While looking for additional integrals of motion of several minimally superintegrable systems in static electric and magnetic fields, we have realized that in some cases Lie point symmetries of Euler-Lagrange equations imply existence of explicitly time-dependent integrals of motion through Noether’s theorem. These integrals can be combined to get an additional time-independent integral for some values of the parameters of the considered systems, thus implying maximal superintegrability. Even for values of the parameters for which the systems don’t exhibit maximal superintegrability in the usual sense they allow a completely algebraic determination of the trajectories (including their time dependence).
{"title":"Superintegrability and time-dependent integrals","authors":"O. Kubů, L. Šnobl","doi":"10.5817/am2019-5-309","DOIUrl":"https://doi.org/10.5817/am2019-5-309","url":null,"abstract":"While looking for additional integrals of motion of several minimally superintegrable systems in static electric and magnetic fields, we have realized that in some cases Lie point symmetries of Euler-Lagrange equations imply existence of explicitly time-dependent integrals of motion through Noether’s theorem. These integrals can be combined to get an additional time-independent integral for some values of the parameters of the considered systems, thus implying maximal superintegrability. Even for values of the parameters for which the systems don’t exhibit maximal superintegrability in the usual sense they allow a completely algebraic determination of the trajectories (including their time dependence).","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"80 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85810711","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}
Let G be a finite group. The main supergraph S(G) is a graph with vertex set G in which two vertices x and y are adjacent if and only if o(x) | o(y) or o(y) | o(x). In this paper, we will show that G ∼= Sz(q) if and only if S(G) ∼= S(Sz(q)), where q = 22m+1 ≥ 8.
{"title":"Recognizability of finite groups by Suzuki group","authors":"A. K. Asboei, S. S. S. Amiri","doi":"10.5817/am2019-4-225","DOIUrl":"https://doi.org/10.5817/am2019-4-225","url":null,"abstract":"Let G be a finite group. The main supergraph S(G) is a graph with vertex set G in which two vertices x and y are adjacent if and only if o(x) | o(y) or o(y) | o(x). In this paper, we will show that G ∼= Sz(q) if and only if S(G) ∼= S(Sz(q)), where q = 22m+1 ≥ 8.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"29 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87207965","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}
We consider some applications of the singular integral equation of the second kind of Fox. Some new solutions to Fox’s integral equation are discussed in relation to number theory.
讨论了第二类福克斯奇异积分方程的一些应用。从数论的角度讨论了福克斯积分方程的一些新解。
{"title":"On instances of Fox’s integral equation connection to the Riemann zeta function","authors":"A. Patkowski","doi":"10.5817/AM2019-3-195","DOIUrl":"https://doi.org/10.5817/AM2019-3-195","url":null,"abstract":"We consider some applications of the singular integral equation of the second kind of Fox. Some new solutions to Fox’s integral equation are discussed in relation to number theory.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"34 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90991009","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}
We establish a decomposition of non-negative Radon measures on Rd which extends that obtained by Strichartz [6] in the setting of α-dimensional measures. As consequences, we deduce some well-known properties concerning the density of non-negative Radon measures. Furthermore, some properties of non-negative Radon measures having their Riesz potential in a Lebesgue space are obtained.
{"title":"On a decomposition of non-negative Radon measures","authors":"B. A. Kpata","doi":"10.5817/am2019-4-203","DOIUrl":"https://doi.org/10.5817/am2019-4-203","url":null,"abstract":"We establish a decomposition of non-negative Radon measures on Rd which extends that obtained by Strichartz [6] in the setting of α-dimensional measures. As consequences, we deduce some well-known properties concerning the density of non-negative Radon measures. Furthermore, some properties of non-negative Radon measures having their Riesz potential in a Lebesgue space are obtained.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"7 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73537369","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}
{"title":"The group ring $mathbb{K}F$ of Richard Thompson’s Group $F$ has no minimal non-zero ideals","authors":"J. Donnelly","doi":"10.5817/am2019-1-23","DOIUrl":"https://doi.org/10.5817/am2019-1-23","url":null,"abstract":"","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"9 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74310290","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}
In this paper, we study the strong convergence of the proximal gradient algorithm with inertial extrapolation term for solving classical minimization problem and finding the fixed points of δ-demimetric mapping in a real Hilbert space. Our algorithm is inspired by the inertial proximal point algorithm and the viscosity approximation method of Moudafi. A strong convergence result is achieved in our result without necessarily imposing the summation condition ∑∞ n=1 βn‖xn−1 − xn‖ < +∞ on the inertial term. Finally, we provide some applications and numerical example to show the efficiency and accuracy of our algorithm. Our results improve and complement many other related results in the literature.
{"title":"A viscosity-proximal gradient method with inertial extrapolation for solving certain minimization problems in Hilbert space","authors":"L. Jolaoso, H. Abass, O. Mewomo","doi":"10.5817/AM2019-3-167","DOIUrl":"https://doi.org/10.5817/AM2019-3-167","url":null,"abstract":"In this paper, we study the strong convergence of the proximal gradient algorithm with inertial extrapolation term for solving classical minimization problem and finding the fixed points of δ-demimetric mapping in a real Hilbert space. Our algorithm is inspired by the inertial proximal point algorithm and the viscosity approximation method of Moudafi. A strong convergence result is achieved in our result without necessarily imposing the summation condition ∑∞ n=1 βn‖xn−1 − xn‖ < +∞ on the inertial term. Finally, we provide some applications and numerical example to show the efficiency and accuracy of our algorithm. Our results improve and complement many other related results in the literature.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"55 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80195906","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}
{"title":"A note on the cohomology ring of the oriented Grassmann manifolds $widetilde{G}_{n,4}$","authors":"T. Rusin","doi":"10.5817/am2019-5-319","DOIUrl":"https://doi.org/10.5817/am2019-5-319","url":null,"abstract":"","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"1479 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77711860","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}
We study the invariant symbolic calculi associated with the unitary irreducible representations of a compact Lie group.
研究紧李群的幺正不可约表示的不变符号微积分。
{"title":"Invariant symbolic calculus for compact Lie groups","authors":"B. Cahen","doi":"10.5817/am2019-3-139","DOIUrl":"https://doi.org/10.5817/am2019-3-139","url":null,"abstract":"We study the invariant symbolic calculi associated with the unitary irreducible representations of a compact Lie group.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"16 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77141946","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}
The aim of this work is to study the existence and uniqueness of solutions of the fractional integro-differential equations $frac{d}{dt}[x(t) - L(x_{t})]= A[x(t)- L(x_{t})]+G(x_{t})+ frac{1}{Gamma (alpha )} int _{- infty }^{t} (t-s)^{alpha - 1} ( int _{- infty }^{s}a(s-xi )x(xi ) d xi )ds+f(t)$, ($alpha > 0$) with the periodic condition $x(0) = x(2pi )$, where $a in L^{1}(mathbb{R}_{+})$ . Our approach is based on the R-boundedness of linear operators $L^{p}$-multipliers and UMD-spaces.
本文研究具有周期条件$x(0) = x(2pi )$的分数阶积分微分方程$frac{d}{dt}[x(t) - L(x_{t})]= A[x(t)- L(x_{t})]+G(x_{t})+ frac{1}{Gamma (alpha )} int _{- infty }^{t} (t-s)^{alpha - 1} ( int _{- infty }^{s}a(s-xi )x(xi ) d xi )ds+f(t)$， ($alpha > 0$)解的存在唯一性，其中$a in L^{1}(mathbb{R}_{+})$。我们的方法是基于线性算子$L^{p}$ -乘数和umd -空间的r -有界性。
{"title":"Existence and uniqueness of solutions of the fractional integro-differential equations in vector-valued function space","authors":"Bahloul Rachid","doi":"10.5817/AM2019-2-97","DOIUrl":"https://doi.org/10.5817/AM2019-2-97","url":null,"abstract":"The aim of this work is to study the existence and uniqueness of solutions of the fractional integro-differential equations $frac{d}{dt}[x(t) - L(x_{t})]= A[x(t)- L(x_{t})]+G(x_{t})+ frac{1}{Gamma (alpha )} int _{- infty }^{t} (t-s)^{alpha - 1} ( int _{- infty }^{s}a(s-xi )x(xi ) d xi )ds+f(t)$, ($alpha > 0$) with the periodic condition $x(0) = x(2pi )$, where $a in L^{1}(mathbb{R}_{+})$ . Our approach is based on the R-boundedness of linear operators $L^{p}$-multipliers and UMD-spaces.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"4 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78728746","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}
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