Authors:G. Mastroianni; I. Notarangelo; L. Szili; P. Vértesi Abstract: We prove some results on the root-distances and the weighted Lebesgue function corresponding to orthogonal polynomials for Laguerre type exponential weights. PubDate: 2018-05-26 DOI: 10.1007/s10474-018-0841-8

Authors:L. Csizmadia; L. Hatvani Abstract: Using purely elementary methods, necessary and sufficient conditions are given for the existence of 2T-periodic and 4T-periodic solutions around the upper equilibrium of the mathematical pendulum when the suspension point is vibrating with period 2T. The equation of the motion is of the form $$\ddot{\theta}-\frac{1}{l}(g+a(t)) \theta=0,$$ where l, g are constants and $$a(t) := \begin{cases} A &\text{if } 2kT\leq t < (2k+1)T,\\ -A &\text{if } (2k+1)T\leq t < (2k+2)T,\end{cases}\quad (k=0,1,\dots);$$ A, T are positive constants. The exact stability zones for the upper equilibrium are presented. PubDate: 2018-05-25 DOI: 10.1007/s10474-018-0835-6

Authors:J. Schleischitz Abstract: We study the rational approximation properties of special manifolds defined by a set of polynomials with rational coefficients. Mostly we will assume the case of all polynomials to depend on only one variable. In this case the manifold can be viewed as a Cartesian product of polynomial curves and it is possible to generalize recent results concerning such curves with similar concepts. There is hope that the method leads to insights on how to treat more general manifolds defined by arbitrary polynomials with rational coefficients. PubDate: 2018-05-25 DOI: 10.1007/s10474-018-0842-7

Authors:J. Hejduk; A. Loranty Abstract: We concentrate on topologies generated by lower and almost-lower density operators on measurable spaces. Among others the existence of the smallest in the sense of inclusion abstract density topology on measurable space is investigated. Moreover, the separation axioms for such topologies are studied. PubDate: 2018-05-25 DOI: 10.1007/s10474-018-0838-3

Authors:J. Davidov; O. Mushkarov Abstract: We construct new twistorial examples of non-Kähler almost Hermitian manifolds with Hermitian Ricci tensor by means of a natural almost Hermitian structures on the twistor space of an almost Hermitian four manifold. PubDate: 2018-05-25 DOI: 10.1007/s10474-018-0833-8

Authors:I. Ghenciu Abstract: The p-Gelfand–Phillips property (1 \({\leq}\) p < ∞) is studied in spaces of operators. Dunford–Pettis type like sets are studied in Banach spaces. We discuss Banach spaces X with the property that every p-convergent operator T: X \({\rightarrow}\) Y is weakly compact, for every Banach space Y. PubDate: 2018-05-25 DOI: 10.1007/s10474-018-0836-5

Authors:H.-F. Liu Abstract: We study the mean value estimate of coefficients of product L-function related to a primitive holomorphic cusp form f(z) of weight k for the full modular group \({SL_{2}(\mathbb{Z})}\) . Upper bounds and asymptotic formulas are established. PubDate: 2018-05-25 DOI: 10.1007/s10474-018-0839-2

Authors:Y. Cao; H. Liu Abstract: We introduce large families of subsets arising from Woods problem and study their cardinalities. Estimates of character sums over the subsets are given. We study the pesudorandom properties of the subsets and show that their well-distribution measures are very high. PubDate: 2018-05-25 DOI: 10.1007/s10474-018-0834-7

Authors:Q. Han; P. Yuan Abstract: Jeśmanowicz [9] conjectured that, for positive integers m and n with m > n, gcd(m,n) = 1 and \({m\not\equiv n\pmod{2}}\) , the exponential Diophantine equation \({(m^2-n^2)^x+(2mn)^y=(m^2+n^2)^z}\) has only the positive integer solution (x, y, z) = (2, 2, 2). We prove the conjecture for \({2 \ mn}\) and m + n has a prime factor p with \({p\not\equiv1\pmod{16}}\) . PubDate: 2018-05-25 DOI: 10.1007/s10474-018-0837-4

Authors:B. Maga Abstract: In the previous decades, the theory of first passage percolation became a highly important area of probability theory. In this work, we will observe what can be said about the corresponding structure if we forget about the probability measure defined on the product space of edges and simply consider topology in the terms of residuality. We focus on interesting questions arising in the probabilistic setup that make sense in this setting, too. We will see that certain classical almost sure events, as the existence of geodesics have residual counterparts, while the notion of the limit shape or time constants gets as chaotic as possible. PubDate: 2018-05-25 DOI: 10.1007/s10474-018-0840-9

Authors:M. M. Bayer Abstract: A renowned theorem of Blind and Mani, with a constructive proof by Kalai and an efficiency proof by Friedman, shows that the whole face lattice of a simple polytope can be determined from its graph. This is part of a broader story of reconstructing face lattices from partial information, first considered comprehensively in Grünbaum’s 1967 book. This survey paper includes varied results and open questions by many researchers on simplicial polytopes, nearly simple polytopes, cubical polytopes, zonotopes, crosspolytopes, and Eulerian posets. PubDate: 2018-05-23 DOI: 10.1007/s10474-018-0804-0

Authors:J. Solymosi; C. Wong Abstract: The boundedness of the kissing numbers of convex bodies has been known to Hadwiger [9] for long. We present an application of it to the sum-product estimate $$\max(\mid{\mathcal{A}+\mathcal{A}}\mid,\mid{\mathcal{A}\mathcal{A}}\mid)\gg \frac {\mid{\mathcal{A}\mid}^{4/3}}{\lceil\log\mid{\mathcal{A}\mid} \rceil^{1/3}}$$ for finite sets \({\mathcal{A}}\) of quaternions and of a certain family of well-conditioned matrices. PubDate: 2018-05-23 DOI: 10.1007/s10474-018-0831-x

Authors:J. H. Rolfes; F. Vallentin Abstract: A general greedy approach to construct coverings of compact metric spaces by metric balls is given and analyzed. The analysis is a continuous version of Chvátal’s analysis of the greedy algorithm for the weighted set cover problem. The approach is demonstrated in an exemplary manner to construct efficient coverings of the n-dimensional sphere and n-dimensional Euclidean space to give short and transparent proofs of several best known bounds obtained from constructions in the literature on sphere coverings. PubDate: 2018-05-08 DOI: 10.1007/s10474-018-0829-4

Authors:M. Balcerowski Abstract: We generalize a theorem proved by R. Ger and T. Kochanek [4]. Hence we obtain the solution of a problem posed by Z. Daróczy, J. Jarczyk and W. Jarczyk [2]. PubDate: 2018-04-24 DOI: 10.1007/s10474-018-0816-9

Authors:F. A. A. Almahdi; K. Louartiti; M. Tamekkante Abstract: Let R be a commutative ring and let \({n >1}\) be an integer. We introduce a simple graph, denoted by \({\Gamma_t(M_n(R))}\) , which we call the trace graph of the matrix ring \({M_n(R)}\) , such that its vertex set is \({M_n(R)^{\ast}}\) and such that two distinct vertices A and B are joined by an edge if and only if \({{\rm Tr} (AB)=0}\) where \({ {\rm Tr} (AB)}\) denotes the trace of the matrix AB. We prove that \({\Gamma_t(M_n(R))}\) is connected with \({{\rm diam}(\Gamma_{t}(M_{n}(R)))=2}\) and \({{\rm gr} (\Gamma_t(M_n(R)))=3}\) . We investigate also the interplay between the ring-theoretic properties of R and the graph-theoretic properties of \({\Gamma_t(M_n(R))}\) . Hence, we use the notion of the irregularity index of a graph to characterize rings with exactly one nontrivial ideal. PubDate: 2018-04-24 DOI: 10.1007/s10474-018-0815-x

Authors:M. Henk; H. Pollehn Abstract: We study the log-Minkowski inequality for centered convex bodies when the cone-volume body is a simplex or a parallelepiped. PubDate: 2018-04-24 DOI: 10.1007/s10474-018-0822-y

Authors:B. Csikós; M. Horváth Abstract: We show that the perimeter of the convex hull of finitely many disks lying in the hyperbolic or Euclidean plane, or in a hemisphere does not increase when the disks are rearranged so that the distances between their centers do not increase. This generalizes the theorem on the monotonicity of the perimeter of the convex hull of a finite set under contractions, proved in the Euclidean plane by V. N. Sudakov [8], R. Alexander [1], V. Capoyleas and J. Pach [3]. We also prove that the area of the intersection of finitely many disks in the hyperbolic plane does not decrease after such a contractive rearrangement. The Euclidean analogue of the latter statement was proved by K. Bezdek and R. Connelly [2]. Both theorems are proved by a suitable adaptation of a recently published method of I. Gorbovickis [4]. PubDate: 2018-04-24 DOI: 10.1007/s10474-018-0820-0

Authors:M. Tărnăuceanu Abstract: Let G be a finite group. We give a criterion of nilpotency of G based on the existence of elements of certain order in each section of G. PubDate: 2018-04-24 DOI: 10.1007/s10474-018-0826-7

Authors:H. Baños; D. Oliveros Abstract: By extending the definition of boxicity, we extend a Hellytype result given by Danzer and Grünbaum on 2-piercings of families of boxes in d-dimensional Euclidean space by lowering the dimension of the boxes in the ambient space. PubDate: 2018-04-24 DOI: 10.1007/s10474-018-0817-8