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Quadrature based innovative techniques concerning nonlinear equations having unknown multiplicity 基于正交的有关未知倍数非线性方程的创新技术
Pub Date : 2024-07-09 DOI: 10.1016/j.exco.2024.100150
Farooq Ahmed Shah , Muhammad Waseem

Solution of nonlinear equations is one of the most frequently encountered issue in engineering and applied sciences. Most of the intricateed engineering problems are modeled in the frame work of nonlinear equation f(x)=0. The significance of iterative algorithms executed by computers in resolving such functions is of paramount importance and undeniable in contemporary times. If we study the simple roots and the roots having multiplicity greater of any nonlinear equations we come to the point that finding the roots of nonlinear equations having multiplicity greater than one is not trivialvia classical iterative methods. Instability or slow convergence rate is faced by these methods, and also sometimes these methods diverge. In this article, we give some innovative and robust iterative techniques for obtaining the approximate solution of nonlinear equations having multiplicity m>1. Quadrature formulas are implemented to obtain iterative techniques for finding roots of nonlinear equations having unknown multiplicity. The derived methods are the variants of modified Newton method with high order of convergence and better accuracy. The convergence criteria of the new techniques are studied by using Taylor series method. Some examples are tested for the sack of implementations of these techniques. Numerical and graphical comparison shows the performance and efficiency of these new techniques.

非线性方程的求解是工程和应用科学中最常遇到的问题之一。大多数错综复杂的工程问题都是在非线性方程 f(x)=0 的框架内建模的。在当代,计算机执行的迭代算法在求解此类函数方面的重要性是毋庸置疑的。如果我们研究任何非线性方程的简单根和乘数大于 1 的根,我们就会发现,通过经典迭代法找到乘数大于 1 的非线性方程的根并非易事。这些方法会面临不稳定性或收敛速度慢的问题,有时还会出现发散现象。在本文中,我们给出了一些创新而稳健的迭代技术,用于求得乘数为 m>1 的非线性方程的近似解。通过实施正交公式,我们获得了求未知乘数非线性方程根的迭代技术。推导出的方法是修正牛顿法的变种,具有高收敛阶数和更好的精度。利用泰勒级数法研究了新技术的收敛标准。通过一些实例对这些技术的实施进行了测试。数值和图形比较显示了这些新技术的性能和效率。
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引用次数: 0
Estimation of time delay functions for design of traffic systems 为设计交通系统估算时延函数
Pub Date : 2024-06-30 DOI: 10.1016/j.exco.2024.100151
N. Hossam, U. Gazder

Main aim of this research was to apply multiple approaches for the development of time delay functions on three highways in Bahrain, namely; Dry Dock Highway, Arad Highway and Zallaq Highway. Four equations were obtained from previous studies and two equations were, additionally, tailored for each of the three highways. The results were used to obtain two parameters that aid in design, optimum flow rate and level of service.

本研究的主要目的是在巴林的三条高速公路(即干船坞高速公路、阿拉德高速公路和扎拉克高速公路)上应用多种方法来开发时间延迟函数。从先前的研究中获得了四个方程,另外还为这三条高速公路各定制了两个方程。研究结果用于获得两个有助于设计的参数,即最佳流速和服务水平。
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引用次数: 0
Studies in fractal–fractional operators with examples 分形-分数算子研究与实例
Pub Date : 2024-06-29 DOI: 10.1016/j.exco.2024.100148
Rabha W. Ibrahim

By using the generalization of the gamma function (p-gamma function: Γp(.)), we introduce a generalization of the fractal–fractional calculus which is called p-fractal fractional calculus. We extend the proposed operators into the symmetric complex domain, specifically the open unit disk. Normalization for each operator is formulated. This allows us to explore the most important geometric properties. Examples are illustrated including the basic power functions.

利用伽马函数的广义化(p-伽马函数:Γp(.)),我们引入了分形-分形微积分的广义,称为 p 分形-分形微积分。我们将提出的算子扩展到对称复数域,特别是开放单位盘。我们对每个算子进行了归一化处理。这使我们能够探索最重要的几何特性。示例包括基本幂函数。
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引用次数: 0
On the extension of quadrant dependence 关于象限依存性的扩展
Pub Date : 2024-06-01 DOI: 10.1016/j.exco.2024.100146
João Lita da Silva

In this short note, it is propounded an extension for quadrant dependence, and shown that some of the original proprieties of this popular concept remain valid, while others are necessarily generalized. A second Borel–Cantelli lemma due to Petrov (Statist. Probab. Lett. 58: 283–286, 2002) is revisited for events enjoying this new dependence notion and demonstrated by means of simpler arguments.

在这篇短文中,我们提出了象限依赖性的扩展,并证明了这一流行概念的某些原始特性仍然有效,而另一些特性则必须加以概括。本文还重新探讨了 Petrov 提出的第二个 Borel-Cantelli Lemma (Statist. Probab. Lett. 58: 283-286, 2002),并通过更简单的论证证明了享有这一新依赖性概念的事件。
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引用次数: 0
Existence conditions for 2-periodic solutions to a non-homogeneous differential equations with piecewise constant argument 带片断常数参数的非均质微分方程 2 周期解的存在条件
Pub Date : 2024-04-29 DOI: 10.1016/j.exco.2024.100145
Mukhiddin I. Muminov , Tirkash A. Radjabov

This paper provides a method of finding 2-periodical solutions for the first-order non-homogeneous differential equations with piecewise constant arguments. All existence conditions are described for 2-periodical solutions and obtained explicit formula for these solutions. An example for the problem that has infinitely many solutions is constructed.

本文提供了一种为具有片常数参数的一阶非均质微分方程寻找 2 周期解的方法。描述了二周期解的所有存在条件,并获得了这些解的明确公式。还构建了一个具有无穷多个解的问题实例。
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引用次数: 0
Hexagonal finite differences for the two-dimensional variable coefficient Poisson equation 二维变系数泊松方程的六边形有限差分
Pub Date : 2024-04-26 DOI: 10.1016/j.exco.2024.100144
R. Itza Balam , M. Uh Zapata , U. Iturrarán-Viveros

For many years, finite differences in hexagonal grids have been developed to solve elliptic problems such as the Poisson and Helmholtz equations. However, these schemes are limited to constant coefficients, which reduces their usefulness in many applications. The main challenge is accurately approximating the diffusive term. This paper presents examples of both successful and unsuccessful attempts to obtain accurate finite differences based on a hexagonal stencil with equilateral triangles to approximate two-dimensional Poisson equations. Local truncation error analysis reveals that a second-order scheme can be achieved if the derivative of the diffusive coefficient is included. Finally, we provide numerical examples to verify the accuracy of the proposed methods.

多年来,人们开发了六边形网格有限差分法来解决泊松方程和亥姆霍兹方程等椭圆问题。然而,这些方案仅限于常数系数,这降低了它们在许多应用中的实用性。主要的挑战在于精确逼近扩散项。本文举例说明了基于等边三角形的六边形模版逼近二维泊松方程以获得精确有限差分的成功和失败尝试。局部截断误差分析表明,如果包含扩散系数的导数,就可以实现二阶方案。最后,我们提供了数值示例来验证所提方法的准确性。
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引用次数: 0
Assemblies as semigroups 作为半群的装配体
Pub Date : 2024-03-20 DOI: 10.1016/j.exco.2024.100143
Ulderico Dardano , Bruno Dinis , Giuseppina Terzo

In this paper we give an algebraic characterization of assemblies in terms of bands of groups. We also consider substructures and homomorphisms of assemblies. We give many examples and counterexamples.

在本文中,我们用群带给出了集合的代数特征。我们还考虑了集合的子结构和同态。我们给出了许多例子和反例。
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引用次数: 0
A closer look at some new lower bounds on the minimum singular value of a matrix 细看矩阵最小奇异值的一些新下限
Pub Date : 2024-02-26 DOI: 10.1016/j.exco.2024.100142
Avleen Kaur , S.H. Lui

There is an extensive body of literature on estimating the eigenvalues of the sum of two symmetric matrices, P+Q, in relation to the eigenvalues of P and Q. Recently, the authors introduced two novel lower bounds on the minimum eigenvalue, λmin(P+Q), under the conditions that matrices P and Q are symmetric positive semi-definite and their sum P+Q is non-singular. These bounds rely on the Friedrichs angle between the range spaces of matrices P and Q, which are denoted by R(P) and R(Q), respectively. In addition, both results led to the derivation of several new lower bounds on the minimum singular value of full-rank matrices. One significant aspect of the two novel lower bounds on λmin(P+Q) is the distinction of the case where R(P) and R(Q) have no principal angles between 0 and π2. This work offers an explanation for the aforementioned scenario and presents a classification of all matrices that meet the specified criteria. Additionally, we offer insight into the rationale behind selecting the decomposition for the subspace R(Q), which is employed to formulate the lower bounds for λmin(P+Q). At last, an example that showcases the potential for improving these two lower bounds is presented.

最近,作者提出了两个关于最小特征值 λmin(P+Q) 的新下限,条件是矩阵 P 和 Q 是对称正半有穷数,并且它们的和 P+Q 是非奇异值。这些界限依赖于矩阵 P 和 Q 的范围空间之间的弗里德里希角,分别用 R(P) 和 R(Q) 表示。此外,这两个结果还推导出了全秩矩阵最小奇异值的几个新下界。关于 λmin(P+Q) 的两个新下界的一个重要方面是区分了 R(P) 和 R(Q) 在 0 和 π2 之间没有主角的情况。本研究对上述情况进行了解释,并对符合特定标准的所有矩阵进行了分类。此外,我们还深入探讨了为子空间 R(Q) 选择分解方法的原理,并利用该分解方法制定了 λmin(P+Q) 的下限。最后,我们将举例说明改进这两个下界的可能性。
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引用次数: 0
The locating chromatic number of generalized Petersen graphs with small order 小阶广义彼得森图的定位色度数
Pub Date : 2024-02-17 DOI: 10.1016/j.exco.2024.100141
Redha Sakri , Moncef Abbas

It was conjectured by Asmiati (2018) that the generalized Petersen graph Pn,k has a locating chromatic number 4 if and only if (noddandk=1) or (n=4andk=2). In this paper, we give a negative answer to the conjecture posed by Asmiati. As a consequence, we are able to exhibit many counterexamples to the recent conjecture proposed, by proving that if (5n12) and (2kn12) and (n,k)(12,5), then χLP(n,k)=4.

Asmiati(2018)猜想,广义彼得森图Pn,k的定位色度数为4,且仅当(noddandk=1)或(n=4andk=2)。在本文中,我们对阿斯米亚蒂提出的猜想给出了否定的答案。因此,我们能够通过证明如果(5≤n≤12)和(2≤k≤⌊n-12⌋)并且(n,k)≠(12,5),那么χLP(n,k)=4,来展示最近提出的猜想的许多反例。
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引用次数: 0
Trifferent codes with small lengths 长度较小的不同代码
Pub Date : 2024-02-07 DOI: 10.1016/j.exco.2024.100139
Sascha Kurz

A code C{0,1,2}n of length n is called trifferent if for any three distinct elements of C there exists a coordinate in which they all differ. By T(n) we denote the maximum cardinality of trifferent codes with length n. The values T(5)=10 and T(6)=13 were recently determined (Fiore et al., 2022). Here we determine T(7)=16, T(8)=20, and T(9)=27. For the latter case n=9 there also exist linear codes attaining the maximum possible cardinality 27.

长度为 n 的代码 C⊆{0,1,2}n,如果 C 的任意三个不同元素都存在一个坐标,且它们都不同,则称为三不同代码。T(5)=10 和 T(6)=13 的值是最近确定的(Fiore 等人,2022 年)。在此,我们确定了 T(7)=16、T(8)=20 和 T(9)=27。对于后一种情况 n=9,也存在达到最大可能心数 27 的线性编码。
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引用次数: 0
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Examples and Counterexamples
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