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Poncelet Pairs via Isogonal Conjugacy 通过等角共轭的Poncelet对
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2026-03-16 DOI: 10.1007/s00010-026-01274-w
Ronaldo Alves Garcia, Liliana Gabriela Gheorghe
{"title":"Poncelet Pairs via Isogonal Conjugacy","authors":"Ronaldo Alves Garcia,&nbsp;Liliana Gabriela Gheorghe","doi":"10.1007/s00010-026-01274-w","DOIUrl":"10.1007/s00010-026-01274-w","url":null,"abstract":"<div><p>The starting point is a pair of a circle <span>({mathcal {D}})</span> and ellipse <span>({mathcal {E}})</span>, which is within <span>({mathcal {D}})</span>, so that there is a triangle inscribed in <span>({mathcal {D}})</span> and circumscribed about <span>({mathcal {E}})</span>. According to the famous Poncelet porism, we know that there is an infinite family of such triangles, so we will call <span>({D,E})</span> a 3-Poncelet pair. Using isogonal conjugacy, we develop a geometric construction that produces new families of circles that also form a 3-Poncelet pair with <span>({mathcal {E}})</span>. In fact, any circle that is the locus of isogonal conjugates of a fixed point with respect to the family of Poncelet triangles of the original 3-Poncelet pair <span>({D,E})</span> serves as an outer circle in a new 3-Poncelet pair with the same inner conic <span>({mathcal {E}})</span>. In the process, two special pairs of circles emerge as guide marks.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"100 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-026-01274-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147559864","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
(C_{2})-cyclic means (C_{2})-循环均值
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2026-03-16 DOI: 10.1007/s00010-026-01277-7
Lucio R. Berrone, Gerardo E. Sbérgamo
{"title":"(C_{2})-cyclic means","authors":"Lucio R. Berrone,&nbsp;Gerardo E. Sbérgamo","doi":"10.1007/s00010-026-01277-7","DOIUrl":"10.1007/s00010-026-01277-7","url":null,"abstract":"<div><p>The concept of <span>(C_{2})</span>-cyclic mean is introduced and studied in this paper. The unique symmetric and sufficiently regular two-variable means that are <span>(C_{2})</span>-cyclic turn out to be quasiarithmetic. Besides a proof of this fact, several related examples and remarks are given.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"100 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147559865","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
Difference-differential fields of continuous functions 连续函数的微分-微分域
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2026-03-10 DOI: 10.1007/s00010-026-01276-8
Seiji Nishioka
{"title":"Difference-differential fields of continuous functions","authors":"Seiji Nishioka","doi":"10.1007/s00010-026-01276-8","DOIUrl":"10.1007/s00010-026-01276-8","url":null,"abstract":"<div><p>The set <span>(mathcal {C})</span> of complex-valued continuous functions on <span>([0,infty ))</span> is a ring for addition and convolution. It has the quotient field <span>(Q(mathcal {C}))</span>, by which J. Mikusiński developed his operational calculus. In this paper, we revisit a derivation and a transforming operator for <span>(Q(mathcal {C}))</span> discussed in his textbook, and define a new transforming operator related to the <i>q</i>-shift operator, which gives structures of a <i>q</i>-difference field and a difference field of Mahler type to <span>(Q(mathcal {C}))</span>.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"100 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-026-01276-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147440878","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
Some distributions on increasing and flattened permutations 递增排列和扁平排列的一些分布
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2026-03-09 DOI: 10.1007/s00010-026-01275-9
Jean-Luc Baril, José L. Ramírez
{"title":"Some distributions on increasing and flattened permutations","authors":"Jean-Luc Baril,&nbsp;José L. Ramírez","doi":"10.1007/s00010-026-01275-9","DOIUrl":"10.1007/s00010-026-01275-9","url":null,"abstract":"<div><p>We examine the distribution and popularity of different parameters (such as the number of descents, runs, valleys, peaks, right-to-left minima, and more) on the sets of increasing and flattened permutations. For each parameter, we provide an exponential generating function for its corresponding distribution and popularity. Additionally, we present one-to-one correspondences between these permutations and some classes of simpler combinatorial objects.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"100 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-026-01275-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441206","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
Migrativity properties of uninorms over fuzzy implications 模糊暗示上一致信息的迁移性
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2026-03-09 DOI: 10.1007/s00010-026-01270-0
Deng Pan, Hongjun Zhou, Michał Baczyński
{"title":"Migrativity properties of uninorms over fuzzy implications","authors":"Deng Pan,&nbsp;Hongjun Zhou,&nbsp;Michał Baczyński","doi":"10.1007/s00010-026-01270-0","DOIUrl":"10.1007/s00010-026-01270-0","url":null,"abstract":"<div><p>Migrativity between fuzzy logical connectives is an important and interesting property in fuzzy logic theory. So far, the migrativity between conjunctive logic connectives including t-norms, uninorms and overlap functions has been extensively studied. Recently, we [23] studied the migrativity of continuous t-conorms over fuzzy implications, which is a theoretical supplement on the migrativity of disjunctive connectives in the literature. It is well known that uninorms are a special kind of aggregation functions, which can be viewed as generalizations of both t-norms and t-conorms, and within this framework, we carry out a continuous deep investigation on the migrativity of uninorms over fuzzy implications in this paper. We first introduce the concept of alpha-migrativity of uninorms over fuzzy implications and then characterize the migrative equation for the uninorms <i>U</i> belonging to one of the usually-studied classes over fuzzy implications whose natural negation is non-vanishing. Finally, we study the <span>(alpha )</span>-migrativity of uninorms over general fuzzy implications and obtain the characterizations of solutions to migrative equations by the ordinal sum of t-conorms (t-norms), where plenty of supporting examples of solutions are given.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"100 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441207","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 Counterexample to Matkowski’s Conjecture for Quasi Graph-Additive Functions 拟图加性函数Matkowski猜想的一个反例
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2026-02-27 DOI: 10.1007/s00010-026-01269-7
Tibor Kiss
{"title":"A Counterexample to Matkowski’s Conjecture for Quasi Graph-Additive Functions","authors":"Tibor Kiss","doi":"10.1007/s00010-026-01269-7","DOIUrl":"10.1007/s00010-026-01269-7","url":null,"abstract":"<div><p>In this paper we investigate a conjecture of Janusz Matkowski concerning the continuous solutions of the functional equation </p><div><div><span>$$begin{aligned}begin{aligned} fbig (f(-x)+xbig )=fbig (-f(x)big )+f(x),qquad xin mathbb {R}. end{aligned}end{aligned}$$</span></div></div><p>Matkowski conjectured that all continuous solutions must necessarily be linear on both the negative and the positive half-line. We show, however, that the family of continuous solutions to the equation in question is far richer than anticipated: there exist continuous solutions that admit an arbitrary part. In addition, we provide a sufficient condition which, in the continuous setting, enforces the conclusion predicted by Matkowski’s Conjecture.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"100 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-026-01269-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147342094","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 isoperimetric problem for hyperideal polyhedra, part I 超多面体的等周问题，第1部分
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2026-02-20 DOI: 10.1007/s00010-025-01253-7
Ren Guo
{"title":"The isoperimetric problem for hyperideal polyhedra, part I","authors":"Ren Guo","doi":"10.1007/s00010-025-01253-7","DOIUrl":"10.1007/s00010-025-01253-7","url":null,"abstract":"<div><p>The isoperimetric problem for hyperbolic hyperideal polyhedra is studied. A convex hyperideal polyhedron, with all vertices beyond the sphere at infinity and equal edge lengths, uniquely maximizes volume among those with the same combinatorial type and surface area. Constructed examples include hyperideal counterparts of all convex uniform polyhedra, certain Johnson solids, and other hyperideal polyhedra with no analogues in Euclidean space.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"100 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147340445","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
The d-distance p-packing domination number: complexity, cycles, and trees d距离p填充支配数：复杂性、循环和树
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2026-02-20 DOI: 10.1007/s00010-026-01266-w
Csilla Bujtás, Vesna Iršič Chenoweth, Sandi Klavžar, Gang Zhang
{"title":"The d-distance p-packing domination number: complexity, cycles, and trees","authors":"Csilla Bujtás,&nbsp;Vesna Iršič Chenoweth,&nbsp;Sandi Klavžar,&nbsp;Gang Zhang","doi":"10.1007/s00010-026-01266-w","DOIUrl":"10.1007/s00010-026-01266-w","url":null,"abstract":"<div><p>A set of vertices <span>(Xsubseteq V(G))</span> is a <i>d</i>-distance dominating set if for every <span>(uin V(G)setminus X)</span> there exists <span>(xin X)</span> such that <span>(d(u,x) le d)</span>, and <i>X</i> is a <i>p</i>-packing if <span>(d(u,v) ge p+1)</span> for every different <span>(u,vin X)</span>. The <i>d</i>-distance <i>p</i>-packing domination number <span>(gamma _d^p(G))</span> of <i>G</i> is the minimum size of a set of vertices of <i>G</i> which is both a <i>d</i>-distance dominating set and a <i>p</i>-packing. It is proved that for every two fixed integers <i>d</i> and <i>p</i> with <span>(2 le d)</span> and <span>(0 le p le 2d-1)</span>, the decision problem whether <span>(gamma _d^p(G) le k)</span> holds is NP-complete for bipartite planar graphs. A necessary and sufficient condition for the existence of a <i>d</i>-distance <i>p</i>-packing dominating set in <span>(C_n)</span> is obtained and <span>(gamma _d^p(C_n))</span> determined for every <i>d</i>, <i>p</i>, and <i>n</i>. For a tree <i>T</i> on <i>n</i> vertices with <span>(ell )</span> leaves and <i>s</i> support vertices it is proved that (i) <span>(gamma _2^0(T) ge frac{n-ell -s+4}{5})</span>, (ii) <span>(lceil frac{n-ell -s+4}{5} rceil le gamma _2^2(T) le leftlfloor frac{n+3s-1}{5} rightrfloor )</span>, and if <span>(d ge 2)</span>, then (iii) <span>(gamma _d^2(T) le frac{n-2sqrt{n}+d+1}{d})</span>. Inequality (i) improves an earlier bound due to Meierling and Volkmann, and independently Raczek, Lemańska, and Cyman, while (iii) extends an earlier result for <span>(gamma _2^2(T))</span> due to Henning. Sharpness of the bounds is discussed and established in most cases. It is also proved that every connected graph <i>G</i> contains a spanning tree <i>T</i> such that <span>(gamma _2^2(T) le gamma _2^2(G))</span>.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"100 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-026-01266-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147340447","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 second differences in product form in two variables 关于两个变量乘积形式的第二个差别的注释
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2026-02-20 DOI: 10.1007/s00010-025-01249-3
Ying Ying Xu, Hou Yu Zhao
{"title":"A note on second differences in product form in two variables","authors":"Ying Ying Xu,&nbsp;Hou Yu Zhao","doi":"10.1007/s00010-025-01249-3","DOIUrl":"10.1007/s00010-025-01249-3","url":null,"abstract":"<div><p>In this paper, we study the class of functions whose second difference admits a product form. In particular, we present the general solutions of the functional equation </p><div><div><span>$$begin{aligned} begin{aligned} f_1(x_1y_1,x_2y_2)-f_1(x_1y_1,x_2y_2^{-1})&amp;-f_2(x_1y_1^{-1},x_2y_2)+f_2(x_1y_1^{-1},x_2y_2^{-1})&amp;=g(x_1,x_2)h(y_1,y_2) end{aligned} end{aligned}$$</span></div></div><p>where <span>(f_1,f_2)</span> are unknown functions and satisfy the conditions </p><div><div><span>$$begin{aligned} begin{aligned}&amp;f_1(x_1y_1z_1,x_2)=f_1(x_1z_1y_1,x_2),f_1(x_1,x_2y_2z_2)=f_1(x_1,x_2z_2y_2),&amp;f_2(x_1y_1z_1,x_2)=f_2(x_1z_1y_1,x_2),f_2(x_1,x_2y_2z_2)=f_2(x_1,x_2z_2y_2) end{aligned} end{aligned}$$</span></div></div><p>for all <span>(x_i,y_i,z_iin G_i(i=1,2))</span>, where <span>(G_i(i=1,2))</span> are arbitrary groups.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"100 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147340446","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 note on the iterative roots of a class of noninjective functions 关于一类非内射函数的迭代根的注释
IF 0.7 3区 数学
Aequationes Mathematicae Pub Date : 2026-02-20 DOI: 10.1007/s00010-025-01261-7
Kiran Antony, Murugan Veerapazham
{"title":"A note on the iterative roots of a class of noninjective functions","authors":"Kiran Antony,&nbsp;Murugan Veerapazham","doi":"10.1007/s00010-025-01261-7","DOIUrl":"10.1007/s00010-025-01261-7","url":null,"abstract":"<div><p>We characterize the iterative roots of a class of noninjective functions using a theorem by Bašić and Hačko originally established for injective functions. It is demonstrated that a certain class of non-decreasing functions on an interval with finitely many discontinuities admit iterative roots of all orders.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"100 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147340444","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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