Pub Date : 2013-08-08DOI: 10.2478/s11533-013-0400-z
Marek Cúth, O. Kalenda
We compare two methods of proving separable reduction theorems in functional analysis — the method of rich families and the method of elementary submodels. We show that any result proved using rich families holds also when formulated with elementary submodels and the converse is true in spaces with fundamental minimal system and in spaces of density ℵ1. We do not know whether the converse is true in general. We apply our results to show that a projectional skeleton may be without loss of generality indexed by ranges of its projections.
{"title":"Rich families and elementary submodels","authors":"Marek Cúth, O. Kalenda","doi":"10.2478/s11533-013-0400-z","DOIUrl":"https://doi.org/10.2478/s11533-013-0400-z","url":null,"abstract":"We compare two methods of proving separable reduction theorems in functional analysis — the method of rich families and the method of elementary submodels. We show that any result proved using rich families holds also when formulated with elementary submodels and the converse is true in spaces with fundamental minimal system and in spaces of density ℵ1. We do not know whether the converse is true in general. We apply our results to show that a projectional skeleton may be without loss of generality indexed by ranges of its projections.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"48 1","pages":"1026-1039"},"PeriodicalIF":0.0,"publicationDate":"2013-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85659173","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 : 2013-08-08DOI: 10.2478/s11533-013-0294-9
Horaţiu-Vasile Boncea, S. Grad
In this paper we present different regularity conditions that equivalently characterize various ɛ-duality gap statements (with ɛ ≥ 0) for constrained optimization problems and their Lagrange and Fenchel-Lagrange duals in separated locally convex spaces, respectively. These regularity conditions are formulated by using epigraphs and ɛ-subdifferentials. When ɛ = 0 we rediscover recent results on stable strong and total duality and zero duality gap from the literature.
{"title":"Characterizations of ɛ-duality gap statements for constrained optimization problems","authors":"Horaţiu-Vasile Boncea, S. Grad","doi":"10.2478/s11533-013-0294-9","DOIUrl":"https://doi.org/10.2478/s11533-013-0294-9","url":null,"abstract":"In this paper we present different regularity conditions that equivalently characterize various ɛ-duality gap statements (with ɛ ≥ 0) for constrained optimization problems and their Lagrange and Fenchel-Lagrange duals in separated locally convex spaces, respectively. These regularity conditions are formulated by using epigraphs and ɛ-subdifferentials. When ɛ = 0 we rediscover recent results on stable strong and total duality and zero duality gap from the literature.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"1 1","pages":"2020-2033"},"PeriodicalIF":0.0,"publicationDate":"2013-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79657406","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 : 2013-07-20DOI: 10.2478/s11533-013-0285-x
Vajk Szécsi
A nearly sharp lower bound on the length of the longest trail in a graph on n vertices and average degree k is given provided the graph is dense enough (k ≥ 12.5).
如果图足够密集(k≥12.5)，则给出n个顶点且平均度为k的图中最长轨迹长度的近似下界。
{"title":"On the minimal length of the longest trail in a fixed edge-density graph","authors":"Vajk Szécsi","doi":"10.2478/s11533-013-0285-x","DOIUrl":"https://doi.org/10.2478/s11533-013-0285-x","url":null,"abstract":"A nearly sharp lower bound on the length of the longest trail in a graph on n vertices and average degree k is given provided the graph is dense enough (k ≥ 12.5).","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"7 1","pages":"1831-1837"},"PeriodicalIF":0.0,"publicationDate":"2013-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89121569","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 : 2013-07-20DOI: 10.2478/s11533-013-0286-9
A. Cantón, A. Granados, D. Pestana, José M. Rodríguez
We prove that under appropriate assumptions adding or removing an infinite amount of edges to a given planar graph preserves its non-hyperbolicity, a result which is shown to be false in general. In particular, we make a conjecture that every tessellation graph of ℝ2 with convex tiles is non-hyperbolic; it is shown that in order to prove this conjecture it suffices to consider tessellation graphs of ℝ2 such that every tile is a triangle and a partial answer to this question is given. A weaker version of this conjecture stating that every tessellation graph of ℝ2 with rectangular tiles is non-hyperbolic is given and partially answered. If this conjecture were true, many tessellation graphs of ℝ2 with tiles which are parallelograms would be non-hyperbolic.
{"title":"Gromov hyperbolicity of planar graphs","authors":"A. Cantón, A. Granados, D. Pestana, José M. Rodríguez","doi":"10.2478/s11533-013-0286-9","DOIUrl":"https://doi.org/10.2478/s11533-013-0286-9","url":null,"abstract":"We prove that under appropriate assumptions adding or removing an infinite amount of edges to a given planar graph preserves its non-hyperbolicity, a result which is shown to be false in general. In particular, we make a conjecture that every tessellation graph of ℝ2 with convex tiles is non-hyperbolic; it is shown that in order to prove this conjecture it suffices to consider tessellation graphs of ℝ2 such that every tile is a triangle and a partial answer to this question is given. A weaker version of this conjecture stating that every tessellation graph of ℝ2 with rectangular tiles is non-hyperbolic is given and partially answered. If this conjecture were true, many tessellation graphs of ℝ2 with tiles which are parallelograms would be non-hyperbolic.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"45 1","pages":"1817-1830"},"PeriodicalIF":0.0,"publicationDate":"2013-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84210938","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 : 2013-07-20DOI: 10.2478/s11533-013-0281-1
D. Stankov, Tzonio G. Tzonev
In this paper we consider several conditions for sequences of points in M(H∞) and establish relations between them. We show that every interpolating sequence for QA of nontrivial points in the corona $$M(H^infty )backslash mathbb{D}$$ of H∞ is a thin sequence for H∞, which satisfies an additional topological condition. The discrete sequences in the Shilov boundary of H∞ necessarily satisfy the same condition.
{"title":"Thin sequences in the corona of H∞","authors":"D. Stankov, Tzonio G. Tzonev","doi":"10.2478/s11533-013-0281-1","DOIUrl":"https://doi.org/10.2478/s11533-013-0281-1","url":null,"abstract":"In this paper we consider several conditions for sequences of points in M(H∞) and establish relations between them. We show that every interpolating sequence for QA of nontrivial points in the corona $$M(H^infty )backslash mathbb{D}$$ of H∞ is a thin sequence for H∞, which satisfies an additional topological condition. The discrete sequences in the Shilov boundary of H∞ necessarily satisfy the same condition.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"25 1","pages":"1843-1849"},"PeriodicalIF":0.0,"publicationDate":"2013-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75574131","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 : 2013-07-20DOI: 10.2478/s11533-013-0288-7
C. Bardaro, A. Boccuto, X. Dimitriou, I. Mantellini
We prove some versions of abstract Korovkin-type theorems in modular function spaces, with respect to filter convergence for linear positive operators, by considering several kinds of test functions. We give some results with respect to an axiomatic convergence, including almost convergence. An extension to non positive operators is also studied. Finally, we give some examples and applications to moment and bivariate Kantorovich-type operators, showing that our results are proper extensions of the corresponding classical ones.
{"title":"Abstract Korovkin-type theorems in modular spaces and applications","authors":"C. Bardaro, A. Boccuto, X. Dimitriou, I. Mantellini","doi":"10.2478/s11533-013-0288-7","DOIUrl":"https://doi.org/10.2478/s11533-013-0288-7","url":null,"abstract":"We prove some versions of abstract Korovkin-type theorems in modular function spaces, with respect to filter convergence for linear positive operators, by considering several kinds of test functions. We give some results with respect to an axiomatic convergence, including almost convergence. An extension to non positive operators is also studied. Finally, we give some examples and applications to moment and bivariate Kantorovich-type operators, showing that our results are proper extensions of the corresponding classical ones.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"3 1","pages":"1774-1784"},"PeriodicalIF":0.0,"publicationDate":"2013-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81882343","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 : 2013-07-20DOI: 10.2478/s11533-013-0284-y
L. A. Kurdachenko, J. Otal
We compare the special rank of the factors of the upper central series and terms of the lower central series of a group. As a consequence we are able to show some generalizations of a theorem of Reinhold Baer.
{"title":"The rank of the factor-group modulo the hypercenter and the rank of the some hypocenter of a group","authors":"L. A. Kurdachenko, J. Otal","doi":"10.2478/s11533-013-0284-y","DOIUrl":"https://doi.org/10.2478/s11533-013-0284-y","url":null,"abstract":"We compare the special rank of the factors of the upper central series and terms of the lower central series of a group. As a consequence we are able to show some generalizations of a theorem of Reinhold Baer.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"105 1","pages":"1732-1741"},"PeriodicalIF":0.0,"publicationDate":"2013-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85880767","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 : 2013-07-20DOI: 10.2478/s11533-013-0287-8
P. Hegedus
This paper deals with a rationality condition for groups. Let n be a fixed positive integer. Suppose every element g of the finite solvable group is conjugate to its nth power gn. Let p be a prime divisor of the order of the group. We conclude that the multiplicative order of n modulo p is small, or p is small.
{"title":"Groups where each element is conjugate to its certain power","authors":"P. Hegedus","doi":"10.2478/s11533-013-0287-8","DOIUrl":"https://doi.org/10.2478/s11533-013-0287-8","url":null,"abstract":"This paper deals with a rationality condition for groups. Let n be a fixed positive integer. Suppose every element g of the finite solvable group is conjugate to its nth power gn. Let p be a prime divisor of the order of the group. We conclude that the multiplicative order of n modulo p is small, or p is small.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"1 1","pages":"1742-1749"},"PeriodicalIF":0.0,"publicationDate":"2013-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89696210","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 : 2013-07-04DOI: 10.2478/s11533-013-0279-8
O. Okunev
We prove that the one-point Lindelöfication of a discrete space of cardinality ω1 is homeomorphic to a subspace of Cp(X) for some hereditarily Lindelöf space X if the axiom holds.
{"title":"The one-point Lindelöfication of an uncountable discrete space can be surlindelöf","authors":"O. Okunev","doi":"10.2478/s11533-013-0279-8","DOIUrl":"https://doi.org/10.2478/s11533-013-0279-8","url":null,"abstract":"We prove that the one-point Lindelöfication of a discrete space of cardinality ω1 is homeomorphic to a subspace of Cp(X) for some hereditarily Lindelöf space X if the axiom holds.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"54 18","pages":"1750-1754"},"PeriodicalIF":0.0,"publicationDate":"2013-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2478/s11533-013-0279-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72492445","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 : 2013-07-04DOI: 10.2478/s11533-013-0280-2
J. Koo, D. Shin
We present some completely normal elements in the maximal real subfields of cyclotomic fields over the field of rational numbers, relying on the criterion for normal element developed in [Jung H.Y., Koo J.K., Shin D.H., Normal bases of ray class fields over imaginary quadratic fields, Math. Z., 2012, 271(1–2), 109–116]. And, we further find completely normal elements in certain abelian extensions of modular function fields in terms of Siegel functions.
{"title":"Completely normal elements in some finite abelian extensions","authors":"J. Koo, D. Shin","doi":"10.2478/s11533-013-0280-2","DOIUrl":"https://doi.org/10.2478/s11533-013-0280-2","url":null,"abstract":"We present some completely normal elements in the maximal real subfields of cyclotomic fields over the field of rational numbers, relying on the criterion for normal element developed in [Jung H.Y., Koo J.K., Shin D.H., Normal bases of ray class fields over imaginary quadratic fields, Math. Z., 2012, 271(1–2), 109–116]. And, we further find completely normal elements in certain abelian extensions of modular function fields in terms of Siegel functions.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"13 1","pages":"1725-1731"},"PeriodicalIF":0.0,"publicationDate":"2013-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78116741","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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