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 Acta Mathematica Hungarica   [SJR: 0.53]   [H-I: 29]   [2 followers]  Follow         Hybrid journal (It can contain Open Access articles)    ISSN (Print) 1588-2632 - ISSN (Online) 0236-5294    Published by Springer-Verlag  [2355 journals]
• On size, order, diameter and edge-connectivity of graphs
• Authors: P. Ali; J. P. Mazorodze; S. Mukwembi; T. Vetrík
Pages: 11 - 24
Abstract: To bound the size (the number of edges) of a graph in terms of other parameters of a graph forms an important family of problems in the extremal graph theory. We present a number of upper bounds on the size of general graphs and triangle-free graphs. We bound the size of any graph and of any triangle-free graph in terms of its order (number of vertices), diameter and edge-connectivity. We also give an upper bound on the size of triangle-free graphs of given order, diameter and minimum degree. All bounds presented in this paper are asymptotically sharp.
PubDate: 2017-06-01
DOI: 10.1007/s10474-017-0699-1
Issue No: Vol. 152, No. 1 (2017)

• Some integrals of hypergeometric functions
• Authors: A. Biró
Pages: 58 - 71
Abstract: We consider a certain definite integral involving the product of two classical hypergeometric functions having complicated arguments. We show the surprising fact that this integral does not depend on the parameters of the hypergeometric functions.
PubDate: 2017-06-01
DOI: 10.1007/s10474-017-0700-z
Issue No: Vol. 152, No. 1 (2017)

• Projections onto closed convex sets in Hilbert spaces
• Authors: A. Domokos; J. M. Ingram; M. M. Marsh
Pages: 114 - 129
Abstract: Let X be a real Hilbert space. We give necessary and sufficient algebraic conditions for a mapping $${F\colon X \to X}$$ with a closed image set to be the metric projection mapping onto a closed convex set. We provide examples that illustrate the necessity of each of the conditions. Our characterizations generalize several results related to projections onto closed convex sets.
PubDate: 2017-06-01
DOI: 10.1007/s10474-017-0691-9
Issue No: Vol. 152, No. 1 (2017)

• Polynomial entropy and expansivity
• Authors: A. Artigue; D. Carrasco-Olivera; I. Monteverde
Pages: 140 - 149
Abstract: We study the polynomial entropy of homeomorphisms on compact metric spaces. We construct a homeomorphism on a compact metric space with vanishing polynomial entropy that it is not equicontinuous. Also we give examples with arbitrarily small polynomial entropy. Finally, we show that expansive homeomorphisms and positively expansive maps of compact metric spaces with infinitely many points have polynomial entropy greater than or equal to 1.
PubDate: 2017-06-01
DOI: 10.1007/s10474-017-0689-3
Issue No: Vol. 152, No. 1 (2017)

• Extendability to summable ideals
• Authors: P. Klinga; A. Nowik
Pages: 150 - 160
Abstract: We continue our work on the ideal version of the Lévy–Steinitz theorem on conditionally convergent series of vectors. In particular, we prove that for each series $${\sum_{n\in\omega}v_n}$$ , $${(v_n)_{n\in\omega} \subset\mathbb{R}^2}$$ , such that its sum range is $${\mathbb{R}^2}$$ and its set of Lévy vectors is of power at least 3, it is possible to find $${A\in\mathcal{I}}$$ such that the sum range of $${\sum_{n\in A}v_n}$$ is still $${\mathbb{R}^2}$$ , for some proper ideal $${\mathcal{I}\subset\mathcal{P}(\omega)}$$ . We also work on the summability of certain known ideals as well as introduce the cardinal number $${\kappa_{M}}$$ as the minimal number of summable ideals required to cover an ideal, and prove some basic properties of it.
PubDate: 2017-06-01
DOI: 10.1007/s10474-017-0704-8
Issue No: Vol. 152, No. 1 (2017)

• On a theorem of Galvin and Nagy
• Authors: P. Komjáth
Pages: 161 - 165
Abstract: We give complete proofs of the results of Galvin and Nagy on a problem of Erdős and Hajnal concerning certain combinatorial games of transfinite length.
PubDate: 2017-06-01
DOI: 10.1007/s10474-017-0705-7
Issue No: Vol. 152, No. 1 (2017)

• Bounded operators on vector-valued weak Orlicz martingale spaces
• Authors: A. Yang
Pages: 186 - 200
Abstract: This paper is devoted to studying the boundedness of sublinear operators on vector-valued weak Orlicz martingale spaces. These results closely depend on the geometrical properties of the Banach space in which the martingales take values. Also the results obtained here extend the corresponding known results from scalar-valued setting to vector-valued setting.
PubDate: 2017-06-01
DOI: 10.1007/s10474-017-0710-x
Issue No: Vol. 152, No. 1 (2017)

• Sharp constants in asymptotic higher order Markov inequalities
• Authors: V. Totik; Y. Zhou
Pages: 227 - 242
Abstract: The best asymptotic constant for k-th order Markov inequality on a general compact set is determined.
PubDate: 2017-06-01
DOI: 10.1007/s10474-017-0709-3
Issue No: Vol. 152, No. 1 (2017)

• A note on property ( $${W_E}$$ W E )
• Authors: A. Liu
Pages: 243 - 256
Abstract: We investigate a new spectrum property ( $${W_E}$$ ), which extends the generalized Weyl theorem. Using the property of consistence in Fredholm and index, we establish for a bounded linear operator T defined on a Hilbert space sufficient and necessary conditions for which the property $${(W_E)}$$ holds. We also explore conditions on Hilbert operators T and S so that property $${(W_E)}$$ holds for $${T\oplus S}$$ . Moreover, we study the permanence of property $${(W_E)}$$ under perturbations by power finite rank operators commuting with T and discuss the relation between property ( $${W_E}$$ ) and hypercyclic operators.
PubDate: 2017-06-01
DOI: 10.1007/s10474-017-0707-5
Issue No: Vol. 152, No. 1 (2017)

• On Chebyshev polynomials in the complex plane
• Authors: V. V. Andrievskii
Abstract: The estimates of the uniform norm of the Chebyshev polynomials associated with a compact set K in the complex plane are established. These estimates are exact (up to a constant factor) in the case where K consists of a finite number of quasiconformal curves or arcs. The case where K is a uniformly perfect subset of the real line is also studied.
PubDate: 2017-07-19
DOI: 10.1007/s10474-017-0720-8

• Cubes and their centers
• Authors: R. Thornton
Abstract: We study the relationship between the sizes of sets B, S in $${\mathbb{R}^n}$$ where B contains the k-skeleton of an axes-parallel cube around each point in S, generalizing the results of Keleti, Nagy, and Shmerkin [6] about such sets in the plane. We find sharp estimates for the possible packing and box-counting dimensions for B and S. These estimates follow from related cardinality bounds for sets containing the discrete skeleta of cubes around a finite set of a given size. The Katona–Kruskal Theorem from hypergraph theory plays an important role. We also find partial results for the Haussdorff dimension and settle an analogous question for the dual polytope of the cube, the orthoplex.
PubDate: 2017-07-19
DOI: 10.1007/s10474-017-0729-z

• An inverse eigenvalue problem for one dimensional Dirac operators
• Authors: M. Kiss
Abstract: We consider an inverse eigenvalue problem for Dirac operators on finite intervals. We show that if for a $${\mu\in\mathbb{C}}$$ the system $${\{\exp{2i\lambda_nx}}$$ , $${\exp{2i\mu x}\}}$$ is closed in $${L^p[-\pi,\pi]}$$ , then there is at most one $${L^p}$$ -potential with the eigenvalues $${\lambda_n}$$ . The result corresponds to the case of Schrödinger operators.
PubDate: 2017-06-21
DOI: 10.1007/s10474-017-0733-3

• Coorbit spaces related to locally compact hypergroups
• Authors: B. H. Sadathoseyni; S. M. Tabatabaie
Abstract: We initiate the study of coorbit spaces on locally compact hypergroups and give some necessary and sufficient conditions for the extended coorbit spaces to be complete.
PubDate: 2017-06-20
DOI: 10.1007/s10474-017-0736-0

• A refinement of Young’s inequality
• Authors: P. Kórus
Abstract: We present an improved version of Young’s inequality as well as an operator inequality version of it. Our result is compared to the latest refinements.
PubDate: 2017-06-20
DOI: 10.1007/s10474-017-0735-1

• f -stability of spacelike hypersurfaces in weighted spacetimes
• Authors: H. F. de Lima; A. M. S. Oliveira; M. S. Santos; M. A. L. Velásquez
Abstract: We establish the notions of f-stability and strong f-stability concerning closed spacelike hypersurfaces immersed with constant f-mean curvature in a conformally stationary spacetime endowed with a conformal timelike vector field V and a weight function f. When V is closed, with the aid of the f-Laplacian of a suitable support function, we characterize f-stable closed spacelike hypersurfaces through the analysis of the first eigenvalue of the Jacobi operator associated to the corresponding variational problem. Furthermore, we obtain sufficient conditions which assure that a strongly f-stable closed spacelike hypersurface must be either f-maximal or isometric to a leaf orthogonal to V.
PubDate: 2017-06-20
DOI: 10.1007/s10474-017-0731-5

• Commutativity of integral quasi-arithmetic means on measure spaces
• Authors: D. Głazowska; P. Leonetti; J. Matkowski; S. Tringali
Abstract: Let $${(X, \mathscr{L}, \lambda)}$$ and $${(Y, \mathscr{M}, \mu)}$$ be finite measure spaces for which there exist $${A \in \mathscr{L}}$$ and $${B \in \mathscr{M}}$$ with $${0 < \lambda(A) < \lambda(X)}$$ and $${0 < \mu(B) < \mu(Y)}$$ , and let $${I\subseteq \mathbf{R}}$$ be a non-empty interval. We prove that, if f and g are continuous bijections $${I \to \mathbf{R}^+}$$ , then the equation $$f^{-1}\Big(\int_X f\Big(g^{-1}\Big(\int_Y g \circ h \,d\mu\Big)\Big)d \lambda\Big) = g^{-1}\Big(\int_Y g\Big(f^{-1}\Big(\int_X f \circ h \,d\lambda\Big)\Big)d \mu\Big)$$ is satisfied by every $${\mathscr{L} \otimes \mathscr{M}}$$ -measurable simple function $${h\colon X \times Y \to I}$$ if and only if f = cg for some $${c \in \mathbf{R}^+}$$ (it is easy to see that the equation is well posed). An analogous, but essentially different result, with f and g replaced by continuous injections $${I \to \mathbf R}$$ and $${\lambda(X)=\mu(Y)=1}$$ , was recently obtained in [7].
PubDate: 2017-06-20
DOI: 10.1007/s10474-017-0734-2

• Cantor type functions in non-integer bases
• Authors: C. Baiocchi; V. Komornik; P. Loreti
Abstract: Cantor’s ternary function is generalized to arbitrary base-change functions in non-integer bases. They turn out to have radically different continuity, differentiability and monotonicity properties, depending on the particular bases involved in their definition.
PubDate: 2017-06-20
DOI: 10.1007/s10474-017-0732-4

• King spaces and compactness
• Authors: V. Gutev
Abstract: Using the framework of weak selections, Nagao and Shakhmatov introduced topological king spaces, and extended the classical “King Chicken Theorem” by showing that each compact space with a continuous weak selection is a king space. They also obtained that several king spaces are compact, and raised the question whether every locally compact (or locally pseudocompact) king space must be compact. In the present paper, we settle this question in the affirmative.
PubDate: 2017-04-18
DOI: 10.1007/s10474-017-0713-7

• Hamiltonicity, minimum degree and leaf number
• Authors: P. Mafuta; S. Mukwembi; S. Munyira; T. Vetrík
Abstract: We prove a new sufficient condition for a connected graph to be Hamiltonian in terms of the leaf number and the minimum degree. Our results give solutions to conjectures on the Hamiltonicity and traceability of graphs. We considerably generalize known results in the area by showing that if G is a connected graph having minimum degree $${\delta}$$ and leaf number L such that $${\delta \ge \frac{L}{2}+1}$$ , then G is Hamiltonian and thus traceable.
PubDate: 2017-04-18
DOI: 10.1007/s10474-017-0716-4

• On lattice-valued maps stemming from the notion of optimal average
• Authors: N. K. Agbeko; W. Fechner; E. Rak
Abstract: The main purpose of this paper is to study certain lattice-valued maps through associated functional equations and inequalities. We deal with morphisms between an algebraic structure and an ordered structure. Next, we solve a separation problem for the inequalities studied. Moreover, we discuss the Hyers-Ulam stability of our main equation. Our research is motivated by the notion of optimal average, which was introduced by the first author in 1994.
PubDate: 2017-04-18
DOI: 10.1007/s10474-017-0719-1

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