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Aequationes Mathematicae最新文献

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Set-valued dynamics related to convex-valued m-mappings 与凸值 m 映射相关的集值动力学
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-07-03 DOI: 10.1007/s00010-024-01103-y
Hamid Khodaei
{"title":"Set-valued dynamics related to convex-valued m-mappings","authors":"Hamid Khodaei","doi":"10.1007/s00010-024-01103-y","DOIUrl":"https://doi.org/10.1007/s00010-024-01103-y","url":null,"abstract":"<p>In this article, we study the set-valued dynamics related to some Euler-Lagrange type functional equations of convex-valued <i>m</i>-mappings. We deal with perturbations of these equations. In order to do this, we use the Banach contraction principle and the Hausdorff distance. Several outcomes on approximate solutions of a few important classic equations are discussed and some applications are given.</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141546758","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
Asymptotic expansions of the Archimedean compounds 阿基米德化合物的渐近展开
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-07-01 DOI: 10.1007/s00010-024-01102-z
Tomislav Burić, Neven Elezović, Lenka Mihoković
{"title":"Asymptotic expansions of the Archimedean compounds","authors":"Tomislav Burić,&nbsp;Neven Elezović,&nbsp;Lenka Mihoković","doi":"10.1007/s00010-024-01102-z","DOIUrl":"10.1007/s00010-024-01102-z","url":null,"abstract":"<div><p>In this paper we present a complete asymptotic expansion of the Archimedean compound of two symmetric homogeneous means and derive recursive algorithms for coefficients in this expansion. We also show some examples and obtain explicit expansions for the Archimedean compounds of the arithmetic, geometric and harmonic means.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508651","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 surface of Apollonius of two ellipsoids 关于两个椭圆体的阿波罗尼奥斯曲面
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-06-27 DOI: 10.1007/s00010-024-01101-0
Attila Végh
{"title":"On surface of Apollonius of two ellipsoids","authors":"Attila Végh","doi":"10.1007/s00010-024-01101-0","DOIUrl":"10.1007/s00010-024-01101-0","url":null,"abstract":"<div><p>Apollonius defined the circle as the set of points that have a given ratio <span>(mu )</span> of distances from two given points, where the ratio is not equal to one. In a more general sense, consider two 0-symmetric, bounded, convex bodies <i>K</i> and <span>(K')</span>, which define two norms. Their unit balls are <i>K</i> and <span>(K')</span>. The surface of Apollonius is defined as the set of points equidistant from the centres of bodies <i>K</i> and <span>(K')</span> with respect to the aforementioned norms. In this paper we demonstrate that the surface of Apollonius of two ellipsoids is a quadratic surface. We also examine the circumstances under which this surface becomes a sphere.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01101-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508652","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
Mathematical models of functional extreme leaning machins: operator-algebraic and free-probabilistic approaches 功能极端倾斜机数学模型：算子代数和自由概率方法
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-06-24 DOI: 10.1007/s00010-024-01096-8
Ilwoo Cho, Palle E. T. Jorgensen
{"title":"Mathematical models of functional extreme leaning machins: operator-algebraic and free-probabilistic approaches","authors":"Ilwoo Cho, Palle E. T. Jorgensen","doi":"10.1007/s00010-024-01096-8","DOIUrl":"https://doi.org/10.1007/s00010-024-01096-8","url":null,"abstract":"<p>In this paper, we establish mathematical models for an arbitrarily fixed functional extreme learning machine (FELM). From a FELM <span>({mathfrak {M}})</span>, we construct a direct graph <i>G</i> induced by <span>({mathfrak {M}})</span>, and then define the graph groupoid <span>({mathbb {G}})</span> of <i>G</i>. Then the graph-groupoid <span>(C^{*})</span>-algebra <span>(M_{G})</span> of <i>G</i> generated by <span>({mathbb {G}})</span> is well-determined. This <span>(C^{*})</span>-algebra <span>(M_{G})</span> is realized on a certain Hilbert space <span>(H_{G})</span> up to a canonical representation. It means that the FELM <span>({mathfrak {M}})</span> is analyzed in a representation-depending structure in terms of operator algebra theory. By defining a natural free probability on <span>(M_{G})</span>, one can have an assessment tool of the operator algebra on <span>(M_{G})</span>, too.</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529648","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 a generalized notion of metrics 关于广义度量概念
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-06-23 DOI: 10.1007/s00010-024-01092-y
Wolf-Jürgen Beyn
{"title":"On a generalized notion of metrics","authors":"Wolf-Jürgen Beyn","doi":"10.1007/s00010-024-01092-y","DOIUrl":"10.1007/s00010-024-01092-y","url":null,"abstract":"<div><p>In these notes we generalize the notion of a (pseudo) metric measuring the distance of two points, to a (pseudo) <i>n</i>-metric which assigns a value to a tuple of <span>(n ge 2)</span> points. Some elementary properties of pseudo <i>n</i>-metrics are provided and their construction via exterior products is investigated. We discuss some examples from the geometry of Euclidean vector spaces leading to pseudo <i>n</i>-metrics on the unit sphere, on the Stiefel manifold, and on the Grassmann manifold. Further, we construct a pseudo <i>n</i>-metric on hypergraphs and discuss the problem of generalizing the Hausdorff metric for closed sets to a pseudo <i>n</i>-metric.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01092-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508654","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
Uniformly-like convex solutions for the polynomial-like iterative equation in Banach spaces 巴拿赫空间多项式迭代方程的均匀类凸解
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-06-22 DOI: 10.1007/s00010-024-01099-5
Hou Yu Zhao, Meng Lian Xia
{"title":"Uniformly-like convex solutions for the polynomial-like iterative equation in Banach spaces","authors":"Hou Yu Zhao, Meng Lian Xia","doi":"10.1007/s00010-024-01099-5","DOIUrl":"https://doi.org/10.1007/s00010-024-01099-5","url":null,"abstract":"<p>Using Schauder’s fixed point theorem and the Banach contraction principle, the existence, uniqueness, and stability of monotone solutions and uniformly-like convex solutions of the polynomial-like iterative functional equation are studied in Banach spaces. Furthermore, the approximate solutions of the corresponding solutions are considered. Some examples are considered for our results.</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141521862","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
A Kannappan-sine subtraction law on semigroups 半群上的 Kannappan 正弦减法法则
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-06-22 DOI: 10.1007/s00010-024-01098-6
Ahmed Jafar, Omar Ajebbar, Elhoucien Elqorachi
{"title":"A Kannappan-sine subtraction law on semigroups","authors":"Ahmed Jafar, Omar Ajebbar, Elhoucien Elqorachi","doi":"10.1007/s00010-024-01098-6","DOIUrl":"https://doi.org/10.1007/s00010-024-01098-6","url":null,"abstract":"<p>Let <i>S</i> be a semigroup, <span>(z_0)</span> a fixed element in <i>S</i> and <span>(sigma :S longrightarrow S)</span> an involutive automorphism. We determine the complex-valued solutions of the Kannappan-sine subtraction law </p><span>$$begin{aligned} f(xsigma (y)z_0)=f(x)g(y)-f(y)g(x),; x,y in S. end{aligned}$$</span><p>As an application we solve the following variant of the Kannappan-sine subtraction law viz. </p><span>$$begin{aligned} f(xsigma (y)z_0)=f(x)g(y)-f(y)g(x)+lambda g(xsigma (y)z_0),;x,y in S, end{aligned}$$</span><p>where <span>(lambda in mathbb {C}^{*})</span>. The continuous solutions on topological semigroups are given and an example to illustrate the main results is also given.</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508653","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
Elephant polynomials 大象多项式
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-06-22 DOI: 10.1007/s00010-024-01095-9
Hélène Guérin, Lucile Laulin, Kilian Raschel
{"title":"Elephant polynomials","authors":"Hélène Guérin, Lucile Laulin, Kilian Raschel","doi":"10.1007/s00010-024-01095-9","DOIUrl":"https://doi.org/10.1007/s00010-024-01095-9","url":null,"abstract":"<p>In this note, we study a family of polynomials that appear naturally when analysing the characteristic functions of the one-dimensional elephant random walk. These polynomials depend on a memory parameter <i>p</i> attached to the model. For certain values of <i>p</i>, these polynomials specialise to classical polynomials, such as the Chebychev polynomials in the simplest case, or generating polynomials of various combinatorial triangular arrays (e.g. Eulerian numbers). Although these polynomials are generically non-orthogonal (except for <span>(p=frac{1}{2})</span> and <span>(p=1)</span>), they have interlacing roots. Finally, we relate some algebraic properties of these polynomials to the probabilistic behaviour of the elephant random walk. Our methods are reminiscent of classical orthogonal polynomial theory and are elementary.\u0000</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532763","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
n-gon centers and central lines 核子中心和中心线
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-06-22 DOI: 10.1007/s00010-024-01100-1
Marta Farré Puiggalí, Luis Felipe Prieto-Martínez
{"title":"n-gon centers and central lines","authors":"Marta Farré Puiggalí,&nbsp;Luis Felipe Prieto-Martínez","doi":"10.1007/s00010-024-01100-1","DOIUrl":"10.1007/s00010-024-01100-1","url":null,"abstract":"<div><p>In this paper we provide a review of the concept of center of an <i>n</i>-gon, generalizing the original idea given by C. Kimberling for triangles. We also generalize the concept of central line for <i>n</i>-gons for <span>(nge 3)</span> and establish its basic properties.\u0000</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141521863","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
Extending EP matrices by means of recent generalized inverses 通过最近的广义倒数扩展 EP 矩阵
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-06-21 DOI: 10.1007/s00010-024-01091-z
D. E. Ferreyra, F. E. Levis, A. N. Priori, N. Thome
{"title":"Extending EP matrices by means of recent generalized inverses","authors":"D. E. Ferreyra,&nbsp;F. E. Levis,&nbsp;A. N. Priori,&nbsp;N. Thome","doi":"10.1007/s00010-024-01091-z","DOIUrl":"10.1007/s00010-024-01091-z","url":null,"abstract":"<div><p>It is well known that a square complex matrix is called EP if it commutes with its Moore–Penrose inverse. In this paper, new classes of matrices which extend this concept are characterized. For that, we consider commutative equalities given by matrices of arbitrary index and generalized inverses recently investigated in the literature. More specifically, these classes are characterized by expressions of type <span>(A^mX=XA^m)</span>, where <i>X</i> is an outer inverse of a given complex square matrix <i>A</i> and <i>m</i> is an arbitrary positive integer. The relationships between the different classes of matrices are also analyzed. Finally, a picture presents an overview of the overall studied classes.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01091-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141521861","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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