Authors:J. A. Martínez-Cadena; R. G. Wilson Pages: 259 - 270 Abstract: Abstract A topological space X is densely countably compact if it possesses a dense subspace D with the property that every infinite subset of D has an accumulation point in X. We study topologies which are maximal with respect to this property; in particular we show that a T 1 densely countably compact space is maximal densely countably compact if and only if it is a scattered Fréchet SC-space of scattering order 2. PubDate: 2017-04-01 DOI: 10.1007/s10474-016-0684-0 Issue No:Vol. 151, No. 2 (2017)

Authors:Z. Garbouj; H. Skhiri Pages: 328 - 360 Abstract: Abstract For a closed linear relation in a Hilbert space the notions of minimum modulus, essential g-ascent, essential ascent and essential descent are introduced and studied. We prove that some results of E. Chafai and M. Mnif [3] related to the stability of the essential descent and descent of a linear relation T everywhere defined such that \({T(0)\subseteq \mathsf{ker}(T)}\) by a finite rank operator F commuting with T, remain valid when F is an everywhere defined linear relation and without the assumption that \({T(0)\subseteq \mathsf{ker}(T)}\) . We studied also the stability of the essential g-ascent and the essential ascent under a finite rank relation. Motivated by the recent work of T. Álvarez and A. Sandovici [1], we extend to a closed linear relation, the well known notion of minimum modulus of a linear operator (H. A. Gindler and A. E. Taylor [7]). Also, we introduce and study the new notion of minimum g-modulus for a linear relation. PubDate: 2017-04-01 DOI: 10.1007/s10474-016-0683-1 Issue No:Vol. 151, No. 2 (2017)

Authors:H. Halas Pages: 462 - 481 Abstract: Abstract The line-inversion and pedal transformation are defined in the quasi-hyperbolic plane and certain properties of these transformations are shown with regard to analogous transformations in the Euclidean [1, 3, 10, 12, 20], hyperbolic [4, 15, 18] isotropic [17, 19] and pseudo-Euclidean plane [5, 6, 7, 14]. As it is natural to observe class curves in the quasi-hyperbolic plane, i.e. line envelopes, the construction of a tangent point on any line of the class curve obtained by the line-inversion and pedal transformation is shown. PubDate: 2017-04-01 DOI: 10.1007/s10474-016-0686-y Issue No:Vol. 151, No. 2 (2017)

Authors:A. Gut; U. Stadtmüller Pages: 510 - 530 Abstract: Abstract Various methods of summation for divergent series have been extended to analogs for sums of i.i.d. random variables. The present paper deals with a special class of matrix weighted sums of i.i.d. random variables where the weights \({a_{n,k}}\) are defined as the weights from Cesàro summability, i.e., \({a_{n,k}=\binom{n-k+\alpha-1}{n-k}/\binom{n+\alpha}{n}}\) , where \({\alpha > 0}\) . A strong law of large numbers (SLLN) has been shown to hold in this setting iff \({E { X }^{1/\alpha}<\infty}\) , but a law of the iterated logarithm (LIL) has been shown for the case \({\alpha \geqq 1}\) only. We will study the case \({0 < \alpha < 1}\) in more detail, giving an LIL for \({1/2 < \alpha < 1}\) and some additional strong limit theorems under appropriate moment conditions for \({1/2 \leqq \alpha < 1}\) . PubDate: 2017-04-01 DOI: 10.1007/s10474-016-0685-z Issue No:Vol. 151, No. 2 (2017)

Authors:V. Gutev Abstract: 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

Authors:P. Mafuta; S. Mukwembi; S. Munyira; T. Vetrík Abstract: 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

Authors:Z. Krčmáriková; W. Steiner; T. Vávra Abstract: Abstract The finiteness property is an important arithmetical property of beta-expansions. We exhibit classes of Pisot numbers β having the negative finiteness property, that is the set of finite (−β)-expansions is equal to \({\mathbb{Z}[\beta^{-1}]}\) . For a class of numbers including the Tribonacci number, we compute the maximal length of the fractional parts arising in the addition and subtraction of (−β)-integers. We also give conditions excluding the negative finiteness property. PubDate: 2017-04-18 DOI: 10.1007/s10474-017-0711-9

Authors:N. K. Agbeko; W. Fechner; E. Rak Abstract: 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

Authors:I. Juhász; J. van Mill Abstract: Abstract We consider nine natural tightness conditions for topological spaces that are all variations on countable tightness, some stronger and some weaker than countable tightness. We investigate the interrelationships between them, presenting examples which show that mostly they are all different. However, a couple of intriguing problems of this type remain open. PubDate: 2017-04-18 DOI: 10.1007/s10474-017-0714-6

Authors:M. Avdispahić; Z. Šabanac Abstract: Abstract A trigonometric series strongly bounded at two points and with coefficients forming a log-quasidecreasing sequence is necessarily the Fourier series of a function belonging to all \({L^{p}}\) spaces, \({1\leq p < \infty}\) . We obtain new results on strong convergence of Fourier series for functions of generalized bounded variation. PubDate: 2017-04-18 DOI: 10.1007/s10474-017-0717-3

Authors:Z. Buczolich Abstract: Abstract We show that there are functions f in the Hölder class \({C^{\alpha}[0,1]}\) , \({1 < \alpha < 2}\) such that \({f _{A}}\) is neither convex nor concave for any \({A\subset [0,1]}\) with \({\overline{{\rm dim}}_\textsc{M}\,A > \alpha-1}\) . Our earlier result shows that for the typical/generic \({f\in C_1^{\alpha}[0,1]}\) , \({0\leq \alpha < 2}\) there is always a set \({A\subset [0,1]}\) such that \({f _A}\) is convex and \({\overline{{\rm dim}}_\textsc{M}\,A=1}\) . The analogous statement for monotone restrictions is the following: there are functions \({f}\) in the Hölder class \({C^{\alpha}[0,1]}\) , \({1/2 \leq \alpha < 1}\) such that \({f _{A}}\) is not monotone on \({A\subset [0,1]}\) with \({\overline{{\rm dim}}_\textsc{M}\,A > \alpha}\) . This statement is not true for the range of parameters \({\alpha < 1/2}\) and the main theorem of this paper for the parameter range \({1< \alpha < 3/2}\) cannot be obtained by integration of the result about monotone restrictions. PubDate: 2017-04-18 DOI: 10.1007/s10474-017-0712-8

Authors:L. Székelyhidi Abstract: Abstract We make an attempt to extend L. Schwartz’s classical result on spectral synthesis to several dimensions. Due to counterexamples of D. I. Gurevich this is impossible for translation invariant varieties. Our idea is to replace translations by proper euclidean motions in higher dimensions. For this purpose we introduce the basic concepts of spectral analysis and synthesis in the non-commutative setting based on Gelfand pairs, where “translation invariance" will be replaced by invariance with respect to a compact group of automorphisms. The role of exponential functions will be played by spherical functions. As an application we obtain the extension of L. Schwartz’s fundamental result. PubDate: 2017-04-18 DOI: 10.1007/s10474-017-0715-5

Authors:R. P. Agarwal; R. R. Mahmoud; S. H. Saker; C. Tunç Abstract: Abstract Some new dynamic inequalities on time scales are established, that reduce in the discrete and the continuous cases to classical inequalities named after Németh and Mohapatra, respectively. The new generalized inequalities resemble intensive classical inequalities known in the literature such as Beesack type inequalities, Copson type inequalities and Hardy–Littlewood type inequalities. The main results will be proved by employing the time scales Hölder inequality and the time scales power rules for integrations that have been proved earlier. PubDate: 2017-04-18 DOI: 10.1007/s10474-017-0718-2

Authors:N. Abughazalah Abstract: Abstract Every semigroup which is a finite disjoint union of copies of the free monogenic semigroup (natural numbers under addition) has soluble word problem and soluble membership problem. Efficient algorithms are given for both problems. PubDate: 2017-03-02 DOI: 10.1007/s10474-017-0687-5

Authors:D. E. Otera; F. G. Russo; C. Tanasi Abstract: Abstract We study the notion of wgsc inverse-representation of finitely presented groups and use the “ \({(\Phi,\Psi)}\) -technique” of Poénaru, in order to prove that the universal cover of a closed 3-manifold admitting a wgsc inverse-representation with an extra finiteness condition is simply connected at infinity. Furthermore, we investigate some new relations between wgsc inverse-representations and the qsf property for groups. PubDate: 2017-02-21 DOI: 10.1007/s10474-017-0698-2

Authors:H. Mishou; H. Nagoshi Abstract: Abstract We establish a joint universality theorem for pairs of functions in the Selberg class under certain conditions. This theorem generalizes and unifies several previous results, which were shown individually. We also give further examples of pairs of jointly universal L-functions, and actually extend the known universality theorem for the symmetric power L-function \({L(s, \mathrm{sym}^m f)}\) associated to a holomorphic Hecke eigen cusp form f for \({\mathrm{SL}_{2} (\mathbb{Z})}\) with \({1 \le m \le 4}\) . PubDate: 2017-02-21 DOI: 10.1007/s10474-017-0696-4

Authors:E. de Amo; M. Díaz Carrillo; J. Fernández-Sánchez Abstract: Abstract Among the members of the celebrated family of functions introduced by Salem in the mid 20th century, there is a particular and very interesting one that we use to relate the dyadic system of numbers representation with the modified Engel system. Various properties are studied for this function, including derivatives and fractal dimensions. PubDate: 2017-02-20 DOI: 10.1007/s10474-017-0690-x

Authors:L. Montejano; E. Roldán-Pensado Abstract: Abstract We develop a concrete way to construct bodies of constant width in dimension three. They are constructed from special embeddings of self-dual graphs. PubDate: 2017-02-20 DOI: 10.1007/s10474-017-0697-3

Authors:P. Frankl; V. Rödl; A. Ruciński Abstract: Abstract Erdős [1] conjectured that for all \({k \geq 2}\) , \({s \geq 1}\) and \({n \geq {k(s+1)}}\) , an n-vertex k-uniform hypergraph \({\mathcal{F}}\) with \({\nu(\mathcal{F})=s}\) cannot have more than \({\max\{\binom{sk+k-1}k,\binom nk-\binom{n-s}k\}}\) edges. It took almost fifty years to prove it for triple systems. In [5] we proved the conjecture for all s and all \({n \geq 4(s+1)}\) . Then Łuczak and Mieczkowska [6] proved the conjecture for sufficiently large s and all n. Soon after, Frankl proved it for all s. Here we present a simpler version of that proof which yields Erdős’ conjecture for \({s \geq 33}\) . Our motivation is to lay down foundations for a possible proof in the much harder case k = 4, at least for large s. PubDate: 2017-02-20 DOI: 10.1007/s10474-017-0692-8

Authors:J. Makó Abstract: Abstract The generalized convexity of the Takagi function was proved by Z. Boros [7]. We give an another proof of this result, which is more transparent. PubDate: 2017-02-20 DOI: 10.1007/s10474-017-0695-5