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Bivariate q-extended Weibull morgenstern family and correlation coefficient formulas for some of its sub-models 二元q扩展Weibull morgenstern族及其部分子模型的相关系数公式
IF 2.2 3区 数学 Q1 MATHEMATICS Pub Date : 2023-01-01 DOI: 10.3934/math.20231292
R. A. Attwa, T. Radwan, E. O. A. Zaid
A bivariate extension of a flexible univariate family is proposed. The new family is called bivariate q-extended Weibull Morgenstern family of distributions which can be constructed based on the Farlie-Gumbel-Morgenstern (FGM) copula technique. After introducing the new family, four sub-models are discussed in detail from the theoretical and numerical coefficient of correlation point of view with pointing to the effect of the $ q $ parameter.
提出了一个柔性单变量族的二元扩展。新的分布族被称为二元q扩展Weibull Morgenstern分布族,它可以基于Farlie-Gumbel-Morgenstern (FGM) copula技术构造。在引入新族后,从理论和数值相关系数的角度详细讨论了四个子模型,并指出q参数的影响。
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引用次数: 0
Maps on $ C^ast $-algebras are skew Lie triple derivations or homomorphisms at one point C^ast $-代数上的映射是一点上的斜李三重导数或同态
IF 2.2 3区 数学 Q1 MATHEMATICS Pub Date : 2023-01-01 DOI: 10.3934/math.20231305
Zhonghua Wang, Xiuhai Fei
In this paper, we show that every continuous linear map between unital $ C^ast $-algebras is skew Lie triple derivable at the identity is a $ ast $-derivation and that every continuous linear map between unital $ C^ast $-algebras which is a skew Lie triple homomorphism at the identity is a Jordan $ ast $-homomorphism.
本文证明了一元C^ast $-代数之间的每一个连续线性映射在单位上都是偏李三重可导的,是一元C^ast $-导数;一元C^ast $-代数之间的每一个连续线性映射在单位上都是偏李三重同态的,是Jordan $ ast $-同态。
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引用次数: 0
Direct connection between Navier and spherical harmonic kernels in elasticity 弹性力学中Navier和球谐核的直接联系
IF 2.2 3区 数学 Q1 MATHEMATICS Pub Date : 2023-01-01 DOI: 10.3934/math.2023158
D. Labropoulou, P. Vafeas, G. Dassios
Linear isotropic elasticity is an interesting branch of continuum mechanics, described by the fundamental laws of Hooke and Newton, which are combined in order to construct the governing generalized Navier equation of the displacement within any material. Implying time-independence and in the absence of external body forces, the latter is reduced to the corresponding form of a homogeneous second-order partial differential equation, whose solution is given via the Papkovich differential representation, which expresses the displacement field in terms of harmonic functions. On the other hand, spherical geometry provides the most widely used framework in real-life applications, concerning interior and exterior problems in elasticity. The present work aims to provide a little progress, by producing ready-to-use basic functions for linear isotropic elasticity in spherical coordinates. Hence, we calculate the Papkovich eigensolutions, generated by the spherical harmonic eigenfunctions, obtaining connections between Navier and spherical harmonic kernels. A set of useful results are provided at the end of the paper in the form of examples, regarding the evaluation of displacement field inside and outside a sphere.
线性各向同性弹性是连续介质力学的一个有趣的分支,由胡克和牛顿的基本定律描述,它们结合在一起,以构建任何材料内位移的控制广义纳维尔方程。在没有外力的情况下,后者被简化为齐次二阶偏微分方程的相应形式,其解通过Papkovich微分表示给出,该表示以调和函数的形式表示位移场。另一方面,球面几何在实际应用中提供了最广泛使用的框架,涉及弹性的内部和外部问题。目前的工作旨在提供一点进展,通过在球坐标下产生现成的线性各向同性弹性的基本函数。因此,我们计算了由球调和本征函数生成的Papkovich本征解,得到了Navier和球调和核之间的联系。最后以实例的形式给出了一组关于球内外位移场计算的有用结果。
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引用次数: 0
Disaster decision-making with a mixing regret philosophy DDAS method in Fermatean fuzzy number fermatan模糊数中混合后悔哲学DDAS方法的灾难决策
IF 2.2 3区 数学 Q1 MATHEMATICS Pub Date : 2023-01-01 DOI: 10.3934/math.2023192
A. Fahmi, Rehan Ahmed, M. Aslam, T. Abdeljawad, Aziz Khan
In this paper, the use of the Fermatean fuzzy number (FFN) in a significant research problem of disaster decision-making by defining operational laws and score function is demonstrated. Generally, decision control authorities need to brand suitable and sensible disaster decisions in the direct conceivable period as unfitting decisions may consequence in enormous financial dead and thoughtful communal costs. To certify that a disaster comeback can be made, professionally, we propose a new disaster decision-making (DDM) technique by the Fermatean fuzzy Schweizer-Sklar environment. First, the Fermatean fuzzy Schweizer-Sklar operators are employed by decision-makers to rapidly analyze their indefinite and vague assessment information on disaster choices. Then, the DDM technique based on the FFN is planned to identify highly devastating disaster choices and the best available choices. Finally, the proposed regret philosophy DDM technique is shown functional to choose the ideal retort explanation for a communal fitness disaster in Pakistan. The dominance and realism of the intended technique are further defensible through a relative study with additional DDM systems.
本文通过定义运行规律和分数函数,证明了Fermatean模糊数(FFN)在一个重大的灾害决策研究问题中的应用。一般来说,决策控制当局需要在直接可想象的时期内制定合适和明智的灾难决策,因为不合适的决策可能导致巨大的财务死亡和深思熟虑的公共成本。为了证明灾难能够卷土重来,我们在专业上提出了一种新的基于fermatan模糊Schweizer-Sklar环境的灾难决策(DDM)技术。首先,决策者利用Fermatean模糊Schweizer-Sklar算子对其不确定和模糊的灾害选择评估信息进行快速分析。然后,计划基于FFN的DDM技术来识别高破坏性灾害选择和最佳可用选择。最后,本文提出的后悔哲学DDM技术在选择巴基斯坦公共健身灾难的理想反驳解释方面具有一定的功能。通过对附加DDM系统的相关研究,可以进一步证明预期技术的主导地位和现实性。
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引用次数: 1
Simulation analysis, properties and applications on a new Burr XII model based on the Bell-X functionalities 基于Bell-X功能的新型Burr XII模型的仿真分析、性能及应用
IF 2.2 3区 数学 Q1 MATHEMATICS Pub Date : 2023-01-01 DOI: 10.3934/math.2023352
A. Alanzi, Muhammad Imran, Muhammad Mohsin Tahir, C. Chesneau, Farrukh Jamal, Saima Shakoor, Waqas Sami
In this article, we make mathematical and practical contributions to the Bell-X family of absolutely continuous distributions. As a main member of this family, a special distribution extending the modeling perspectives of the famous Burr XII (BXII) distribution is discussed in detail. It is called the Bell-Burr XII (BBXII) distribution. It stands apart from the other extended BXII distributions because of its flexibility in terms of functional shapes. On the theoretical side, a linear representation of the probability density function and the ordinary and incomplete moments are among the key properties studied in depth. Some commonly used entropy measures, namely Rényi, Havrda and Charvat, Arimoto, and Tsallis entropy, are derived. On the practical (inferential) side, the associated parameters are estimated using seven different frequentist estimation methods, namely the methods of maximum likelihood estimation, percentile estimation, least squares estimation, weighted least squares estimation, Cramér von-Mises estimation, Anderson-Darling estimation, and right-tail Anderson-Darling estimation. A simulation study utilizing all these methods is offered to highlight their effectiveness. Subsequently, the BBXII model is successfully used in comparisons with other comparable models to analyze data on patients with acute bone cancer and arthritis pain. A group acceptance sampling plan for truncated life tests is also proposed when an item's lifetime follows a BBXII distribution. Convincing results are obtained.
在本文中,我们对绝对连续分布的Bell-X族做出了数学和实际的贡献。作为该家族的主要成员,详细讨论了扩展了著名的Burr XII (BXII)分布的建模视角的特殊分布。它被称为贝尔-伯尔十二(BBXII)分布。它与其他扩展BXII发行版的区别在于它在功能形状方面的灵活性。在理论方面,概率密度函数的线性表示以及普通矩和不完全矩是深入研究的关键性质。推导了一些常用的熵测度,即r尼、Havrda和Charvat、Arimoto和Tsallis熵。在实际(推理)方面,使用七种不同的频率估计方法对相关参数进行估计,即最大似然估计、百分位数估计、最小二乘估计、加权最小二乘估计、cram von-Mises估计、Anderson-Darling估计和右尾Anderson-Darling估计。利用所有这些方法进行了仿真研究,以突出它们的有效性。随后,BBXII模型成功用于与其他可比较模型的比较,分析急性骨癌和关节炎疼痛患者的数据。当一个项目的寿命遵循BBXII分布时,还提出了截断寿命试验的组验收抽样计划。得到了令人信服的结果。
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引用次数: 1
Some new criteria for judging $ mathcal{H} $-tensors and their applications $ mathcal{H} $-张量的几个新判据及其应用
IF 2.2 3区 数学 Q1 MATHEMATICS Pub Date : 2023-01-01 DOI: 10.3934/math.2023381
Wenbin Gong, Yaqiang Wang
$ mathcal{H} $-tensors play a key role in identifying the positive definiteness of even-order real symmetric tensors. Some criteria have been given since it is difficult to judge whether a given tensor is an $ mathcal{H} $-tensor, and their range of judgment has been limited. In this paper, some new criteria, from an increasing constant $ k $ to scale the elements of a given tensor can expand the range of judgment, are obtained. Moreover, as an application of those new criteria, some sufficient conditions for judging positive definiteness of even-order real symmetric tensors are proposed. In addition, some numerical examples are presented to illustrate those new results.
$ mathcal{H} $-张量在确定偶阶实对称张量的正定性方面起着关键作用。由于很难判断给定张量是否为$ mathcal{H} $-张量,因此给出了一些准则,并且它们的判断范围受到限制。本文给出了从一个递增的常数$ k $缩放给定张量的元素可以扩大判断范围的一些新准则。此外,作为这些新准则的应用,给出了判定偶阶实对称张量正确定性的几个充分条件。此外,还给出了一些数值算例来说明这些新结果。
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引用次数: 0
Existence and compatibility of positive solutions for boundary value fractional differential equation with modified analytic kernel 修正解析核边值分数阶微分方程正解的存在性与相容性
IF 2.2 3区 数学 Q1 MATHEMATICS Pub Date : 2023-01-01 DOI: 10.3934/math.2023390
A. Kalsoom, Sehar Afsheen, A. Azam, Faryad Ali
In this article, a Green's function for a fractional boundary value problem in connection with modified analytic kernel has been constructed to study the existence of multiple solutions of a type of characteristic fractional boundary value problems. It is done here by using a well-known result: Krasnoselskii fixed point theorem. Moreover, a practical example is created to understand the importance of main results regarding the existence of solution of a boundary value fractional differential problem with homogeneous conditions. This example analytically and graphically, explains circumstances under which the Green's functions with different types of differential operator are compatible.
本文构造了一类带有修正解析核的分数阶边值问题的格林函数,研究了一类特征性分数阶边值问题多解的存在性。这里用一个著名的结果:Krasnoselskii不动点定理。并通过一个实例说明了齐次条件下边值分数阶微分问题解存在性的主要结果的重要性。这个例子以解析和图解的方式解释了不同类型的微分算子的格林函数兼容的情况。
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引用次数: 0
Blowup for $ {{rm{C}}}^{1} $ solutions of Euler equations in $ {{rm{R}}}^{N} $ with the second inertia functional of reference 放大了$ {{rm{C}}}^{1} $的欧拉方程的解,在$ {{rm{R}}}}^{N} $中有第二个参考惯性泛函
IF 2.2 3区 数学 Q1 MATHEMATICS Pub Date : 2023-01-01 DOI: 10.3934/math.2023412
Manwai Yuen

The compressible Euler equations are an elementary model in mathematical fluid mechanics. In this article, we combine the Sideris and Makino-Ukai-Kawashima's classical functional techniques to study the new second inertia functional of reference:

for the blowup phenomena of $ C^{1} $ solutions $ (rho, vec{u}) $ with the support of $ left({ rho-bar{rho}}, vec{u}right) $, and with a positive constant $ { bar{rho}} $ for the adiabatic index $ gamma > 1 $. We find that if the total reference mass

and the total reference energy

with a positive constant $ K $ is sufficiently large, then the corresponding solution blows up on or before any finite time $ T > 0 $.

The compressible Euler equations are an elementary model in mathematical fluid mechanics. In this article, we combine the Sideris and Makino-Ukai-Kawashima's classical functional techniques to study the new second inertia functional of reference: begin{document}$ { H}_{ref}{ (t) = }frac{1}{2}int_{Omega(t)}left( { rho-bar{rho}}right) leftvert { vec{x} }rightvert ^{2}dV{{ , }} $end{document} for the blowup phenomena of $ C^{1} $ solutions $ (rho, vec{u}) $ with the support of $ left({ rho-bar{rho}}, vec{u}right) $, and with a positive constant $ { bar{rho}} $ for the adiabatic index $ gamma > 1 $. We find that if the total reference mass begin{document}$ M_{ref}(0) = { int_{{bf R}^{N}}} (rho_{0}({ vec{x}})-bar{rho})dVgeq0, $end{document} and the total reference energy begin{document}$ E_{ref}(0) = int_{{bf R}^{N}}left( frac{1}{2}rho_{0}({ vec {x}})leftvert vec{u}_{0}({ vec{x}})rightvert ^{2}+frac {K}{gamma-1}left( rho_{0}^{gamma}({ vec{x}})-bar{rho }^{gamma}right) right) dV, $end{document} with a positive constant $ K $ is sufficiently large, then the corresponding solution blows up on or before any finite time $ T > 0 $.
{"title":"Blowup for $ {{rm{C}}}^{1} $ solutions of Euler equations in $ {{rm{R}}}^{N} $ with the second inertia functional of reference","authors":"Manwai Yuen","doi":"10.3934/math.2023412","DOIUrl":"https://doi.org/10.3934/math.2023412","url":null,"abstract":"<abstract><p>The compressible Euler equations are an elementary model in mathematical fluid mechanics. In this article, we combine the Sideris and Makino-Ukai-Kawashima's classical functional techniques to study the new second inertia functional of reference:</p> <p><disp-formula> <label/> <tex-math id=\"FE1\"> begin{document}$ { H}_{ref}{ (t) = }frac{1}{2}int_{Omega(t)}left( { rho-bar{rho}}right) leftvert { vec{x} }rightvert ^{2}dV{{ , }} $end{document} </tex-math></disp-formula></p> <p>for the blowup phenomena of $ C^{1} $ solutions $ (rho, vec{u}) $ with the support of $ left({ rho-bar{rho}}, vec{u}right) $, and with a positive constant $ { bar{rho}} $ for the adiabatic index $ gamma > 1 $. We find that if the total reference mass</p> <p><disp-formula> <label/> <tex-math id=\"FE2\"> begin{document}$ M_{ref}(0) = { int_{{bf R}^{N}}} (rho_{0}({ vec{x}})-bar{rho})dVgeq0, $end{document} </tex-math></disp-formula></p> <p>and the total reference energy</p> <p><disp-formula> <label/> <tex-math id=\"FE3\"> begin{document}$ E_{ref}(0) = int_{{bf R}^{N}}left( frac{1}{2}rho_{0}({ vec {x}})leftvert vec{u}_{0}({ vec{x}})rightvert ^{2}+frac {K}{gamma-1}left( rho_{0}^{gamma}({ vec{x}})-bar{rho }^{gamma}right) right) dV, $end{document} </tex-math></disp-formula></p> <p>with a positive constant $ K $ is sufficiently large, then the corresponding solution blows up on or before any finite time $ T > 0 $.</p></abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70182449","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
Stability, bifurcation, and chaos control in a discrete predator-prey model with strong Allee effect 具有强Allee效应的离散捕食-食饵模型的稳定性、分岔和混沌控制
IF 2.2 3区 数学 Q1 MATHEMATICS Pub Date : 2023-01-01 DOI: 10.3934/math.2023408
Ali Al Khabyah, Rizwan Ahmed, M. Akram, S. Akhtar
This work considers a discrete-time predator-prey system with a strong Allee effect. The existence and topological classification of the system's possible fixed points are investigated. Furthermore, the existence and direction of period-doubling and Neimark-Sacker bifurcations are explored at the interior fixed point using bifurcation theory and the center manifold theorem. A hybrid control method is used for controlling chaos and bifurcations. Some numerical examples are presented to verify our theoretical findings. Numerical simulations reveal that the discrete model has complex dynamics. Moreover, it is shown that the system with the Allee effect requires a much longer time to reach its interior fixed point.
本文考虑了一个具有强Allee效应的离散时间捕食者-猎物系统。研究了系统可能不动点的存在性和拓扑分类。进一步利用分岔理论和中心流形定理,探讨了内不动点上周期加倍分岔和neimmark - sacker分岔的存在性和方向。采用混合控制方法控制混沌和分岔。给出了一些数值算例来验证我们的理论结果。数值模拟结果表明,离散模型具有复杂的动力学特性。此外,研究还表明,有Allee效应的系统需要更长的时间才能到达其内部不动点。
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引用次数: 4
q-Spherical fuzzy rough sets and their usage in multi-attribute decision-making problems q-球面模糊粗糙集及其在多属性决策问题中的应用
IF 2.2 3区 数学 Q1 MATHEMATICS Pub Date : 2023-01-01 DOI: 10.3934/math.2023415
Ahmad Bin Azim, Ahmad Aloqaily, Asad Ali, Sumbal Ali, Nabil Mlaiki, F. Hussain
This article's purpose is to investigate and generalize the concepts of rough set, in addition to the q-spherical fuzzy set, and to introduce a novel concept that is called q-spherical fuzzy rough set (q-SFRS). This novel approach avoids the complications of more recent ideas like the intuitionistic fuzzy rough set, Pythagorean fuzzy rough set, and q-rung orthopair fuzzy rough set. Since mathematical operations known as "aggregation operators" are used to bring together sets of data. Popular aggregation operations include the arithmetic mean and the weighted mean. The key distinction between the weighted mean and the arithmetic mean is that the latter allows us to weight the various values based on their importance. Various aggregation operators make different assumptions about the input (data kinds) and the kind of information that may be included in the model. Because of this, some new q-spherical fuzzy rough weighted arithmetic mean operator and q-spherical fuzzy rough weighted geometric mean operator have been introduced. The developed operators are more general. Because the picture fuzzy rough weighted arithmetic mean (PFRWAM) operator, picture fuzzy rough weighted geometric mean (PFRWGM) operator, spherical fuzzy rough weighted arithmetic mean (SFRWAM) operator and spherical fuzzy rough weighted geometric mean (SFRWGM) operator are all the special cases of the q-SFRWAM and q-SFRWGM operators. When parameter q = 1, the q-SFRWAM operator reduces the PFRWAM operator, and the q-SFRWGM operator reduces the PFRWGM operator. When parameter q = 2, the q-SFRWAM operator reduces the SFRWAM operator, and the q-SFRWGM operator reduces the SFRWGM operator. Besides, our approach is more flexible, and decision-makers can choose different values of parameter q according to the different risk attitudes. In addition, the basic properties of these newly presented operators have been analyzed in great depth and expounded upon. Additionally, a technique called multi-criteria decision-making (MCDM) has been established, and a detailed example has been supplied to back up the recently introduced work. An evaluation of the offered methodology is established at the article's conclusion. The results of this research show that, compared to the q-spherical fuzzy set, our method is better and more effective.
本文的目的是研究和推广粗糙集的概念,除了q球模糊集,并引入一个新的概念,称为q球模糊粗糙集(q-SFRS)。这种新颖的方法避免了诸如直觉模糊粗糙集、毕达哥拉斯模糊粗糙集和q-rung正形模糊粗糙集等新近思想的复杂性。因为称为“聚合运算符”的数学运算是用来将数据集合在一起的。常用的聚合操作包括算术平均值和加权平均值。加权平均数和算术平均数之间的关键区别在于,算术平均数允许我们根据其重要性对各种值进行加权。不同的聚合操作符对输入(数据类型)和可能包含在模型中的信息类型做出不同的假设。为此,引入了新的q球模糊粗糙加权算术平均算子和q球模糊粗糙加权几何平均算子。发达的运营商更为普遍。因为图像模糊粗糙加权算术平均数(PFRWAM)算子、图像模糊粗糙加权几何平均数(PFRWGM)算子、球面模糊粗糙加权算术平均数(SFRWAM)算子和球面模糊粗糙加权几何平均数(SFRWGM)算子都是q-SFRWAM和q-SFRWGM算子的特例。当参数q = 1时,q- sfrwam算子约简PFRWAM算子,q- sfrwgm算子约简PFRWGM算子。当参数q = 2时,q-SFRWAM算子约简SFRWAM算子,q-SFRWGM算子约简SFRWGM算子。此外,我们的方法更加灵活,决策者可以根据不同的风险态度选择不同的参数q值。此外,还对这些新出现的算子的基本性质进行了深入的分析和阐述。此外,还建立了一种称为多标准决策(MCDM)的技术,并提供了一个详细的示例来支持最近介绍的工作。在文章的结论中建立了对所提供方法的评估。研究结果表明,与q球模糊集相比,我们的方法更好、更有效。
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引用次数: 1
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AIMS Mathematics
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