发布求助
文献互助 智能选刊 最新文献

Aequationes Mathematicae最新文献

筛选
英文 中文
Position of the centroid of a planar convex body 平面凸体的中心点位置
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-04-23 DOI: 10.1007/s00010-024-01058-0
Marek Lassak
{"title":"Position of the centroid of a planar convex body","authors":"Marek Lassak","doi":"10.1007/s00010-024-01058-0","DOIUrl":"10.1007/s00010-024-01058-0","url":null,"abstract":"<div><p>It is well known that any planar convex body <i>A</i> permits to inscribe an affine-regular hexagon <span>(H_A)</span>. We prove that the centroid of <i>A</i> belongs to the homothetic image of <span>(H_A)</span> with ratio <span>(frac{4}{21})</span> and the center in the center of <span>(H_A)</span>. This ratio cannot be decreased.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 3","pages":"687 - 695"},"PeriodicalIF":0.9,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01058-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140669872","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
Matrix inequalities between (f(A)sigma f(B)) and (Asigma B) $$f(A)sigma f(B)$$ 与 $$Asigma B$ 之间的矩阵不等式
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-04-23 DOI: 10.1007/s00010-024-01059-z
Manisha Devi, Jaspal Singh Aujla, Mohsen Kian, Mohammad Sal Moslehian
{"title":"Matrix inequalities between (f(A)sigma f(B)) and (Asigma B)","authors":"Manisha Devi,&nbsp;Jaspal Singh Aujla,&nbsp;Mohsen Kian,&nbsp;Mohammad Sal Moslehian","doi":"10.1007/s00010-024-01059-z","DOIUrl":"10.1007/s00010-024-01059-z","url":null,"abstract":"<div><p>Let <i>A</i> and <i>B</i> be <span>(ntimes n)</span> positive definite complex matrices, let <span>(sigma )</span> be a matrix mean, and let <span>(f: [0,infty )rightarrow [0,infty ))</span> be a differentiable convex function with <span>(f(0)=0)</span>. We prove that </p><div><div><span>$$begin{aligned} f^{prime }(0)(A sigma B)le frac{f(m)}{m}(Asigma B)le f(A)sigma f(B)le frac{f(M)}{M}(Asigma B)le f^{prime }(M)(Asigma B), end{aligned}$$</span></div></div><p>where <i>m</i> represents the smallest eigenvalues of <i>A</i> and <i>B</i> and <i>M</i> represents the largest eigenvalues of <i>A</i> and <i>B</i>. If <i>f</i> is differentiable and concave, then the reverse inequalities hold. We use our result to improve some known subadditivity inequalities involving unitarily invariant norms under certain mild conditions. In particular, if <i>f</i>(<i>x</i>)/<i>x</i> is increasing, then </p><div><div><span>$$begin{aligned} |||f(A)+f(B)|||le frac{f(M)}{M} |||A+B|||le |||f(A+B)||| end{aligned}$$</span></div></div><p>holds for all <i>A</i> and <i>B</i> with <span>(Mle A+B)</span>. Furthermore, we apply our results to explore some related inequalities. As an application, we present a generalization of Minkowski’s determinant inequality.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 2","pages":"539 - 554"},"PeriodicalIF":0.9,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140799775","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
Rotation number of 2-interval piecewise affine maps 两区间片断仿射映射的旋转数
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-04-22 DOI: 10.1007/s00010-024-01064-2
José Pedro Gaivão, Michel Laurent, Arnaldo Nogueira
{"title":"Rotation number of 2-interval piecewise affine maps","authors":"José Pedro Gaivão,&nbsp;Michel Laurent,&nbsp;Arnaldo Nogueira","doi":"10.1007/s00010-024-01064-2","DOIUrl":"10.1007/s00010-024-01064-2","url":null,"abstract":"<div><p>We study maps of the unit interval whose graph is made up of two increasing segments and which are injective in an extended sense. Such maps <span>(f_{varvec{p}})</span> are parametrized by a quintuple <span>(varvec{p})</span> of real numbers satisfying inequations. Viewing <span>(f_{varvec{p}})</span> as a circle map, we show that it has a rotation number <span>(rho (f_{varvec{p}}))</span> and we compute <span>(rho (f_{varvec{p}}))</span> as a function of <span>(varvec{p})</span> in terms of Hecke–Mahler series. As a corollary, we prove that <span>(rho (f_{varvec{p}}))</span> is a rational number when the components of <span>(varvec{p})</span> are algebraic numbers.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 2","pages":"511 - 530"},"PeriodicalIF":0.9,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01064-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140799835","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
Curves that allow the motion of a regular polygon 允许正多边形运动的曲线
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-04-15 DOI: 10.1007/s00010-024-01054-4
David Rochera
{"title":"Curves that allow the motion of a regular polygon","authors":"David Rochera","doi":"10.1007/s00010-024-01054-4","DOIUrl":"10.1007/s00010-024-01054-4","url":null,"abstract":"<div><p>This paper characterizes curves where a regular polygon of either a variable side length or a constant side length is allowed to rotate during <i>k</i> full revolutions while having its vertices on the curve during the motion. A constructive method to generate these curves is given based on the curve described by the polygon centers (centroids) during the motion and some examples are shown. Moreover, if the regular polygon divides the curve perimeter into parts of equal length, it is proved that the curve is either a rotational symmetric curve in the case of a variable side length or a circle otherwise. Finally, in the case of a regular polygon of constant side length rotating along a curve, a simple relation between the algebraic areas of such a curve and the curve of polygon centers is revisited.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 2","pages":"377 - 395"},"PeriodicalIF":0.9,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01054-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140577789","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
A characterization of the Euclidean ball via antipodal points 通过对跖点描述欧几里得球的特征
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-04-11 DOI: 10.1007/s00010-024-01055-3
Xuguang Lu
{"title":"A characterization of the Euclidean ball via antipodal points","authors":"Xuguang Lu","doi":"10.1007/s00010-024-01055-3","DOIUrl":"10.1007/s00010-024-01055-3","url":null,"abstract":"<div><p>Arising from an equilibrium state of a Fermi–Dirac particle system at the lowest temperature, a new characterization of the Euclidean ball is proved: a compact set <span>(Ksubset {{{mathbb {R}}}^n})</span> (having at least two elements) is an <i>n</i>-dimensional Euclidean ball if and only if for every pair <span>(x, yin partial K)</span> and every <span>(sigma in {{{mathbb {S}}}^{n-1}})</span>, either <span>(frac{1}{2}(x+y)+frac{1}{2}|x-y|sigma in K)</span> or <span>(frac{1}{2}(x+y)-frac{1}{2}|x-y|sigma in K)</span>. As an application, a measure version of this characterization of the Euclidean ball is also proved and thus the previous result proved for <span>(n=3)</span> on the classification of equilibrium states of a Fermi–Dirac particle system holds also true for all <span>(nge 2)</span>.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 3","pages":"637 - 660"},"PeriodicalIF":0.9,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01055-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140577781","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
The cosine addition and subtraction formulas on non-abelian groups 非阿贝尔群的余弦加减公式
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-04-10 DOI: 10.1007/s00010-024-01052-6
Omar Ajebbar, Elhoucien Elqorachi, Henrik Stetkær
{"title":"The cosine addition and subtraction formulas on non-abelian groups","authors":"Omar Ajebbar,&nbsp;Elhoucien Elqorachi,&nbsp;Henrik Stetkær","doi":"10.1007/s00010-024-01052-6","DOIUrl":"10.1007/s00010-024-01052-6","url":null,"abstract":"<div><p>Let <i>G</i> be a topological group, and let <i>C</i>(<i>G</i>) denote the algebra of continuous, complex valued functions on <i>G</i>. We determine the solutions <span>(f,g,h in C(G))</span> of the Levi-Civita equation </p><div><div><span>$$begin{aligned} g(xy) = g(x)g(y) + f(x)h(y), x,y in G, end{aligned}$$</span></div></div><p>that extends the cosine addition law. As a corollary we obtain the solutions <span>(f,g in C(G))</span> of the cosine subtraction law <span>(g(xy^*) = g(x)g(y) + f(x)f(y))</span>, <span>(x,y in G)</span> where <span>(x mapsto x^*)</span> is a continuous involution of <i>G</i>. That <span>(x mapsto x^*)</span> is an involution, means that <span>((xy)^* = y^*x^*)</span> and <span>(x^{**} = x)</span> for all <span>(x,y in G)</span>.\u0000</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 6","pages":"1657 - 1676"},"PeriodicalIF":0.9,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01052-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140577778","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 some classes of multiplicative functions 关于几类乘法函数
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-04-09 DOI: 10.1007/s00010-024-01053-5
Pentti Haukkanen
{"title":"On some classes of multiplicative functions","authors":"Pentti Haukkanen","doi":"10.1007/s00010-024-01053-5","DOIUrl":"10.1007/s00010-024-01053-5","url":null,"abstract":"<div><p>An arithmetical function <i>f</i> is multiplicative if <span>(f(1)=1)</span> and <span>(f(mn)=f(m)f(n))</span> whenever <i>m</i> and <i>n</i> are coprime. We study connections between certain subclasses of multiplicative functions, such as strongly multiplicative functions, over-multiplicative functions and totients. It appears, among others, that the over-multiplicative functions are exactly same as the totients and the strongly multiplicative functions are exactly same as the so-called level totients. All these functions satisfy nice arithmetical identities which are recursive in character.\u0000</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 2","pages":"531 - 537"},"PeriodicalIF":0.9,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01053-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140577947","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
A note on the Radiant formula and its relations to the sliced Wasserstein distance 关于辐射公式及其与瓦瑟斯坦切分距离关系的说明
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-04-06 DOI: 10.1007/s00010-024-01049-1
Gennaro Auricchio
{"title":"A note on the Radiant formula and its relations to the sliced Wasserstein distance","authors":"Gennaro Auricchio","doi":"10.1007/s00010-024-01049-1","DOIUrl":"10.1007/s00010-024-01049-1","url":null,"abstract":"<div><p>In this note, we show that the squared Wasserstein distance can be expressed as the average over the sphere of one dimensional Wasserstein distances. We name this new expression for the Wasserstein Distance <i>Radiant Formula</i>. Using this formula, we are able to highlight new connections between the Wasserstein distances and the Sliced Wasserstein distance, an alternative Wasserstein-like distance that is cheaper to compute.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 5","pages":"1317 - 1332"},"PeriodicalIF":0.9,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01049-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140578027","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
Global centers of a family of cubic systems 立方体系统家族的全球中心
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-04-05 DOI: 10.1007/s00010-024-01051-7
Raul Felipe Appis, Jaume Llibre
{"title":"Global centers of a family of cubic systems","authors":"Raul Felipe Appis,&nbsp;Jaume Llibre","doi":"10.1007/s00010-024-01051-7","DOIUrl":"10.1007/s00010-024-01051-7","url":null,"abstract":"<div><p>Consider the family of polynomial differential systems of degree 3, or simply cubic systems </p><div><div><span>$$ x' = y, quad y' = -x + a_1 x^2 + a_2 xy + a_3 y^2 + a_4 x^3 + a_5 x^2 y + a_6 xy^2 + a_7 y^3, $$</span></div></div><p>in the plane <span>(mathbb {R}^2)</span>. An equilibrium point <span>((x_0,y_0))</span> of a planar differential system is a <i>center</i> if there is a neighborhood <span>(mathcal {U})</span> of <span>((x_0,y_0))</span> such that <span>(mathcal {U} backslash {(x_0,y_0)})</span> is filled with periodic orbits. When <span>(mathbb {R}^2setminus {(x_0,y_0)})</span> is filled with periodic orbits, then the center is a <i>global center</i>. For this family of cubic systems Lloyd and Pearson characterized in Lloyd and Pearson (Comput Math Appl 60:2797–2805, 2010) when the origin of coordinates is a center. We classify which of these centers are global centers.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 5","pages":"1373 - 1389"},"PeriodicalIF":0.9,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01051-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140577776","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 iterative roots of injective functions 论注入函数的迭代根
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-03-26 DOI: 10.1007/s00010-024-01047-3
Bojan Bašić, Stefan Hačko
{"title":"On iterative roots of injective functions","authors":"Bojan Bašić,&nbsp;Stefan Hačko","doi":"10.1007/s00010-024-01047-3","DOIUrl":"10.1007/s00010-024-01047-3","url":null,"abstract":"<div><p>In 1951 Łojasiewicz found a necessary and sufficient condition for the existence of a <i>q</i>-iterative root of an arbitrary bijective function <i>g</i> for any <span>(qge 2)</span>. In this article we extend this result to the injective case. More precisely, a necessary and sufficient condition for the existence of an iterative root of an injective function is proved, and in the case of existence, the characterization and enumeration of all iterative roots are given. Furthermore, we devise a construction by which all iterative roots of an injective function can be constructed (provided that the considered function has at least one iterative root). As an illustration, we apply the developed theory to several results from the literature to obtain somewhat more elegant and shorter proofs of those results.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 3","pages":"697 - 726"},"PeriodicalIF":0.9,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140301117","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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：604180095
Book学术官方微信