates a linear function to represent the effect of tumor antigen stimulation and a logistic model to describe the tumor growth in the absence of immune response. We analyze the oscillatory behavior of tumor levels from three perspectives: the intrinsic growth rate of tumor, the killing rate of lymphocytes against tumor cells, and the stimulation effect of tumor antigens on the immune system. Supported by theoretical analysis of Hopf bifurcation, we observe distinct differences among these factors. The oscillation occurs between two critical values for the intrinsic growth rate and the killing rate of lymphocytes, while for the stimulation effect of tumor antigens, there is a single critical value that triggers the oscillation. Numerical simulations show that strong tumor antigen stimulation can induce long-term dormancy in tumor growth. Furthermore, we establish the equivalence between the local and global stability of the tumor-free equilibrium using the fluctuation lemma and derive a sufficient condition on the global attractivity of the tumor-present equilibrium by constructing auxiliary convergent sequences.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"10016-10027"},"PeriodicalIF":2.1,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950176","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":"Asymptotic Properties of a Stochastic SIR Model With Regime Switching and Mean-Reverting Ornstein–Uhlenbeck Process","authors":"Wei Wei,&nbsp;Wei Xu,&nbsp;Deli Wang","doi":"10.1002/mma.10875","DOIUrl":"https://doi.org/10.1002/mma.10875","url":null,"abstract":"<div>\u0000 \u0000 <p>The goal of this paper is to investigate a new mean-reverting Ornstein–Uhlenbeck process based stochastic SIR model with regime switching for diseases transmission that still is a threat to human health and life. In this paper, the deterministic model is extended to the stochastic switched form by incorporating the Ornstein–Uhlenbeck process and Markov switching to account the environmental noise. Firstly, with the Lyapunov functions, the existence of global unique positive solution is proved. Then, the sufficient criteria that control the disease's extinction and persistence of the disease are identified through the Khasminskii theory and stochastic comparison theorem. Epidemiologically, it is found that the larger proportions of the intensity of volatility and the speed of reversion can suppress the outbreak of diseases. At last, numerical simulations are provided to verify our theoretical findings and study the effects of Markov switching and Ornstein–Uhlenbeck process on the spread of the disease.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"10152-10161"},"PeriodicalIF":2.1,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143949733","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":"Alternative Variational Iteration Elzaki Transform Method for Solving Time-Fractional Generalized Burgers-Fisher Equation in Porous Media Flow Modeling","authors":"Jyoti U. Yadav,&nbsp;Twinkle R. Singh","doi":"10.1002/mma.10848","DOIUrl":"https://doi.org/10.1002/mma.10848","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we have studied the time-fractional generalized Burgers-Fisher equation, which has applications in turbulence modeling, image processing, and biology. A new method called the alternative variational iteration Elzaki transform method (AVIETM) has been used to achieve the results. We employed the proposed method to obtain a solution for the time-fractional generalized Burgers-Fisher equation. The convergence and uniqueness of the solutions for the proposed method have been analyzed and discussed. The validity of the AVIETM is shown by numerical simulation and graphs. The method's accuracy have been shown by comparing the results to exact for various values of the fractional order. The obtained results demonstrate that the proposed AVIETM method is straightforward, highly accurate, and efficient.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"9853-9865"},"PeriodicalIF":2.1,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950018","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":"Explicit Solution for the Bagley–Torvik Equation With Variable Coefficients","authors":"Huiwen Wang,&nbsp;Fang Li","doi":"10.1002/mma.10862","DOIUrl":"https://doi.org/10.1002/mma.10862","url":null,"abstract":"<div>\u0000 \u0000 <p>Analytical solutions to the Bagley–Torvik equation with variable coefficients are difficult to be obtained, so most previous research focused on numerical solutions. In this paper, with the help of a fractional integral equation, we obtain an explicit representation of a unique exact solution of the initial value problem for the Bagley–Torvik equation with variable coefficients in a weighted space. We present three examples and give numerical simulations as an application.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"10008-10015"},"PeriodicalIF":2.1,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950017","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":"Scattering Limit of the Diffusion Approximate Model in Radiation Hydrodynamics","authors":"Peng Jiang,&nbsp;Chunjin Lin","doi":"10.1002/mma.10844","DOIUrl":"https://doi.org/10.1002/mma.10844","url":null,"abstract":"<div>\u0000 \u0000 <p>The multidimensional gray model in radiation hydrodynamics describing the energy and momentum exchanges between the fluid and the radiation field is considered. This exchange is accomplished by the absorption, scattering, and emission of photons. In the nonequilibrium frame, the scattering process is the dominated. Through the asymptotic expansion of the radiation intensity, an diffusion approximate model with small parameters is obtained from the gray one, which consists of compressible Euler equations and radiation diffusion equation. In this paper, we will discuss the scattering limit problem of the diffusion approximation model. We will show that when the scattering process tends to stop (i.e., the small parameter tends to zero), the smooth solution of the diffusion approximation model converges to the smooth solution of the so-called nonequilibrium model in radiation hydrodynamics. Both of these models are widely used in the study of radiation hydrodynamics.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"9809-9818"},"PeriodicalIF":2.1,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950019","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":"Random Sampling and Reconstruction of Non-Decaying Signals From Weighted Multiply Generated Shift-Invariant Spaces","authors":"Wei Li,&nbsp;Jinping Wang","doi":"10.1002/mma.10771","DOIUrl":"https://doi.org/10.1002/mma.10771","url":null,"abstract":"<div>\u0000 \u0000 <p>It is a classical assumption in sampling theory that the input signal is square-integrable. However, non-decaying signals are prevalent in science and engineering. They do not decay and even grow at infinity, such as realizations of Brownian and Lévy processes. In this paper, we consider the problem of random sampling of non-decaying signals from weighted multiply generated shift-invariant spaces. We obtain that with overwhelming probability, the random sampling stability holds uniformly for all non-decaying signals in certain compact subsets of the weighted multiply generated shift-invariant spaces when the sampling size is sufficiently large. Furthermore, we consider a reconstruction algorithm for a subspace of the weighted multiply generated shift-invariant spaces and provide the probability that the algorithm succeeds.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 8","pages":"9007-9019"},"PeriodicalIF":2.1,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143909010","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}