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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
European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4934
Thomas Wunderli
{"title":"Approximation of BV space-defined Functionals Containing Piecewise Integrands with L¹ Condition","authors":"Thomas Wunderli","doi":"10.29020/nybg.ejpam.v16i4.4934","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4934","url":null,"abstract":"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} $g(x,p)$ &amp; if $|p|leq beta $ $psi (x)|p|+k(x)$ &amp; if $|p|>beta .$% end{tabular}% right. end{equation*}% We show for each $uin BVleft( Omega right) cap L^{p}left( Omega right) ,$ $1leq p<infty ,$ there exist $u_{k}in W^{1,1}left( Omega right) cap C^{infty }left( Omega right) cap L^{p}left( Omega right) $ so that $% %TCIMACRO{TeXButton{mathcal G}{mathcal{G}}}% %BeginExpansion mathcal{G}% %EndExpansion (u_{k})rightarrow %TCIMACRO{TeXButton{mathcal G}{mathcal{G}}}% %BeginExpansion mathcal{G}% %EndExpansion (u).$ Approximation theorems in $BV$ are used to prove existence results for the strong solution to the time flow $u_{t}=func{div}left( nabla _{p}varphi (x,Duright) )$ in $L^{1}((0,infty );BVleft( Omega right) cap L^{p}left( Omega right) ),$ typically with additional boundary condition or penalty term in $u$ to ensure uniqueness. The functions in this work are not covered by previous approximation theorems since for fixed $p$ we have $varphi (x,p)in L^{1}left( Omega right) $ which do not in general hold for assumptions on $varphi $ in earlier work.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136069448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4986
Young Hee Geum
{"title":"Study on the Dynamical Analysis of a Family of Optimal Third Order Multiple-zero Finder","authors":"Young Hee Geum","doi":"10.29020/nybg.ejpam.v16i4.4986","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4986","url":null,"abstract":"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.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"41 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068680","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4923
Amjad Alghamdi
{"title":"The SL(2,R) Group Representations on Spaces of Holomorphic Functions on the Unit Disc","authors":"Amjad Alghamdi","doi":"10.29020/nybg.ejpam.v16i4.4923","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4923","url":null,"abstract":"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&gt;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.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"41 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068683","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
European Journal of Pure and Applied 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
{"title":"Kernel Estimation of the Quintile Share Ratio index of Inequality for Heavy-tailed Income distributions","authors":"None Modou Kebe, El Hadji Deme, None Tchilabalo Abozou Kpanzou, Solym Mawaki Manou-Abi, None Ebrima Sisawo","doi":"10.29020/nybg.ejpam.v16i4.4765","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4765","url":null,"abstract":"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.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"25 10","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4951
Buddhi Prasad Sapkota, Jivandhar Jnawali
{"title":"New Variants of Newton's Method for Solving Nonlinear Equations","authors":"Buddhi Prasad Sapkota, Jivandhar Jnawali","doi":"10.29020/nybg.ejpam.v16i4.4951","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4951","url":null,"abstract":"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.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4939
Dwi Nur Yunianti, Noor Hidayat, Raden Sulaiman, Abdul Rouf Alghofari
{"title":"Some Properties of Operations in the Collection of Intuitionistic Fuzzy Sets : A Novel Approach","authors":"Dwi Nur Yunianti, Noor Hidayat, Raden Sulaiman, Abdul Rouf Alghofari","doi":"10.29020/nybg.ejpam.v16i4.4939","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4939","url":null,"abstract":"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.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"130 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136069655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4916
Kailash Yadav, Ateq Alsaadi
{"title":"A Comparative Study of Numerical Solution of Second-order Singular Differential Equations Using Bernoulli Wavelet Techniques","authors":"Kailash Yadav, Ateq Alsaadi","doi":"10.29020/nybg.ejpam.v16i4.4916","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4916","url":null,"abstract":"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.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"32 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139310106","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
European Journal of Pure and Applied 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
{"title":"Metrical Fixed Point Results on lowercase{b}-multiplicative metric spaces employing binary relaion","authors":"Ibtesam Eid AlShammari, Shahbaz Ali, Q.H. Khan, T. Rashid, Cenap Ozel","doi":"10.29020/nybg.ejpam.v16i4.4953","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4953","url":null,"abstract":"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.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068672","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Geodetic Roman Dominating Functions in a Graph 图中的测地罗马支配函数
European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4962
Rona Jane Gamayot Fortosa, Sergio Canoy
{"title":"Geodetic Roman Dominating Functions in a Graph","authors":"Rona Jane Gamayot Fortosa, Sergio Canoy","doi":"10.29020/nybg.ejpam.v16i4.4962","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4962","url":null,"abstract":"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.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI: 10.29020/nybg.ejpam.v16i4.4822
Wachirarak Orosram
{"title":"On the Diophantine Equation (p+n)^x+p^y=z^2 where p and p+n are Prime Numbers","authors":"Wachirarak Orosram","doi":"10.29020/nybg.ejpam.v16i4.4822","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4822","url":null,"abstract":"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&gt;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}).","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"25 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068994","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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