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Magneto‐hydrodynamic equations and parametric flag microlocal quantities at binary time interval 二进制时间间隔的磁流体动力学方程和参数标志微局域量
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-07 DOI: 10.1002/mma.10386
Zhenzhen Lou, Qixiang Yang, Jianxun He
{"title":"Magneto‐hydrodynamic equations and parametric flag microlocal quantities at binary time interval","authors":"Zhenzhen Lou, Qixiang Yang, Jianxun He","doi":"10.1002/mma.10386","DOIUrl":"https://doi.org/10.1002/mma.10386","url":null,"abstract":"In this paper, we establish the well‐posedness of the Cauchy problem for incompressible magneto‐hydrodynamic equations by using parametric Meyer wavelets. The velocity field and magnetic field are expanded according to parametric wavelets given by a discrete set of thresholds. The evolution of these two types of fields is described by the relationship of parameterized flag microlocal quantities over binary time intervals. The corresponding iteration space is defined by the decay of the single norm, and the single norm is defined by the parametric flag microlocal quantities at a set of binary time interval.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141934958","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
On the analyzing of bifurcation properties of the one‐dimensional Mackey–Glass model by using a generalized approach 用广义方法分析一维麦基-格拉斯模型的分岔特性
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-07 DOI: 10.1002/mma.10381
Shuai Zhang, Yaya Wang, Hongyin Geng, Wei Gao, Esin Ilhan, Haci Mehmet Baskonus
{"title":"On the analyzing of bifurcation properties of the one‐dimensional Mackey–Glass model by using a generalized approach","authors":"Shuai Zhang, Yaya Wang, Hongyin Geng, Wei Gao, Esin Ilhan, Haci Mehmet Baskonus","doi":"10.1002/mma.10381","DOIUrl":"https://doi.org/10.1002/mma.10381","url":null,"abstract":"The goal of this work is to look at how a nonlinear model describes hematopoiesis and its complexities utilizing commonly used techniques with historical and material links. Based on time delay, the Mackey–Glass model is explored in two instances. To offer a range, the relevance of the parameter impacting stability (bifurcation) is recorded. The power spectrum of the considered model is collected in order to analyze the periodic behavior of a solution in a differential equation. The complex nature of the system is relayed on a parameter which is illustrated in the bifurcation plot. Due to the fact that the considered model is associated with blood‐related diseases, the effect coefficients are effectively captured. The corresponding parameters‐based consequences of the generalized model in different order are deduced. The parametric charts for both examples reveal intriguing results. The current work enables investigations into complex real‐world problems as well as forecasts of essential techniques.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141968794","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
Testing the hypothesis of a nested block covariance matrix structure with applications to medicine and natural sciences 测试嵌套块协方差矩阵结构的假设，并将其应用于医学和自然科学
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-06 DOI: 10.1002/mma.10377
Carlos A. Coelho, Mina Norouzirad, Filipe J. Marques
{"title":"Testing the hypothesis of a nested block covariance matrix structure with applications to medicine and natural sciences","authors":"Carlos A. Coelho, Mina Norouzirad, Filipe J. Marques","doi":"10.1002/mma.10377","DOIUrl":"https://doi.org/10.1002/mma.10377","url":null,"abstract":"This paper addresses the challenge of testing the hypothesis of what the authors call a nested block circular‐compound symmetric (NBCCS) covariance structure for the population covariance matrix. This is a covariance structure which has an outer block compound symmetric structure, where the diagonal blocks are themselves block circular matrices, while the off‐diagonal blocks are formed by all equal matrices. The NBCCS null hypothesis is decomposed into sub‐hypotheses, allowing this way for a simpler way to obtain a likelihood ratio test and its associated statistic. The exact moments of this statistic are derived, and its distribution is carefully examined. Given the complicated nature of this distribution, highly precise near‐exact distributions were developed. Numerical studies are conducted to assess the proximity between these near‐exact distributions and the exact distribution, highlighting the performance of these approximations, even in the case of very small sample sizes. Furthermore, three datasets, on bone mineral content, metabolic rates of glucose, and soil moisture are used to exemplify the practical application of the methodology derived in this study.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141934960","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
Dynamic analysis of a class of fractional‐order dry friction oscillators 一类分数阶干摩擦振荡器的动态分析
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-06 DOI: 10.1002/mma.10371
Jialin Si, Jiaquan Xie, Peng Zhao, Haijun Wang, Jinbin Wang, Yan Hao, Jiani Ren, Wei Shi
{"title":"Dynamic analysis of a class of fractional‐order dry friction oscillators","authors":"Jialin Si, Jiaquan Xie, Peng Zhao, Haijun Wang, Jinbin Wang, Yan Hao, Jiani Ren, Wei Shi","doi":"10.1002/mma.10371","DOIUrl":"https://doi.org/10.1002/mma.10371","url":null,"abstract":"This article investigates a class of Duffing nonlinear dynamic systems with fractional‐order dry friction and conducts in‐depth research on the stability, chaotic characteristics, and erosion of the safety basin of this system; the results are verified through numerical simulation. First, the average method is used to approximate the amplitude–frequency relationship of the system, and the accuracy of the analytical results is verified through numerical experiments. Second, the Melnikov method is used to obtain the conditions for the system to enter chaos in the Smale horseshoe sense, and the Melnikov curve is drawn for further verification. Then, bifurcation diagrams are drawn for the changes in various parameters in the system, with a focus on analyzing the influence of friction factors on chaotic bifurcation. By applying the definition and calculation principle of the maximum Lyapunov exponent, and drawing and utilizing the maximum Lyapunov exponent graph, the chaotic state that the system enters under different parameters is more clearly defined. Finally, the evolution law of the safety basin under various parameter changes, especially dry friction changes, is analyzed, and the erosion and bifurcation mechanism of the safety basin is studied. Comparing with the bifurcation diagram, it reveals that chaos primarily contributes to the erosion of the safety basin.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141934790","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
A highly accurate and efficient Genocchi‐based spectral technique applied to singular fractional order boundary value problems 基于 Genocchi 的高精度高效光谱技术应用于奇异分数阶边界值问题
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-06 DOI: 10.1002/mma.10366
Mohammad Izadi, Khursheed J. Ansari, Hari M. Srivastava
{"title":"A highly accurate and efficient Genocchi‐based spectral technique applied to singular fractional order boundary value problems","authors":"Mohammad Izadi, Khursheed J. Ansari, Hari M. Srivastava","doi":"10.1002/mma.10366","DOIUrl":"https://doi.org/10.1002/mma.10366","url":null,"abstract":"This article focuses on an efficient and highly accurate approximate solver for a class of generalized singular boundary value problems (SBVPs) having nonlinearity and with two‐term fractional derivatives. The involved fractional derivative operators are given in the form of Liouville–Caputo. The developed algorithm for solving the generalized SBVPs consists of two main stages. The first stage is devoted to an iterative quasilinearization method (QLM) to conquer the (strong) nonlinearity of the governing SBVPs. Secondly, we employ the generalized Genocchi polynomials (GGPs) to treat the resulting sequence of linearized SBVPs numerically. An upper error estimate for the Genocchi series solution in the norm is obtained via a rigorous error analysis. The main benefit of the presented QLM‐GGPs procedure is that the required number of iteration in the first stage is within a few steps, and an accurate polynomial solution is obtained through computer implementations in the second stage. Three widely applicable test cases are investigated to observe the efficacy as well as the high‐order accuracy of the QLM‐GGPs algorithm. The comparable accuracy and robustness of the presented algorithm are validated by doing comparisons with the results of some well‐established available computational methods. It is apparently shown that the QLM‐GGPs algorithm provides a promising tool to solve strongly nonlinear SBVPs with two‐term fractional derivatives accurately and efficiently.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141934791","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
Impulsive integro‐differential inclusions with nonlocal conditions: Existence and Ulam's type stability 具有非局部条件的脉冲积分微分夹杂：存在性和乌拉姆型稳定性
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-06 DOI: 10.1002/mma.10387
Abdelhamid Bensalem, Abdelkrim Salim, Mouffak Benchohra
{"title":"Impulsive integro‐differential inclusions with nonlocal conditions: Existence and Ulam's type stability","authors":"Abdelhamid Bensalem, Abdelkrim Salim, Mouffak Benchohra","doi":"10.1002/mma.10387","DOIUrl":"https://doi.org/10.1002/mma.10387","url":null,"abstract":"This article focuses on the existence and Ulam–Hyers–Rassias stability outcomes pertaining to a specific category of impulsive integro‐differential inclusions (with instantaneous and non‐instantaneous impulses). These problems are examined using resolvent operators, drawing from the Grimmer perspective. Our analysis is based on Bohnenblust–Karlin's and Darbo's fixed point theorems for multivalued mappings in Banach spaces. Additionally, we provide an illustrative example to reinforce and demonstrate the validity of our findings.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141968797","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
Global existence and uniform boundedness in a diffusive food chain model with direct and indirect prey‐taxis 具有直接和间接猎物税的扩散食物链模型中的全球存在性和均匀有界性
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-06 DOI: 10.1002/mma.10369
Inkyung Ahn, Wonhyung Choi, Changwook Yoon
{"title":"Global existence and uniform boundedness in a diffusive food chain model with direct and indirect prey‐taxis","authors":"Inkyung Ahn, Wonhyung Choi, Changwook Yoon","doi":"10.1002/mma.10369","DOIUrl":"https://doi.org/10.1002/mma.10369","url":null,"abstract":"In this paper, we propose a food chain model in which the primary predator moves directly toward areas of high prey density. Simultaneously, the primary predator, which serves as the prey for the secondary predator, indirectly influences the directional movements of the secondary predator through cues such as chemical signals, scents, or excretions. We investigate whether the distinct influences of direct taxis and indirect taxis, as observed in prey–predator dynamics, are also manifested in the proposed food chain model. Our study demonstrates that the model, which incorporates both direct and indirect prey‐taxis, possesses bounded and global solutions up to three‐dimensional space.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141934959","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
Mathematical analysis of a non‐convex optimal control problem for age‐structured mosquito populations 年龄结构蚊虫种群非凸优化控制问题的数学分析
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-06 DOI: 10.1002/mma.10389
Cícero Alfredo da Silva Filho, José Luiz Boldrini
{"title":"Mathematical analysis of a non‐convex optimal control problem for age‐structured mosquito populations","authors":"Cícero Alfredo da Silva Filho, José Luiz Boldrini","doi":"10.1002/mma.10389","DOIUrl":"https://doi.org/10.1002/mma.10389","url":null,"abstract":"We present a rigorous mathematical analysis of a non‐convex optimal control problem for mosquito populations. The nonlinear model for the dynamics of the mosquito population takes in consideration the iterations among the immature (aquatic) subpopulation, the adult winged subpopulation, and the environment resources; the immature subpopulation is assumed to be age‐structured. Moreover, the action of certain control mechanisms on these subpopulations is also taken in account. The cost functional to be minimized is non‐convex. The proof of the existence of an optimal control is done by using fixed point arguments and a special minimizing sequence obtained with the help of Ekeland's variational principle.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141968796","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
Fractional Newton‐type integral inequalities by means of various function classes 利用各种函数类的分数牛顿型积分不等式
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-05 DOI: 10.1002/mma.10378
Fatih Hezenci, Hüseyin Budak
{"title":"Fractional Newton‐type integral inequalities by means of various function classes","authors":"Fatih Hezenci, Hüseyin Budak","doi":"10.1002/mma.10378","DOIUrl":"https://doi.org/10.1002/mma.10378","url":null,"abstract":"The authors of the paper present a method to examine some Newton‐type inequalities for various function classes using Riemann‐Liouville fractional integrals. Namely, some fractional Newton‐type inequalities are established by using convex functions. In addition, several fractional Newton‐type inequalities are proved by using bounded functions by fractional integrals. Moreover, we construct some fractional Newton‐type inequalities for Lipschitzian functions. Furthermore, several Newton‐type inequalities are acquired by fractional integrals of bounded variation. Finally, we provide our results by using special cases of obtained theorems and examples.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141968800","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
Quantum (or q$$ q $$‐) operator equations and associated partial differential equations for bivariate Laguerre polynomials with applications to the q$$ q $$‐Hille‐Hardy type formulas 双变量拉盖尔多项式的量子（或 q$$ q$- ）算子方程和相关偏微分方程，以及 q$$ q$-Hille-Hardy 型公式的应用
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-05 DOI: 10.1002/mma.10328
Jian Cao, H. M. Srivastava, Yue Zhang
{"title":"Quantum (or q$$ q $$‐) operator equations and associated partial differential equations for bivariate Laguerre polynomials with applications to the q$$ q $$‐Hille‐Hardy type formulas","authors":"Jian Cao, H. M. Srivastava, Yue Zhang","doi":"10.1002/mma.10328","DOIUrl":"https://doi.org/10.1002/mma.10328","url":null,"abstract":"Based on the extensive application of the ‐series and ‐polynomials including (for example) the ‐Laguerre polynomials in several fields of the mathematical and physical sciences, we attach great importance to the equations and related application issues involving the ‐Laguerre polynomials. The mission of this paper is to find the general ‐operational equation together with the expansion issue of the bivariate ‐Laguerre polynomials from the perspective of ‐partial differential equations. We also give some applications including some ‐Hille‐Hardy type formulas. In addition, we present the Rogers‐type formulas and the ‐type generating functions for the bivariate ‐Laguerre polynomials by the technique based upon ‐operational equations. Moreover, we derive a new generalized Andrews‐Askey integral and a new transformation identity involving the bivariate ‐Laguerre polynomials by applying ‐operational equations.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141934963","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
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