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Approximation of BV space-defined Functionals Containing Piecewise Integrands with L¹ Condition L¹条件下含分段积分的BV空间定义泛函的逼近
Q1 MATHEMATICS Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4934
Thomas Wunderli
We prove an approximation result for a class of functionals $% %TCIMACRO{TeXButton{mathcal G}{mathcal{G}}}% %BeginExpansion mathcal{G}% %EndExpansion (u)=int_{Omega }varphi (x,Du)$ defined on $BVleft( Omega right) $ where $varphi (cdot ,Du)in L^{1}left( Omega right) ,$ $Omega subset %TCIMACRO{U{211d} }% %BeginExpansion mathbb{R} %EndExpansion ^{N}$ bounded, $varphi (x,p)$ convex, radially symmetric and of the form begin{equation*} varphi (x,p)=left{ begin{tabular}{ll} $g(x,p)$ & if $|p|leq beta $ $psi (x)|p|+k(x)$ & if $|p|>beta .$% end{tabular}% right. end{equation*}% We show for each $uin BVleft( Omega right) cap L^{p}left( Omega right) ,$ $1leq p
我们证明了一类泛函$% %TCIMACRO{TeXButton{mathcal G}{mathcal{G}} % %BeginExpansion mathcal{G}% % endexpand (u)=int_{Omega}varphi (x,Du)$定义在$BVleft(Omega right) $上,其中$varphi (cdot,Du)in L^{1}left(Omega right) $,$ $Omega 子集%TCIMACRO{ u {211d}}% BeginExpansion mathbb{R} % endexpand ^{N}$有界,$ varphi (x,p)$凸,径向对称的形式为begin{equation*} varphi (x,p)=left{begin{tabular}{ll} $g(x,p)$ &如果$|p|leq beta $ $psi (x)|p|+k(x)$ &如果$|p|>beta .$% end{tabular}% right。我们显示每个$u在BV左(Omega 右) cap L^{p}左(Omega 右),$ $1leq p<infty,$ $存在$u_{k}在W^{1,1}左(Omega 右) cap C^{infty}左(Omega 右) cap L^{p}左(Omega 右)$因此$% %TCIMACRO{TeXButton{mathcal G}{mathcal{G}} % %BeginExpansion mathcal{G}} % %BeginExpansion mathcal{G}} % %BeginExpansion mathcal{G}} % % endexpand (u_{k})right row %TCIMACRO{TeXButton{mathcal G}} {mathcal{G}} % %BeginExpansion mathcal{G}% % endexpand (u).$ BV$中的近似定理被使用证明时间流$u_{t}=func{div}left(nabla _{p}varphi (x,Duright))$ in $L^{1}((0,infty))$的强解的存在性结果;BVleft(Omega right) cap L^{p}left(Omega right))$通常在$u$中附加边界条件或惩罚项以确保唯一性。本工作中的函数没有被先前的近似定理所涵盖,因为对于固定的$p$,我们有$varphi (x,p)in L^{1}left(Omega right) $,这在早期的工作中通常不适用于$varphi $的假设。
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引用次数: 0
Study on the Dynamical Analysis of a Family of Optimal Third Order Multiple-zero Finder 一类最优三阶多重寻零器的动力学分析研究
Q1 MATHEMATICS Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4986
Young Hee Geum
We study the complex dynamics by analyzing the dynamical planes associated with the family of third order multiple root finders and the parameter spaces related to the free critical points. The conjugacy maps with the theoretical results of dynamical analysis for the iterative schemes are investigated. In addition, the various experiments are implemented to draw the dynamics of the cubic-order schemes as well as existing methods.
通过分析与三阶多重寻根器族相关的动力平面和与自由临界点相关的参数空间来研究复动力学。研究了迭代格式与动力学分析理论结果的共轭映射。此外,还进行了各种实验来绘制三阶格式的动态以及现有的方法。
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引用次数: 0
The SL(2,R) Group Representations on Spaces of Holomorphic Functions on the Unit Disc 单位圆盘上全纯函数空间上的SL(2,R)群表示
Q1 MATHEMATICS Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4923
Amjad Alghamdi
We can realise the representations of the group SL(2,R) on the unit disc. This is due to an isomorphism between the group SL(2,R) and the group SU(1,1). The discrete series representations for the group SL(2,R)given bypi_{n}(g)varphi(z)=varphi (frac{d z-b}{a-cz} )(a-c z)^{-n}, where n is an integer number,is on the Bergman space where n>2 .Lang studies the discrete series on the group in the upper half-plane and on the unit disc. For n=1, the SL(2,R) representation is called the mock discrete series. The representation space of the mock discrete series is the Hardy space.In this article we describe the SL(2,R) representation on the Dirichlet space.
我们可以在单位圆盘上实现群SL(2,R)的表示。这是由于群SL(2,R)和群SU(1,1)之间的同构。由pi _n{(g) }varphi (z)= varphi (frac{d z-b}{a-cz})(a-c z)^{-n}给出的群SL(2,R)的离散级数表示,其中n为整数,在Bergman空间中,n&gt;2 . lang研究了群在上半平面和单位盘上的离散级数。对于n=1, SL(2,R)表示称为模拟离散级数。模拟离散级数的表示空间是Hardy空间。在本文中,我们描述了Dirichlet空间上的SL(2,R)表示。
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引用次数: 0
Kernel Estimation of the Quintile Share Ratio index of Inequality for Heavy-tailed Income distributions 重尾收入分布的五分位数份额比不平等指数的核估计
Q1 MATHEMATICS Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4765
None Modou Kebe, El Hadji Deme, None Tchilabalo Abozou Kpanzou, Solym Mawaki Manou-Abi, None Ebrima Sisawo
Evidence from micro-data shows that capital incomes are exceedingly volatile, which makes up a disproportionately high contribution to the overall inequality in populations with the heavy-tailed nature on the income distributions for many countries. The quintile share ratio (QSR) is a recently introduced measure of income inequality, also forming part of the European Laeken indicators and which cover four important dimensions of social inclusion (health, education, employment and financial poverty). In 2001, the European Council decided that income inequality in the European Union member states should be described using a number of indicators including the QSR. Non-parametric estimation has been developed on the QSR index for heavy-tailed capital incomes distributions. However, this method of estimation does not give satisfactory statistical performances, since it suffers badly from under coverage, and so we cannot rely on the non-parametric estimator. Hence, we need another estimator in the case of heavy tailed populations. This is the reason why we introduce, in this paper, a class of semi-parametric estimators of theQSR index of economic inequality for heavy-tailed income distributions. Our methodology is basedon the extreme value theory, which offers adequate statistical results for such distributions. Weestablish their asymptotic distribution, and through a simulation study, we illustrate their behaviorin terms of the absolute bias and the median squared error. The simulation results clearly showthat our estimators work well.
来自微观数据的证据表明,资本收入极不稳定,这对许多国家收入分配具有重尾性质的人口的总体不平等造成了不成比例的高贡献。五分位数份额比率(QSR)是最近引入的收入不平等衡量标准,也是欧洲拉肯指标的一部分,涵盖社会包容的四个重要方面(健康、教育、就业和金融贫困)。2001年,欧洲理事会决定,欧盟成员国的收入不平等应该用一系列指标来描述,其中包括质量评价体系。对重尾资本收入分布的QSR指数进行了非参数估计。然而,这种估计方法不能给出令人满意的统计性能,因为它受到覆盖不足的严重影响,因此我们不能依赖于非参数估计器。因此,对于重尾种群,我们需要另一个估计量。这就是为什么我们在本文中引入了一类重尾收入分配的经济不平等qsr指数的半参数估计量。我们的方法基于极值理论,该理论为这种分布提供了充分的统计结果。我们建立了它们的渐近分布,并通过模拟研究,从绝对偏差和中位数平方误差的角度说明了它们的行为。仿真结果清楚地表明我们的估计器工作良好。
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引用次数: 0
New Variants of Newton's Method for Solving Nonlinear Equations 求解非线性方程的牛顿方法的新变体
Q1 MATHEMATICS Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4951
Buddhi Prasad Sapkota, Jivandhar Jnawali
Two Newton-type iterative techniques have been created in this work to locate the true root of univariate nonlinear equations. One of these can be acquired by modifying the double Newton's method in a straightforward manner, while the other can be gotten by modifying the midpoint Newton's method. The iterative approach developed by McDougall and Wortherspoon is employed for the change. The study demonstrates that the modified double Newton's approach outperforms the current one in terms of both convergence order and efficiency index, even though both methods assess the same amount of functions and derivatives every iteration. In comparison to the midpoint Newton's technique, which has a convergence order of 3, the modified midpoint Newton's method has a convergence order of 5.25 and requires two extra functions to be evaluated per iteration. In order to evaluate the effectiveness of recently introduced approaches with current methods, some numerical examples are shown in the final section.
在这项工作中,创建了两种牛顿型迭代技术来定位单变量非线性方程的真根。其中一个可以通过对双牛顿法的简单修改得到,另一个可以通过对中点牛顿法的修改得到。这种变化采用了McDougall和Wortherspoon开发的迭代方法。研究表明,改进的双牛顿方法在收敛阶和效率指标方面都优于当前的方法,尽管两种方法每次迭代评估相同数量的函数和导数。与中点牛顿法的收敛阶为3相比,改进的中点牛顿法的收敛阶为5.25,并且每次迭代需要计算两个额外的函数。为了评价最近介绍的方法与现有方法的有效性,在最后一节中给出了一些数值例子。
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引用次数: 0
Some Properties of Operations in the Collection of Intuitionistic Fuzzy Sets : A Novel Approach 直觉模糊集集合中运算的若干性质:一种新方法
Q1 MATHEMATICS Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4939
Dwi Nur Yunianti, Noor Hidayat, Raden Sulaiman, Abdul Rouf Alghofari
In this paper, we introduce collection of intuitionistic fuzzy sets as a new concept of intuitionistic fuzzy sets. In ordinary, universal set in intuitionistic fuzzy sets is classical set. So in this paper, we generalize the universal set as a collection or family of intuitionistic fuzzy sets. We also present intersection and union operation on collection of of intuitionistic fuzzy sets and show that the operations hold commutative, assosiative, idempotent, and De Morgan’s laws properties.
本文引入直觉模糊集集合作为直觉模糊集的一个新概念。一般情况下,直觉模糊集中的全称集是经典集。因此,本文将全称集推广为直觉模糊集的集合或族。给出了直觉模糊集合集合上的交并运算,并证明了这些运算具有交换律、结合律、幂等律和De Morgan定律的性质。
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引用次数: 0
A Comparative Study of Numerical Solution of Second-order Singular Differential Equations Using Bernoulli Wavelet Techniques 使用伯努利小波技术数值求解二阶奇异微分方程的比较研究
IF 0.7 Q1 MATHEMATICS Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4916
Kailash Yadav, Ateq Alsaadi
The main objective of this article is to discuss a numerical method for solving singular differential equations based on wavelets. Singular differential equations are first transformed into a system of linear algebraic equations, and then the linear system’s solution produces the unknown coefficients. Along with its estimated error, the convergence of the approximative solution is alsodetermined. Some numerical examples are thought to show that Bernoulli wavelet is better than Chebyshev and Legendre wavelet and other existing techniques.
本文的主要目的是讨论一种基于小波的求解奇异微分方程的数值方法。奇异微分方程首先被转化为线性代数方程组,然后线性方程组的解产生未知系数。在估计误差的同时,还确定了近似解的收敛性。一些数值实例表明,伯努利小波优于切比雪夫小波、勒让德小波和其他现有技术。
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引用次数: 0
Metrical Fixed Point Results on lowercase{b}-multiplicative metric spaces employing binary relaion 采用二元关系的小写{b}乘性度量空间上的测量不动点结果
Q1 MATHEMATICS Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4953
Ibtesam Eid AlShammari, Shahbaz Ali, Q.H. Khan, T. Rashid, Cenap Ozel
In this manuscrit, we establish some results on the existence and uniqueness of fixed points by using b-multiplicative metric spaces(MMS) endowed with a binary relation. we also find result on the coincidence of points involving a pair of mappings. Finally some examples are presented to illustrate the suitability of our results.
本文利用具有二元关系的b乘度量空间,建立了不动点存在唯一性的一些结果。我们还得到了涉及一对映射的点重合的结果。最后通过算例说明了所得结果的适用性。
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引用次数: 0
Geodetic Roman Dominating Functions in a Graph 图中的测地罗马支配函数
Q1 MATHEMATICS Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4962
Rona Jane Gamayot Fortosa, Sergio Canoy
Let $G$ be a connected graph. A function $f: V(G)rightarrow {0,1,2}$ is a textit{geodetic Roman dominating function} (or GRDF) if every vertex $u$ for which $f(u)=0$ is adjacent to at least one vertex $v$ for which $f(v)=2$ and $V_1 cup V_2$ is a geodetic set in $G$. The weight of a geodetic Roman dominating function $f$, denoted by $omega_{G}^{gR}(f)$, is given by $omega_{G}^{gR}(f)=sum_{v in V(G)}f(v)$. The minimum weight of a GRDF on $G$, denoted by $gamma_{gR}(G)$, is called the textit{geodetic Roman domination number} of $G$. In this paper, we give some properties of geodetic Roman domination and determine the geodetic Roman domination number of some graphs.
让 $G$ 做一个连通图。函数 $f: V(G)rightarrow {0,1,2}$ 是? textit{罗马大地测量的支配作用} (或GRDF),如果每个顶点 $u$ 为了什么? $f(u)=0$ 至少与一个顶点相邻 $v$ 为了什么? $f(v)=2$ 和 $V_1 cup V_2$ 大地测量仪设置好了吗 $G$. 罗马大地测量法的主导功能的重量 $f$,表示为 $omega_{G}^{gR}(f)$,由 $omega_{G}^{gR}(f)=sum_{v in V(G)}f(v)$. GRDF的最小重量 $G$,表示为 $gamma_{gR}(G)$,叫做 textit{大地测量罗马统治数} 的 $G$. 本文给出了测地罗马支配的一些性质,并确定了一些图的测地罗马支配数。
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引用次数: 0
On the Diophantine Equation (p+n)^x+p^y=z^2 where p and p+n are Prime Numbers 关于丢番图方程(p+n)^x+p^y=z^2其中p和p+n是素数
Q1 MATHEMATICS Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4822
Wachirarak Orosram
In this paper, we study the Diophantine equation (p+n)^x+p^y=z^2, where p, p+n are prime numbers and n is a positive integer such that n equiv mod 4. In case p=3 and n=4, Rao{7} showed that the non-negative integer solutions are (x,y,z)=(0,1,2) and (1,2,4) In case p>3 and pequiv 3pmod4, if n-1 is a prime number and 2n-1 is not prime number, then the non-negative integer solution (x, y, z) is (0, 1,sqrt {p+1}) or ( 1, 0, sqrt{p+n+1}). In case pequiv 1pmod4, the non-negative integer solution (x,y,z) is also (0, 1,sqrt {p+1}) or ( 1,0, sqrt{p+n+1}).
本文研究了Diophantine方程(p+n)^x+p^y=z^2,其中p、p+n为素数,且n为正整数,使得n对4等价。在p=3和n=4的情况下,Rao{7}证明了非负整数解为(x,y,z)=(0,1,2)和(1,2,4);在p>3和pequiv 3pmod4的情况下,如果n-1是素数,2n-1不是素数,则非负整数解(x,y,z)为(0,1,sqrt{p+ 1})或(1,0,sqrt {p+n+1})。在pequiv 1pmod4的情况下,非负整数解(x,y,z)也是(0,1,sqrt {p+1})或(1,0,sqrt{p+n+1})。
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引用次数: 1
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European Journal of Pure and Applied Mathematics
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