Pub Date : 2013-09-04DOI: 10.2478/s11533-013-0306-9
J. Jaros, K. Takaši, J. Manojlovic
Positive solutions of the nonlinear second-order differential equation $(p(t)|x'|^{alpha - 1} x')' + q(t)|x|^{beta - 1} x = 0,alpha > beta > 0,$ are studied under the assumption that p, q are generalized regularly varying functions. An application of the theory of regular variation gives the possibility of obtaining necessary and sufficient conditions for existence of three possible types of intermediate solutions, together with the precise information about asymptotic behavior at infinity of all solutions belonging to each type of solution classes.
{"title":"Asymptotic analysis of positive solutions of generalized Emden-Fowler differential equations in the framework of regular variation","authors":"J. Jaros, K. Takaši, J. Manojlovic","doi":"10.2478/s11533-013-0306-9","DOIUrl":"https://doi.org/10.2478/s11533-013-0306-9","url":null,"abstract":"Positive solutions of the nonlinear second-order differential equation $(p(t)|x'|^{alpha - 1} x')' + q(t)|x|^{beta - 1} x = 0,alpha > beta > 0,$ are studied under the assumption that p, q are generalized regularly varying functions. An application of the theory of regular variation gives the possibility of obtaining necessary and sufficient conditions for existence of three possible types of intermediate solutions, together with the precise information about asymptotic behavior at infinity of all solutions belonging to each type of solution classes.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"23 1","pages":"2215-2233"},"PeriodicalIF":0.0,"publicationDate":"2013-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87082806","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 : 2013-09-04DOI: 10.2478/s11533-013-0307-8
N. I. Zhukova, A. Y. Dolgonosova
The category of foliations is considered. In this category morphisms are differentiable maps sending leaves of one foliation into leaves of the other foliation. We prove that the automorphism group of a foliation with transverse linear connection is an infinite-dimensional Lie group modeled on LF-spaces. This result extends the corresponding result of Macias-Virgós and Sanmartín Carbón for Riemannian foliations. In particular, our result is valid for Lorentzian and pseudo-Riemannian foliations.
{"title":"The automorphism groups of foliations with transverse linear connection","authors":"N. I. Zhukova, A. Y. Dolgonosova","doi":"10.2478/s11533-013-0307-8","DOIUrl":"https://doi.org/10.2478/s11533-013-0307-8","url":null,"abstract":"The category of foliations is considered. In this category morphisms are differentiable maps sending leaves of one foliation into leaves of the other foliation. We prove that the automorphism group of a foliation with transverse linear connection is an infinite-dimensional Lie group modeled on LF-spaces. This result extends the corresponding result of Macias-Virgós and Sanmartín Carbón for Riemannian foliations. In particular, our result is valid for Lorentzian and pseudo-Riemannian foliations.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"56 1","pages":"2076-2088"},"PeriodicalIF":0.0,"publicationDate":"2013-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80224320","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 : 2013-08-23DOI: 10.2478/s11533-013-0299-4
A. Ballester-Bolinches, Enric Cosme Llópez, R. Esteban-Romero
In this paper we describe some algorithms to identify permutable and Sylow-permutable subgroups of finite groups, Dedekind and Iwasawa finite groups, and finite T-groups (groups in which normality is transitive), PT-groups (groups in which permutability is transitive), and PST-groups (groups in which Sylow permutability is transitive). These algorithms have been implemented in a package for the computer algebra system GAP.
{"title":"Algorithms for permutability in finite groups","authors":"A. Ballester-Bolinches, Enric Cosme Llópez, R. Esteban-Romero","doi":"10.2478/s11533-013-0299-4","DOIUrl":"https://doi.org/10.2478/s11533-013-0299-4","url":null,"abstract":"In this paper we describe some algorithms to identify permutable and Sylow-permutable subgroups of finite groups, Dedekind and Iwasawa finite groups, and finite T-groups (groups in which normality is transitive), PT-groups (groups in which permutability is transitive), and PST-groups (groups in which Sylow permutability is transitive). These algorithms have been implemented in a package for the computer algebra system GAP.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"81 4","pages":"1914-1922"},"PeriodicalIF":0.0,"publicationDate":"2013-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2478/s11533-013-0299-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72435446","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 : 2013-08-23DOI: 10.2478/s11533-013-0304-y
A. Rozkosz
We consider the Cauchy problem for an infinite-dimensional Ornstein-Uhlenbeck equation perturbed by gradient of a potential. We prove some results on existence and uniqueness of mild solutions of the problem. We also provide stochastic representation of mild solutions in terms of linear backward stochastic differential equations determined by the Ornstein-Uhlenbeck operator and the potential.
{"title":"On mild solutions of gradient systems in Hilbert spaces","authors":"A. Rozkosz","doi":"10.2478/s11533-013-0304-y","DOIUrl":"https://doi.org/10.2478/s11533-013-0304-y","url":null,"abstract":"We consider the Cauchy problem for an infinite-dimensional Ornstein-Uhlenbeck equation perturbed by gradient of a potential. We prove some results on existence and uniqueness of mild solutions of the problem. We also provide stochastic representation of mild solutions in terms of linear backward stochastic differential equations determined by the Ornstein-Uhlenbeck operator and the potential.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"2012 1","pages":"1994-2004"},"PeriodicalIF":0.0,"publicationDate":"2013-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78688017","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 : 2013-08-23DOI: 10.2478/s11533-013-0298-5
S. Burciu
A description of the commutator of a normal subcategory of the fusion category of representation Rep A of a semisimple Hopf algebra A is given. Formulae for the kernels of representations of Drinfeld doubles D(G) of finite groups G are presented. It is shown that all these kernels are normal Hopf subalgebras.
{"title":"Kernels of representations of Drinfeld doubles of finite groups","authors":"S. Burciu","doi":"10.2478/s11533-013-0298-5","DOIUrl":"https://doi.org/10.2478/s11533-013-0298-5","url":null,"abstract":"A description of the commutator of a normal subcategory of the fusion category of representation Rep A of a semisimple Hopf algebra A is given. Formulae for the kernels of representations of Drinfeld doubles D(G) of finite groups G are presented. It is shown that all these kernels are normal Hopf subalgebras.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"56 16","pages":"1900-1913"},"PeriodicalIF":0.0,"publicationDate":"2013-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2478/s11533-013-0298-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72537108","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 : 2013-08-23DOI: 10.2478/s11533-013-0291-z
D. Halverson, Dušan D. Repovš
We show that all finite-dimensional resolvable generalized manifolds with the piecewise disjoint arc-disk property are codimension one manifold factors. We then show how the piecewise disjoint arc-disk property and other general position properties that detect codimension one manifold factors are related. We also note that in every example presently known to the authors of a codimension one manifold factor of dimension n ≥ 4 determined by general position properties, the piecewise disjoint arc-disk property is satisfied.
{"title":"Detecting codimension one manifold factors with the piecewise disjoint arc-disk property and related properties","authors":"D. Halverson, Dušan D. Repovš","doi":"10.2478/s11533-013-0291-z","DOIUrl":"https://doi.org/10.2478/s11533-013-0291-z","url":null,"abstract":"We show that all finite-dimensional resolvable generalized manifolds with the piecewise disjoint arc-disk property are codimension one manifold factors. We then show how the piecewise disjoint arc-disk property and other general position properties that detect codimension one manifold factors are related. We also note that in every example presently known to the authors of a codimension one manifold factor of dimension n ≥ 4 determined by general position properties, the piecewise disjoint arc-disk property is satisfied.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"67 1","pages":"1932-1948"},"PeriodicalIF":0.0,"publicationDate":"2013-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75359974","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 : 2013-08-23DOI: 10.2478/s11533-013-0301-1
L. S. Efremova, G. Freiling
We consider Sturm-Liouville differential operators on a finite interval with discontinuous potentials having one jump. As the main result we obtain a procedure of recovering the location of the discontinuity and the height of the jump. Using our result, we apply a generalized Rundell-Sacks algorithm of Rafler and Böckmann for a more effective reconstruction of the potential and present some numerical examples.
{"title":"Numerical solution of inverse spectral problems for Sturm-Liouville operators with discontinuous potentials","authors":"L. S. Efremova, G. Freiling","doi":"10.2478/s11533-013-0301-1","DOIUrl":"https://doi.org/10.2478/s11533-013-0301-1","url":null,"abstract":"We consider Sturm-Liouville differential operators on a finite interval with discontinuous potentials having one jump. As the main result we obtain a procedure of recovering the location of the discontinuity and the height of the jump. Using our result, we apply a generalized Rundell-Sacks algorithm of Rafler and Böckmann for a more effective reconstruction of the potential and present some numerical examples.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"102 1","pages":"2044-2051"},"PeriodicalIF":0.0,"publicationDate":"2013-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75888292","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 : 2013-08-23DOI: 10.2478/s11533-013-0300-2
J. Zieliński
Lotka-Volterra systems appear in population biology, plasma physics, laser physics and derivation theory, among many others. We determine the rings of constants of four-variable Lotka-Volterra derivations with four parameters C1, C2, C3, C4 ∈ k, where k is a field of characteristic zero. Thus, we give a full description of polynomial first integrals of the respective systems of differential equations.
{"title":"Rings of constants of four-variable Lotka-Volterra systems","authors":"J. Zieliński","doi":"10.2478/s11533-013-0300-2","DOIUrl":"https://doi.org/10.2478/s11533-013-0300-2","url":null,"abstract":"Lotka-Volterra systems appear in population biology, plasma physics, laser physics and derivation theory, among many others. We determine the rings of constants of four-variable Lotka-Volterra derivations with four parameters C1, C2, C3, C4 ∈ k, where k is a field of characteristic zero. Thus, we give a full description of polynomial first integrals of the respective systems of differential equations.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"15 1","pages":"1923-1931"},"PeriodicalIF":0.0,"publicationDate":"2013-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81688667","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 : 2013-08-23DOI: 10.2478/s11533-013-0303-z
Arya Jamshidi, F. Sady
In this paper we first consider a real-linear isometry T from a certain subspace A of C(X) (endowed with supremum norm) into C(Y) where X and Y are compact Hausdorff spaces and give a result concerning the description of T whenever A is a uniform algebra on X. The result is improved for the case where T(A) is, in addition, a complex subspace of C(Y). We also give a similar description for the case where A is a function space on X and the range of T is a real subspace of C(Y) satisfying a ceratin separating property. Next similar results are obtained for real-linear isometries between spaces of Lipschitz functions on compact metric spaces endowed with a certain complete norm.
{"title":"Real-linear isometries between certain subspaces of continuous functions","authors":"Arya Jamshidi, F. Sady","doi":"10.2478/s11533-013-0303-z","DOIUrl":"https://doi.org/10.2478/s11533-013-0303-z","url":null,"abstract":"In this paper we first consider a real-linear isometry T from a certain subspace A of C(X) (endowed with supremum norm) into C(Y) where X and Y are compact Hausdorff spaces and give a result concerning the description of T whenever A is a uniform algebra on X. The result is improved for the case where T(A) is, in addition, a complex subspace of C(Y). We also give a similar description for the case where A is a function space on X and the range of T is a real subspace of C(Y) satisfying a ceratin separating property. Next similar results are obtained for real-linear isometries between spaces of Lipschitz functions on compact metric spaces endowed with a certain complete norm.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"117 1","pages":"2034-2043"},"PeriodicalIF":0.0,"publicationDate":"2013-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89117877","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 : 2013-08-23DOI: 10.2478/s11533-013-0302-0
W. Rump
The concept of quantale was created in 1984 to develop a framework for non-commutative spaces and quantum mechanics with a view toward non-commutative logic. The logic of quantales and its algebraic semantics manifests itself in a class of partially ordered algebras with a pair of implicational operations recently introduced as quantum B-algebras. Implicational algebras like pseudo-effect algebras, generalized BL- or MV-algebras, partially ordered groups, pseudo-BCK algebras, residuated posets, cone algebras, etc., are quantum B-algebras, and every quantum B-algebra can be recovered from its spectrum which is a quantale. By a two-fold application of the functor “spectrum”, it is shown that quantum B-algebras have a completion which is again a quantale. Every quantale Q is a quantum B-algebra, and its spectrum is a bigger quantale which repairs the deficiency of the inverse residuals of Q. The connected components of a quantum B-algebra are shown to be a group, a fact that applies to normal quantum B-algebras arising in algebraic number theory, as well as to pseudo-BCI algebras and quantum BL-algebras. The logic of quantum B-algebras is shown to be complete.
{"title":"Quantum B-algebras","authors":"W. Rump","doi":"10.2478/s11533-013-0302-0","DOIUrl":"https://doi.org/10.2478/s11533-013-0302-0","url":null,"abstract":"The concept of quantale was created in 1984 to develop a framework for non-commutative spaces and quantum mechanics with a view toward non-commutative logic. The logic of quantales and its algebraic semantics manifests itself in a class of partially ordered algebras with a pair of implicational operations recently introduced as quantum B-algebras. Implicational algebras like pseudo-effect algebras, generalized BL- or MV-algebras, partially ordered groups, pseudo-BCK algebras, residuated posets, cone algebras, etc., are quantum B-algebras, and every quantum B-algebra can be recovered from its spectrum which is a quantale. By a two-fold application of the functor “spectrum”, it is shown that quantum B-algebras have a completion which is again a quantale. Every quantale Q is a quantum B-algebra, and its spectrum is a bigger quantale which repairs the deficiency of the inverse residuals of Q. The connected components of a quantum B-algebra are shown to be a group, a fact that applies to normal quantum B-algebras arising in algebraic number theory, as well as to pseudo-BCI algebras and quantum BL-algebras. The logic of quantum B-algebras is shown to be complete.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"24 1","pages":"1881-1899"},"PeriodicalIF":0.0,"publicationDate":"2013-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75982337","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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