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An Unconditionally Stable Numerical Method for Space Tempered Fractional Convection-Diffusion Models 空间节制分数对流扩散模型的无条件稳定数值方法
IF 1.4 4区 数学 Q1 MATHEMATICS Pub Date : 2024-05-31 DOI: 10.1155/2024/6710903
Zeshan Qiu
A second-order numerical method for two-sided tempered fractional convection-diffusion equations is studied in this paper, both convection term and diffusion term are approximated by the tempered weighted and shifted Grünwald difference operators, the first time partial derivative is discretized by the Crank–Nicolson method, and then a class of second-order numerical schemes is derived. By means of matrix method, numerical schemes are proved to be unconditionally stable and convergent with order . The validity of the proposed numerical scheme is verified by numerical experiments.
本文研究了双面节制分式对流扩散方程的二阶数值方法,对流项和扩散项都用节制加权和移位格吕内瓦尔德差分算子近似,第一次偏导数用 Crank-Nicolson 方法离散,然后推导出一类二阶数值方案。通过矩阵法证明了数值方案的无条件稳定性和阶收敛性。通过数值实验验证了所提出数值方案的有效性。
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引用次数: 0
On the Exterior Degree of a Finite-Dimensional Lie Algebra 论有限维李代数的外度
IF 1.4 4区 数学 Q1 MATHEMATICS Pub Date : 2024-05-30 DOI: 10.1155/2024/5596170
Afsaneh Shamsaki, Mohsen Parvizi, Ahmad Erfanian
In this paper, we define the exterior degree for a finite-dimensional Lie algebra over the field and give upper and lower bounds. Also, we give some relations between this concept and commutativity degree, capability, and Schur multiplier.
在本文中,我们定义了域上有限维李代数的外部度,并给出了上界和下界。此外,我们还给出了这一概念与交换度、能力和舒尔乘数之间的一些关系。
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引用次数: 0
Study of Hybrid Problems under Exponential Type Fractional-Order Derivatives 指数型分阶导数下的混合问题研究
IF 1.4 4区 数学 Q1 MATHEMATICS Pub Date : 2024-05-29 DOI: 10.1155/2024/2274198
Mohammed S. Abdo, Sahar Ahmed Idris, M. Daher Albalwi, Tomadir Ahmed Idris
In this investigation, we develop a theory for the hybrid boundary value problem for fractional differential equations subject to three-point boundary conditions, including the antiperiodic hybrid boundary condition. On suggested problems, the third-order Caputo–Fabrizio derivative is the fractional operator applied. In this regard, the corresponding hybrid fractional integral equation is obtained by the Caputo–Fabrizio operator’s properties with the Green function’s aid. Then, we apply Dhage’s nonlinear alternative to the Schaefer type to prove the existence results. Finally, two examples are provided to confirm the validity of our main results.
在这项研究中,我们发展了受三点边界条件(包括反周期混合边界条件)限制的分数微分方程的混合边界值问题理论。在建议的问题中,三阶 Caputo-Fabrizio 导数是应用的分数算子。在这方面,利用卡普托-法布里齐奥算子的性质和格林函数的辅助,可以得到相应的混合分数积分方程。然后,我们应用 Dhage 的非线性替代 Schaefer 类型来证明存在性结果。最后,我们提供了两个例子来证实我们主要结果的正确性。
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引用次数: 0
Hankel Determinants for the Logarithmic Coefficients of a Subclass of Close-to-Star Functions 近星函数子类对数系数的汉克尔决定因素
IF 1.4 4区 数学 Q1 MATHEMATICS Pub Date : 2024-05-29 DOI: 10.1155/2024/1315252
Dong Guo, Huo Tang, Jun Zhang, Qingbing Xu, Zongtao Li
Suppose that <svg height="11.5564pt" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 36.9885 11.5564" width="36.9885pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"></path></g><g transform="matrix(.013,0,0,-0.013,9.659,0)"></path></g><g transform="matrix(.013,0,0,-0.013,21.515,0)"></path></g><g transform="matrix(.013,0,0,-0.013,26.013,0)"></path></g><g transform="matrix(.013,0,0,-0.013,32.253,0)"></path></g></svg> is a class of close-to-star functions. In this paper, we investigated the estimate of Zalcman functional on the logarithmic coefficients and the third Hankel determinant for the class <svg height="11.5564pt" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 36.9885 11.5564" width="36.9885pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g198-20"></use></g><g transform="matrix(.013,0,0,-0.013,9.659,0)"><use xlink:href="#g198-21"></use></g><g transform="matrix(.013,0,0,-0.013,21.515,0)"><use xlink:href="#g113-41"></use></g><g transform="matrix(.013,0,0,-0.013,26.013,0)"><use xlink:href="#g113-50"></use></g><g transform="matrix(.013,0,0,-0.013,32.253,0)"><use xlink:href="#g113-42"></use></g></svg> with the determinant entry of logarithmic coefficients. Also, we obtained the sharp bounds of Zalcman functional <svg height="13.639pt" style="vertical-align:-4.35067pt" version="1.1" viewbox="-0.0498162 -9.28833 34.116 13.639" width="34.116pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.031,3.132)"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.463,3.132)"></path></g><g transform="matrix(.0091,0,0,-0.0091,11.619,3.132)"></path></g><g transform="matrix(.013,0,0,-0.013,16.59,0)"><use xlink:href="#g113-41"></use></g><g transform="matrix(.013,0,0,-0.013,21.088,0)"></path></g><g transform="matrix(.013,0,0,-0.013,29.441,0)"><use xlink:href="#g113-42"></use></g></svg> and <svg height="13.639pt" style="vertical-align:-4.35067pt" version="1.1" viewbox="-0.0498162 -9.28833 34.116 13.639" width="34.116pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-75"></use></g><g transform="matrix(.0091,0,0,-0.0091,5.031,3.132)"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.463,3.132)"><use xlink:href="#g50-45"></use></g><g transform="matrix(.0091,0,0,-0.0091,11.62,3.132)"><use xlink:href="#g50-52"></use></g><g transform="matrix(.013,0,0,-0.013,16.59,0)"><use xlink:href="#g113-41"></use></g><g transform="matrix(.013,0,0,-0.013,21.088,0)"><use xlink:href="#g113-103"></use></g><g transform="matrix(.013,0,0,-0.013,29.441,0)"><use xlink:href="#g113-42"></use></g></svg> for the class <span><svg height="11.5564pt" style=
假设是一类近似星函数。本文研究了 Zalcman 函数对对数系数的估计和带有对数系数行列式项的类的第三汉克尔行列式。此外,我们还得到了...类的扎尔克曼函数和...类的汉克尔行列式的尖锐边界。
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引用次数: 0
Existence Results for the System of Fractional-Order Sequential Integrodifferential Equations via Liouville–Caputo Sense 通过利乌维尔-卡普托原理求分数阶序列积分微分方程系统的存在性结果
IF 1.4 4区 数学 Q1 MATHEMATICS Pub Date : 2024-05-27 DOI: 10.1155/2024/6889622
Muath Awadalla, Manigandan Murugesan, Subramanian Muthaiah, Jihan Alahmadi
We investigate the conditions for the existence and uniqueness of solutions in a nonlinear system of sequential fractional differential equations using the Liouville–Caputo type with varying orders. This system is enriched by nonlocal coupled integral boundary conditions. The desired outcomes are attained by employing traditional fixed-point theorems. It is essential to emphasize that the fixed-point approach proves to be an effective method for establishing the existence of solutions in boundary value problems. Furthermore, we provide constructed examples to illustrate the obtained results.
我们研究了一个非线性序列分数微分方程系统中的解的存在性和唯一性条件,该系统采用的是具有不同阶数的 Liouville-Caputo 型。非局部耦合积分边界条件丰富了该系统。通过使用传统的定点定理,可以获得理想的结果。必须强调的是,定点法被证明是建立边界值问题解存在性的有效方法。此外,我们还提供了一些构造实例来说明所获得的结果。
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引用次数: 0
Characterizing Topologically Dense Injective Acts and Their Monoid Connections 拓扑密集注入行为的特征及其单体连接
IF 1.4 4区 数学 Q1 MATHEMATICS Pub Date : 2024-05-27 DOI: 10.1155/2024/2966461
Masoomeh Hezarjaribi Dastaki, Hamid Rasouli, Hasan Barzegar
In this paper, we explore the concept of topologically dense injectivity of monoid acts. It is shown that topologically dense injective acts constitute a class strictly larger than the class of ordinary injective ones. We determine a number of acts satisfying topologically dense injectivity. Specifically, any strongly divisible as well as strongly torsion free -act over a monoid is topologically dense injective if and only if is a left reversible monoid. Furthermore, we establish a counterpart of the Skornjakov criterion and also identify a class of acts satisfying the Baer criterion for topologically dense injectivity. Lastly, some homological classifications for monoids by means of this type of injectivity of monoid acts are also provided.
本文探讨了单元行为的拓扑致密可注入性概念。研究表明,拓扑致密注入行为构成了一个严格大于普通注入行为的类别。我们确定了一些满足拓扑密集注入性的行为。具体地说,当且仅当一个左可逆单元上的强可分和强无扭行为是拓扑致密注入行为时,该单元上的任何强可分和强无扭行为都是拓扑致密注入行为。此外,我们还建立了斯科恩贾科夫准则的对应准则,并确定了一类满足贝尔准则的拓扑致密注入性行为。最后,我们还通过这类单形行为的注入性为单形提供了一些同构分类。
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引用次数: 0
Study on the Solutions of Impulsive Integrodifferential Equations of Mixed Type Based on Infectious Disease Dynamical Systems 基于传染病动态系统的混合型脉冲积分微分方程解法研究
IF 1.4 4区 数学 Q1 MATHEMATICS Pub Date : 2024-05-25 DOI: 10.1155/2024/6167434
Haiyan Li, Yuheng Guo, Min Wang
Since ancient times, infectious diseases have been a major source of harm to human health. Therefore, scientists have established many mathematical models in the history of fighting infectious diseases to study the law of infection and then analyzed the practicability and effectiveness of various prevention and control measures, providing a scientific basis for human prevention and research of infectious diseases. However, due to the great differences in the transmission mechanisms and modes of many diseases, there are many kinds of infectious disease dynamic models, which make the research more and more difficult. With the continuous progress of infectious disease research technology, people have adopted more ways to prevent and interfere with the derivation and spread of infectious disease, which will make the state of infectious disease system change in an instant. The mutation of this state can be described more scientifically and reasonably by the mathematical impulse dynamic system, which makes the research more practical. Based on this, a time-delay differential system model of infectious disease under impulse effect was established by means of impulse differential equation theory. A class of periodic boundary value problems for impulsive integrodifferential equations of mixed type with integral boundary conditions was studied. The existence of periodic solutions of these equations was obtained by using the comparison theorem, upper and lower solution methods, and the monotone iteration technique. Finally, combined with the practical application, the established time-delay differential system model was applied to the prediction of the stability and persistence of the infectious disease dynamic system, and the correctness of the conclusion was further verified. This study provides some reference for the prevention and treatment of infectious diseases.
自古以来,传染病一直是危害人类健康的重要根源。因此,科学家们在防治传染病的历史上建立了许多数学模型,研究传染规律,进而分析各种防治措施的实用性和有效性,为人类预防和研究传染病提供了科学依据。然而,由于许多疾病的传播机制和方式存在很大差异,传染病动态模型种类繁多,给研究带来了越来越大的难度。随着传染病研究技术的不断进步,人们采用了更多的方式来预防和干扰传染病的衍生和传播,这将使传染病系统的状态在瞬间发生变化。这种状态的突变可以用数学脉冲动力系统来描述,更加科学合理,使研究更具实用性。在此基础上,利用脉冲微分方程理论建立了脉冲效应下的传染病时延微分系统模型。研究了一类带积分边界条件的混合型脉冲积分微分方程的周期性边界值问题。利用比较定理、上下解法和单调迭代技术,得到了这些方程的周期解的存在性。最后,结合实际应用,将建立的时延微分系统模型应用于传染病动态系统稳定性和持续性的预测,进一步验证了结论的正确性。本研究为传染病的防治提供了一定的参考。
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引用次数: 0
Geometric Classifications of Perfect Fluid Space-Time Admit Conformal Ricci-Bourguignon Solitons 完美流体时空的几何分类可容纳共形里奇-布尔吉农孤子
IF 1.4 4区 数学 Q1 MATHEMATICS Pub Date : 2024-05-25 DOI: 10.1155/2024/6674726
Noura Alhouiti, Soumendu Roy, Santu Dey, Fatemah Mofarreh, Akram Ali, Yanlin Li
This paper is dedicated to the study of the geometric composition of a perfect fluid space-time with a conformal Ricci-Bourguignon soliton, which is the extended version of the soliton to the Ricci-Bourguignon flow. Here, we have delineated the conditions for conformal Ricci-Bourguignon soliton to be expanding, steady, or shrinking. We have studied certain curvature conditions on the spacetime that admit conformal Ricci-Bourguignon soliton. We have also discussed conformal Ricci-Bourguignon soliton on some special types of perfect fluid spacetime such as dust fluid, dark fluid, and radiation era.
本文致力于研究完美流体时空与共形里奇-布尔基尼孤子的几何构成,共形里奇-布尔基尼孤子是对里奇-布尔基尼流孤子的扩展版本。在这里,我们划分了共形里奇-布尔吉尼孤子膨胀、稳定或收缩的条件。我们研究了接纳共形里奇-布尔吉尼孤子的时空的某些曲率条件。我们还讨论了完美流体时空中一些特殊类型的共形里奇-布尔基尼孤子,如尘埃流体、暗流体和辐射时代。
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引用次数: 0
A Note on Weakly Semiprime Ideals and Their Relationship to Prime Radical in Noncommutative Rings 关于非交换环中的弱半素数理想及其与素根的关系的说明
IF 1.4 4区 数学 Q1 MATHEMATICS Pub Date : 2024-05-24 DOI: 10.1155/2024/9142090
Alaa Abouhalaka
In this paper, we introduce the concept of weakly semiprime ideals and weakly -systems in noncommutative rings. We establish the equivalence between an ideal being a weakly semiprime ideal and being a weakly -system. We provide alternative definitions and explore the properties of weakly semiprime ideals. Additionally, we investigate scenarios where all ideals in a given ring are weakly semiprime and demonstrate that in Noetherian rings, where every ideal is weakly semiprime, the prime radical and the Jacobson radical coincide.
本文介绍了非交换环中弱半理想和弱-系统的概念。我们建立了弱半枚举理想与弱-系统之间的等价关系。我们提供了弱半整数理想的替代定义,并探讨了弱半整数理想的性质。此外,我们还研究了给定环中所有理想都是弱半枚举的情况,并证明在诺特环中,每个理想都是弱半枚举,质根和雅各布森根重合。
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引用次数: 0
On the Comparative Analysis among Topological Indices for Rhombus Silicate and Oxide Structures 论菱形硅酸盐和氧化物结构拓扑指标的比较分析
IF 1.4 4区 数学 Q1 MATHEMATICS Pub Date : 2024-05-24 DOI: 10.1155/2024/2773913
Aqsa Sattar, Muhammad Javaid, Mamo Abebe Ashebo
A topological index (TI) is a numeric digit that signalizes the whole chemical structure of a molecular network. TIs are helpful in predicting the bioactivity of molecular substances in investigations of quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR). TIs correlate various chemical and physical attributes of chemical substances such as melting and freezing point, strain energy, stability, temperature, volume, density, and pressure. There are several distance-based descriptors available in the literature, but connection-based TIs are considered more effective than degree-based TIs in measuring the chemical characteristics of molecular compounds. The present study focuses on computing the connection-based TIs for the most significant type of chemical structures, namely, rhombus silicate and rhombus oxide networks. At the end, we compare these structures on the basis of their computed result.
拓扑指数(TI)是表示分子网络整体化学结构的数字。在定量结构-活性关系(QSAR)和定量结构-性质关系(QSPR)研究中,拓扑指数有助于预测分子物质的生物活性。距离描述符与化学物质的各种化学和物理属性相关联,如熔点和凝固点、应变能、稳定性、温度、体积、密度和压力。文献中有多种基于距离的描述符,但在测量分子化合物的化学特性方面,基于连接的 TI 被认为比基于度的 TI 更有效。本研究主要针对最重要的化学结构类型,即菱形硅酸盐和菱形氧化物网络,计算基于连接的 TI。最后,我们根据计算结果对这些结构进行了比较。
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引用次数: 0
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Journal of Mathematics
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