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Annales Mathematicae Silesianae最新文献

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A Further Generalization of limn→∞n!/nn=1/e {lim _{n to infty }}root n of {n!/n} = 1/e limn的进一步推广→∞n/nn=1/e
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2022-04-18 DOI: 10.2478/amsil-2022-0006
Reza Farhadian, R. Jakimczuk
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引用次数: 1
Report of Meeting: The Twenty-first Katowice–Debrecen Winter Seminar on Functional Equations and Inequalities Brenna (Poland), February 2–5, 2022 会议报告：第二十一届卡托维兹-德布勒森函数方程和不等式冬季研讨会布伦纳（波兰），2022年2月2日至5日
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2022-03-22 DOI: 10.2478/amsil-2022-0003
{"title":"Report of Meeting: The Twenty-first Katowice–Debrecen Winter Seminar on Functional Equations and Inequalities Brenna (Poland), February 2–5, 2022","authors":"","doi":"10.2478/amsil-2022-0003","DOIUrl":"https://doi.org/10.2478/amsil-2022-0003","url":null,"abstract":"","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42540638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Variant of D’Alembert’s Functional Equation on Semigroups with Endomorphisms 具有自同态的半群上D 'Alembert泛函方程的一个变体
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2022-03-01 DOI: 10.2478/amsil-2022-0004
A. Akkaoui, M. El Fatini, B. Fadli
{"title":"A Variant of D’Alembert’s Functional Equation on Semigroups with Endomorphisms","authors":"A. Akkaoui, M. El Fatini, B. Fadli","doi":"10.2478/amsil-2022-0004","DOIUrl":"https://doi.org/10.2478/amsil-2022-0004","url":null,"abstract":"Abstract Let S be a semigroup, and let φ, ψ: S → S be two endomorphisms (which are not necessarily involutive). Our main goal in this paper is to solve the following generalized variant of d’Alembert’s functional equation f(xϕ(y))+f(ψ(y)x)=2f(x)f(y),      x,y ∈ S, fleft( {xvarphi left( y right)} right) + fleft( {psi left( y right)x} right) = 2fleft( x right)fleft( y right),,,,,,,x,y, in ,S, where f : S → ℂ is the unknown function by expressing its solutions in terms of multiplicative functions. Some consequences of this result are presented.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"36 1","pages":"1 - 14"},"PeriodicalIF":0.4,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46964586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Deepest Nodes in Marked Ordered Trees 标记有序树中的最深节点
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2022-02-11 DOI: 10.2478/amsil-2022-0015
H. Prodinger
{"title":"Deepest Nodes in Marked Ordered Trees","authors":"H. Prodinger","doi":"10.2478/amsil-2022-0015","DOIUrl":"https://doi.org/10.2478/amsil-2022-0015","url":null,"abstract":"Abstract A variation of ordered trees, where each rightmost edge might be marked or not, if it does not lead to an endnode, is investigated. These marked ordered trees were introduced by E. Deutsch et al. to model skew Dyck paths. We study the number of deepest nodes in such trees. Explicit generating functions are established and the average number of deepest nodes, which approaches 53 {5 over 3} when the number of nodes gets large. This is to be compared to standard ordered trees where the average number of deepest nodes approaches 2.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"36 1","pages":"215 - 227"},"PeriodicalIF":0.4,"publicationDate":"2022-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44651290","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Gauss Congruences in Algebraic Number Fields 代数数域中的高斯同余
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2022-01-17 DOI: 10.2478/amsil-2022-0002
Paweł Gładki, Mateusz Pulikowski
{"title":"Gauss Congruences in Algebraic Number Fields","authors":"Paweł Gładki, Mateusz Pulikowski","doi":"10.2478/amsil-2022-0002","DOIUrl":"https://doi.org/10.2478/amsil-2022-0002","url":null,"abstract":"Abstract In this miniature note we generalize the classical Gauss congruences for integers to rings of integers in algebraic number fields.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"36 1","pages":"53 - 56"},"PeriodicalIF":0.4,"publicationDate":"2022-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43324350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Parametric Functional Equation Originating from Number Theory 一个源于数论的参数函数方程
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2022-01-17 DOI: 10.2478/amsil-2022-0001
A. Mouzoun, D. Zeglami, Y. Aissi
{"title":"A Parametric Functional Equation Originating from Number Theory","authors":"A. Mouzoun, D. Zeglami, Y. Aissi","doi":"10.2478/amsil-2022-0001","DOIUrl":"https://doi.org/10.2478/amsil-2022-0001","url":null,"abstract":"Abstract Let S be a semigroup and α, β ∈ ℝ. The purpose of this paper is to determine the general solution f : ℝ2 → S of the following parametric functional equation f(x1+x2+αy1y2,x1y2+x2y1+βy1y2)=f(x1,y1)f(x2,y2), fleft( {{x_1} + {x_2} + alpha {y_1}{y_2},{x_1}{y_2} + {x_2}{y_1} + beta {y_1}{y_2}} right) = fleft( {{x_1},{y_1}} right)fleft( {{x_2},{y_2}} right), for all (x1, y1), (x2, y2) ∈ ℝ2, that generalizes some functional equations arising from number theory and is connected with the characterizations of the determinant of matrices.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"36 1","pages":"71 - 91"},"PeriodicalIF":0.4,"publicationDate":"2022-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45605607","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Jacobsthal Representation Hybrinomials Jacobthal表示Hybrinomials
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2021-11-27 DOI: 10.2478/amsil-2021-0014
M. Liana, A. Szynal-Liana, I. Włoch
{"title":"Jacobsthal Representation Hybrinomials","authors":"M. Liana, A. Szynal-Liana, I. Włoch","doi":"10.2478/amsil-2021-0014","DOIUrl":"https://doi.org/10.2478/amsil-2021-0014","url":null,"abstract":"Abstract Jacobsthal numbers are a special case of numbers defined recursively by the second order linear relation and for these reasons they are also named as numbers of the Fibonacci type. They have many interpretations, representations and applications in distinct areas of mathematics. In this paper we present the Jacobsthal representation hybrinomials, i.e. polynomials, which are a generalization of Jacobsthal hybrid numbers.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"36 1","pages":"57 - 70"},"PeriodicalIF":0.4,"publicationDate":"2021-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42006595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Separately Continuous Function Not Somewhat Continuous 一个单独连续的函数，不是某种程度上连续的
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2021-10-11 DOI: 10.2478/amsil-2021-0013
Wojciech Bielas
{"title":"A Separately Continuous Function Not Somewhat Continuous","authors":"Wojciech Bielas","doi":"10.2478/amsil-2021-0013","DOIUrl":"https://doi.org/10.2478/amsil-2021-0013","url":null,"abstract":"Abstract We construct a separately continuous function f : ℚ × ℚ → [0; 1] and a dense subset D ⊆ ℚ × ℚ such that f[D] is not dense in f[ℚ × ℚ], in other words, f is separately continuous and not somewhat (feebly) continuous.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"36 1","pages":"26 - 29"},"PeriodicalIF":0.4,"publicationDate":"2021-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48100550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Cosine-Sine Functional Equation on Semigroups 半群上的余弦正弦函数方程
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2021-10-05 DOI: 10.2478/amsil-2021-0012
B. Ebanks
{"title":"The Cosine-Sine Functional Equation on Semigroups","authors":"B. Ebanks","doi":"10.2478/amsil-2021-0012","DOIUrl":"https://doi.org/10.2478/amsil-2021-0012","url":null,"abstract":"Abstract The primary object of study is the “cosine-sine” functional equation f(xy) = f(x)g(y)+g(x)f(y)+h(x)h(y) for unknown functions f, g, h : S → ℂ, where S is a semigroup. The name refers to the fact that it contains both the sine and cosine addition laws. This equation has been solved on groups and on semigroups generated by their squares. Here we find the solutions on a larger class of semigroups and discuss the obstacles to finding a general solution for all semigroups. Examples are given to illustrate both the results and the obstacles. We also discuss the special case f(xy) = f(x)g(y) + g(x)f(y) − g(x)g(y) separately, since it has an independent direct solution on a general semigroup. We give the continuous solutions on topological semigroups for both equations.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"36 1","pages":"30 - 52"},"PeriodicalIF":0.4,"publicationDate":"2021-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46287940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
A Note on Amalgamated Rings Along an Ideal 关于沿理想的并合环的一个注记
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2021-08-30 DOI: 10.2478/amsil-2021-0010
M. Nowakowska
{"title":"A Note on Amalgamated Rings Along an Ideal","authors":"M. Nowakowska","doi":"10.2478/amsil-2021-0010","DOIUrl":"https://doi.org/10.2478/amsil-2021-0010","url":null,"abstract":"Abstract Ring properties of amalgamated products are investigated. We offer new, elementary arguments which extend results from [5] and [12] to noncommutative setting and also give new properties of amalgamated rings.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"35 1","pages":"282 - 288"},"PeriodicalIF":0.4,"publicationDate":"2021-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42586040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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