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Reconstruction properties of selective Rips complexes 选择性Rips配合物的重构性质
IF 0.4 4区 数学
Glasnik Matematicki Pub Date : 2022-06-28 DOI: 10.3336/gm.57.1.06
Boštjan Lemež, Žiga Virk
{"title":"Reconstruction properties of selective Rips complexes","authors":"Boštjan Lemež, Žiga Virk","doi":"10.3336/gm.57.1.06","DOIUrl":"https://doi.org/10.3336/gm.57.1.06","url":null,"abstract":"Selective Rips complexes associated to two parameters are certain subcomplexes of Rips complexes consisting of thin simplices. They are designed to detect more closed geodesics than their Rips counterparts. In this paper we introduce a general definition of selective Rips complexes with countably many parameters and prove basic reconstruction properties associated with them. In particular, we prove that selective Rips complexes of a closed Riemannian manifold (X) attain the homotopy type of (X) at small scales.\u0000We also completely classify the resulting persistent fundamental group and (1)-dimensional persistent homology.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":"112 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79631741","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: 3
The finite coarse shape - inverse systems approach and intrinsic approach 有限粗形逆系统方法和本征方法
IF 0.4 4区 数学
Glasnik Matematicki Pub Date : 2022-06-28 DOI: 10.3336/gm.57.1.07
I. Jelić, Nikola Koceić Bilan
{"title":"The finite coarse shape - inverse systems approach and intrinsic approach","authors":"I. Jelić, Nikola Koceić Bilan","doi":"10.3336/gm.57.1.07","DOIUrl":"https://doi.org/10.3336/gm.57.1.07","url":null,"abstract":"Given an arbitrary category (mathcal{C}), a category (pro^{*^f})-(mathcal{C}) is constructed such that the known (pro)-(mathcal{C}) category may be considered as a subcategory of (pro^{*^f})-(mathcal{C}) and that (pro^{*^f})-(mathcal{C}) may be considered as a subcategory of (pro^*)-(mathcal{C}). Analogously to the construction of the shape category (Sh_{(mathcal{C},mathcal{D})}) and the coarse category (Sh^*_{(mathcal{C},mathcal{D})}), an (abstract) finite coarse shape category (Sh^{*^f}_{(mathcal{C},mathcal{D})}) is obtained. Between these three categories appropriate faithful functors are defined. The finite coarse shape is also defined by an intrinsic approach using the notion of the (epsilon)-continuity. The isomorphism of the finite coarse shape categories obtained by these two approaches is constructed. Besides, an overview of some basic properties related to the notion of the (epsilon)-continuity is given.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":"36 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81040806","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
A generalized two-sweep shift splitting methodfor non-Hermitian positive definite linear systems 非厄米正定线性系统的广义双扫描位移分裂方法
IF 0.4 4区 数学
Glasnik Matematicki Pub Date : 2022-06-28 DOI: 10.3336/gm.57.1.10
Shiliang Wu, Cuixia Li
{"title":"A generalized two-sweep shift splitting method\u0000for non-Hermitian positive definite linear systems","authors":"Shiliang Wu, Cuixia Li","doi":"10.3336/gm.57.1.10","DOIUrl":"https://doi.org/10.3336/gm.57.1.10","url":null,"abstract":"In this paper, based on the shift splitting of the\u0000coefficient matrix, a generalized two-sweep shift splitting (GTSS)\u0000method is introduced to solve the non-Hermitian positive definite\u0000linear systems. Theoretical analysis shows that the GTSS method is\u0000convergent to the unique solution of the linear systems under a\u0000loose restriction on the iteration parameter. Numerical experiments\u0000are reported to the efficiency of the GTSS method.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":"88 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79386358","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
Exponential moments of simultaneous hitting time for non-atomic Markov chains 非原子马尔可夫链同时撞击时间的指数矩
IF 0.4 4区 数学
Glasnik Matematicki Pub Date : 2022-06-28 DOI: 10.3336/gm.57.1.09
V. Golomoziy
{"title":"Exponential moments of simultaneous hitting time for non-atomic Markov chains","authors":"V. Golomoziy","doi":"10.3336/gm.57.1.09","DOIUrl":"https://doi.org/10.3336/gm.57.1.09","url":null,"abstract":"This paper is devoted to studying the first simultaneous hitting time of a given set by two discrete-time, inhomogeneous Markov chains with values in general phase space. Established conditions for the existence of the hitting time's exponential moment. Computable bounds for the exponential moment are obtained under the condition of stochastic dominance.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":"28 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89365397","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
Three kinds of numerical indices of (l_p)-spaces (l_p) -空间的三种数值指标
IF 0.4 4区 数学
Glasnik Matematicki Pub Date : 2022-06-28 DOI: 10.3336/gm.57.1.04
Sung Guen Kim
{"title":"Three kinds of numerical indices of (l_p)-spaces","authors":"Sung Guen Kim","doi":"10.3336/gm.57.1.04","DOIUrl":"https://doi.org/10.3336/gm.57.1.04","url":null,"abstract":"In this paper, we investigate the polynomial numerical index (n^{(k)}(l_p),) the symmetric multilinear numerical index\u0000(n_s^{(k)}(l_p),) and the multilinear numerical index (n_m^{(k)}(l_p)) of (l_p) spaces, for (1leq pleq infty.) First we prove that (n_{s}^{(k)}(l_1)=n_{m}^{(k)}(l_1)=1,) for every (kgeq 2.)\u0000We show that for (1 lt p lt infty,) (n_I^{(k)}(l_p^{j+1})leq n_I^{(k)}(l_p^j),) for every (jin mathbb{N}) and (n_I^{(k)}(l_p)=lim_{jto infty}n_I^{(k)}(l_p^j),) for every (I=s, m,) where (l_p^j=(mathbb{C}^j, |cdot|_p)) or ((mathbb{R}^j, |cdot|_p).)\u0000We also show the following inequality between ( n_s^{(k)}(l_p^j)) and (n^{(k)}(l_p^j)): let (1 lt p lt infty) and (kin mathbb{N}) be\u0000fixed. Then\u0000[\u0000\u0000\u0000\u0000c(k: l_p^j)^{-1}~n^{(k)}(l_p^j)leq n_s^{(k)}(l_p^j)leq n^{(k)}(l_p^j),\u0000\u0000\u0000]\u0000for every (jin mathbb{N}cup{infty},) where\u0000(l_p^{infty}:=l_p,)\u0000[\u0000\u0000\u0000\u0000c(k: l_p)=infBig{M>0: |check{Q}|leq M|Q|,mbox{ for every}~Qin {mathcal P}(^k l_p)Big}\u0000\u0000\u0000]\u0000and (check{Q}) denotes the symmetric (k)-linear form associated with (Q.) From this inequality, we deduce that if (l_{p}) is a complex space, then (lim_{jto infty} n_s^{(j)}(l_p)=lim_{jto infty} n_m^{(j)}(l_p)=0,) for every (1lt p lt infty.)","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":"32 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85497616","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
Equivalent topologies on the contracting boundary 契约边界上的等价拓扑
IF 0.4 4区 数学
Glasnik Matematicki Pub Date : 2022-06-16 DOI: 10.3336/gm.58.1.06
Vivian He
{"title":"Equivalent topologies on the contracting boundary","authors":"Vivian He","doi":"10.3336/gm.58.1.06","DOIUrl":"https://doi.org/10.3336/gm.58.1.06","url":null,"abstract":"The contracting boundary of a proper geodesic metric space generalizes the Gromov boundary of a hyperbolic space. It consists of contracting geodesics up to bounded Hausdorff distances. Another generalization of the Gromov boundary is the (kappa)–Morse boundary with a sublinear function (kappa). The two generalizations model the Gromov boundary based on different characteristics of geodesics in Gromov hyperbolic spaces. It was suspected that the (kappa)–Morse boundary contains the contracting boundary. We will prove this conjecture: when (kappa =1) is the constant function, the 1-Morse boundary and the contracting boundary are equivalent as topological spaces.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":"385 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84976005","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: 3
Big flip graphs and their automorphism groups 大翻转图及其自同构群
IF 0.4 4区 数学
Glasnik Matematicki Pub Date : 2022-01-27 DOI: 10.3336/gm.58.1.09
Assaf Bar-Natan, Advay Goel, Brendan Halstead, P. Hamrick, Sumedh Shenoy, R. Verma
{"title":"Big flip graphs and their automorphism groups","authors":"Assaf Bar-Natan, Advay Goel, Brendan Halstead, P. Hamrick, Sumedh Shenoy, R. Verma","doi":"10.3336/gm.58.1.09","DOIUrl":"https://doi.org/10.3336/gm.58.1.09","url":null,"abstract":"In this paper, we study the relationship between the mapping class\u0000 group of an infinite-type surface and the simultaneous flip graph,\u0000 a variant of the flip graph for infinite-type surfaces defined by\u0000 Fossas and Parlier [6]. We show that the extended\u0000 mapping class group is isomorphic to a proper subgroup of the\u0000 automorphism group of the flip graph, unlike in the finite-type\u0000 case. This shows that Ivanov's metaconjecture, which states that\u0000 any “sufficiently rich\" object associated to a finite-type surface\u0000 has the extended mapping class group as its automorphism group, does\u0000 not extend to simultaneous flip graphs of infinite-type surfaces.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":"337 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75792637","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
Pillai's conjecture for polynomials 多项式的皮莱猜想
IF 0.4 4区 数学
Glasnik Matematicki Pub Date : 2022-01-26 DOI: 10.3336/gm.58.1.05
Sebastian Heintze
{"title":"Pillai's conjecture for polynomials","authors":"Sebastian Heintze","doi":"10.3336/gm.58.1.05","DOIUrl":"https://doi.org/10.3336/gm.58.1.05","url":null,"abstract":"In this paper we study the polynomial version of Pillai's conjecture on the exponential Diophantine equation\u0000 \u0000 -17ex p^n - q^m = f.\u0000\u0000 We prove that for any non-constant polynomial ( f ) there are only finitely many quadruples ( (n,m,deg p,deg q) ) consisting of integers ( n,m geq 2 ) and non-constant polynomials ( p,q ) such that Pillai's equation holds.\u0000 Moreover, we will give some examples that there can still be infinitely many possibilities for the polynomials ( p,q ).","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":"60 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73306295","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
On the Ramanujan-Nagell type Diophantine equation (Dx^2+k^n=B) 关于Ramanujan-Nagell型丢番图方程 (Dx^2+k^n=B)
IF 0.4 4区 数学
Glasnik Matematicki Pub Date : 2021-12-23 DOI: 10.3336/gm.56.2.04
Zhong-Can Zhang, A. Togbé
{"title":"On the Ramanujan-Nagell type Diophantine equation (Dx^2+k^n=B)","authors":"Zhong-Can Zhang, A. Togbé","doi":"10.3336/gm.56.2.04","DOIUrl":"https://doi.org/10.3336/gm.56.2.04","url":null,"abstract":"In this paper, we prove that the Ramanujan-Nagell type Diophantine equation (Dx^2+k^n=B) has at most three nonnegative integer solutions ((x, n)) for (k) a prime and (B, D) positive integers.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":"68 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88532954","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
On homotopy nilpotency 关于同伦幂零
IF 0.4 4区 数学
Glasnik Matematicki Pub Date : 2021-12-23 DOI: 10.3336/gm.56.2.10
M. Golasiński
{"title":"On homotopy nilpotency","authors":"M. Golasiński","doi":"10.3336/gm.56.2.10","DOIUrl":"https://doi.org/10.3336/gm.56.2.10","url":null,"abstract":"We review established and recent results on the homotopy nilpotence of spaces. In particular, the homotopy nilpotency of the loop spaces (Omega(G/K)) of homogenous spaces (G/K) for a compact Lie group (G) and its closed homotopy nilpotent subgroup (K lt G) is discussed.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":"2008 12","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72538159","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
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