Abstract: In this paper, the authors establish the global structure of one-signed periodic solutions of the first-order functional differential equation $$\begin{aligned} u'(t)=a(t)u(t)-\lambda f(t,u(t-\tau (t))),\qquad t\in \mathbb {R} \end{aligned}$$ by using unilateral bifurcation theorem, where the nonlinearity \(f\in C(\mathbb {R}\times \mathbb {R},\ \mathbb {R})\) is T-periodic with first variable and having nontrivial zeros, \(a\in C(\mathbb {R},[0,\ \infty ))\) is T-periodic function with \(\int _{0}^{T}a(t)dt>0\) , \(\tau \in C(\mathbb {R},\mathbb {R})\) is T-periodic function, \(\lambda >0\) is a parameter. PubDate: 2019-03-21 DOI: 10.1007/s00605-019-01286-6

Abstract: The normal covering number \(\gamma (G)\) of a finite, non-cyclic group G is the minimum number of proper subgroups such that each element of G lies in some conjugate of one of these subgroups. We find lower bounds linear in n for \(\gamma (S_n)\) , when n is even, and for \(\gamma (A_n)\) , when n is odd. PubDate: 2019-03-20 DOI: 10.1007/s00605-019-01287-5

Abstract: We present characterizations of democratic property for systems of translates on a general locally compact abelian group, along a lattice in that group.. That way we generalize the results from Hernández et al. (J Approx Theory 171:105–127, 2013) on systems of integer translates. Furthermore, we investigate the possibilities of more operative characterizations for lattices with torsion group structure, mainly through examples and counterexamples. PubDate: 2019-03-19 DOI: 10.1007/s00605-019-01285-7

Abstract: Let \((u_{n})_{n \ge 0}\) be a non-degenerate binary recurrence sequence with positive discriminant and p be a fixed prime number. In this paper, we are interested in finding a finiteness result for the solutions of the Diophantine equation \(u_{n_{1}} + u_{n_{2}} + \cdots + u_{n_{t}} = p^{z}\) with \(n_1> n_2> \cdots > n_t\ge 0\) . Moreover, we explicitly find all the powers of three which are sums of three balancing numbers using lower bounds for linear forms in logarithms. Further, we use a variant of the Baker–Davenport reduction method in Diophantine approximation due to Dujella and Pethő. PubDate: 2019-03-16 DOI: 10.1007/s00605-019-01282-w

Abstract: In this article, let \(\mu \) be a self-conformal measure, we discuss the dimensions of divergence points of self-conformal measures with the open set condition. Our main result is that the set \(\{x\in \mathrm{{{\,\mathrm{supp}\,}}}\mu : A(\frac{\log \mu (B(x,r))}{\log r})=I\}\) is not Taylor fractal and the set \(\{x\in \mathrm{{{\,\mathrm{supp}\,}}}\mu : A(\frac{\log \mu (B(x,r))}{\log r})\subseteq I\}\) is Taylor fractal. PubDate: 2019-03-14 DOI: 10.1007/s00605-019-01283-9

Abstract: In this paper, we first establish the sharp version of Landau–Bloch type theorem for strongly bounded harmonic mappings by considering the Landau–Bloch type theorem of a one-parameter family of holomorphic mappings. Next, we will establish two sharp versions of Landau–Bloch type theorems for certain harmonic mappings. Finally, we also pose several conjectures for the sharp version of Landau–Bloch type theorem for bounded harmonic mappings. PubDate: 2019-03-14 DOI: 10.1007/s00605-019-01284-8

Abstract: A group G is called automatically continuous if any homomorphism from a completely metrizable or locally compact Hausdorff group to G has open kernel. In this paper, we study preservation of automatic continuity under group-theoretic constructions, focusing mainly on groups of size less than continuum. In particular, we consider group extensions and graph products. As a consequence, we establish automatic continuity of virtually poly-free groups, and hence of non-exceptional spherical Artin groups. On the other hand, we show that if G is automatically continuous, then so is any finitely generated residually G group, hence, for instance, all finitely generated residually free groups are automatically continuous. PubDate: 2019-03-13 DOI: 10.1007/s00605-019-01281-x

Abstract: We use properties of the sequences of zeros of certain spaces of analytic functions in the unit disc \({\mathbb {D}}\) to study the question of characterizing the weighted superposition operators which map one of these spaces into another. We also prove that for a large class of Banach spaces of analytic functions in \({\mathbb {D}}\) , Y, we have that if the superposition operator \(S_\varphi \) associated to the entire function \(\varphi \) is a bounded operator from X, a certain Banach space of analytic functions in \(\mathbb D\) , into Y, then the superposition operator \(S_{\varphi ^\prime }\) maps X into Y. PubDate: 2019-03-06 DOI: 10.1007/s00605-019-01279-5

Abstract: A recent model for the flow of the Antarctic Circumpolar Current, formulated in spherical coordinates as a Dirichlet boundary-value problem for a nonlinear elliptic partial differential equation, reduces for flows with no azimuthal variations to a two-point boundary-value problem for a second-order ordinary differential equation. We provide some general settings for which these apparently simpler solutions are the unique solutions, due to an inherent symmetry of the model. PubDate: 2019-03-01 DOI: 10.1007/s00605-017-1147-6

Abstract: We answer a recent question of Bustamante concerning a representation formula for Bernstein operators. PubDate: 2019-03-01 DOI: 10.1007/s00605-018-1164-0

Abstract: Smooth molecular decompositions for holomorphic Besov and Triebel–Lizorkin spaces on the unit disk of the complex plane are constructed. The decompositions are used to obtain a boundedness result for Fourier multipliers. As further applications, we provide equivalent norms for the spaces under consideration, we consider the implications of the results on Hardy and Hardy–Sobolev spaces, and we study boundedness of coefficient multipliers. PubDate: 2019-03-01 DOI: 10.1007/s00605-018-1251-2

Abstract: Let A and G be finite groups of relatively prime orders and suppose that A acts on G via automorphisms. We demonstrate that if G has a maximal A-invariant subgroup M that is nilpotent and the Sylow 2-subgroup of M has class at most 2, then G is soluble. This result extends, in the context of coprime action, a solubility criterion given by W.E. Deskins. PubDate: 2019-03-01 DOI: 10.1007/s00605-018-1256-x

Abstract: In this article we characterize the polynomial maps \(F:\mathbb {C}^n\rightarrow \mathbb {C}^n\) for which \(F^{-1}(0)\) is finite and their multiplicity \(\mu (F)\) is equal to \(n!\mathrm V_n(\widetilde{\Gamma }_{+}(F))\) , where \(\widetilde{\Gamma }_{+}(F)\) is the global Newton polyhedron of F. As an application, we derive a characterization of those polynomial maps whose multiplicity is maximal with respect to a fixed Newton filtration. PubDate: 2019-03-01 DOI: 10.1007/s00605-018-1204-9

Abstract: We prove some results concerning the boundary of a convex set in \(\mathbb {H}^n\) . This includes the convergence of curvature measures under Hausdorff convergence of the sets, the study of normal points, and, for convex surfaces, a generalized Gauss equation and some natural characterizations of the regular part of the Gaussian curvature measure. PubDate: 2019-03-01 DOI: 10.1007/s00605-018-1194-7

Abstract: In this paper we introduce the notion of a categorical Mackey functor. This categorical notion allows us to obtain new Mackey functors by passing to Quillen’s K-theory of the corresponding abelian categories. In the case of an action by monoidal autoequivalences on a monoidal category the Mackey functor obtained at the level of Grothendieck rings has in fact a Green functor structure. PubDate: 2019-03-01 DOI: 10.1007/s00605-018-1156-0

Abstract: Using the follower/predecessor/extender set sequences defined by the first author, we define quantities which we call the follower/predecessor/extender entropies, which can be associated to any shift space. We analyze the behavior of these quantities under conjugacies and factor maps, most notably showing that extender entropy is a conjugacy invariant and that having follower entropy zero is a conjugacy invariant. We give some applications, including examples of shift spaces with equal entropy which can be distinguished by extender entropy, and examples of shift spaces which can be shown to not be isomorphic to their inverse by using follower/predecessor entropy. PubDate: 2019-03-01 DOI: 10.1007/s00605-018-1224-5

Abstract: The main purpose of this paper is to study the characterizations of John spaces. We obtain five equivalent characterizations for length John spaces. As an application, we establish a dimension-free quasisymmetric invariance of length John spaces. This result is new also in the case of the Euclidean space. PubDate: 2019-03-01 DOI: 10.1007/s00605-018-1231-6

Abstract: A cut vertex of a graph is a vertex whose removal causes the resulting graph to have more connected components. We show that the prime divisor character degree graph of a solvable group has at most one cut vertex. We also prove that a solvable group whose prime divisor character degree graph has a cut vertex has at most two normal nonabelian Sylow subgroups. We determine the structures of those solvable groups whose prime divisor character degree graph has a cut vertex and has two normal nonabelian Sylow subgroups. Finally, we characterize a subgroup determined by the prime associated with the cut vertex in terms of the structure of the prime divisor character degree graph. PubDate: 2019-03-01 DOI: 10.1007/s00605-019-01276-8

Authors:Henna Koivusalo; Michał Rams Abstract: Let \((\Sigma , \sigma )\) be a dynamical system, and let \(U\subset \Sigma \) . Consider the survivor set $$\begin{aligned} \Sigma _U=\left\{ x\in \Sigma \mid \sigma ^n(x)\notin U\,\text {for all}\,n\right\} \end{aligned}$$ of points that never enter the subset U. We study the size of this set in the case when \(\Sigma \) is the symbolic space associated to a self-affine set \(\Lambda \) , calculating the dimension of the projection of \(\Sigma _U\) as a subset of \(\Lambda \) and finding an asymptotic formula for the dimension in terms of the Käenmäki measure of the hole as the hole shrinks to a point. Our results hold when the set U is a cylinder set in two cases: when the matrices defining \(\Lambda \) are diagonal; and when they are such that the pressure is differentiable at its zero point, and the Käenmäki measure is a strong-Gibbs measure. PubDate: 2018-05-22 DOI: 10.1007/s00605-018-1187-6