On the Recursive Sequence

The boundedness, global attractivity, oscillatory and asymptotic periodicity of the nonnegative solutions of the difference equation?in the title is investigated, where all the coefficients are nonnegative real numbers. The paper is motivated by an open problem proposed by Ladas [Open problems and conjectures, J. Differ. Equations?Appl., 5 (1999), 211–215].     

Mixing in the Absence of the Shrinking Target Property

Using reparametrizations of linear flows, we show that thereexist area-preserving real analytic maps of the three-dimensionaltorus that are ‘mixing of all orders’ and do notenjoy the monotone shrinking target property. Prior to that,we give a short proof of a result of Kurzweil from 1955: namely,that a translation T of the torus T^d has the monotone shrinkingtarget property if and only if the vector is badly approximable(that is, of constant type). 2000 Mathematics Subject Classification37E45, 37A25, 11J13. 2000 Mathematics Subject Classification37E45, 37A25, 11J13.     

On a Lie-theoretic approach to generalized doubly stochastic matrices and applications

In this article, we study generalized doubly stochastic matrices using the theory of Lie groups and Lie algebras. Applications to the inverse eigenvalue problem for symmetric doubly stochastic matrices are presented.     

Topologically mixing and minimal but not ergodic, analytic transformation onT 5

We give an example of an analytic transformation onT ⁵ that conserves the Haar measure, that is minimal and topologically mixing, but is not ergodic.     

Synthesis of tin oxides SnO2–x in the entire composition range (x = 0 to 1) by ion‐beam sputter‐deposition

Ion‐beam sputter‐deposition (IBSD) was used to reactively deposit tin oxide crystalline films at oxygen fluxes of 3–15 sccm and at substrate temperatures of 100–600 °C. Analysing the samples by X‐ray diffraction and Raman spectro‐ scopy yields a map of the crystalline structures in dependence on the growth parameters. In addition to SnO₂, pure SnO films of high quality and an intermediate phase such as Sn₂O₃ or Sn₃O₄ can be reproducibly obtained. Thus, IBSD is, to our knowledge, the only thin‐film deposition technique verified yet to reliably produce samples in the entire composition range of tin oxides. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Polyazapodands Derived from Biphenyl. Study of their Behaviour as Conformationally Regulated Fluorescent Sensors

Eight new polyazapodands containing a 4,4′-substituted biphenyl moiety have been synthesised. Four (7, 8, 9 and 11) are functionalised on positions 4 and 4′ with a nitro group and four (1, 2, 3 and 10) with a dimethylamino substituent. Comparison of the emission behaviour of 1, 2, 3 with that of the reference compounds 10 and tetramthylbenzidine, clearly suggests that a modification in the dihedral angle between the biphenyl rings is an important factor in determining the fluorescent response of the molecule. The fluorescence is pH dependent, due to the formation of intramolecular hydrogen bonds between protonated aliphatic nitrogens and a carbonyl oxygen, which influences the aforementioned dihedral angle. A crystal structure resolved by X-ray diffraction of 7·2HCl has been determined, and confirms the dependence of the angle and the rigidity on the hydrogen bonding. The complexation properties of these ligands have been studied with Zn²⁺, Cd²⁺, Ni²⁺, Cu²⁺ and Pb²⁺, which show that the number of amino groups within the pendants has a strong influence on the nature of the complexation and the fluorescent response of each ligand.