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Annales Mathematicae Silesianae最新文献

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Refinements of Some Classical Inequalities Involving Sinc and Hyperbolic Sinc Functions 涉及Sinc函数和双曲Sinc函数的一些经典不等式的改进
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2022-11-23 DOI: 10.2478/amsil-2022-0019
Yogesh J. Bagul, Sumedh B. Thool, C. Chesneau, R. Dhaigude
{"title":"Refinements of Some Classical Inequalities Involving Sinc and Hyperbolic Sinc Functions","authors":"Yogesh J. Bagul, Sumedh B. Thool, C. Chesneau, R. Dhaigude","doi":"10.2478/amsil-2022-0019","DOIUrl":"https://doi.org/10.2478/amsil-2022-0019","url":null,"abstract":"Abstract Several bounds of trigonometric-exponential and hyperbolic-exponential type for sinc and hyperbolic sinc functions are presented. In an attempt to generalize the results, some known inequalities are sharpened and extended. Hyperbolic versions are also established, along with extensions.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"37 1","pages":"1 - 15"},"PeriodicalIF":0.4,"publicationDate":"2022-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43360382","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
On Weights Which Admit Harmonic Bergman Kernel and Minimal Solutions of Laplace’s Equation 关于拉普拉斯方程的调和Bergman核权和极小解
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2022-09-01 DOI: 10.2478/amsil-2022-0016
T. Ł. Żynda
{"title":"On Weights Which Admit Harmonic Bergman Kernel and Minimal Solutions of Laplace’s Equation","authors":"T. Ł. Żynda","doi":"10.2478/amsil-2022-0016","DOIUrl":"https://doi.org/10.2478/amsil-2022-0016","url":null,"abstract":"Abstract In this paper we consider spaces of weight square-integrable and harmonic functions L2H(Ω, µ). Weights µ for which there exists reproducing kernel of L2H(Ω, µ) are named ’admissible weights’ and such kernels are named ’harmonic Bergman kernels’. We prove that if only weight of integration is integrable in some negative power, then it is admissible. Next we construct a weight µ on the unit circle which is non-admissible and using Bell-Ligocka theorem we show that such weights exist for a large class of domains in ℝ2. Later we conclude from the classical result of reproducing kernel Hilbert spaces theory that if the set {f ∈ L2H(Ω, µ)|f(z) = c} for admissible weight µ is non-empty, then there is exactly one element with minimal norm. Such an element in this paper is called ’a minimal (z, c)-solution in weight µ of Laplace’s equation on Ω’ and upper estimates for it are given.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"36 1","pages":"238 - 252"},"PeriodicalIF":0.4,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46744271","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
Gleason–Kahane–Żelazko Theorem for Bilinear Maps 双线性映射的Gleason–Kahane–Żelazko定理
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2022-09-01 DOI: 10.2478/amsil-2022-0017
A. Zivari-kazempour
{"title":"Gleason–Kahane–Żelazko Theorem for Bilinear Maps","authors":"A. Zivari-kazempour","doi":"10.2478/amsil-2022-0017","DOIUrl":"https://doi.org/10.2478/amsil-2022-0017","url":null,"abstract":"Abstract Let A and B be two unital Banach algebras and 𝔘 = A × B. We prove that the bilinear mapping φ: 𝔘 → ℂ is a bi-Jordan homomorphism if and only if φ is unital, invertibility preserving and jointly continuous. Additionally, if A is commutative, then φ is a bi-homomorphism.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"36 1","pages":"228 - 237"},"PeriodicalIF":0.4,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42732415","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
On the Two-Dimensional Version of the Sperner Lemma and Brouwer’s Theorem 关于Sperner引理和Brouwer定理的二维版本
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2022-09-01 DOI: 10.2478/amsil-2022-0012
Eugeniusz Barcz
{"title":"On the Two-Dimensional Version of the Sperner Lemma and Brouwer’s Theorem","authors":"Eugeniusz Barcz","doi":"10.2478/amsil-2022-0012","DOIUrl":"https://doi.org/10.2478/amsil-2022-0012","url":null,"abstract":"Abstract In this work the Brouwer fixed point theorem for a triangle was proved by two methods based on the Sperner Lemma. One of the two proofs of Sperner’s Lemma given in the paper was carried out using the so-called index.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"36 1","pages":"106 - 114"},"PeriodicalIF":0.4,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46577687","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
On Quaternion Gaussian Bronze Fibonacci Numbers 关于四元数高斯青铜斐波那契数
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2022-09-01 DOI: 10.2478/amsil-2022-0013
P. Catarino, S. Ricardo
{"title":"On Quaternion Gaussian Bronze Fibonacci Numbers","authors":"P. Catarino, S. Ricardo","doi":"10.2478/amsil-2022-0013","DOIUrl":"https://doi.org/10.2478/amsil-2022-0013","url":null,"abstract":"Abstract In the present work, a new sequence of quaternions related to the Gaussian Bronze numbers is defined and studied. Binet’s formula, generating function and certain properties and identities are provided. Tridiagonal matrices are considered to determine the general term of this sequence.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"36 1","pages":"129 - 150"},"PeriodicalIF":0.4,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48774279","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
General Limit Formulae Involving Prime Numbers 涉及素数的一般极限公式
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2022-09-01 DOI: 10.2478/amsil-2022-0014
Reza Farhadian, R. Jakimczuk
{"title":"General Limit Formulae Involving Prime Numbers","authors":"Reza Farhadian, R. Jakimczuk","doi":"10.2478/amsil-2022-0014","DOIUrl":"https://doi.org/10.2478/amsil-2022-0014","url":null,"abstract":"Abstract Let pn be the n th prime number. In this note, we study strictly increasing sequences of positive integers An such that the limit limn→∞ (A1A2 · · · An)1/pn = e holds. This limit formula is in fact a generalization of some previously known results. Furthermore, some other generalizations are established.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"36 1","pages":"176 - 183"},"PeriodicalIF":0.4,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44834290","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
On Generalized Jacobsthal and Jacobsthal–Lucas Numbers 关于广义Jacobsthal数和Jacobsthal - lucas数
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2022-07-01 DOI: 10.2478/amsil-2022-0011
D. Bród, Adrian Michalski
{"title":"On Generalized Jacobsthal and Jacobsthal–Lucas Numbers","authors":"D. Bród, Adrian Michalski","doi":"10.2478/amsil-2022-0011","DOIUrl":"https://doi.org/10.2478/amsil-2022-0011","url":null,"abstract":"Abstract Jacobsthal numbers and Jacobsthal–Lucas numbers are some of the most studied special integer sequences related to the Fibonacci numbers. In this study, we introduce one parameter generalizations of Jacobsthal numbers and Jacobsthal–Lucas numbers. We define two sequences, called generalized Jacobsthal sequence and generalized Jacobsthal–Lucas sequence. We give generating functions, Binet’s formulas for these numbers. Moreover, we obtain some identities, among others Catalan’s, Cassini’s identities and summation formulas for the generalized Jacobsthal numbers and the generalized Jacobsthal–Lucas numbers. These properties generalize the well-known results for classical Jacobsthal numbers and Jacobsthal–Lucas numbers. Additionally, we give a matrix representation of the presented numbers.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"36 1","pages":"115 - 128"},"PeriodicalIF":0.4,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44558961","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
Classification of Odometers: A Short Elementary Proof 里程表的分类:一个简短的初等证明
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2022-05-28 DOI: 10.2478/amsil-2022-0010
Roman Hric, Miroslav Výbošťok
{"title":"Classification of Odometers: A Short Elementary Proof","authors":"Roman Hric, Miroslav Výbošťok","doi":"10.2478/amsil-2022-0010","DOIUrl":"https://doi.org/10.2478/amsil-2022-0010","url":null,"abstract":"Abstract The paper deals with odometers (i.e. adding machines) of general type. We give a characterization of self-conjugacies of odometers which enables us to present an elementary proof of a classification of odometers given by Buescu and Stewart in [2]. The paper might also serve as a very quick introduction to odometers.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"36 1","pages":"184 - 192"},"PeriodicalIF":0.4,"publicationDate":"2022-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41844843","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
A Levi–Civita Equation on Monoids, Two Ways Monoids上的Levi–Civita方程，两种方法
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2022-05-12 DOI: 10.2478/amsil-2022-0009
B. Ebanks
{"title":"A Levi–Civita Equation on Monoids, Two Ways","authors":"B. Ebanks","doi":"10.2478/amsil-2022-0009","DOIUrl":"https://doi.org/10.2478/amsil-2022-0009","url":null,"abstract":"Abstract We consider the Levi–Civita equation f(xy)=g1(x)h1(y)+g2(x)h2(y) fleft( {xy} right) = {g_1}left( x right){h_1}left( y right) + {g_2}left( x right){h_2}left( y right) for unknown functions f, g1, g2, h1, h2 : S → ℂ, where S is a monoid. This functional equation contains as special cases many familiar functional equations, including the sine and cosine addition formulas. In a previous paper we solved this equation on groups and on monoids generated by their squares under the assumption that f is central. Here we solve the equation on monoids by two different methods. The first method is elementary and works on a general monoid, assuming only that the function f is central. The second way uses representation theory and assumes that the monoid is commutative. The solutions are found (in both cases) with the help of the recently obtained solution of the sine addition formula on semigroups. We also find the continuous solutions on topological monoids.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"36 1","pages":"151 - 166"},"PeriodicalIF":0.4,"publicationDate":"2022-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43969992","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: 2
A Functional Equation with Biadditive Functions 一个具有可加性函数的函数方程
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2022-05-02 DOI: 10.2478/amsil-2022-0008
Radosław Łukasik
{"title":"A Functional Equation with Biadditive Functions","authors":"Radosław Łukasik","doi":"10.2478/amsil-2022-0008","DOIUrl":"https://doi.org/10.2478/amsil-2022-0008","url":null,"abstract":"Abstract Let S, H, X be groups. For two given biadditive functions A : S2 → X, B : H2 → X and for two unknown mappings T : S → H, g : S → S we will study the functional equation B(T (x), T (y)) = A(x, g(y)), x, y ∈ S, which is a generalization of the orthogonality equation in Hilbert spaces.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"36 1","pages":"193 - 205"},"PeriodicalIF":0.4,"publicationDate":"2022-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49327778","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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