Pub Date : 2014-05-08DOI: 10.2478/s11533-014-0417-y
W. Fish, R. Fray, E. Mwambene
For k ≥ 1, the odd graph denoted by O(k), is the graph with the vertex-set Ω{k}, the set of all k-subsets of Ω = {1, 2, …, 2k +1}, and any two of its vertices u and v constitute an edge [u, v] if and only if u ∩ v = /0. In this paper the binary code generated by the adjacency matrix of O(k) is studied. The automorphism group of the code is determined, and by identifying a suitable information set, a 2-PD-set of the order of k4 is determined. Lastly, the relationship between the dual code from O(k) and the code from its graph-theoretical complement $overline {O(k)} $, is investigated.
{"title":"Binary codes and partial permutation decoding sets from the odd graphs","authors":"W. Fish, R. Fray, E. Mwambene","doi":"10.2478/s11533-014-0417-y","DOIUrl":"https://doi.org/10.2478/s11533-014-0417-y","url":null,"abstract":"For k ≥ 1, the odd graph denoted by O(k), is the graph with the vertex-set Ω{k}, the set of all k-subsets of Ω = {1, 2, …, 2k +1}, and any two of its vertices u and v constitute an edge [u, v] if and only if u ∩ v = /0. In this paper the binary code generated by the adjacency matrix of O(k) is studied. The automorphism group of the code is determined, and by identifying a suitable information set, a 2-PD-set of the order of k4 is determined. Lastly, the relationship between the dual code from O(k) and the code from its graph-theoretical complement $overline {O(k)} $, is investigated.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"126 1","pages":"1362-1371"},"PeriodicalIF":0.0,"publicationDate":"2014-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86847386","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}
Pub Date : 2014-05-08DOI: 10.2478/s11533-014-0419-9
David G. L. Wang
Generalizing Reiner’s notion of set partitions of type Bn, we define colored Bn-partitions by coloring the elements in and not in the zero-block respectively. Considering the generating function of colored Bn-partitions, we get the exact formulas for the expectation and variance of the number of non-zero-blocks in a random colored Bn-partition. We find an asymptotic expression of the total number of colored Bn-partitions up to an error of O(n−1/2log7/2n], and prove that the centralized and normalized number of non-zero-blocks is asymptotic normal over colored Bn-partitions.
{"title":"On colored set partitions of type Bn","authors":"David G. L. Wang","doi":"10.2478/s11533-014-0419-9","DOIUrl":"https://doi.org/10.2478/s11533-014-0419-9","url":null,"abstract":"Generalizing Reiner’s notion of set partitions of type Bn, we define colored Bn-partitions by coloring the elements in and not in the zero-block respectively. Considering the generating function of colored Bn-partitions, we get the exact formulas for the expectation and variance of the number of non-zero-blocks in a random colored Bn-partition. We find an asymptotic expression of the total number of colored Bn-partitions up to an error of O(n−1/2log7/2n], and prove that the centralized and normalized number of non-zero-blocks is asymptotic normal over colored Bn-partitions.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"304 1","pages":"1372-1381"},"PeriodicalIF":0.0,"publicationDate":"2014-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73190838","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}
Pub Date : 2014-05-08DOI: 10.2478/s11533-014-0410-5
Piotr Bartłomiejczyk, P. Nowak-Przygodzki
We prove that for n > 1 the space of proper maps P0(n, k) and the space of local maps F0(n, k) are not homotopy equivalent.
证明了当n > 1时，固有映射空间P0(n, k)与局部映射空间F0(n, k)不是同伦等价的。
{"title":"On the homotopy equivalence of the spaces of proper and local maps","authors":"Piotr Bartłomiejczyk, P. Nowak-Przygodzki","doi":"10.2478/s11533-014-0410-5","DOIUrl":"https://doi.org/10.2478/s11533-014-0410-5","url":null,"abstract":"We prove that for n > 1 the space of proper maps P0(n, k) and the space of local maps F0(n, k) are not homotopy equivalent.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"190 1","pages":"1330-1336"},"PeriodicalIF":0.0,"publicationDate":"2014-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89037095","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}
Pub Date : 2014-05-08DOI: 10.2478/s11533-014-0414-1
Przemysław Liszka
Very recently bounds for the Lq spectra of inhomogeneous self-similar measures satisfying the Inhomogeneous Open Set Condition (IOSC), being the appropriate version of the standard Open Set Condition (OSC), were obtained. However, if the IOSC is not satisfied, then almost nothing is known for such measures. In the paper we study the Lq spectra and Rényi dimension of generalized inhomogeneous self-similar measures, for which we allow an infinite number of contracting similarities and probabilities depending on positions. As an application of the results, we provide a systematic approach to obtaining non-trivial bounds for the Lq spectra and Rényi dimension of inhomogeneous self-similar measures not satisfying the IOSC and of homogeneous ones not satisfying the OSC. We also provide some non-trivial bounds without any separation conditions.
{"title":"The Lq spectra and Rényi dimension of generalized inhomogeneous self-similar measures","authors":"Przemysław Liszka","doi":"10.2478/s11533-014-0414-1","DOIUrl":"https://doi.org/10.2478/s11533-014-0414-1","url":null,"abstract":"Very recently bounds for the Lq spectra of inhomogeneous self-similar measures satisfying the Inhomogeneous Open Set Condition (IOSC), being the appropriate version of the standard Open Set Condition (OSC), were obtained. However, if the IOSC is not satisfied, then almost nothing is known for such measures. In the paper we study the Lq spectra and Rényi dimension of generalized inhomogeneous self-similar measures, for which we allow an infinite number of contracting similarities and probabilities depending on positions. As an application of the results, we provide a systematic approach to obtaining non-trivial bounds for the Lq spectra and Rényi dimension of inhomogeneous self-similar measures not satisfying the IOSC and of homogeneous ones not satisfying the OSC. We also provide some non-trivial bounds without any separation conditions.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"58 2 1","pages":"1305-1319"},"PeriodicalIF":0.0,"publicationDate":"2014-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90937155","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}
Pub Date : 2014-05-08DOI: 10.2478/s11533-013-0399-1
M. Gromov
Groping our way toward a theory of singular spaces with positive scalar curvatures we look at the Dirac operator and a generalized Plateau problem in Riemannian manifolds with corners. Using these, we prove that the set of C2-smooth Riemannian metrics g on a smooth manifold X, such that scalg(x) ≥ κ(x), is closed under C0-limits of Riemannian metrics for all continuous functions κ on X. Apart from that our progress is limited but we formulate many conjectures. All along, we emphasize geometry, rather than topology of manifolds with their scalar curvatures bounded from below.
{"title":"Dirac and Plateau billiards in domains with corners","authors":"M. Gromov","doi":"10.2478/s11533-013-0399-1","DOIUrl":"https://doi.org/10.2478/s11533-013-0399-1","url":null,"abstract":"Groping our way toward a theory of singular spaces with positive scalar curvatures we look at the Dirac operator and a generalized Plateau problem in Riemannian manifolds with corners. Using these, we prove that the set of C2-smooth Riemannian metrics g on a smooth manifold X, such that scalg(x) ≥ κ(x), is closed under C0-limits of Riemannian metrics for all continuous functions κ on X. Apart from that our progress is limited but we formulate many conjectures. All along, we emphasize geometry, rather than topology of manifolds with their scalar curvatures bounded from below.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"25 1","pages":"1109-1156"},"PeriodicalIF":0.0,"publicationDate":"2014-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80194322","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}
Pub Date : 2014-05-08DOI: 10.2478/s11533-014-0421-2
Augustine O. Munagi
The study of parity-alternating permutations of {1, 2, … n} is extended to permutations containing a prescribed number of parity successions — adjacent pairs of elements of the same parity. Several enumeration formulae are computed for permutations containing a given number of parity successions, in conjunction with further parity and length restrictions. The objects are classified using direct construction and elementary combinatorial techniques. Analogous results are derived for circular permutations.
{"title":"Parity-alternating permutations and successions","authors":"Augustine O. Munagi","doi":"10.2478/s11533-014-0421-2","DOIUrl":"https://doi.org/10.2478/s11533-014-0421-2","url":null,"abstract":"The study of parity-alternating permutations of {1, 2, … n} is extended to permutations containing a prescribed number of parity successions — adjacent pairs of elements of the same parity. Several enumeration formulae are computed for permutations containing a given number of parity successions, in conjunction with further parity and length restrictions. The objects are classified using direct construction and elementary combinatorial techniques. Analogous results are derived for circular permutations.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"14 1","pages":"1390-1402"},"PeriodicalIF":0.0,"publicationDate":"2014-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73310235","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}
Pub Date : 2014-04-16DOI: 10.2478/s11533-014-0405-2
K. Adaricheva, A. Romanowska, Jonathan D. H. Smith
Modes are idempotent and entropic algebras. While the mode structure of sets of submodes has received considerable attention in the past, this paper is devoted to the study of mode structure on sets of mode homomorphisms. Connections between the two constructions are established. A detailed analysis is given for the algebra of homomorphisms from submodes of one mode to submodes of another. In particular, it is shown that such algebras can be decomposed as Płonka sums of more elementary homomorphism algebras. Some critical examples are examined.
{"title":"The algebra of mode homomorphisms","authors":"K. Adaricheva, A. Romanowska, Jonathan D. H. Smith","doi":"10.2478/s11533-014-0405-2","DOIUrl":"https://doi.org/10.2478/s11533-014-0405-2","url":null,"abstract":"Modes are idempotent and entropic algebras. While the mode structure of sets of submodes has received considerable attention in the past, this paper is devoted to the study of mode structure on sets of mode homomorphisms. Connections between the two constructions are established. A detailed analysis is given for the algebra of homomorphisms from submodes of one mode to submodes of another. In particular, it is shown that such algebras can be decomposed as Płonka sums of more elementary homomorphism algebras. Some critical examples are examined.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"14 1","pages":"1265-1277"},"PeriodicalIF":0.0,"publicationDate":"2014-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81930977","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}
Pub Date : 2014-04-16DOI: 10.2478/s11533-014-0408-z
R. Skiba
We construct a cohomological index of the Fuller type for set-valued flows in normed linear spaces satisfying the properties of existence, excision, additivity, homotopy and topological invariance. In particular, the constructed index detects periodic orbits and stationary points of set-valued dynamical systems, i.e., those generated by differential inclusions. The basic methods to calculate the index are also presented.
{"title":"A cohomological index of Fuller type for parameterized set-valued maps in normed spaces","authors":"R. Skiba","doi":"10.2478/s11533-014-0408-z","DOIUrl":"https://doi.org/10.2478/s11533-014-0408-z","url":null,"abstract":"We construct a cohomological index of the Fuller type for set-valued flows in normed linear spaces satisfying the properties of existence, excision, additivity, homotopy and topological invariance. In particular, the constructed index detects periodic orbits and stationary points of set-valued dynamical systems, i.e., those generated by differential inclusions. The basic methods to calculate the index are also presented.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"137 1","pages":"1164-1197"},"PeriodicalIF":0.0,"publicationDate":"2014-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86360499","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}
Pub Date : 2014-04-04DOI: 10.2478/s11533-014-0401-6
A. Osȩkowski
We study sharp weak-type inequalities for a wide class of Fourier multipliers resulting from modulation of the jumps of Lévy processes. In particular, we obtain optimal estimates for second-order Riesz transforms, which lead to interesting a priori bounds for smooth functions on ℝd. The proofs rest on probabilistic methods: we deduce the above inequalities from the corresponding estimates for martingales. To obtain the lower bounds, we exploit the properties of laminates, important probability measures on the space of matrices of dimension 2×2, and some transference-type arguments.
{"title":"Sharp weak-type inequalities for Fourier multipliers and second-order Riesz transforms","authors":"A. Osȩkowski","doi":"10.2478/s11533-014-0401-6","DOIUrl":"https://doi.org/10.2478/s11533-014-0401-6","url":null,"abstract":"We study sharp weak-type inequalities for a wide class of Fourier multipliers resulting from modulation of the jumps of Lévy processes. In particular, we obtain optimal estimates for second-order Riesz transforms, which lead to interesting a priori bounds for smooth functions on ℝd. The proofs rest on probabilistic methods: we deduce the above inequalities from the corresponding estimates for martingales. To obtain the lower bounds, we exploit the properties of laminates, important probability measures on the space of matrices of dimension 2×2, and some transference-type arguments.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"24 1","pages":"1198-1213"},"PeriodicalIF":0.0,"publicationDate":"2014-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81791518","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}
Pub Date : 2014-04-04DOI: 10.2478/s11533-014-0403-4
I. Biswas, A. Hogadi, Yogish I. Holla
Let X be an irreducible smooth complex projective curve of genus g, with g ≥ 2. Let N be a connected component of the moduli space of semistable principal PGLr (ℂ)-bundles over X; it is a normal unirational complex projective variety. We prove that the Brauer group of a desingularization of N is trivial.
{"title":"Unramified Brauer group of the moduli spaces of PGLr(ℂ)-bundles over curves","authors":"I. Biswas, A. Hogadi, Yogish I. Holla","doi":"10.2478/s11533-014-0403-4","DOIUrl":"https://doi.org/10.2478/s11533-014-0403-4","url":null,"abstract":"Let X be an irreducible smooth complex projective curve of genus g, with g ≥ 2. Let N be a connected component of the moduli space of semistable principal PGLr (ℂ)-bundles over X; it is a normal unirational complex projective variety. We prove that the Brauer group of a desingularization of N is trivial.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"1 1","pages":"1157-1163"},"PeriodicalIF":0.0,"publicationDate":"2014-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89611897","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}
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