Pub Date : 2014-07-20DOI: 10.2478/s11533-014-0416-z
Z. Aliyev
In this paper, we consider the nonlinear fourth order eigenvalue problem. We show the existence of family of unbounded continua of nontrivial solutions bifurcating from the line of trivial solutions. These global continua have properties similar to those found in Rabinowitz and Berestycki well-known global bifurcation theorems.
{"title":"Some global results for nonlinear fourth order eigenvalue problems","authors":"Z. Aliyev","doi":"10.2478/s11533-014-0416-z","DOIUrl":"https://doi.org/10.2478/s11533-014-0416-z","url":null,"abstract":"In this paper, we consider the nonlinear fourth order eigenvalue problem. We show the existence of family of unbounded continua of nontrivial solutions bifurcating from the line of trivial solutions. These global continua have properties similar to those found in Rabinowitz and Berestycki well-known global bifurcation theorems.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"3 12","pages":"1811-1828"},"PeriodicalIF":0.0,"publicationDate":"2014-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2478/s11533-014-0416-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72388288","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 : 2014-07-20DOI: 10.2478/s11533-014-0445-7
Yu. M. Movsisyan, V. Aslanyan
A De Morgan quasilattice is an algebra satisfying hyperidentities of the variety of De Morgan algebras (lattices). In this paper we give a functional representation of the free n-generated De Morgan quasilattice with two binary and one unary operations. Namely, we define the concept of super-De Morgan function and prove that the free De Morgan quasilattice with two binary and one unary operations on nfree generators is isomorphic to the De Morgan quasilattice of super-De Morgan functions of nvariables.
De Morgan拟格是一种满足各种De Morgan代数(格)的超恒等式的代数。本文给出了具有两个二元操作和一个一元操作的自由n生成De Morgan拟格的泛函表示。即定义了超De Morgan函数的概念，并证明了在非自由生成元上具有两个二元操作和一个一元操作的自由De Morgan拟格与非变量的超De Morgan函数的De Morgan拟格是同构的。
{"title":"Super-De Morgan functions and free De Morgan quasilattices","authors":"Yu. M. Movsisyan, V. Aslanyan","doi":"10.2478/s11533-014-0445-7","DOIUrl":"https://doi.org/10.2478/s11533-014-0445-7","url":null,"abstract":"A De Morgan quasilattice is an algebra satisfying hyperidentities of the variety of De Morgan algebras (lattices). In this paper we give a functional representation of the free n-generated De Morgan quasilattice with two binary and one unary operations. Namely, we define the concept of super-De Morgan function and prove that the free De Morgan quasilattice with two binary and one unary operations on nfree generators is isomorphic to the De Morgan quasilattice of super-De Morgan functions of nvariables.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"18 1","pages":"1749-1761"},"PeriodicalIF":0.0,"publicationDate":"2014-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84310232","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 : 2014-07-20DOI: 10.2478/s11533-014-0433-y
A. Smajdor, W. Smajdor
Let K be a closed convex cone with nonempty interior in a real Banach space and let cc(K) denote the family of all nonempty convex compact subsets of K. If {Ft: t ≥ 0} is a regular cosine family of continuous additive set-valued functions Ft: K → cc(K) such that x ∈ Ft(x) for t ≥ 0 and x ∈ K, then $F_t circ F_s (x) = F_s circ F_t (x)fors,t geqslant 0andx in K$.
{"title":"Commutativity of set-valued cosine families","authors":"A. Smajdor, W. Smajdor","doi":"10.2478/s11533-014-0433-y","DOIUrl":"https://doi.org/10.2478/s11533-014-0433-y","url":null,"abstract":"Let K be a closed convex cone with nonempty interior in a real Banach space and let cc(K) denote the family of all nonempty convex compact subsets of K. If {Ft: t ≥ 0} is a regular cosine family of continuous additive set-valued functions Ft: K → cc(K) such that x ∈ Ft(x) for t ≥ 0 and x ∈ K, then $F_t circ F_s (x) = F_s circ F_t (x)fors,t geqslant 0andx in K$.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"33 1","pages":"1871-1881"},"PeriodicalIF":0.0,"publicationDate":"2014-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87365708","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 : 2014-07-20DOI: 10.2478/s11533-014-0447-5
Eunmi Pak, Y. Suh
Regarding the generalized Tanaka-Webster connection, we considered a new notion of $$mathfrak{D}^ bot$$-parallel structure Jacobi operator for a real hypersurface in a complex two-plane Grassmannian G2(ℂm+2) and proved that a real hypersurface in G2(ℂm+2) with generalized Tanaka-Webster $$mathfrak{D}^ bot$$-parallel structure Jacobi operator is locally congruent to an open part of a tube around a totally geodesic quaternionic projective space ℍPn in G2(ℂm+2), where m = 2n.
{"title":"Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster $$mathfrak{D}^ bot$$-parallel structure Jacobi operator","authors":"Eunmi Pak, Y. Suh","doi":"10.2478/s11533-014-0447-5","DOIUrl":"https://doi.org/10.2478/s11533-014-0447-5","url":null,"abstract":"Regarding the generalized Tanaka-Webster connection, we considered a new notion of $$mathfrak{D}^ bot$$-parallel structure Jacobi operator for a real hypersurface in a complex two-plane Grassmannian G2(ℂm+2) and proved that a real hypersurface in G2(ℂm+2) with generalized Tanaka-Webster $$mathfrak{D}^ bot$$-parallel structure Jacobi operator is locally congruent to an open part of a tube around a totally geodesic quaternionic projective space ℍPn in G2(ℂm+2), where m = 2n.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"254 1","pages":"1840-1851"},"PeriodicalIF":0.0,"publicationDate":"2014-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82933467","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 : 2014-07-20DOI: 10.2478/s11533-014-0448-4
Francisco Perdomo, Ángel Plaza
The Longest-Edge (LE) bisection of a triangle is obtained by joining the midpoint of its longest edge with the opposite vertex. Here two properties of the longest-edge bisection scheme for triangles are proved. For any triangle, the number of distinct triangles (up to similarity) generated by longest-edge bisection is finite. In addition, if LE-bisection is iteratively applied to an initial triangle, then minimum angle of the resulting triangles is greater or equal than a half of the minimum angle of the initial angle. The novelty of the proofs is the use of an hyperbolic metric in a shape space for triangles.
{"title":"Properties of triangulations obtained by the longest-edge bisection","authors":"Francisco Perdomo, Ángel Plaza","doi":"10.2478/s11533-014-0448-4","DOIUrl":"https://doi.org/10.2478/s11533-014-0448-4","url":null,"abstract":"The Longest-Edge (LE) bisection of a triangle is obtained by joining the midpoint of its longest edge with the opposite vertex. Here two properties of the longest-edge bisection scheme for triangles are proved. For any triangle, the number of distinct triangles (up to similarity) generated by longest-edge bisection is finite. In addition, if LE-bisection is iteratively applied to an initial triangle, then minimum angle of the resulting triangles is greater or equal than a half of the minimum angle of the initial angle. The novelty of the proofs is the use of an hyperbolic metric in a shape space for triangles.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"2 1","pages":"1796-1810"},"PeriodicalIF":0.0,"publicationDate":"2014-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76323551","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 : 2014-07-20DOI: 10.2478/s11533-014-0449-3
T. Haynes, Michael A. Henning, Lucas C. van der Merwe, Anders Yeo
A graph is diameter-2-critical if its diameter is two and the deletion of any edge increases the diameter. Let G be a diameter-2-critical graph of order n. Murty and Simon conjectured that the number of edges in G is at most ⌊n2/4⌋ and that the extremal graphs are the complete bipartite graphs K⌊n/2⌋,⌊n/2⌉. Fan [Discrete Math. 67 (1987), 235–240] proved the conjecture for n ≤ 24 and for n = 26, while Füredi [J. Graph Theory 16 (1992), 81–98] proved the conjecture for n > n0 where n0 is a tower of 2’s of height about 1014. The conjecture has yet to be proven for other values of n. Let Δ denote the maximum degree of G. We prove the following maximum degree theorems for diameter-2-critical graphs. If Δ ≥ 0.7 n, then the Murty-Simon Conjecture is true. If n ≥ 2000 and Δ ≥ 0.6789 n, then the Murty-Simon Conjecture is true.
{"title":"A maximum degree theorem for diameter-2-critical graphs","authors":"T. Haynes, Michael A. Henning, Lucas C. van der Merwe, Anders Yeo","doi":"10.2478/s11533-014-0449-3","DOIUrl":"https://doi.org/10.2478/s11533-014-0449-3","url":null,"abstract":"A graph is diameter-2-critical if its diameter is two and the deletion of any edge increases the diameter. Let G be a diameter-2-critical graph of order n. Murty and Simon conjectured that the number of edges in G is at most ⌊n2/4⌋ and that the extremal graphs are the complete bipartite graphs K⌊n/2⌋,⌊n/2⌉. Fan [Discrete Math. 67 (1987), 235–240] proved the conjecture for n ≤ 24 and for n = 26, while Füredi [J. Graph Theory 16 (1992), 81–98] proved the conjecture for n > n0 where n0 is a tower of 2’s of height about 1014. The conjecture has yet to be proven for other values of n. Let Δ denote the maximum degree of G. We prove the following maximum degree theorems for diameter-2-critical graphs. If Δ ≥ 0.7 n, then the Murty-Simon Conjecture is true. If n ≥ 2000 and Δ ≥ 0.6789 n, then the Murty-Simon Conjecture is true.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"13 1","pages":"1882-1889"},"PeriodicalIF":0.0,"publicationDate":"2014-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83915958","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 : 2014-07-20DOI: 10.2478/s11533-014-0443-9
Dina A. Abuzaid, Randa Ben Mahmoud, H. Chtioui, Afef Rigane
In this paper, we consider the problem of the existence of conformal metrics with prescribed scalar curvature on the standard sphere Sn, n ≥ 3. We give new existence and multiplicity results based on a new Euler-Hopf formula type. Our argument also has the advantage of extending well known results due to Y. Li [16].
{"title":"Topological tools for the prescribed scalar curvature problem on Sn","authors":"Dina A. Abuzaid, Randa Ben Mahmoud, H. Chtioui, Afef Rigane","doi":"10.2478/s11533-014-0443-9","DOIUrl":"https://doi.org/10.2478/s11533-014-0443-9","url":null,"abstract":"In this paper, we consider the problem of the existence of conformal metrics with prescribed scalar curvature on the standard sphere Sn, n ≥ 3. We give new existence and multiplicity results based on a new Euler-Hopf formula type. Our argument also has the advantage of extending well known results due to Y. Li [16].","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"51 1","pages":"1829-1839"},"PeriodicalIF":0.0,"publicationDate":"2014-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74661937","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 : 2014-07-20DOI: 10.2478/s11533-014-0444-8
L. A. Kurdachenko, S. Atlıhan, N. N. Semko
The main aim of this article is to examine infinite groups whose non-abelian subgroups are subnormal. In this sense we obtain here description of such locally finite groups and, as a consequence we show several results related to such groups.
{"title":"On the structure of groups whose non-abelian subgroups are subnormal","authors":"L. A. Kurdachenko, S. Atlıhan, N. N. Semko","doi":"10.2478/s11533-014-0444-8","DOIUrl":"https://doi.org/10.2478/s11533-014-0444-8","url":null,"abstract":"The main aim of this article is to examine infinite groups whose non-abelian subgroups are subnormal. In this sense we obtain here description of such locally finite groups and, as a consequence we show several results related to such groups.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"1 1","pages":"1762-1771"},"PeriodicalIF":0.0,"publicationDate":"2014-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88671157","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 : 2014-07-20DOI: 10.2478/s11533-014-0446-6
Tolga Karayayla
In this paper, the automorphism groups of relatively minimal rational elliptic surfaces with section which have constant J-maps are classified. The ground field is ℂ. The automorphism group of such a surface β: B → ℙ1, denoted by Aut(B), consists of all biholomorphic maps on the complex manifold B. The group Aut(B) is isomorphic to the semi-direct product MW(B) ⋊ Autσ (B) of the Mordell-Weil groupMW(B) (the group of sections of B), and the subgroup Autσ (B) of the automorphisms preserving a fixed section σ of B which is called the zero section on B. The Mordell-Weil group MW(B) is determined by the configuration of singular fibers on the elliptic surface B due to Oguiso and Shioda [9]. In this work, the subgroup Autσ (B) is determined with respect to the configuration of singular fibers of B. Together with a previous paper [4] where the case with non-constant J-maps was considered, this completes the classification of automorphism groups of relatively minimal rational elliptic surfaces with section.
{"title":"Automorphism groups of rational elliptic surfaces with section and constant J-map","authors":"Tolga Karayayla","doi":"10.2478/s11533-014-0446-6","DOIUrl":"https://doi.org/10.2478/s11533-014-0446-6","url":null,"abstract":"In this paper, the automorphism groups of relatively minimal rational elliptic surfaces with section which have constant J-maps are classified. The ground field is ℂ. The automorphism group of such a surface β: B → ℙ1, denoted by Aut(B), consists of all biholomorphic maps on the complex manifold B. The group Aut(B) is isomorphic to the semi-direct product MW(B) ⋊ Autσ (B) of the Mordell-Weil groupMW(B) (the group of sections of B), and the subgroup Autσ (B) of the automorphisms preserving a fixed section σ of B which is called the zero section on B. The Mordell-Weil group MW(B) is determined by the configuration of singular fibers on the elliptic surface B due to Oguiso and Shioda [9]. In this work, the subgroup Autσ (B) is determined with respect to the configuration of singular fibers of B. Together with a previous paper [4] where the case with non-constant J-maps was considered, this completes the classification of automorphism groups of relatively minimal rational elliptic surfaces with section.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"52 1","pages":"1772-1795"},"PeriodicalIF":0.0,"publicationDate":"2014-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91202273","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 : 2014-06-29DOI: 10.2478/s11533-014-0432-z
Tamotsu Izumida, Ken-Ichi Mitani, K. Saito
AbstractIn this paper, we consider a generalized triangle inequality of the following type: $$left| {x_1 + cdots + x_n } right|^p leqslant frac{{left| {x_1 } right|^p }} {{mu _1 }} + cdots + frac{{left| {x_2 } right|^p }} {{mu _n }}left( {for all x_1 , ldots ,x_n in X} right),$$ where (X, ‖·‖) is a normed space, (µ1, ..., µn) ∈ ℝn and p > 0. By using ψ-direct sums of Banach spaces, we present another approach to characterizations of the above inequality which is given by [Dadipour F., Moslehian M.S., Rassias J.M., Takahasi S.-E., Nonlinear Anal., 2012, 75(2), 735–741].
{"title":"Another approach to characterizations of generalized triangle inequalities in normed spaces","authors":"Tamotsu Izumida, Ken-Ichi Mitani, K. Saito","doi":"10.2478/s11533-014-0432-z","DOIUrl":"https://doi.org/10.2478/s11533-014-0432-z","url":null,"abstract":"AbstractIn this paper, we consider a generalized triangle inequality of the following type: $$left| {x_1 + cdots + x_n } right|^p leqslant frac{{left| {x_1 } right|^p }}\u0000{{mu _1 }} + cdots + frac{{left| {x_2 } right|^p }}\u0000{{mu _n }}left( {for all x_1 , ldots ,x_n in X} right),$$ where (X, ‖·‖) is a normed space, (µ1, ..., µn) ∈ ℝn and p > 0. By using ψ-direct sums of Banach spaces, we present another approach to characterizations of the above inequality which is given by [Dadipour F., Moslehian M.S., Rassias J.M., Takahasi S.-E., Nonlinear Anal., 2012, 75(2), 735–741].","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"115 1","pages":"1615-1623"},"PeriodicalIF":0.0,"publicationDate":"2014-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76083525","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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