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Aequationes Mathematicae最新文献

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Casting light on integer compositions 照亮整数组成
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-06-21 DOI: 10.1007/s00010-024-01094-w
Aubrey Blecher, Arnold Knopfmacher, Michael Mays
{"title":"Casting light on integer compositions","authors":"Aubrey Blecher, Arnold Knopfmacher, Michael Mays","doi":"10.1007/s00010-024-01094-w","DOIUrl":"https://doi.org/10.1007/s00010-024-01094-w","url":null,"abstract":"<p>Integer compositions of <i>n</i> are viewed as bargraphs with <i>n</i> circular nodes or square cells in which the <i>i</i>th part of the composition <span>(x_i)</span> is given by the <i>i</i>th column of the bargraph with <span>(x_i)</span> nodes or cells. The sun is at infinity in the north west of our two dimensional model and each node/cell may or may not be lit depending on whether it stands in the shadow cast by another node/cell to its left. We study the number of lit nodes in an integer composition of <i>n</i> and later we modify this to yield the number of lit square cells. We then count the number of columns being lit which leads naturally to those cases where only the first column is lit. We prove the theorem that the generating function for the latter is the same as the generating function for compositions in which the first part is strictly smallest. This theorem has interesting <i>q</i>-series identities as corollaries which allow us to deduce in a simple way the asymptotics for both the number of lit nodes and columns as <span>(n rightarrow infty )</span>.</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141521860","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
Operators with a non-trivial closed invariant affine subspace 具有非三维封闭不变仿射子空间的算子
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-06-20 DOI: 10.1007/s00010-024-01090-0
Janko Bračič
{"title":"Operators with a non-trivial closed invariant affine subspace","authors":"Janko Bračič","doi":"10.1007/s00010-024-01090-0","DOIUrl":"10.1007/s00010-024-01090-0","url":null,"abstract":"<div><p>We are concerned with the question of the existence of an invariant proper affine subspace for an operator <i>A</i> on a complex Banach space. It turns out that the presence of the number 1 in the spectrum of <i>A</i> or in the spectrum of its adjoint operator <span>(A^*)</span> is crucial. For instance, an algebraic operator has an invariant proper affine subspace if and only if 1 is its eigenvalue. For an arbitrary operator <i>A</i>, we show that it has an invariant proper hyperplane if and only if 1 is an eigenvalue of <span>(A^*)</span>. If <i>A</i> is a power bounded operator, then every invariant proper affine subspace is contained in an invariant proper hyperplane, moreover, <i>A</i> has a non-trivial invariant cone.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01090-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532712","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
Spherical and hyperbolic bicentric polygons 球面和双曲双心多边形
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-06-17 DOI: 10.1007/s00010-024-01088-8
Ren Guo
{"title":"Spherical and hyperbolic bicentric polygons","authors":"Ren Guo","doi":"10.1007/s00010-024-01088-8","DOIUrl":"https://doi.org/10.1007/s00010-024-01088-8","url":null,"abstract":"<p>Relations of circumradius, inradius and the distance between the circumcenter and incenter of Euclidean bicentric polygons are generalized into spherical geometry and hyperbolic geometry. The asymptotic behavior of these generalized formulas with small circumradius are studied. Relations for hyperbolic hyper-ideal bicentric polygons are derived.</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508655","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
Hyers–Ulam stability of integral equations with infinite delay 具有无限延迟的积分方程的 Hyers-Ulam 稳定性
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-30 DOI: 10.1007/s00010-024-01080-2
Davor Dragičević, Mihály Pituk
{"title":"Hyers–Ulam stability of integral equations with infinite delay","authors":"Davor Dragičević,&nbsp;Mihály Pituk","doi":"10.1007/s00010-024-01080-2","DOIUrl":"10.1007/s00010-024-01080-2","url":null,"abstract":"<div><p>Integral equations with infinite delay are considered as functional equations in a Banach space. Two types of Hyers–Ulam stability criteria are established. First, it is shown that a linear autonomous equation is Hyers–Ulam stable if and only if it has no characteristic value with zero real part. Second, it is proved that the Hyers–Ulam stability of a linear autonomous equation is preserved under sufficiently small nonlinear perturbations. The proofs are based on a recently developed decomposition theory of linear integral equations with infinite delay.\u0000</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01080-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192185","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
Another approach to K-subadditivity K 次加成的另一种方法
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-27 DOI: 10.1007/s00010-024-01083-z
Eliza Jabłońska
{"title":"Another approach to K-subadditivity","authors":"Eliza Jabłońska","doi":"10.1007/s00010-024-01083-z","DOIUrl":"https://doi.org/10.1007/s00010-024-01083-z","url":null,"abstract":"<p>In the paper the notion of weakly <i>K</i>-subadditive set-valued maps is introduced in such a way that <i>F</i> is weakly <i>K</i>-superadditive if and only if <span>(-F)</span> is weakly <i>K</i>-subadditive. This new definition is a natural generalization of <i>K</i>-subadditive set-valued maps from Jabłońska and Nikodem (Aequ Math 95:1221–1231, 2021), for which opposite set-valued maps need not be <i>K</i>-subadditive. Among others, we prove that every weakly <i>K</i>-subadditive set-valued map which is <i>K</i>–upper bounded on a “large” set has to be locally weakly <i>K</i>-upper bounded and weakly <i>K</i>-lower bounded at every point of the domain. This theorem completes an analogous result for <i>K</i>-subadditive set-valued maps which are weakly <i>K</i>-upper bounded on “large” sets from Jabłońska and Nikodem (Aequ Math 95:1221–1231, 2021).</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141170855","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
Smooth solutions of a class of iterative functional equations 一类迭代函数方程的平稳解
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-27 DOI: 10.1007/s00010-024-01085-x
Weiwei Shi, Xiao Tang
{"title":"Smooth solutions of a class of iterative functional equations","authors":"Weiwei Shi,&nbsp;Xiao Tang","doi":"10.1007/s00010-024-01085-x","DOIUrl":"10.1007/s00010-024-01085-x","url":null,"abstract":"<div><p>Imposing some conditions on derivatives of the known functions, using the Fiber Contraction Theorem we prove the existence of <span>(C^1)</span> solutions of a class of iterative functional equations which involves iterates of the unknown functions and a nonlinear term.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141170962","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 evolutes of curves in the isotropic plane 论各向同性平面内曲线的演变
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-25 DOI: 10.1007/s00010-024-01086-w
R. Pacheco, S. D. Santos
{"title":"On evolutes of curves in the isotropic plane","authors":"R. Pacheco, S. D. Santos","doi":"10.1007/s00010-024-01086-w","DOIUrl":"https://doi.org/10.1007/s00010-024-01086-w","url":null,"abstract":"<p>We associate to each spacelike curve in the isotropic plane a null curve in the Lorentzian 3-space. We relate the isotropic geometry of the first to the Lorentzian geometry of the second. We prove a version of the Tait–Kneser theorem for curves in the isotropic plane. Some explicit examples are given.</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153218","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
Angular structure of Reuleaux cones 鲁莱欧锥的角度结构
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-25 DOI: 10.1007/s00010-024-01063-3
José Pedro Moreno, Alberto Seeger
{"title":"Angular structure of Reuleaux cones","authors":"José Pedro Moreno, Alberto Seeger","doi":"10.1007/s00010-024-01063-3","DOIUrl":"https://doi.org/10.1007/s00010-024-01063-3","url":null,"abstract":"<p>In this note we exhibit some examples of proper cones that have the property of being of constant opening angle. In particular, we analyze the class of Reuleaux cones in <span>(mathbb {R}^n)</span> with <span>(nge 3)</span>. Such cones are constructed as intersection of <i>n</i> revolutions cones <span>(textrm{Rev}(g_1,psi ),ldots , textrm{Rev}(g_n,psi ))</span> whose incenters <span>(g_1,ldots , g_n)</span> are unit vectors forming a common angle. The half-aperture angle <span>(psi )</span> of each revolution cone corresponds to the common angle between the incenters. A major result of this work is that a Reuleaux cone in <span>(mathbb {R}^n)</span> is of constant opening angle if and only if <span>(n= 3)</span>. Reuleaux cones in dimension higher than 3 are not of constant opening angle, but such mathematical objects are still of interest. In the same way that a Reuleaux triangle is a “rounded” version of an equilateral triangle, a Reuleaux cone can be viewed as a rounded version of an equiangular simplicial cone and, therefore, it has a lot of symmetry in it.</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153159","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 variable-order fractional derivatives with respect to another function 关于另一个函数的变阶分数导数
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-24 DOI: 10.1007/s00010-024-01082-0
Ricardo Almeida
{"title":"On the variable-order fractional derivatives with respect to another function","authors":"Ricardo Almeida","doi":"10.1007/s00010-024-01082-0","DOIUrl":"https://doi.org/10.1007/s00010-024-01082-0","url":null,"abstract":"","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141101425","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
Alienation of the quadratic, exponential and d’Alembert functional equations 二次函数方程、指数函数方程和达朗贝尔函数方程的异化
IF 0.8 3区 数学
Aequationes Mathematicae Pub Date : 2024-05-20 DOI: 10.1007/s00010-024-01084-y
Marcin Adam
{"title":"Alienation of the quadratic, exponential and d’Alembert functional equations","authors":"Marcin Adam","doi":"10.1007/s00010-024-01084-y","DOIUrl":"https://doi.org/10.1007/s00010-024-01084-y","url":null,"abstract":"","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141122168","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
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