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Some arithmetic functions of factorials in Lucas sequences Lucas序列中阶乘的几个算术函数
IF 0.4 4区 数学
Glasnik Matematicki Pub Date : 2021-06-24 DOI: 10.3336/gm.56.1.02
E. F. Bravo, Jhon J. Bravo
{"title":"Some arithmetic functions of factorials in Lucas sequences","authors":"E. F. Bravo, Jhon J. Bravo","doi":"10.3336/gm.56.1.02","DOIUrl":"https://doi.org/10.3336/gm.56.1.02","url":null,"abstract":"We prove that if {un}n≥ 0 is a nondegenerate Lucas sequence, then there are only finitely many effectively computable positive integers n such that |un|=f(m!), where f is either the sum-of-divisors function, or the sum-of-proper-divisors function, or the Euler phi function. We also give a theorem that holds for a more general class of integer sequences and illustrate our results through a few specific examples. This paper is motivated by a previous work of Iannucci and Luca who addressed the above problem with Catalan numbers and the sum-of-proper-divisors function.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82535494","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}
引用次数: 1
Extremal behaviour of ± 1-valued completely multiplicative functions in function fields 函数场中±1值完全乘法函数的极值行为
IF 0.4 4区 数学
Glasnik Matematicki Pub Date : 2021-06-24 DOI: 10.3336/gm.56.1.06
Nikola Lelas
{"title":"Extremal behaviour of ± 1-valued completely multiplicative functions in function fields","authors":"Nikola Lelas","doi":"10.3336/gm.56.1.06","DOIUrl":"https://doi.org/10.3336/gm.56.1.06","url":null,"abstract":"We investigate the classical Pólya and Turán conjectures in the context of rational function fields over finite fields 𝔽q. Related to these two conjectures we investigate the sign of truncations of Dirichlet L-functions at point s=1 corresponding to quadratic characters over 𝔽q[t], prove a variant of a theorem of Landau for arbitrary sets of monic, irreducible polynomials over 𝔽q[t] and calculate the mean value of certain variants of the Liouville function over 𝔽q[t].","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85639479","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}
引用次数: 0
Angular right symmetricity of bounded linear operators on Hilbert spaces Hilbert空间上有界线性算子的角右对称性
IF 0.4 4区 数学
Glasnik Matematicki Pub Date : 2021-06-24 DOI: 10.3336/gm.56.1.09
S. M. S. Nabavi Sales
{"title":"Angular right symmetricity of bounded linear operators on Hilbert spaces","authors":"S. M. S. Nabavi Sales","doi":"10.3336/gm.56.1.09","DOIUrl":"https://doi.org/10.3336/gm.56.1.09","url":null,"abstract":"We introduce and characterize angular right symmetric and approximate angular right symmetric points of the algebra of all bounded linear operators defined on either real or complex Hilbert spaces.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84137215","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}
引用次数: 1
Approximate inverse limits and (m,n)-dimensions 近似逆极限和(m,n)维
IF 0.4 4区 数学
Glasnik Matematicki Pub Date : 2021-06-24 DOI: 10.3336/gm.56.1.11
J. Peters
{"title":"Approximate inverse limits and (m,n)-dimensions","authors":"J. Peters","doi":"10.3336/gm.56.1.11","DOIUrl":"https://doi.org/10.3336/gm.56.1.11","url":null,"abstract":"This paper introduces shape boundary regions in descriptive proximity forms of CW (Closure-finite Weak) spaces as a source of amiable fixed subsets as well as almost amiable fixed subsets of descriptive proximally continuous (dpc) maps. A dpc map is an extension of an Efremovič-Smirnov proximally continuous (pc) map introduced during the early-1950s by V.A. Efremovič and Yu.M. Smirnov. Amiable fixed sets and the Betti numbers of their free Abelian group representations are derived from dpc's relative to the description of the boundary region of the sets. Almost amiable fixed sets are derived from dpc's by relaxing the matching description requirement for the descriptive closeness of the sets. This relaxed form of amiable fixed sets works well for applications in which closeness of fixed sets is approximate rather than exact. A number of examples of amiable fixed sets are given in terms of wide ribbons. A bi-product of this work is a variation of the Jordan curve theorem and a fixed cell complex theorem, which is an extension of the Brouwer fixed point theorem.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86545938","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}
引用次数: 0
Approximation of nilpotent orbits for simple Lie groups 单李群幂零轨道的逼近
IF 0.4 4区 数学
Glasnik Matematicki Pub Date : 2021-01-21 DOI: 10.3336/gm.56.2.06
Lucas Fresse, S. Mehdi
{"title":"Approximation of nilpotent orbits for simple Lie groups","authors":"Lucas Fresse, S. Mehdi","doi":"10.3336/gm.56.2.06","DOIUrl":"https://doi.org/10.3336/gm.56.2.06","url":null,"abstract":"We propose a systematic and topological study of limits (lim_{nuto 0^+}G_mathbb{R}cdot(nu x)) of continuous families of adjoint orbits for a non-compact simple real Lie group (G_mathbb{R}). This limit is always a finite union of nilpotent orbits. We describe explicitly these nilpotent orbits in terms of Richardson orbits in the case of hyperbolic semisimple elements. We also show that one can approximate minimal nilpotent orbits or even nilpotent orbits by elliptic semisimple orbits. The special cases of (mathrm{SL}_n(mathbb{R})) and (mathrm{SU}(p,q)) are computed in detail.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72426004","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}
引用次数: 2
On some partial orders on a certain subset of the power set of rings 在环幂集的某个子集上的某些偏序上
IF 0.4 4区 数学
Glasnik Matematicki Pub Date : 2020-12-23 DOI: 10.3336/gm.55.2.01
G. Dolinar, B. Kuzma, J. Marovt, B. Ungor, Jadranska ulica Si Ljubljana Slovenia Imfm, Razlagova Maribor Slovenia Business
{"title":"On some partial orders on a certain subset of the power set of rings","authors":"G. Dolinar, B. Kuzma, J. Marovt, B. Ungor, Jadranska ulica Si Ljubljana Slovenia Imfm, Razlagova Maribor Slovenia Business","doi":"10.3336/gm.55.2.01","DOIUrl":"https://doi.org/10.3336/gm.55.2.01","url":null,"abstract":"Let 𝓡 be a ring with identity and let 𝓙𝓡 be a collection of subsets of 𝓡 such that their left and right annihilators are generated by the same idempotent. % from 𝓡. We extend the notion of the sharp, the left-sharp, and the right-sharp partial orders to 𝓙𝓡, present equivalent definitions of these orders, and study their properties. We also extend the concept of the core and the dual core orders to 𝓙𝓡, show that they are indeed partial orders when 𝓡 is a Baer *-ring, and connect them with one-sided sharp and star partial orders.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77724324","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}
引用次数: 0
A note on the exponential Diophantine equation (A^2n)^x+(B^2n)^y=((A^2+B^2)n)^z 关于指数丢番图方程(A^2n)^x+(B^2n)^y=(A^2+B^2)n)^z的注释
IF 0.4 4区 数学
Glasnik Matematicki Pub Date : 2020-12-23 DOI: 10.3336/gm.55.2.03
M. Le, G. Soydan
{"title":"A note on the exponential Diophantine equation (A^2n)^x+(B^2n)^y=((A^2+B^2)n)^z","authors":"M. Le, G. Soydan","doi":"10.3336/gm.55.2.03","DOIUrl":"https://doi.org/10.3336/gm.55.2.03","url":null,"abstract":"Let A, B be positive integers such that min{A,B}>1, gcd(A,B) = 1 and 2|B. In this paper, using an upper bound for solutions of ternary purely exponential Diophantine equations due to R. Scott and R. Styer, we prove that, for any positive integer n, if A >B3/8, then the equation (A2 n)x + (B2 n)y = ((A2 + B2)n)z has no positive integer solutions (x,y,z) with x > z > y; if B>A3/6, then it has no solutions (x,y,z) with y>z>x. Thus, combining the above conclusion with some existing results, we can deduce that, for any positive integer n, if B ≡ 2 (mod 4) and A >B3/8, then this equation has only the positive integer solution (x,y,z)=(1,1,1).","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77546414","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}
引用次数: 1
Čech systems and approximate inverse systems Čech系统和近似逆系统
IF 0.4 4区 数学
Glasnik Matematicki Pub Date : 2020-12-23 DOI: 10.3336/gm.55.2.12
Vlasta Matijević, L. Rubin
{"title":"Čech systems and approximate inverse systems","authors":"Vlasta Matijević, L. Rubin","doi":"10.3336/gm.55.2.12","DOIUrl":"https://doi.org/10.3336/gm.55.2.12","url":null,"abstract":"We generalize a result of the first author who proved that the Čech system of open covers of a Hausdorff arc-like space cannot induce an approximate system of the nerves of these covers under any choices of the meshes and the projections.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77712637","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}
引用次数: 0
otally real Thue inequalities over imaginary quadratic fields: an improvement 虚二次域上的全实Thue不等式:一个改进
IF 0.4 4区 数学
Glasnik Matematicki Pub Date : 2020-12-23 DOI: 10.3336/gm.55.2.02
Istv'an Ga'al, Borka Jadrijevic, László Remete
{"title":"otally real Thue inequalities over imaginary quadratic fields: an improvement","authors":"Istv'an Ga'al, Borka Jadrijevic, László Remete","doi":"10.3336/gm.55.2.02","DOIUrl":"https://doi.org/10.3336/gm.55.2.02","url":null,"abstract":"In this paper we significantly improve our previous results of reducing relative Thue inequalities to absolute ones.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74098370","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}
引用次数: 0
Dirichlet product and the multiple Dirichlet series over function fields 狄利克雷积和函数域上的多重狄利克雷级数
IF 0.4 4区 数学
Glasnik Matematicki Pub Date : 2020-12-23 DOI: 10.3336/gm.55.2.06
Y. Hamahata
{"title":"Dirichlet product and the multiple Dirichlet series over function fields","authors":"Y. Hamahata","doi":"10.3336/gm.55.2.06","DOIUrl":"https://doi.org/10.3336/gm.55.2.06","url":null,"abstract":"We define the Dirichlet product for multiple arithmetic functions over function fields and consider the ring of the multiple Dirichlet series over function fields. We apply our results to absolutely convergent multiple Dirichlet series and obtain some zero-free regions for them.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73849772","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}
引用次数: 0
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