Pub Date : 2021-06-29DOI: 10.1556/012.2021.58.2.1498
A. Frolov
Fifty years ago P. Erdős and A. Rényi published their famous paper on the new law of large numbers. In this survey, we describe numerous results and achievements which are related with this paper or motivated by it during these years.
{"title":"The Erdős–Rényi Law and Strong Limit Theorems of Probability","authors":"A. Frolov","doi":"10.1556/012.2021.58.2.1498","DOIUrl":"https://doi.org/10.1556/012.2021.58.2.1498","url":null,"abstract":"Fifty years ago P. Erdős and A. Rényi published their famous paper on the new law of large numbers. In this survey, we describe numerous results and achievements which are related with this paper or motivated by it during these years.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"153 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73402219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-29DOI: 10.1556/012.2021.58.2.1496
K. Ayadi, Chiheb ben Bechir, Iheb Elouaer
We exhibit some explicit continued fraction expansions and their representation series in different fields. Some of these continued fractions have a type of symmetry, known as folding symmetry. We will extracted those whose are specialized.
{"title":"On Some Continued Fractions and Series","authors":"K. Ayadi, Chiheb ben Bechir, Iheb Elouaer","doi":"10.1556/012.2021.58.2.1496","DOIUrl":"https://doi.org/10.1556/012.2021.58.2.1496","url":null,"abstract":"We exhibit some explicit continued fraction expansions and their representation series in different fields. Some of these continued fractions have a type of symmetry, known as folding symmetry. We will extracted those whose are specialized.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"23 2 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78002478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, we study a family of subgraphs of the Farey graph, denoted as ℱN for every N ∈ ℕ. We show that ℱN is connected if and only if N is either equal to one or a prime power. We introduce a class of continued fractions referred to as ℱN -continued fractions for each N > 1. We establish a relation between ℱN-continued fractions and certain paths from infinity in the graph ℱN. Using this correspondence, we discuss the existence and uniqueness of ℱN-continued fraction expansions of real numbers.
{"title":"Farey-Subgraphs and Continued Fractions","authors":"S. Kushwaha, R. Sarma","doi":"10.1556/012.2022.01525","DOIUrl":"https://doi.org/10.1556/012.2022.01525","url":null,"abstract":"In this article, we study a family of subgraphs of the Farey graph, denoted as ℱN for every N ∈ ℕ. We show that ℱN is connected if and only if N is either equal to one or a prime power. We introduce a class of continued fractions referred to as ℱN -continued fractions for each N > 1. We establish a relation between ℱN-continued fractions and certain paths from infinity in the graph ℱN. Using this correspondence, we discuss the existence and uniqueness of ℱN-continued fraction expansions of real numbers.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83205719","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-04-14DOI: 10.1556/012.2021.58.1.1486
B. Wehrfritz
We study the effect on sections of a soluble-by-finite group G of finite rank of an almost fixed-point-free automorphism φ of G of finite order. We also elucidate the structure of G if φ has order 4 and if G is also (torsion-free)-by-finite. The latter extends recent work of Xu, Zhou and Liu.
{"title":"Automorphisms of Finite Order of Soluble Groups of Finite Rank","authors":"B. Wehrfritz","doi":"10.1556/012.2021.58.1.1486","DOIUrl":"https://doi.org/10.1556/012.2021.58.1.1486","url":null,"abstract":"We study the effect on sections of a soluble-by-finite group G of finite rank of an almost fixed-point-free automorphism φ of G of finite order. We also elucidate the structure of G if φ has order 4 and if G is also (torsion-free)-by-finite. The latter extends recent work of Xu, Zhou and Liu.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"258 1","pages":"19-31"},"PeriodicalIF":0.7,"publicationDate":"2021-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77076415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-04-14DOI: 10.1556/012.2021.58.1.1488
Y. Tan, Qingcai Zhang
In this paper, we investigate the uniqueness of algebroid functions in angular domain by the method of conformal mapping. We discuss the relations between the Borel directions and uniquenss with the multiple values of algebroid functions and obtain some results which extend some uniqueness results of meromorphic functions to that of algebroid functions.
{"title":"Borel Directions and the Uniqueness of Algebroid Functions Dealing with Multiple Values","authors":"Y. Tan, Qingcai Zhang","doi":"10.1556/012.2021.58.1.1488","DOIUrl":"https://doi.org/10.1556/012.2021.58.1.1488","url":null,"abstract":"In this paper, we investigate the uniqueness of algebroid functions in angular domain by the method of conformal mapping. We discuss the relations between the Borel directions and uniquenss with the multiple values of algebroid functions and obtain some results which extend some uniqueness results of meromorphic functions to that of algebroid functions.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"74 1","pages":"104-118"},"PeriodicalIF":0.7,"publicationDate":"2021-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90783267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-04-14DOI: 10.1556/012.2021.58.1.1478
B. Simonov
The paper provides a detailed study of inequalities of complete moduli of smoothness of functions with transformed Fourier series by moduli of smoothness of initial functions. Upper and lower estimates of the norms and best approximations of the functions with transformed Fourier series by the best approximations of initial functions are also obtained.
{"title":"Estimates of Functions with Transformed Double Fourier Series","authors":"B. Simonov","doi":"10.1556/012.2021.58.1.1478","DOIUrl":"https://doi.org/10.1556/012.2021.58.1.1478","url":null,"abstract":"The paper provides a detailed study of inequalities of complete moduli of smoothness of functions with transformed Fourier series by moduli of smoothness of initial functions. Upper and lower estimates of the norms and best approximations of the functions with transformed Fourier series by the best approximations of initial functions are also obtained.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"14 11","pages":"32-83"},"PeriodicalIF":0.7,"publicationDate":"2021-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72366457","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-04-14DOI: 10.1556/012.2021.58.1.1485
Changwen Li
The major aim of the note is to give new brief proofs of the results in the paper “The influence of weakly H -subgroups on the structure of finite groups” [Studia Scientiarum Mathematicarum Hungarica, 51 (1), 27–40 (2014)].
本文的主要目的是对论文“The influence of weak H -subgroups on structure of finite groups”[匈牙利数学科学研究，51(1)，27-40(2014)]中的结果给出新的简要证明。
{"title":"A Note on Weakly 𐒎 -Subgroups","authors":"Changwen Li","doi":"10.1556/012.2021.58.1.1485","DOIUrl":"https://doi.org/10.1556/012.2021.58.1.1485","url":null,"abstract":"The major aim of the note is to give new brief proofs of the results in the paper “The influence of weakly H -subgroups on the structure of finite groups” [Studia Scientiarum Mathematicarum Hungarica, 51 (1), 27–40 (2014)].","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"59 1","pages":"15-18"},"PeriodicalIF":0.7,"publicationDate":"2021-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74375671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-04-14DOI: 10.1556/012.2021.58.1.1487
Jinjia Li, M. Zhang, Hao Zhao
Let N be a sufficiently large integer. In this paper, it is proved that, with at most O(N 119/270+s) exceptions, all even positive integers up to N can be represented in the form where p1, p2, p3, p4, p5, p6 are prime numbers.
{"title":"Exceptional Set in Waring–Goldbach Problem Involving Squares, Cubes and Sixth Powers","authors":"Jinjia Li, M. Zhang, Hao Zhao","doi":"10.1556/012.2021.58.1.1487","DOIUrl":"https://doi.org/10.1556/012.2021.58.1.1487","url":null,"abstract":"Let N be a sufficiently large integer. In this paper, it is proved that, with at most O(N 119/270+s) exceptions, all even positive integers up to N can be represented in the form where p1, p2, p3, p4, p5, p6 are prime numbers.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"5 1","pages":"84-103"},"PeriodicalIF":0.7,"publicationDate":"2021-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81259127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In stochastic geometry there are several instances of threshold phenomena in high dimensions: the behavior of a limit of some expectation changes abruptly when some parameter passes through a critical value. This note continues the investigation of the expected face numbers of polyhedral random cones, when the dimension of the ambient space increases to infinity. In the focus are the critical values of the observed threshold phenomena, as well as threshold phenomena for differences instead of quotients.
{"title":"Another Look at Threshold Phenomena for Random Cones","authors":"D. Hug, R. Schneider","doi":"10.1556/012.2021.01513","DOIUrl":"https://doi.org/10.1556/012.2021.01513","url":null,"abstract":"In stochastic geometry there are several instances of threshold phenomena in high dimensions: the behavior of a limit of some expectation changes abruptly when some parameter passes through a critical value. This note continues the investigation of the expected face numbers of polyhedral random cones, when the dimension of the ambient space increases to infinity. In the focus are the critical values of the observed threshold phenomena, as well as threshold phenomena for differences instead of quotients.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"5 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87925857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
For each Montesinos knot K, we propose an efficient method to explicitly determine the irreducible SL(2, )-character variety, and show that it can be decomposed as χ0(K)⊔χ1(K)⊔χ2(K)⊔χ'(K), where χ0(K) consists of trace-free characters χ1(K) consists of characters of “unions” of representations of rational knots (or rational link, which appears at most once), χ2(K) is an algebraic curve, and χ'(K) consists of finitely many points when K satisfies a generic condition.
{"title":"The Sl(2, )-Character Variety of a Montesinos Knot","authors":"Haimiao Chen","doi":"10.1556/012.2022.01519","DOIUrl":"https://doi.org/10.1556/012.2022.01519","url":null,"abstract":"For each Montesinos knot K, we propose an efficient method to explicitly determine the irreducible SL(2, )-character variety, and show that it can be decomposed as χ0(K)⊔χ1(K)⊔χ2(K)⊔χ'(K), where χ0(K) consists of trace-free characters χ1(K) consists of characters of “unions” of representations of rational knots (or rational link, which appears at most once), χ2(K) is an algebraic curve, and χ'(K) consists of finitely many points when K satisfies a generic condition.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83042662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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