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Aequationes Mathematicae最新文献

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An explicit example of an iteration group in the ring of formal power series 形式幂级数环中迭代群的一个显式实例
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-06 DOI: 10.1007/s00010-024-01070-4
Wojciech Jabłoński
{"title":"An explicit example of an iteration group in the ring of formal power series","authors":"Wojciech Jabłoński","doi":"10.1007/s00010-024-01070-4","DOIUrl":"10.1007/s00010-024-01070-4","url":null,"abstract":"<div><p>We give an example of some iteration group in a ring of formal power series over a field of characteristic 0. It allows us to obtain an explicit formula for some one-parameter group of (truncated) formal power series under an additional condition. Consequently, we are able to show some non-commutative groups of solutions of the third Aczél-Jabotinsky differential equation in the ring of truncated formal power series.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01070-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140885006","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
Skew Dyck paths with air pockets 带气孔的斜戴克路径
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-03 DOI: 10.1007/s00010-024-01065-1
Jean-Luc Baril, Rémi Maréchal, Helmut Prodinger
{"title":"Skew Dyck paths with air pockets","authors":"Jean-Luc Baril, Rémi Maréchal, Helmut Prodinger","doi":"10.1007/s00010-024-01065-1","DOIUrl":"https://doi.org/10.1007/s00010-024-01065-1","url":null,"abstract":"<p>We yield bivariate generating function for the number of <i>n</i>-length partial skew Dyck paths with air pockets (DAPs) ending at a given ordinate. We also give an asymptotic approximation for the average ordinate of the endpoint in all partial skew DAPs of a given length. Similar studies are made for two subclasses of skew DAPs, namely valley-avoiding and zigzagging, valley-avoiding skew DAPs. We express these results as Riordan arrays. Finally, we present two one-to-one correspondences with binary words avoiding the patterns 00 and 0110, and palindromic compositions with parts in <span>({2,1,3,5,7,ldots })</span>.</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140885005","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
Equalities for mixed operations of Moore–Penrose and group inverses of a matrix 摩尔-彭罗斯混合运算和矩阵的群逆运算的等式
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-03 DOI: 10.1007/s00010-024-01072-2
Yongge Tian
{"title":"Equalities for mixed operations of Moore–Penrose and group inverses of a matrix","authors":"Yongge Tian","doi":"10.1007/s00010-024-01072-2","DOIUrl":"https://doi.org/10.1007/s00010-024-01072-2","url":null,"abstract":"<p>This article shows how to establish expansion formulas for calculating the nested operations <span>((A^{dag })^{#})</span>, <span>((A^{#})^{dag })</span>, <span>(((A^{dag })^{#})^{dag })</span>, <span>(((A^{#})^{dag })^{#})</span>, <span>(ldots )</span> of generalized inverses, where <span>((cdot )^{dag })</span> denotes the Moore–Penrose inverse of a matrix and <span>((cdot )^{#})</span> denotes the group inverse of a square matrix. As applications of the formulas obtained, the author constructs and classifies some groups of matrix equalities involving the above nested operations, and derives necessary and sufficient conditions for them to hold.</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140885072","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
Rotations on the triangular grid: angles of changes of the neighborhood motion map 三角形网格的旋转：邻域运动图的变化角度
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-02 DOI: 10.1007/s00010-024-01062-4
Müge Saadetoğlu, Benedek Nagy, Aydın Avkan
{"title":"Rotations on the triangular grid: angles of changes of the neighborhood motion map","authors":"Müge Saadetoğlu,&nbsp;Benedek Nagy,&nbsp;Aydın Avkan","doi":"10.1007/s00010-024-01062-4","DOIUrl":"10.1007/s00010-024-01062-4","url":null,"abstract":"<div><p>Digital image processing is a well-known field that applies various mathematical methods. Among other parts of image processing the study of digital rotations is an important field that is applied in our everyday life. Digital images are understood in a discrete domain, usually on a periodic grid. On the triangular grid, the digitized rotations of a main triangle pixel (trixel) together with its side neighbors are considered. Given a main triangle pixel lying anywhere on the plane, and the centre of rotation taken to be the midpoint of any triangle pixel, we calculate the rotation angles where the neighborhood motion map (NMM) changes. This occurs when the respective locations of the side neighbor trixels change. An algorithm to compute angles for the following neighborhood motion map changes is also given.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140839754","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
All solutions to a Schröder type functional equation 施罗德函数式方程的所有解
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-04-27 DOI: 10.1007/s00010-024-01069-x
Raymond Mortini, Rudolf Rupp
{"title":"All solutions to a Schröder type functional equation","authors":"Raymond Mortini, Rudolf Rupp","doi":"10.1007/s00010-024-01069-x","DOIUrl":"https://doi.org/10.1007/s00010-024-01069-x","url":null,"abstract":"<p>We determine the solutions on various intervals in <span>([0,infty [)</span> to the functional equation <span>(f(x^m)=r f(x))</span> for real <i>r</i> and positive <i>m</i>. Explicit formulas, involving periodic functions, are given for the set <span>({mathcal {S}})</span> of all solutions. The formulas for <span>(r&lt;0)</span> are more complicated. An approach to <span>({mathcal {S}})</span> with the help of the axiom of choice is also given. A special attention is laid on solutions that are continuous on <span>([0,infty [)</span> or on various open subintervals. We also describe solutions satisfying some asymptotic properties at the boundary of these intervals.</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140799833","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 when the union of two algebraic sets is algebraic 关于两个代数集合的结合何时是代数集合
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-04-26 DOI: 10.1007/s00010-024-01041-9
Erhard Aichinger, Mike Behrisch, Bernardo Rossi
{"title":"On when the union of two algebraic sets is algebraic","authors":"Erhard Aichinger, Mike Behrisch, Bernardo Rossi","doi":"10.1007/s00010-024-01041-9","DOIUrl":"https://doi.org/10.1007/s00010-024-01041-9","url":null,"abstract":"<p>In universal algebraic geometry, an algebra is called an <i>equational domain</i> if the union of two algebraic sets is algebraic. We characterize equational domains, with respect to polynomial equations, inside congruence permutable varieties, and with respect to term equations, among all algebras of size two and all algebras of size three with a cyclic automorphism. Furthermore, for each size at least three, we prove that, modulo term equivalence, there is a continuum of equational domains of that size.</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140799837","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
Some investigations on the U-partial order induced by uninorms 对非矩阵诱导的 U 偏序的一些研究
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-04-26 DOI: 10.1007/s00010-024-01048-2
Emel Aşıcı, Radko Mesiar
{"title":"Some investigations on the U-partial order induced by uninorms","authors":"Emel Aşıcı,&nbsp;Radko Mesiar","doi":"10.1007/s00010-024-01048-2","DOIUrl":"10.1007/s00010-024-01048-2","url":null,"abstract":"<div><p>In this paper, we study on the <span>( preceq _U )</span>-partial order induced by uninorms. We also investigate some properties direct product of two uninorms on bounded lattices. We investigate some properties of the set of incomparable elements with respect to <span>( preceq _U )</span>-partial. Then, we investigate the relation between the set of comparable elements and the distributivity property for uninorms on the unit interval [0, 1] . Finally, we define a total order induced by internal uninorms.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140799836","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
General hyperstability criteria for Jensen-type equations 詹森型方程的一般超稳定性标准
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-04-26 DOI: 10.1007/s00010-024-01066-0
Dan M. Dăianu
{"title":"General hyperstability criteria for Jensen-type equations","authors":"Dan M. Dăianu","doi":"10.1007/s00010-024-01066-0","DOIUrl":"10.1007/s00010-024-01066-0","url":null,"abstract":"<div><p>We provide two large classes of control functions that ensure the hyperstability of Jensen-type equations on restricted domains. Among other consequences, we obtain improvements on similar results known in the literature for some Aoki–Rassias-type control functions and hyperstability results for some equations whose solutions are Jensen functions compounded with radical-type functions or with trigonometric functions.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01066-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140799779","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 total isolation in graphs 关于图形中的完全隔离
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-04-25 DOI: 10.1007/s00010-024-01057-1
Geoffrey Boyer, Wayne Goddard, Michael A. Henning
{"title":"On total isolation in graphs","authors":"Geoffrey Boyer, Wayne Goddard, Michael A. Henning","doi":"10.1007/s00010-024-01057-1","DOIUrl":"https://doi.org/10.1007/s00010-024-01057-1","url":null,"abstract":"<p>An isolating set in a graph is a set <i>S</i> of vertices such that removing <i>S</i> and its neighborhood leaves no edge; it is total isolating if <i>S</i> induces a subgraph with no vertex of degree 0. We show that most graphs have a partition into two disjoint total isolating sets and characterize the exceptions. Using this we show that apart from the 7-cycle, every connected graph of order <span>(nge 4)</span> has a total isolating set of size at most <i>n</i>/2, which is best possible.\u0000</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140799778","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
Twisted coefficients on coarse spaces and their corona 粗糙空间上的扭曲系数及其日冕
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-04-24 DOI: 10.1007/s00010-024-01061-5
Elisa Hartmann
{"title":"Twisted coefficients on coarse spaces and their corona","authors":"Elisa Hartmann","doi":"10.1007/s00010-024-01061-5","DOIUrl":"10.1007/s00010-024-01061-5","url":null,"abstract":"<div><p>To a metric space <i>X</i> we associate a compact topological space <span>(nu '({X}))</span> called the corona of <i>X</i>. Then a coarse map <span>(f:Xrightarrow Y)</span> between metric spaces is mapped to a continuous map <span>(nu '({f}):nu '({X})rightarrow nu '({Y}))</span> between coronas. Sheaf cohomology assigned to a coarse metric space is preserved and reflected by the corona functor. This work reveals new tools to analyze the Higson corona.\u0000</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01061-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140799777","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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