Mathematical Methods in the Applied Sciences最新文献

Construction of Bernstein-Based Words and Their Patterns 伯恩斯坦词的结构及其模式

IF 1.8 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-07-07 DOI: 10.1002/mma.11066

Irem Kucukoglu, Yilmaz Simsek

{"title":"Construction of Bernstein-Based Words and Their Patterns","authors":"Irem Kucukoglu, Yilmaz Simsek","doi":"10.1002/mma.11066","DOIUrl":"https://doi.org/10.1002/mma.11066","url":null,"abstract":"<p>In this paper, with inspiration of the definition of Bernstein basis functions and their recurrence relation, we give construction of a new word family that we refer Bernstein-based words. By classifying these special words as the first and second kinds, we investigate their some fundamental properties involving periodicity and symmetricity. Providing schematic algorithms based on tree diagrams, we also illustrate the construction of the Bernstein-based words. For their symbolic computation, we also give computational implementations of Bernstein-based words in the Wolfram Language. By executing these implementations, we present some tables of Bernstein-based words and their decimal equivalents. In addition, we present black–white and four-colored patterns arising from the Bernstein-based words with their potential applications in computational science and engineering. We also give some finite sums and generating functions for the lengths of the Bernstein-based words. We show that these functions are of relationships with the Catalan numbers, the centered \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <annotation>$$ m $$</annotation>\u0000 </semantics></math>-gonal numbers, the Laguerre polynomials, certain finite sums, and hypergeometric functions. We also raise some open questions and provide some comments on our results. Finally, we investigate relationships between the slopes of the Bernstein-based words and the Farey fractions.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 13","pages":"12819-12836"},"PeriodicalIF":1.8,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.11066","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144767499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Qualitative Behavior of a Discrete-Time Predator–Prey Model With Holling-Type III Functional Response and Gompertz Growth of Prey 具有holling - III型功能响应和猎物Gompertz生长的离散时间捕食者-猎物模型的定性行为

IF 1.8 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-06-25 DOI: 10.1002/mma.11087

M. B. Almatrafi, Messaoud Berkal, M. Y. Hamada

引用次数: 0

Novel and Reliable Techniques for Two-Dimensional Stochastic Itô–Volterra Fredholm Integral Equations 二维随机Itô-Volterra Fredholm积分方程的新颖可靠技术

IF 1.8 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-06-21 DOI: 10.1002/mma.11070

S. Saha Ray

引用次数: 0

Nonlinear Dynamics and Chaos Analysis of Fractional-Order Nonlinear System From Novel Winding Mechanical Equipment 新型缠绕机械设备分数阶非线性系统的非线性动力学与混沌分析

IF 1.8 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-06-15 DOI: 10.1002/mma.11086

Jianglin Liu, Xinlei Fang, Jiaquan Xie, Yujie Duan, Haofei Du, Jianguo Liang

{"title":"Nonlinear Dynamics and Chaos Analysis of Fractional-Order Nonlinear System From Novel Winding Mechanical Equipment","authors":"Jianglin Liu, Xinlei Fang, Jiaquan Xie, Yujie Duan, Haofei Du, Jianguo Liang","doi":"10.1002/mma.11086","DOIUrl":"https://doi.org/10.1002/mma.11086","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, the approximate solutions, resonance features, Poincaré section, dynamic bifurcation properties, chaotic jerky dynamics, chaotic attractors, Lyapunov exponent calculation, and pathways to the chaos of a novel class of fractional-order nonlinear winding mechanical systems are investigated. Firstly, the approximate solution and the expression of the amplitude–frequency relationship of the fractional-order nonlinear system are obtained by using the L-P perturbation method and the average method, respectively, and the stability analysis of the system, which is based on Lyapunov's first method, is carried out. Secondly, the effects of fractional-order, internal excitation amplitude, and cubic term coefficients on the amplitude–frequency characteristic curves are investigated separately. Then, the Poincaré section and the global dynamic bifurcation behavior of the system are studied, along with the effect of different types of damping, cubic terms, and internal excitation amplitudes on the dynamic bifurcation of the system. In addition, the homoclinic and heteroclinic orbits of the system are investigated, and the necessary condition for the heteroclinic orbit cross-section intersection of the system and chaos in the sense of Smale horseshoe is given by the Melnikov method. Finally, a preliminary investigation of the three-dimensional chaotic jerky dynamical system is carried out, and the computation of the chaotic, hyperchaotic, and equilibrium attractors of the system as well as the Lyapunov exponent is investigated.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 13","pages":"13078-13099"},"PeriodicalIF":1.8,"publicationDate":"2025-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144768065","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}

引用次数: 0

Complex Dynamical Analysis of Two Prey-One Predator Model in a Patch Environment Utilizing Spectral Bound 利用谱界分析斑块环境下两猎物-一捕食者模型的复杂动力学

IF 1.8 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-06-13 DOI: 10.1002/mma.11054

Min Zhang, Xuenan Sun, Weipeng Zhang

引用次数: 0

Asymptotic Analysis of Stokes Flow Through a Filter Stokes流通过滤波器的渐近分析

IF 1.8 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-06-12 DOI: 10.1002/mma.11072

Georges Griso, Larysa Khilkova, Julia Orlik

引用次数: 0

Periodic Orbits of MAX and MIN Multistate Networks 最大和最小多状态网络的周期轨道

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-06-10 DOI: 10.1002/mma.10944

Juan A. Aledo, Jose P. Llano, Leila Sharifan, Jose C. Valverde

{"title":"Periodic Orbits of MAX and MIN Multistate Networks","authors":"Juan A. Aledo, Jose P. Llano, Leila Sharifan, Jose C. Valverde","doi":"10.1002/mma.10944","DOIUrl":"https://doi.org/10.1002/mma.10944","url":null,"abstract":"<p>This work presents a generalization of Boolean networks to multistate networks over a complement-closed set \u0000<span></span><math>\u0000 <mrow>\u0000 <mi>𝒞</mi>\u0000 </mrow></math>, which can be finite or infinite. Specifically, we focus on MAX (and MIN) multistate networks, whose dynamics are governed by global arbitrary \u0000<span></span><math>\u0000 <mrow>\u0000 <mi>𝒞</mi>\u0000 </mrow></math>-maxterm (or \u0000<span></span><math>\u0000 <mrow>\u0000 <mi>𝒞</mi>\u0000 </mrow></math>-minterm) functions, which extend the well-known maxterm (or minterm) Boolean functions. More specifically, we tackle the problem of analyzing the combinatorial dynamics of these networks. As a result, we determine the types of periodic orbits that can exist and coexist jointly, when all vertices are self-loop and the graph is undirected. In particular, we show that only fixed points and 2-periodic orbits can appear in these systems by employing tools coming from algebra and graph theory. That is, regardless of the (finite or infinite) number of elements, the types of periodic orbits remain the same as those of MAX and MIN Boolean networks. However, we demonstrate that the coexistence of fixed points and 2-periodic orbits is possible in these networks, which contrasts with the known results for the Boolean case. Moreover, we provide sufficient and necessary conditions to characterize the existence of fixed points and 2-periodic orbits, as well as their coexistence.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 12","pages":"11620-11629"},"PeriodicalIF":2.1,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.10944","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144582083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The Lifespan of Solutions for a Boussinesq-Type Model boussinesq型模型解的生命周期

IF 1.8 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-06-10 DOI: 10.1002/mma.11067

Faramarz Tahamtani, Mohammad Shahrouzi

{"title":"The Lifespan of Solutions for a Boussinesq-Type Model","authors":"Faramarz Tahamtani, Mohammad Shahrouzi","doi":"10.1002/mma.11067","DOIUrl":"https://doi.org/10.1002/mma.11067","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper investigates a class of Boussinesq-type equations in a bounded domain \u0000<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>$$ Omega subset {mathbb{R}}&amp;#x0005E;n $$</annotation>\u0000 </semantics></math> subject to clamped or hinged boundary conditions. The local existence of weak solutions is proven using the classical Faedo-Galerkin method in conjunction with the contraction mapping principle. Within the framework of potential wells, the global existence of solutions and energy decay are established when the solution resides in a subset that is smaller than the stable set. Also, it is shown that solutions exhibit exponential growth either when they belong to the unstable set or when the initial energy is negative. Furthermore, the blow-up of solutions is proven by combining the potential well framework with concavity arguments. For solutions with sufficiently positive initial energy, an upper bound for the blow-up time is derived, while a suitable functional is employed to establish a lower bound for the blow-up time.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 13","pages":"12837-12850"},"PeriodicalIF":1.8,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144767420","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}

引用次数: 0

Space-Time Smoothness and Parsimony in Covariance Functions 协方差函数的时空平滑性和简约性

IF 1.8 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-06-09 DOI: 10.1002/mma.11100

Tarik Faouzi, Emilio Porcu, Moreno Bevilacqua

{"title":"Space-Time Smoothness and Parsimony in Covariance Functions","authors":"Tarik Faouzi, Emilio Porcu, Moreno Bevilacqua","doi":"10.1002/mma.11100","DOIUrl":"https://doi.org/10.1002/mma.11100","url":null,"abstract":"<p>This paper challenges the trade off between computational efficiency and statistical accuracy within the framework of Gaussian space-time processes. Under such a framework, the space-time dependence is completely specified through the space-time covariance function. We compare different classes of space-time covariance functions depending on their supports: when the support is full, information is complete but estimation and prediction are costly. When the support is compact, we only have partial information, but computations are way more efficient. We take a special approach to preserving smoothness at the origin of the covariance when inducing parsimony. This is particularly important because, for Gaussian processes, smoothness is directly linked to the geometric properties of the Gaussian fields, in concert with optimal prediction under certain asymptotic regimes. The instrument used for such comparisons is <i>compatibility</i>, which is in turn a function of equivalence of Gaussian measures under fixed domain asymptotics. We find the parametric restrictions on some classes of covariance functions with compact support to be compatible with those having full support. Such a result has precise consequences in terms of estimation and prediction of Gaussian processes.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 13","pages":"13247-13259"},"PeriodicalIF":1.8,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.11100","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144767824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On Two Classes of q-Fractional Differential, Nonhybrid Equation and Hybrid Inclusion, Via Multiterm–Point-Strip Conditions 基于多项点条条件的两类q分数阶微分非杂化方程和杂化包含

IF 1.8 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-06-09 DOI: 10.1002/mma.11071

Mohammadreza Shahbazi, Azizollah Babakhani, Mohammad Esmael Samei, Gastão S. F. Frederico

{"title":"On Two Classes of q-Fractional Differential, Nonhybrid Equation and Hybrid Inclusion, Via Multiterm–Point-Strip Conditions","authors":"Mohammadreza Shahbazi, Azizollah Babakhani, Mohammad Esmael Samei, Gastão S. F. Frederico","doi":"10.1002/mma.11071","DOIUrl":"https://doi.org/10.1002/mma.11071","url":null,"abstract":"<div>\u0000 \u0000 <p>In this research, achieving the results of existence and stability for two classes of \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>q</mi>\u0000 </mrow>\u0000 <annotation>$$ q $$</annotation>\u0000 </semantics></math>-fractional differential, in the first step, a nonhybrid equations under nonhybrid, integro, multiterm–point-strip type conditions and in the second step, a hybrid integro inclusions, is of interest to the authors. To do these aims, some techniques and nonlinear theorems such as the Kuratowski measures based on the Sadovskii's theorem, Krasnoselskii–Zabreiko criterion, and Dhage's technique are used. We generalize the Gronwall inequality in relation to \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>q</mi>\u0000 </mrow>\u0000 <annotation>$$ q $$</annotation>\u0000 </semantics></math>-fractional differential nonhybrid equation with integro, multiterm–point-strip conditions. Further, the two cases of stabilities criteria have been taken into account. To examine the correctness of the outcomes, we provide some illustrative applications along with conclusion at the end.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 13","pages":"12890-12912"},"PeriodicalIF":1.8,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144767825","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}

引用次数: 0