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Aequationes Mathematicae最新文献

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Disprove of a conjecture on the double Roman domination number 推翻关于双罗马支配数的猜想
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-02-16 DOI: 10.1007/s00010-023-01029-x
Z. Shao, R. Khoeilar, H. Karami, M. Chellali, S. M. Sheikholeslami
{"title":"Disprove of a conjecture on the double Roman domination number","authors":"Z. Shao,&nbsp;R. Khoeilar,&nbsp;H. Karami,&nbsp;M. Chellali,&nbsp;S. M. Sheikholeslami","doi":"10.1007/s00010-023-01029-x","DOIUrl":"10.1007/s00010-023-01029-x","url":null,"abstract":"<div><p>A double Roman dominating function (DRDF) on a graph <span>(G=(V,E))</span> is a function <span>(f:Vrightarrow {0,1,2,3})</span> having the property that if <span>(f(v)=0)</span>, then vertex <i>v</i> must have at least two neighbors assigned 2 under <i>f</i> or one neighbor <i>w</i> with <span>(f(w)=3)</span>, and if <span>(f(v)=1)</span>, then vertex <i>v</i> must have at least one neighbor <i>w</i> with <span>(f(w)ge 2)</span>. The weight of a DRDF is the sum of its function values over all vertices, and the double Roman domination number <span>(gamma _{dR}(G))</span> is the minimum weight of a DRDF on <i>G</i>. Khoeilar et al. (Discrete Appl. Math. 270:159–167, 2019) proved that if <i>G</i> is a connected graph of order <i>n</i> with minimum degree two different from <span>(C_{5})</span> and <span>(C_{7})</span>, then <span>(gamma _{dR}(G)le frac{11}{10}n.)</span> Moreover, they presented an infinite family of graphs <span>({mathcal {G}})</span> attaining the upper bound, and conjectured that <span>({mathcal {G}})</span> is the only family of extremal graphs reaching the bound. In this paper, we disprove this conjecture by characterizing all extremal graphs for this bound.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 1","pages":"241 - 260"},"PeriodicalIF":0.9,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139903233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Exponential semi-polynomials and their characterization on semigroups 指数半多项式及其在半群上的表征
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-02-13 DOI: 10.1007/s00010-024-01032-w
Bruce Ebanks
{"title":"Exponential semi-polynomials and their characterization on semigroups","authors":"Bruce Ebanks","doi":"10.1007/s00010-024-01032-w","DOIUrl":"https://doi.org/10.1007/s00010-024-01032-w","url":null,"abstract":"<p>Exponential semi-polynomials on semigroups are natural generalizations of exponential polynomials on groups. We show that several of the standard properties of exponential polynomials on groups also hold for exponential semi-polynomials on semigroups. The main result is that for topological commutative monoids <i>S</i> belonging to a certain class, a function in <i>C</i>(<i>S</i>) is an exponential semi-polynomial if and only if it is contained in a finite dimensional translation invariant linear subspace. We also show that some standard results about polynomials on commutative semigroups are in fact valid on all semigroups.</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"25 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139754939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generalized Vincze’s functional equations on any group in connection with the maximum functional equation 与最大函数方程有关的任意群上的广义文采函数方程
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-02-03 DOI: 10.1007/s00010-023-01031-3
Muhammad Sarfraz, Zhou Jiang, Qi Liu, Yongjin Li
{"title":"Generalized Vincze’s functional equations on any group in connection with the maximum functional equation","authors":"Muhammad Sarfraz,&nbsp;Zhou Jiang,&nbsp;Qi Liu,&nbsp;Yongjin Li","doi":"10.1007/s00010-023-01031-3","DOIUrl":"10.1007/s00010-023-01031-3","url":null,"abstract":"<div><p>In this research paper, we investigate a generalization of Vincze’s type functional equations involving several (up to four) unknown functions in connection with the maximum functional equation as </p><div><div><span>$$begin{aligned} max {psi (xy), psi (xy^{-1})}&amp;= psi (x)eta (y)+psi (y), max {psi (xy), psi (xy^{-1})}&amp;= psi (x)eta (y)+chi (y), max {psi (xy), psi (xy^{-1})}&amp;= phi (x)eta (y), max {psi (xy), psi (xy^{-1})}&amp;= phi (x)eta (y)+chi (y), end{aligned}$$</span></div></div><p>where <i>G</i> is an arbitrary group, <span>(x, y in G)</span>, and <span>(psi , eta , chi , phi :G rightarrow mathbb {R})</span> are unknown functions.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 1","pages":"173 - 188"},"PeriodicalIF":0.9,"publicationDate":"2024-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139678461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Correction to: Cosine subtraction laws 更正：余弦减法法则
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-01-29 DOI: 10.1007/s00010-023-01027-z
Bruce Ebanks
{"title":"Correction to: Cosine subtraction laws","authors":"Bruce Ebanks","doi":"10.1007/s00010-023-01027-z","DOIUrl":"10.1007/s00010-023-01027-z","url":null,"abstract":"","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 1","pages":"347 - 347"},"PeriodicalIF":0.9,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140490105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Vortex filament flows for curves in a 3-dimensional pseudo-Riemannian manifold 三维伪黎曼流形中曲线的涡丝流
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-01-24 DOI: 10.1007/s00010-023-01030-4
Zühal Küçükarslan Yüzbai, Nevin Ertug Gürbüz, Hyun Chul Lee, Dae Won Yoon
{"title":"Vortex filament flows for curves in a 3-dimensional pseudo-Riemannian manifold","authors":"Zühal Küçükarslan Yüzbai,&nbsp;Nevin Ertug Gürbüz,&nbsp;Hyun Chul Lee,&nbsp;Dae Won Yoon","doi":"10.1007/s00010-023-01030-4","DOIUrl":"10.1007/s00010-023-01030-4","url":null,"abstract":"<div><p>In this work, we focus on the evolution of the vortex filament flow <span>(frac{partial gamma }{partial t} = frac{partial gamma }{partial s} wedge frac{D}{ds}frac{partial gamma }{partial s})</span> for spacelike and timelike curves in a 3-dimensional pseudo-Riemannian manifold. We study the relations between a partial differential equation and the vortex filament flow for spacelike and timelike curves. As a result, we prove that the vortex filament flow of the spacelike curve in a 3-dimensional pseudo-Riemannian manifold with constant sectional curvature is equivalent to the heat equation, and the flow of the timelike curve is equivalent to the non-linear Schrödinger equation. Also, we give some examples to illustrate the vortex filament flow.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 1","pages":"261 - 274"},"PeriodicalIF":0.9,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139559943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
(varepsilon )-isometries in (l^n_1) $$l^n_1$$ 中的 $$varepsilon $$ 等分线
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-01-17 DOI: 10.1007/s00010-023-01023-3
Igor A. Vestfrid
{"title":"(varepsilon )-isometries in (l^n_1)","authors":"Igor A. Vestfrid","doi":"10.1007/s00010-023-01023-3","DOIUrl":"10.1007/s00010-023-01023-3","url":null,"abstract":"<div><p>We show that every <span>(varepsilon )</span>-isometry of the unit ball in <span>(l^n_1)</span> can be uniformly approximated by an affine surjective isometry to within <span>(Cnvarepsilon )</span> for some absolute constant <i>C</i>.\u0000</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 6","pages":"1647 - 1655"},"PeriodicalIF":0.9,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139482949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Notes on the arithmetic–geometric mean inequality 关于算术几何平均数不等式的说明
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-01-17 DOI: 10.1007/s00010-023-01025-1
Ahmad Al-Natoor, Omar Hirzallah, Fuad Kittaneh
{"title":"Notes on the arithmetic–geometric mean inequality","authors":"Ahmad Al-Natoor,&nbsp;Omar Hirzallah,&nbsp;Fuad Kittaneh","doi":"10.1007/s00010-023-01025-1","DOIUrl":"10.1007/s00010-023-01025-1","url":null,"abstract":"<div><p>In this paper, we give a matrix version of an equivalent form of the classical arithmetic–geometric mean inequality for two positive scalars. Applications and generalizations of our results are also given.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 6","pages":"1489 - 1502"},"PeriodicalIF":0.9,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139482887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Correction to: Regularity properties of k-Brjuno and Wilton functions 更正：k-Brjuno 和威尔顿函数的正则特性
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-01-17 DOI: 10.1007/s00010-023-01028-y
Seul Bee Lee, Stefano Marmi, Izabela Petrykiewicz, Tanja I. Schindler
{"title":"Correction to: Regularity properties of k-Brjuno and Wilton functions","authors":"Seul Bee Lee,&nbsp;Stefano Marmi,&nbsp;Izabela Petrykiewicz,&nbsp;Tanja I. Schindler","doi":"10.1007/s00010-023-01028-y","DOIUrl":"10.1007/s00010-023-01028-y","url":null,"abstract":"","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 1","pages":"349 - 350"},"PeriodicalIF":0.9,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-023-01028-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140505080","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the ({A_{!mathbb {C}}})-rank of multidigraphs 关于多图的 $${A_{!
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2023-12-26 DOI: 10.1007/s00010-023-01020-6
Sasmita Barik, Sane Umesh Reddy
{"title":"On the ({A_{!mathbb {C}}})-rank of multidigraphs","authors":"Sasmita Barik,&nbsp;Sane Umesh Reddy","doi":"10.1007/s00010-023-01020-6","DOIUrl":"10.1007/s00010-023-01020-6","url":null,"abstract":"<div><p>The complex adjacency matrix <span>({A_{!mathbb {C}}}(G))</span> for a multidigraph <i>G</i> is introduced in Barik and Sahoo (AKCE Int J Graphs Comb 17(1):466–479, 2020). We study the rank of multidigraphs corresponding to the complex adjacency matrix and call it <span>({A_{!mathbb {C}}})</span>-rank. It is known that a connected graph <i>G</i> has rank 2 if and only if <i>G</i> is a complete bipartite graph, and has rank 3 if and only if it is a complete tripartite graph (Cheng in Electron J Linear Algebra 16:60–67, 2007). We observe that these results hold as special cases for multidigraphs but are not sufficient. In this article, we characterize all multidigraphs with <span>({A_{!mathbb {C}}})</span>-rank 2 and 3, respectively.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 1","pages":"189 - 213"},"PeriodicalIF":0.9,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139054274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","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 state of the second part of Hilbert’s fifth problem 关于希尔伯特第五问题第二部分的状况
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2023-12-22 DOI: 10.1007/s00010-023-01021-5
Antal Járai
{"title":"On the state of the second part of Hilbert’s fifth problem","authors":"Antal Járai","doi":"10.1007/s00010-023-01021-5","DOIUrl":"10.1007/s00010-023-01021-5","url":null,"abstract":"<div><p>In the second part of his fifth problem Hilbert asks for functional equations “In how far are the assertions which we can make in the case of differentiable functions true under proper modifications without this assumption.” In the case of the general functional equation </p><div><div><span>$$begin{aligned} f(x)=hBigl (x,y,bigl (g_1(x,y)bigr ),ldots ,bigl (g_n(x,y)bigr )Bigr ) end{aligned}$$</span></div></div><p>for the unknown function <i>f</i> under natural condition for the given functions it is proved on compact manifolds that <span>(fin C^{-1})</span> implies <span>(fin C^{infty })</span> and practically the general case can also be treated. The natural conditions imply that the dimension of <i>x</i> cannot be larger than the dimension of <i>y</i>. If we remove this condition, then we have to add another condition. In this survey paper a new problem for this second case is formulated and results are summarised for both cases.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"97 5-6","pages":"1173 - 1184"},"PeriodicalIF":0.9,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-023-01021-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138946533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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