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Aequationes Mathematicae最新文献

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Adjacencies for recognition of digital Jordan surfaces 用于识别数字约旦曲面的邻接关系
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-09-25 DOI: 10.1007/s00010-024-01123-8
Josef Šlapal
{"title":"Adjacencies for recognition of digital Jordan surfaces","authors":"Josef Šlapal","doi":"10.1007/s00010-024-01123-8","DOIUrl":"10.1007/s00010-024-01123-8","url":null,"abstract":"<div><p>For every positive integer, we introduce an adjacency in the digital space <span>({mathbb {Z}}^3)</span>. Connectedness in the graph obtained is then used to define and study digital Jordan surfaces. The surfaces are acquired as polyhedral surfaces bounding the digital polyhedra that can be face-to-face tiled with digital cubes, triangular prisms, square pyramids, and tetrahedra.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 3","pages":"989 - 1001"},"PeriodicalIF":0.9,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01123-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144073674","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 Li–Zheng theorem 论李正定理
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-09-23 DOI: 10.1007/s00010-024-01120-x
Gennadiy Feldman
{"title":"On the Li–Zheng theorem","authors":"Gennadiy Feldman","doi":"10.1007/s00010-024-01120-x","DOIUrl":"10.1007/s00010-024-01120-x","url":null,"abstract":"<div><p>By the well-known I. Kotlarski lemma, if <span>(xi _1)</span>, <span>(xi _2)</span>, and <span>(xi _3)</span> are independent real-valued random variables with nonvanishing characteristic functions, <span>(L_1=xi _1-xi _3)</span> and <span>(L_2=xi _2-xi _3)</span>, then the distribution of the random vector <span>((L_1, L_2))</span> determines the distributions of the random variables <span>(xi _j)</span> up to shift. Siran Li and Xunjie Zheng generalized this result for the linear forms <span>(L_1=xi _1+a_2xi _2+a_3xi _3)</span> and <span>(L_2=b_2xi _2+b_3xi _3+xi _4)</span> assuming that all <span>(xi _j)</span> have first and second moments, <span>(xi _2)</span> and <span>(xi _3)</span> are identically distributed, and <span>(a_j)</span>, <span>(b_j)</span> satisfy some conditions. In the article, we give a simpler proof of this theorem. In doing so, we also prove that the condition of existence of moments can be omitted. Moreover, we prove an analogue of the Li–Zheng theorem for independent random variables with values in the field of <i>p</i>-adic numbers, in the field of integers modulo <i>p</i>, where <span>(pne 2)</span>, and in the discrete field of rational numbers.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 3","pages":"927 - 947"},"PeriodicalIF":0.9,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144073863","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 minimality of the Winterbottom shape 论温特巴顿形状的最小性
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-09-17 DOI: 10.1007/s00010-024-01122-9
Shokhrukh Yu. Kholmatov
{"title":"On the minimality of the Winterbottom shape","authors":"Shokhrukh Yu. Kholmatov","doi":"10.1007/s00010-024-01122-9","DOIUrl":"10.1007/s00010-024-01122-9","url":null,"abstract":"<div><p>In this short note we prove that the Winterbottom shape (Winterbottom in Acta Metallurgica 15:303-310, 1967) is a volume-constraint minimizer of the corresponding anisotropic capillary functional.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 2","pages":"733 - 739"},"PeriodicalIF":0.9,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01122-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142266631","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
Two-sided delay-difference equations and evolution maps 双侧延迟差分方程和演化图
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-09-14 DOI: 10.1007/s00010-024-01121-w
Luís Barreira, Claudia Valls
{"title":"Two-sided delay-difference equations and evolution maps","authors":"Luís Barreira,&nbsp;Claudia Valls","doi":"10.1007/s00010-024-01121-w","DOIUrl":"10.1007/s00010-024-01121-w","url":null,"abstract":"<div><p>We establish the equivalence of hyperbolicity and of two other properties for a two-sided linear delay-difference equation and its evolution map. These two properties are the admissibility with respect to various pairs of spaces, and the Ulam–Hyers stability of the equation, again with respect to various spaces. This gives characterizations of important properties of a linear dynamical system in terms of corresponding properties of the autonomous dynamical system determined by the associated evolution map.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 3","pages":"1235 - 1259"},"PeriodicalIF":0.9,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142266632","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
Arithmetic properties for generalized cubic partitions and overpartitions modulo a prime 广义立方分区和以质数为模数的过分区的算术性质
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-09-10 DOI: 10.1007/s00010-024-01116-7
Tewodros Amdeberhan, James A. Sellers, Ajit Singh
{"title":"Arithmetic properties for generalized cubic partitions and overpartitions modulo a prime","authors":"Tewodros Amdeberhan,&nbsp;James A. Sellers,&nbsp;Ajit Singh","doi":"10.1007/s00010-024-01116-7","DOIUrl":"10.1007/s00010-024-01116-7","url":null,"abstract":"<div><p>A cubic partition is an integer partition wherein the even parts can appear in two colors. In this paper, we introduce the notion of generalized cubic partitions and prove a number of new congruences akin to the classical Ramanujan-type. We emphasize two methods of proofs, one elementary (relying significantly on functional equations) and the other based on modular forms. We close by proving analogous results for generalized overcubic partitions.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 3","pages":"1197 - 1208"},"PeriodicalIF":0.9,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194427","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
Min-phase-isometries on the unit sphere of (mathcal {L}^infty (Gamma ))-type spaces $$mathcal {L}^infty (Gamma )$$ 型空间单位球上的最小相位等分线
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-09-10 DOI: 10.1007/s00010-024-01119-4
Dongni Tan, Lu Yuan, Peng Yang
{"title":"Min-phase-isometries on the unit sphere of (mathcal {L}^infty (Gamma ))-type spaces","authors":"Dongni Tan,&nbsp;Lu Yuan,&nbsp;Peng Yang","doi":"10.1007/s00010-024-01119-4","DOIUrl":"10.1007/s00010-024-01119-4","url":null,"abstract":"<div><p>We show that every surjective mapping <i>f</i> between the unit spheres of two real <span>(mathcal {L}^infty (Gamma ))</span>-type spaces satisfies </p><div><div><span>$$begin{aligned} min {Vert f(x)+f(y)Vert ,Vert f(x)-f(y)Vert }=min {Vert x+yVert ,Vert x-yVert }quad (x,yin S_X) end{aligned}$$</span></div></div><p>if and only if <i>f</i> is phase-equivalent to an isometry, i.e., there is a phase-function <span>(varepsilon )</span> from the unit sphere of the <span>(mathcal {L}^infty (Gamma ))</span>-type space onto <span>({-1,1})</span> such that <span>(varepsilon cdot f)</span> is a surjective isometry between the unit spheres of two real <span>(mathcal {L}^infty (Gamma ))</span>-type spaces, and furthermore, this isometry can be extended to a linear isometry on the whole space <span>(mathcal {L}^infty (Gamma ))</span>. We also give an example to show that these are not true if “min” is replaced by “max”.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 6","pages":"1475 - 1487"},"PeriodicalIF":0.9,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194428","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
Multivariable generalizations of bivariate means via invariance 通过不变性对二元均值进行多变量概括
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-09-09 DOI: 10.1007/s00010-024-01113-w
Paweł Pasteczka
{"title":"Multivariable generalizations of bivariate means via invariance","authors":"Paweł Pasteczka","doi":"10.1007/s00010-024-01113-w","DOIUrl":"10.1007/s00010-024-01113-w","url":null,"abstract":"<div><p>For a given <i>p</i>-variable mean <span>(M :I^p rightarrow I)</span> (<i>I</i> is a subinterval of <span>({mathbb {R}})</span>), following (Horwitz in J Math Anal Appl 270(2):499–518, 2002) and (Lawson and Lim in Colloq Math 113(2):191–221, 2008), we can define (under certain assumptions) its <span>((p+1))</span>-variable <span>(beta )</span>-invariant extension as the unique solution <span>(K :I^{p+1} rightarrow I)</span> of the functional equation </p><div><div><span>$$begin{aligned}&amp;Kbig (M(x_2,dots ,x_{p+1}),M(x_1,x_3,dots ,x_{p+1}),dots ,M(x_1,dots ,x_p)big )&amp;quad =K(x_1,dots ,x_{p+1}), text { for all }x_1,dots ,x_{p+1} in I end{aligned}$$</span></div></div><p>in the family of means. Applying this procedure iteratively we can obtain a mean which is defined for vectors of arbitrary lengths starting from the bivariate one. The aim of this paper is to study the properties of such extensions.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 3","pages":"841 - 861"},"PeriodicalIF":0.9,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01113-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194426","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 multiplicative functions which are additive on positive cubes 关于正立方体上相加的乘法函数
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-09-09 DOI: 10.1007/s00010-024-01118-5
Poo-Sung Park
{"title":"On multiplicative functions which are additive on positive cubes","authors":"Poo-Sung Park","doi":"10.1007/s00010-024-01118-5","DOIUrl":"10.1007/s00010-024-01118-5","url":null,"abstract":"<div><p>Let <span>(k ge 3)</span>. If a multiplicative function <i>f</i> satisfies </p><div><div><span>$$begin{aligned} f(a_1^3 + a_2^3 + cdots + a_k^3) = f(a_1^3) + f(a_2^3) + cdots + f(a_k^3) end{aligned}$$</span></div></div><p>for all <span>(a_1, a_2, ldots , a_k in {mathbb {N}})</span>, then <i>f</i> is the identity function. The set of positive cubes is said to be a <i>k</i>-additive uniqueness set for multiplicative functions. But, the condition <span>(k=2)</span> can be satisfied by infinitely many multiplicative functions. In additon, if <span>(k ge 3)</span> and a multiplicative function <i>g</i> satisfies </p><div><div><span>$$begin{aligned} g(a_1^3 + a_2^3 + cdots + a_k^3) = g(a_1)^3 + g(a_2)^3 + cdots + g(a_k)^3 end{aligned}$$</span></div></div><p>for all <span>(a_1, a_2, ldots , a_k in {mathbb {N}})</span>, then <i>g</i> is the identity function. However, when <span>(k=2)</span>, there exist three different types of multiplicative functions.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 6","pages":"1457 - 1474"},"PeriodicalIF":0.9,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194425","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
Three inequalities that characterize the exponential function 指数函数的三个不等式
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-09-06 DOI: 10.1007/s00010-024-01115-8
David M. Bradley
{"title":"Three inequalities that characterize the exponential function","authors":"David M. Bradley","doi":"10.1007/s00010-024-01115-8","DOIUrl":"10.1007/s00010-024-01115-8","url":null,"abstract":"<div><p>Three functional inequalities are shown to uniquely characterize the exponential function. Each of the three inequalities is indispensable in the sense that no two of the three suffice.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 3","pages":"1261 - 1264"},"PeriodicalIF":0.9,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194455","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
Overpartitions in terms of 2-adic valuation 从 2-adic 估值角度看过度分区
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-09-06 DOI: 10.1007/s00010-024-01117-6
Mircea Merca
{"title":"Overpartitions in terms of 2-adic valuation","authors":"Mircea Merca","doi":"10.1007/s00010-024-01117-6","DOIUrl":"10.1007/s00010-024-01117-6","url":null,"abstract":"<div><p>In this paper, we consider the 2-adic valuation of integers and provide an alternative representation for the generating function of the number of overpartitions of an integer. As a consequence of this result, we obtain a new formula and a new combinatorial interpretation for the number of overpartitions of an integer. This formula implies a certain type of partitions with restrictions for which we provide two Ramanujan-type congruences and present as open problems two infinite families of linear inequalities. Connections between overpartitions and the game of <i>m</i>-Modular Nim with two heaps are presented in this context.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 3","pages":"1153 - 1173"},"PeriodicalIF":0.9,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01117-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194429","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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