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Enhancing the accuracy and efficiency of two uniformly convergent numerical solvers for singularly perturbed parabolic convection–diffusion–reaction problems with two small parameters 提高两个均匀收敛数值求解器对具有两个小参数的奇异扰动抛物对流-扩散-反应问题的精度和效率
IF 2 3区 数学 Q1 Mathematics Pub Date : 2024-01-01 DOI: 10.1515/dema-2023-0144
K. Ansari, Mohammad Izadi, S. Noeiaghdam
This study is devoted to designing two hybrid computational algorithms to find approximate solutions for a class of singularly perturbed parabolic convection–diffusion–reaction problems with two small parameters. In our approaches, the time discretization is first performed by the well-known Rothe method and Taylor series procedures, which reduce the underlying model problem into a sequence of boundary value problems (BVPs). Hence, a matrix collocation technique based on novel shifted Delannoy functions (SDFs) is employed to solve each BVP at each time step. We show that our proposed hybrid approximate techniques are uniformly convergent in order O ( Δ τ s + M 1 2 ) {mathcal{O}}left(Delta {tau }^{s}+{M}^{-tfrac{1}{2}}) for
本研究致力于设计两种混合计算算法,为一类具有两个小参数的奇异扰动抛物对流-扩散-反应问题找到近似解。在我们的方法中,首先通过著名的罗特方法和泰勒级数程序进行时间离散化,从而将基础模型问题简化为一系列边界值问题(BVP)。因此,我们采用了一种基于新颖的移位德兰诺伊函数(SDF)的矩阵配位技术来求解每个时间步的每个 BVP。我们的研究表明,我们提出的混合近似技术以 O ( Δ τ s + M - 1 2 ) 的顺序均匀收敛。 {mathcal{O}}left(Delta {tau }^{s}+{M}^{-tfrac{1}{2}}) for s = 1 , 2 s=1,2 ,其中 Δ τ Delta tau 是时间步长,M M 是近似中使用的 SDF 数量。进行了数值模拟,以明确数值结果与理论结果之间的良好一致性。计算结果与文献中的现有数值相比更加精确。
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引用次数: 0
Higher-order circular intuitionistic fuzzy time series forecasting methodology: Application of stock change index 高阶循环直觉模糊时间序列预测方法:股票变动指数的应用
IF 2 3区 数学 Q1 Mathematics Pub Date : 2024-01-01 DOI: 10.1515/dema-2023-0115
Shahzaib Ashraf, Muhammad Sohail, Muhammad Shakir Chohan, Siriluk Paokanta, Choonkil Park
Abstract This article presents a higher-order circular intuitionistic fuzzy time series forecasting method for predicting the stock change index, which is shown to be an improvement over traditional time series forecasting methods. The method is based on the principles of circular intuitionistic fuzzy set theory. It uses both positive and negative membership values and a circular radius to handle uncertainty and imprecision in the data. The circularity of the time series is also taken into consideration, leading to more accurate and robust forecasts. The higher-order forecasting capability of this method provides more comprehensive predictions compared to previous methods. One of the key challenges we face when using the amount featured as a case study in our article to project the future value of ratings is the influence of the stock market index. Through rigorous experiments and comparison with traditional time series forecasting methods, the results of the study demonstrate that the proposed higher-order circular intuitionistic fuzzy time series forecasting method is a superior approach for predicting the stock change index.
摘要 本文提出了一种预测股票变动指数的高阶循环直觉模糊时间序列预测方法,证明该方法比传统的时间序列预测方法有所改进。该方法基于循环直觉模糊集理论的原理。它使用正负成员值和圆形半径来处理数据中的不确定性和不精确性。同时还考虑了时间序列的圆周性,从而得出更准确、更稳健的预测。与之前的方法相比,该方法的高阶预测能力提供了更全面的预测。在使用我们文章中的案例研究金额来预测评级的未来价值时,我们面临的主要挑战之一是股票市场指数的影响。通过严格的实验以及与传统时间序列预测方法的比较,研究结果表明所提出的高阶循环直觉模糊时间序列预测方法是预测股票变化指数的一种优越方法。
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引用次数: 0
L-Fuzzy fixed point results in ℱ -metric spaces with applications ℱ度量空间中的 L-模糊定点结果及其应用
IF 2 3区 数学 Q1 Mathematics Pub Date : 2024-01-01 DOI: 10.1515/dema-2022-0206
Durdana Lateef
Abstract Jleli and Samet in [On a new generalization of metric spaces, J. Fixed Point Theory Appl. 20 (2018), 128 (20 pages)] introduced the notion of ℱ -metric space as a generalization of traditional metric space and proved Banach contraction principle in the setting of this generalized metric space. The objective of this article is to use ℱ -metric space and establish some common fixed point theorems for ( β beta - ψ psi )-contractions. Our results expand, generalize, and consolidate several known results in the literature. As applications of the main result, the solution for fuzzy initial-value problems in the background of a generalized Hukuhara derivative was discussed.
摘要 Jleli和Samet在[On a new generalization of metric spaces, J. Fixed Point Theory Appl. 20 (2018), 128 (20 pages)]中引入了ℱ-度量空间的概念,作为传统度量空间的广义化,并证明了该广义度量空间环境下的巴拿赫收缩原理。本文的目的是利用ℱ -度量空间,建立( β beta - ψ psi )-收缩的一些常见定点定理。我们的结果扩展、概括并巩固了文献中的几个已知结果。作为主要结果的应用,讨论了广义赫库哈拉导数背景下模糊初值问题的求解。
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引用次数: 0
On parameterized inequalities for fractional multiplicative integrals 论分数乘法积分的参数化不等式
IF 2 3区 数学 Q1 Mathematics Pub Date : 2024-01-01 DOI: 10.1515/dema-2023-0155
Wen Sheng Zhu, B. Meftah, Hongyan Xu, Fahd Jarad, A. Lakhdari
In this article, we present a one-parameter fractional multiplicative integral identity and use it to derive a set of inequalities for multiplicatively s s -convex mappings. These inequalities include new discoveries and improvements upon some well-known results. Finally, we provide an illustrative example with graphical representations, along with some applications to special means of real numbers within the domain of multiplicative calculus.
在本文中,我们提出了一个单参数分数乘法积分特性,并利用它推导出了一组乘法 s s -凸映射的不等式。这些不等式包括对一些著名结果的新发现和改进。最后,我们提供了一个具有图形表示的示例,以及在乘法微积分领域中对实数特殊手段的一些应用。
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引用次数: 0
Spectral collocation method for convection-diffusion equation 对流扩散方程的谱配位法
IF 2 3区 数学 Q1 Mathematics Pub Date : 2024-01-01 DOI: 10.1515/dema-2023-0110
Jin Li, Yongling Cheng
Spectral collocation method, named linear barycentric rational interpolation collocation method (LBRICM), for convection-diffusion (C-D) equation with constant coefficient is considered. We change the discrete linear equations into the matrix equation. Different from the classical methods to solve the C-D equation, we solve the C-D equation with the time variable and space variable obtained at the same time. Furthermore, the convergence rate of the C-D equation by LBRICM is proved. Numerical examples are presented to test our analysis.
针对具有恒定系数的对流-扩散(C-D)方程,考虑了名为线性巴里中心有理插值配位法(LBRICM)的谱配位方法。我们将离散线性方程转换为矩阵方程。与经典的 C-D 方程求解方法不同,我们在求解 C-D 方程时同时得到了时间变量和空间变量。此外,我们还证明了 LBRICM 对 C-D 方程的收敛率。我们还给出了数值实例来检验我们的分析。
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引用次数: 0
On the asymptotics of eigenvalues for a Sturm-Liouville problem with symmetric single-well potential 论具有对称单井势的 Sturm-Liouville 问题特征值的渐近性
IF 2 3区 数学 Q1 Mathematics Pub Date : 2024-01-01 DOI: 10.1515/dema-2023-0129
E. Başkaya
In this article, Sturm-Liouville problem with one boundary condition including an eigenparameter is considered, and the asymptotic expansion of its eigenparameter is calculated. The problem also has a symmetric single-well potential, which is an important function in quantum mechanics.
本文考虑了一个边界条件包括一个特征参数的 Sturm-Liouville 问题,并计算了其特征参数的渐近展开。该问题还有一个对称单井势,这是量子力学中的一个重要函数。
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引用次数: 0
LADM procedure to find the analytical solutions of the nonlinear fractional dynamics of partial integro-differential equations 用 LADM 程序求解非线性分式偏积分微分方程的解析解
IF 2 3区 数学 Q1 Mathematics Pub Date : 2024-01-01 DOI: 10.1515/dema-2023-0101
Qasim Khan, Hassan Khan, P. Kumam, Fairouz Tchier, Gurpreet Singh
Generally, fractional partial integro-differential equations (FPIDEs) play a vital role in modeling various complex phenomena. Because of the several applications of FPIDEs in applied sciences, mathematicians have taken a keen interest in developing and utilizing the various techniques for its solutions. In this context, the exact and analytical solutions are not very easy to investigate the solution of FPIDEs. In this article, a novel analytical approach that is known as the Laplace adomian decomposition method is implemented to calculate the solutions of FPIDEs. We obtain the approximate solution of the nonlinear FPIDEs. The results are discussed using graphs and tables. The graphs and tables have shown the greater accuracy of the suggested method compared to the extended cubic-B splice method. The accuracy of the suggested method is higher at all fractional orders of the derivatives. A sufficient degree of accuracy is achieved with fewer calculations with a simple procedure. The presented method requires no parametrization or discretization and, therefore, can be extended for the solutions of other nonlinear FPIDEs and their systems.
一般来说,分数偏积分微分方程(FPIDE)在模拟各种复杂现象中发挥着重要作用。由于 FPIDEs 在应用科学中的多种应用,数学家们对开发和利用各种技术求解 FPIDEs 产生了浓厚的兴趣。在这种情况下,要研究 FPIDE 的解法,精确和分析解法并不十分容易。本文采用了一种被称为拉普拉斯阿多米分解法的新型分析方法来计算 FPIDE 的解。我们得到了非线性 FPIDE 的近似解。我们使用图形和表格对结果进行了讨论。图和表显示,与扩展立方 B 拼接法相比,建议方法的精度更高。在导数的所有分数阶上,建议方法的精度都更高。计算量少,程序简单,就能达到足够的精确度。提出的方法无需参数化或离散化,因此可扩展用于其他非线性 FPIDE 及其系统的求解。
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引用次数: 0
Nonparametric methods of statistical inference for double-censored data with applications 双删失数据的非参数统计推断方法及其应用
IF 2 3区 数学 Q1 Mathematics Pub Date : 2024-01-01 DOI: 10.1515/dema-2023-0126
Asamh S. M. Al Luhayb
This article introduces new nonparametric statistical methods for prediction in case of data containing right-censored observations and left-censored observations simultaneously. The methods can be considered as new versions of Hill’s A ( n ) {A}_{left(n)} assumption for double-censored data. Two bounds are derived to predict the survival function for one future observation X n + 1 {X}_{n+1} based on each version, and these bounds are compared through two examples. Two interesting features are provided based on the proposed methods. The first one is the detailed graphical presentation of the effects of right and left censoring. The second feature is that the lower and upper survival functions can be derived.
本文介绍了在数据同时包含右删失观测值和左删失观测值的情况下进行预测的新的非参数统计方法。这些方法可被视为希尔的 A ( n ) {A}_{left(n)} 假设的新版本。根据每种版本,我们都得出了预测一个未来观测值 X n + 1 {X}_{n+1} 的生存函数的两个边界,并通过两个例子对这些边界进行了比较。基于所提出的方法,有两个有趣的特点。第一个特点是通过详细的图表展示了左右剔除的影响。第二个特点是可以导出下生存函数和上生存函数。
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引用次数: 0
Decay rate of the solutions to the Cauchy problem of the Lord Shulman thermoelastic Timoshenko model with distributed delay 具有分布延迟的舒尔曼勋爵热弹性季莫申科模型考奇问题解的衰减率
IF 2 3区 数学 Q1 Mathematics Pub Date : 2024-01-01 DOI: 10.1515/dema-2023-0143
A. Choucha, S. Boulaaras, Rashid Jan, M. Alnegga
In this study, we address a Cauchy problem within the context of the one-dimensional Timoshenko system, incorporating a distributed delay term. The heat conduction aspect is described by the Lord-Shulman theory. Our demonstration establishes that the dissipation resulting from the coupling of the Timoshenko system with Lord-Shulman’s heat conduction is sufficiently robust to stabilize the system, albeit with a gradual decay rate. To support our findings, we convert the system into a first-order form and, utilizing the energy method in Fourier space, and derive point wise estimates for the Fourier transform of the solution. These estimates, in turn, provide evidence for the slow decay of the solution.
在本研究中,我们在一维季莫申科系统的背景下,结合分布式延迟项,解决了一个柯西问题。热传导方面由 Lord-Shulman 理论描述。我们的论证证明,季莫申科系统与 Lord-Shulman 热传导的耦合所产生的耗散足以稳定系统,尽管衰减率是渐进的。为了支持我们的发现,我们将系统转换为一阶形式,并利用傅里叶空间的能量法,得出了解的傅里叶变换的点智估计值。这些估计值反过来又为解的缓慢衰减提供了证据。
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引用次数: 0
The essential norm of bounded diagonal infinite matrices acting on Banach sequence spaces 作用于巴拿赫序列空间的有界对角无限矩阵的本质规范
IF 2 3区 数学 Q1 Mathematics Pub Date : 2024-01-01 DOI: 10.1515/dema-2023-0263
Julio C. Ramos Fernández, María A. Rivera-Sarmiento, M. Salas-Brown
We calculate the essential norm of bounded diagonal infinite matrices acting on Köthe sequence spaces. As a consequence of our result, we obtain a recent criteria for the compactness of multiplication operator acting on Köthe sequence spaces.
我们计算了作用于 Köthe 序列空间的有界对角无限矩阵的基本规范。由于我们的结果,我们得到了作用于柯特序列空间的乘法算子紧凑性的最新标准。
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引用次数: 0
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Demonstratio Mathematica
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