Nevanlinna–Pick Problem and Uniqueness of Left Inverses in Convex Domains,Symmetrized Bidisc and Tetrablock

In the paper we discuss the problem of uniqueness of left inverses (solutions of two-point Nevanlinna–Pick problem) in bounded convex domains, strongly linearly convex domains, the symmetrized bidisc and the tetrablock.     

New characterizations of the Takagi function via functional equations

We provide two new characterizations of the Takagi function as the unique bounded solution of some systems of two functional equations. The results are independent of those obtained by Kairies (Wy? Szko? Ped Krakow Rocznik Nauk Dydakt Prace Mat 196:73–82, 1998), Kairies (Aequ Math 53:207–241, 1997), Kairies (Aequ Math 58:183–191, 1999) and Kairies et al. (Rad Mat 4:361–374, 1989; Errata, Rad Mat 5:179–180, 1989).     

Time decay of the solution to the Cauchy problem for a three-dimensional model of nonsimple thermoelasticity

This paper is devoted to the investigation of the solution to the Cauchy problem for a system of partial differential equations describing thermoelasticity of nonsimple materials in a three-dimensional space. The model of linear dynamical thermoelasticity of nonsimple materials is considered as the system of partial differential equations of fourth order. In this paper, we proposed a convenient evolutionary method of approach to the system of equations of nonsimple thermoelasticity. We proved the L^p−L^q time decay estimates for the solution to the Cauchy problem for linear thermoelasticity of nonsimple materials.     

Joint universality for dependent <Emphasis Type="Italic">L</Emphasis>-functions

We prove that, for arbitrary Dirichlet L-functions \(L(s;\chi _1),\ldots ,L(s;\chi _n)\) (including the case when \(\chi _j\) is equivalent to \(\chi _k\) for \(j\ne k\)), suitable shifts of type \(L(s+i\alpha _jt^{a_j}\log ^{b_j}t;\chi _j)\) can simultaneously approximate any given set of analytic functions on a simply connected compact subset of the right open half of the critical strip, provided the pairs \((a_j,b_j)\) are distinct and satisfy certain conditions. Moreover, we consider a discrete analogue of this problem where t runs over the set of positive integers.     

Product numerical range in a space with tensor product structure

We study operators acting on a tensor product Hilbert space and investigate their product numerical range, product numerical radius and separable numerical range. Concrete bounds for the product numerical range for Hermitian operators are derived. Product numerical range of a non-Hermitian operator forms a subset of the standard numerical range containing the barycenter of the spectrum. While the latter set is convex, the product range needs not to be convex nor simply connected. The product numerical range of a tensor product is equal to the Minkowski product of numerical ranges of individual factors.     

Can 2‐acylpyrroles form an intramolecular hydrogen bond?

The formation of intramolecular hydrogen bonding by certain N‐substituted 2‐acylpyrroles has been demonstrated by B3LYP/aug‐cc‐pVDZ calculations, the quantum theory of atoms in molecules, and the natural bond orbital method. Total electron energy densities H_BCP at the bond critical point of the H?O bond were applied to analyze the strength of these interactions. The relations between quantum theory of atoms in molecules, carbonyl stretching vibrational modes ν_{C = O}, and natural bond orbital parameters associated with the formation of the C–H?O interaction have been established. The short contacts were found experimentally in the crystal structure of a new 2‐acylpyrrole derivative 5‐chloro‐2‐oxopentyl‐1‐(5‐chloro‐2‐oxopentyl)pyrrolo‐2‐carboxylate. The influence of 2‐ and N‐substitution of 2‐acylpyrroles on C‐H?O interaction energy is discussed. It was found that the methylene group may act as a proton donor leading to a red‐shift or blue‐shift phenomenon of the ν_C–H stretching mode. Copyright © 2015 John Wiley & Sons, Ltd.     

On α-Limit Sets in Lorenz Maps

The aim of this paper is to show that α-limit sets in Lorenz maps do not have to be completely invariant. This highlights unexpected dynamical behavior in these maps, showing gaps existing in the literature. Similar result is obtained for unimodal maps on [0,1]. On the basis of provided examples, we also present how the performed study on the structure of α-limit sets is closely connected with the calculation of the topological entropy.