Pub Date : 2014-01-10DOI: 10.2478/s11533-013-0367-9
L. Olszowy
This paper is concerned with the existence of mild solutions for impulsive semilinear differential equations with nonlocal conditions. Using the technique of measures of noncompactness in Banach and Fréchet spaces of piecewise continuous functions, existence results are obtained both on bounded and unbounded intervals, when the impulsive functions and the nonlocal item are not compact in the space of piecewise continuous functions but they are continuous and Lipschitzian with respect to some measure of noncompactness, and the linear part generates only a strongly continuous evolution system.
{"title":"Existence of mild solutions for semilinear differential equations with nonlocal and impulsive conditions","authors":"L. Olszowy","doi":"10.2478/s11533-013-0367-9","DOIUrl":"https://doi.org/10.2478/s11533-013-0367-9","url":null,"abstract":"This paper is concerned with the existence of mild solutions for impulsive semilinear differential equations with nonlocal conditions. Using the technique of measures of noncompactness in Banach and Fréchet spaces of piecewise continuous functions, existence results are obtained both on bounded and unbounded intervals, when the impulsive functions and the nonlocal item are not compact in the space of piecewise continuous functions but they are continuous and Lipschitzian with respect to some measure of noncompactness, and the linear part generates only a strongly continuous evolution system.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"49 1","pages":"623-635"},"PeriodicalIF":0.0,"publicationDate":"2014-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76253032","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 : 2014-01-03DOI: 10.2478/s11533-013-0364-z
J. Ndogmo, F. Mahomed
An expression for the coefficients of a linear iterative equation in terms of the parameters of the source equation is given both for equations in standard form and for equations in reduced normal form. The operator that generates an iterative equation of a general order in reduced normal form is also obtained and some other properties of iterative equations are established. An expression for the parameters of the source equation of the transformed equation under equivalence transformations is obtained, and this gives rise to the derivation of important symmetry properties for iterative equations. The transformation mapping a given iterative equation to the canonical form is obtained in terms of the simplest determining equation, and several examples of application are discussed.
{"title":"On certain properties of linear iterative equations","authors":"J. Ndogmo, F. Mahomed","doi":"10.2478/s11533-013-0364-z","DOIUrl":"https://doi.org/10.2478/s11533-013-0364-z","url":null,"abstract":"An expression for the coefficients of a linear iterative equation in terms of the parameters of the source equation is given both for equations in standard form and for equations in reduced normal form. The operator that generates an iterative equation of a general order in reduced normal form is also obtained and some other properties of iterative equations are established. An expression for the parameters of the source equation of the transformed equation under equivalence transformations is obtained, and this gives rise to the derivation of important symmetry properties for iterative equations. The transformation mapping a given iterative equation to the canonical form is obtained in terms of the simplest determining equation, and several examples of application are discussed.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"103 1","pages":"648-657"},"PeriodicalIF":0.0,"publicationDate":"2014-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72877069","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 : 2013-10-08DOI: 10.2478/s11533-013-0311-z
L. Holá
We show that a completely regular space Y is a p-space (a Čech-complete space, a locally compact space) if and only if given a dense subspace A of any topological space X and a continuous f: A → Y there are a p-embedded subset (resp. a Gδ-subset, an open subset) M of X containing A and a quasicontinuous subcontinuous extension f*: M → Y of f continuous at every point of A. A result concerning a continuous extension to a residual set is also given.
{"title":"Functional characterizations of p-spaces","authors":"L. Holá","doi":"10.2478/s11533-013-0311-z","DOIUrl":"https://doi.org/10.2478/s11533-013-0311-z","url":null,"abstract":"We show that a completely regular space Y is a p-space (a Čech-complete space, a locally compact space) if and only if given a dense subspace A of any topological space X and a continuous f: A → Y there are a p-embedded subset (resp. a Gδ-subset, an open subset) M of X containing A and a quasicontinuous subcontinuous extension f*: M → Y of f continuous at every point of A. A result concerning a continuous extension to a residual set is also given.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"48 1","pages":"2197-2202"},"PeriodicalIF":0.0,"publicationDate":"2013-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87956089","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 : 2013-10-08DOI: 10.2478/s11533-013-0319-4
T. Preu
We give explicit formulas for reducing the problem of determining whether a given 2-cocycle is a coboundary and if so finding a lifting 1-cochain to a system of norm equations.
{"title":"Effective lifting of 2-cocycles for Galois cohomology","authors":"T. Preu","doi":"10.2478/s11533-013-0319-4","DOIUrl":"https://doi.org/10.2478/s11533-013-0319-4","url":null,"abstract":"We give explicit formulas for reducing the problem of determining whether a given 2-cocycle is a coboundary and if so finding a lifting 1-cochain to a system of norm equations.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"95 1","pages":"2138-2149"},"PeriodicalIF":0.0,"publicationDate":"2013-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91199149","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 : 2013-10-08DOI: 10.2478/s11533-013-0313-x
I. Protasov
Let G be a group and PG be the Boolean algebra of all subsets of G. A mapping Δ: PG → PG defined by Δ(A) = {g ∈ G: gA ∩ A is infinite} is called the combinatorial derivation. The mapping Δ can be considered as an analogue of the topological derivation d: PX→ PX, A ↦ Ad, where X is a topological space and Ad is the set of all limit points of A. We study the behaviour of subsets of G under action of Δ and its inverse mapping ∇. For example, we show that if G is infinite and I is an ideal in PG such that Δ(A) ∈ I and ∇(A) ⊆ I for each A ∈ I then I = PG.
{"title":"The combinatorial derivation and its inverse mapping","authors":"I. Protasov","doi":"10.2478/s11533-013-0313-x","DOIUrl":"https://doi.org/10.2478/s11533-013-0313-x","url":null,"abstract":"Let G be a group and PG be the Boolean algebra of all subsets of G. A mapping Δ: PG → PG defined by Δ(A) = {g ∈ G: gA ∩ A is infinite} is called the combinatorial derivation. The mapping Δ can be considered as an analogue of the topological derivation d: PX→ PX, A ↦ Ad, where X is a topological space and Ad is the set of all limit points of A. We study the behaviour of subsets of G under action of Δ and its inverse mapping ∇. For example, we show that if G is infinite and I is an ideal in PG such that Δ(A) ∈ I and ∇(A) ⊆ I for each A ∈ I then I = PG.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"1 1","pages":"2176-2181"},"PeriodicalIF":0.0,"publicationDate":"2013-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72881642","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 : 2013-10-08DOI: 10.2478/s11533-013-0312-y
S. Camp-Mora
A subgroup H of a group G is called ascendant-by-finite in G if there exists a subgroup K of H such that K is ascendant in G and the index of K in H is finite. It is proved that a locally finite group with every subgroup ascendant-by-finite is locally nilpotent-by-finite. As a consequence, it is shown that the Gruenberg radical has finite index in the whole group.
{"title":"Groups with every subgroup ascendant-by-finite","authors":"S. Camp-Mora","doi":"10.2478/s11533-013-0312-y","DOIUrl":"https://doi.org/10.2478/s11533-013-0312-y","url":null,"abstract":"A subgroup H of a group G is called ascendant-by-finite in G if there exists a subgroup K of H such that K is ascendant in G and the index of K in H is finite. It is proved that a locally finite group with every subgroup ascendant-by-finite is locally nilpotent-by-finite. As a consequence, it is shown that the Gruenberg radical has finite index in the whole group.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"21 1","pages":"2182-2185"},"PeriodicalIF":0.0,"publicationDate":"2013-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78630919","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 : 2013-10-08DOI: 10.2478/s11533-013-0310-0
Z. Finta
For certain generalized Bernstein operators {Ln} we show that there exist no i, j ∈ {1, 2, 3,…}, i < j, such that the functions ei(x) = xi and ej (x) = xj are preserved by Ln for each n = 1, 2,… But there exist infinitely many ei such that e0(x) = 1 and ej (x) = xj are its fixed points.
{"title":"Bernstein type operators having 1 and xj as fixed points","authors":"Z. Finta","doi":"10.2478/s11533-013-0310-0","DOIUrl":"https://doi.org/10.2478/s11533-013-0310-0","url":null,"abstract":"For certain generalized Bernstein operators {Ln} we show that there exist no i, j ∈ {1, 2, 3,…}, i < j, such that the functions ei(x) = xi and ej (x) = xj are preserved by Ln for each n = 1, 2,… But there exist infinitely many ei such that e0(x) = 1 and ej (x) = xj are its fixed points.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"37 1","pages":"2257-2261"},"PeriodicalIF":0.0,"publicationDate":"2013-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86823477","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 : 2013-10-08DOI: 10.2478/s11533-013-0290-0
R. Laver, Sheila K. Miller
The left distributive law is the law a· (b· c) = (a·b) · (a· c). Left distributive algebras have been classically used in the study of knots and braids, and more recently free left distributive algebras have been studied in connection with large cardinal axioms in set theory. We provide a survey of results on the free left distributive algebra on one generator, A, and a new, simplified proof of the existence of a normal form for terms in A. Topics included are: the confluence of A, the linearity of the iterated left division ordering
{"title":"The free one-generated left distributive algebra: basics and a simplified proof of the division algorithm","authors":"R. Laver, Sheila K. Miller","doi":"10.2478/s11533-013-0290-0","DOIUrl":"https://doi.org/10.2478/s11533-013-0290-0","url":null,"abstract":"The left distributive law is the law a· (b· c) = (a·b) · (a· c). Left distributive algebras have been classically used in the study of knots and braids, and more recently free left distributive algebras have been studied in connection with large cardinal axioms in set theory. We provide a survey of results on the free left distributive algebra on one generator, A, and a new, simplified proof of the existence of a normal form for terms in A. Topics included are: the confluence of A, the linearity of the iterated left division ordering <L of A, the connections of A to the braid groups, and an extension P of A obtained by freely adding a composition operation. This is followed by a simplified proof of the division algorithm for P, which produces a normal form for terms in A and is a powerful tool in the study of A.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"17 1","pages":"2150-2175"},"PeriodicalIF":0.0,"publicationDate":"2013-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78030164","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 : 2013-09-25DOI: 10.2478/s11533-014-0441-y
V. Marchenko
We extend a theorem of Kato on similarity for sequences of projections in Hilbert spaces to the case of isomorphic Schauder decompositions in certain Banach spaces. To this end we use ℓψ-Hilbertian and ∞-Hilbertian Schauder decompositions instead of orthogonal Schauder decompositions, generalize the concept of an orthogonal Schauder decomposition to the case of Banach spaces and introduce the class of Banach spaces with Schauder-Orlicz decompositions. Furthermore, we generalize the notions of type, cotype, infratype and M-cotype of a Banach space and study the properties of unconditional Schauder decompositions in Banach spaces possessing certain geometric structure.
{"title":"Isomorphic Schauder decompositions in certain Banach spaces","authors":"V. Marchenko","doi":"10.2478/s11533-014-0441-y","DOIUrl":"https://doi.org/10.2478/s11533-014-0441-y","url":null,"abstract":"We extend a theorem of Kato on similarity for sequences of projections in Hilbert spaces to the case of isomorphic Schauder decompositions in certain Banach spaces. To this end we use ℓψ-Hilbertian and ∞-Hilbertian Schauder decompositions instead of orthogonal Schauder decompositions, generalize the concept of an orthogonal Schauder decomposition to the case of Banach spaces and introduce the class of Banach spaces with Schauder-Orlicz decompositions. Furthermore, we generalize the notions of type, cotype, infratype and M-cotype of a Banach space and study the properties of unconditional Schauder decompositions in Banach spaces possessing certain geometric structure.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"99 1","pages":"1714-1732"},"PeriodicalIF":0.0,"publicationDate":"2013-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78607733","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/s11533-013-0309-6
M. Fiedler, Frank J. Hall
This paper extends some properties of the generalized complementary basic matrices, in particular, in a combinatorial direction. These include inheritance (such as for Alternating Sign Matrices), spectral, and sign pattern matrix (including sign nonsingularity) properties.
{"title":"Combinatorial aspects of generalized complementary basic matrices","authors":"M. Fiedler, Frank J. Hall","doi":"10.2478/s11533-013-0309-6","DOIUrl":"https://doi.org/10.2478/s11533-013-0309-6","url":null,"abstract":"This paper extends some properties of the generalized complementary basic matrices, in particular, in a combinatorial direction. These include inheritance (such as for Alternating Sign Matrices), spectral, and sign pattern matrix (including sign nonsingularity) properties.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"21 1","pages":"2186-2196"},"PeriodicalIF":0.0,"publicationDate":"2013-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82270887","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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