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Incidence Functions of the Exponential Divisor Poset 指数除数 Poset 的发生函数
Mathematica Pannonica Pub Date : 2024-06-13 DOI: 10.1556/314.2024.00011
P. Haukkanen
{"title":"Incidence Functions of the Exponential Divisor Poset","authors":"P. Haukkanen","doi":"10.1556/314.2024.00011","DOIUrl":"https://doi.org/10.1556/314.2024.00011","url":null,"abstract":"A positive integer is said to be an exponential divisor or an e-divisor of if 𝑑𝑖 ∣ 𝑛𝑖 for all prime divisors 𝑝𝑖 of 𝑛. In addition, 1 is an e-divisor of 1. It is easy to see that ℤ+ is a poset under the e-divisibility relation. Utilizing this observation we show that e-convolution of arithmetical functions is an example of the convolution of incidence functions of posets. We also note that the identity, units and the Möbius function are preserved in this process.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"68 38","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141346526","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 Mixed 𝐵-Concatenations of Pell and Pell–Lucas Numbers which are Pell Numbers 论属于佩尔数的佩尔数和佩尔-卢卡斯数的混合𝐵-协集
Mathematica Pannonica Pub Date : 2024-06-13 DOI: 10.1556/314.2024.00010
K. N. Adédji, Marija Bliznac Trebješanin
{"title":"On Mixed 𝐵-Concatenations of Pell and Pell–Lucas Numbers which are Pell Numbers","authors":"K. N. Adédji, Marija Bliznac Trebješanin","doi":"10.1556/314.2024.00010","DOIUrl":"https://doi.org/10.1556/314.2024.00010","url":null,"abstract":"Let (𝑃𝑛)𝑛≥0 and (𝑄𝑛)𝑛≥0 be the Pell and Pell–Lucas sequences. Let 𝑏 be a positive integer such that 𝑏 ≥ 2. In this paper, we prove that the following two Diophantine equations 𝑃𝑛 = 𝑏𝑑𝑃𝑚 + 𝑄𝑘 and 𝑃𝑛 = 𝑏𝑑𝑄𝑚 + 𝑃𝑘 with 𝑑, the number of digits of 𝑃𝑘 or 𝑄𝑘 in base 𝑏, have only finitely many solutions in nonnegative integers (𝑚, 𝑛, 𝑘, 𝑏, 𝑑). Also, we explicitly determine these solutions in cases 2 ≤ 𝑏 ≤ 10.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"41 15","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141345919","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
Answer to a 1971 Question of Grätzer and Lakser on Pseudocomplemented Lattices 对格拉策和拉克塞尔 1971 年关于伪补网格问题的答复
Mathematica Pannonica Pub Date : 2024-06-04 DOI: 10.1556/314.2024.00005
Jonathan David Farley
{"title":"Answer to a 1971 Question of Grätzer and Lakser on Pseudocomplemented Lattices","authors":"Jonathan David Farley","doi":"10.1556/314.2024.00005","DOIUrl":"https://doi.org/10.1556/314.2024.00005","url":null,"abstract":"Grätzer and Lakser asked in the 1971 Transactions of the American Mathematical Society if the pseudocomplemented distributive lattices in the amalgamation class of the subvariety generated by 𝟐𝑛 ⊕ 𝟏 can be characterized by the property of not having a *-homomorphism onto 𝟐𝑖 ⊕ 𝟏 for 1 < 𝑖 < 𝑛.In this article, their question from 1971 is answered.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"222 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141387369","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
*-Rickart Property For Rings with Involution *-具有内卷性的环的里卡特性质
Mathematica Pannonica Pub Date : 2024-05-15 DOI: 10.1556/314.2024.00008
Muhammad T. Tajuddin, Usama A. Aburawash, Muhammad Saad
{"title":"*-Rickart Property For Rings with Involution","authors":"Muhammad T. Tajuddin, Usama A. Aburawash, Muhammad Saad","doi":"10.1556/314.2024.00008","DOIUrl":"https://doi.org/10.1556/314.2024.00008","url":null,"abstract":"This paper introduces and examines the concept of a *-Rickart *-ring, and proves that every Rickart *-ring is also a *-Rickart *-ring. A necessary and sufficient condition for a *-Rickart *-ring to be a Rickart *-ring is also provided. The relationship between *-Rickart *-rings and *-Baer *-rings is investigated, and several properties of *-Rickart *-rings are presented. The paper demonstrates that the property of *-Rickart extends to both the center and *-corners of a *-ring, and investigates the extension of a *-Rickart *-ring to its polynomial *-ring. Additionally, *-Rickart *-rings with descending chain condition on *-biideals are studied, and all *-Rickart (*-Baer) *-rings with finitely many elements are classified.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"14 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140974270","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 Bloch Spaces with Differentiable Strictly Positive Weights 具有可微严格正权重的布洛赫空间
Mathematica Pannonica Pub Date : 2024-02-23 DOI: 10.1556/314.2024.00004
Ding Nan, H. Wulan
{"title":"The Bloch Spaces with Differentiable Strictly Positive Weights","authors":"Ding Nan, H. Wulan","doi":"10.1556/314.2024.00004","DOIUrl":"https://doi.org/10.1556/314.2024.00004","url":null,"abstract":"In this paper, some basic characterizations of a weighted Bloch space with the differentiable strictly positive weight 𝜔 on the unit disc are given, including the growth, the higher order or free derivative descriptions, and integral characterizations of functions in the space.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"60 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140436925","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
Construction of New Operators by Composition of Integral-Type Operators and Discrete Operators 通过积分型算子与离散算子的组合构建新算子
Mathematica Pannonica Pub Date : 2024-02-01 DOI: 10.1556/314.2024.00001
Ulrich Abel, Vijay Gupta
{"title":"Construction of New Operators by Composition of Integral-Type Operators and Discrete Operators","authors":"Ulrich Abel, Vijay Gupta","doi":"10.1556/314.2024.00001","DOIUrl":"https://doi.org/10.1556/314.2024.00001","url":null,"abstract":"In this paper, we propose some new positive linear approximation operators, which are obtained from a composition of certain integral type operators with certain discrete operators. It turns out that the new operators can be expressed in discrete form. We provide representations for their coefficients. Furthermore, we study their approximation properties and determine their moment generating functions, which may be useful in finding several other convergence results in different settings.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"312 16","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139832134","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
Construction of New Operators by Composition of Integral-Type Operators and Discrete Operators 通过积分型算子与离散算子的组合构建新算子
Mathematica Pannonica Pub Date : 2024-02-01 DOI: 10.1556/314.2024.00001
Ulrich Abel, Vijay Gupta
{"title":"Construction of New Operators by Composition of Integral-Type Operators and Discrete Operators","authors":"Ulrich Abel, Vijay Gupta","doi":"10.1556/314.2024.00001","DOIUrl":"https://doi.org/10.1556/314.2024.00001","url":null,"abstract":"In this paper, we propose some new positive linear approximation operators, which are obtained from a composition of certain integral type operators with certain discrete operators. It turns out that the new operators can be expressed in discrete form. We provide representations for their coefficients. Furthermore, we study their approximation properties and determine their moment generating functions, which may be useful in finding several other convergence results in different settings.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"4 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139891975","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 Density Theorem for Dedekind Zeta Functions Dedekind Zeta 函数的密度定理
Mathematica Pannonica Pub Date : 2023-12-13 DOI: 10.1556/314.2023.00023
János Pintz
{"title":"A Density Theorem for Dedekind Zeta Functions","authors":"János Pintz","doi":"10.1556/314.2023.00023","DOIUrl":"https://doi.org/10.1556/314.2023.00023","url":null,"abstract":"We apply a recent general zero density theorem of us (valid for a large class of complex functions) to improve earlier density theorems of Heath-Brown and Paul–Sankaranarayanan for Dedekind zeta functions attached to a number field 𝐾 of degree 𝑛 with 𝑛 > 2.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"107 3‐5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138976904","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
How to Approach Stability of Bi-Continuous Semigroups? 如何处理双连续半群的稳定性？
Mathematica Pannonica Pub Date : 2023-11-24 DOI: 10.1556/314.2023.00029
Christian Budde
{"title":"How to Approach Stability of Bi-Continuous Semigroups?","authors":"Christian Budde","doi":"10.1556/314.2023.00029","DOIUrl":"https://doi.org/10.1556/314.2023.00029","url":null,"abstract":"This paper serves as a kick-off to address the question of how to define and investigate the stability of bi-continuous semigroups. We will see that the mixed topology is the key concept in this framework.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139241130","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 Simultaneous Sign Changes of Coefficients of Rankin–Selberg L-Functions over a Certain Integral Binary Quadratic Form 论兰金-塞尔伯格 L 函数系数在特定二元二次积分形式上的同时符号变化
Mathematica Pannonica Pub Date : 2023-11-17 DOI: 10.1556/314.2023.00026
Guodong Hua
{"title":"On the Simultaneous Sign Changes of Coefficients of Rankin–Selberg L-Functions over a Certain Integral Binary Quadratic Form","authors":"Guodong Hua","doi":"10.1556/314.2023.00026","DOIUrl":"https://doi.org/10.1556/314.2023.00026","url":null,"abstract":"In this paper, we consider the simultaneous sign changes of coefficients of Rankin–Selberg L-functions associated to two distinct Hecke eigenforms supported at positive integers represented by some certain primitive reduced integral binary quadratic form with negative discriminant D. We provide a quantitative result for the number of sign changes of such sequence in the interval (x, 2x] for sufficiently large x.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"33 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139265363","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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