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].     

Conjugation and hydrogen bonding in a curcumin analogue

The strongly yellow‐coloured compound 5‐(5‐methyl‐2,3,4,5‐tetra­hydro­furan‐2‐yl)‐1‐phenyl­pent‐4‐ene‐1,3‐dione, C₁₆H₁₄O₃, has different substituents on each side of the dione group. The mol­ecule is essentially planar and the structure indicates a continuous conjugation from the furyl moiety to the carbonyl O atom in the enol group, as well as a strong conjugation within the enol group itself. The enol H atom is bonded to the O atom closest to the furyl group. Weak hydrogen bonds are indicated and comments about the colour of the compound are given.     

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.     

A substructure-based SAR model for odor perception in humans relevant to health risk assessments

The ability of humans to perceive odors is a very complex phenomenon involving the selective binding of molecules to approximately 1000 olfactory receptors. Accordingly, the derivation of a substructure-based SAR model can be expected to be problematic. Yet, based upon published data on odor thresholds of volatile organic chemicals, we were able to derive such an SAR model. An examination of the structural determinants and related modulators indicates that lipophilicity is a major contributor to olfactory perception. The availability of a substructure-based SAR model permits an examination of the relationship between the presence in the environment of odorous chemicals and public health risks.     

Dynamics in dumbbell domains I. Continuity of the set of equilibria

We analyze the dynamics of a reaction-diffusion equation with homogeneous Neumann boundary conditions in a dumbbell domain. We provide an appropriate functional setting to treat this problem and, as a first step, we show in this paper the continuity of the set of equilibria and of its linear unstable manifolds.     

Bioassay-guided isolation of an anti-ulcer compound, tagitinin C, from Tithonia diversifolia: role of nitric oxide, prostaglandins and sulfhydryls

Tithonia diversifolia is a medicinal plant from the Municipality of Suchiapa, Chiapas, Mexico, that according to local folk medicine is considered useful in the treatment of gastric ulcers. The aim of the present study was to investigate the gastroprotective activity of T. diversifolia by using an ethanol-induced gastric ulcer experimental model in male Wistar rats. The results showed that T. diversifolia had gastroprotective activity, and that the dichloromethane extract had the highest protective activity (close to 90% when using doses between 10 to 100 mg/kg), and that further the compound tagitinin C isolated from this extract was the main active gastroprotective agent. Rats treated with tagitinin C suspended in Tween 80 at 1, 3, 10 and 30 mg/kg showed 37.7, 70.1, 100, and 100% gastroprotection, respectively. The effect elicited by tagitinin C (30 mg/kg) was not attenuated by pretreatment with either N(G)-nitro-L-arginine methyl ester (70 mg/kg, i.p.), a nitric oxide (NO) synthase inhibitor, N-ethylmaleimide (10 mg/kg, s.c.), a blocker of sulfhydryl groups, or indomethacin (10 mg/kg, s.c.), a blocker of prostaglandin synthesis, which suggests that the gastroprotective mechanism of action of this sesquiterpene lactone does not involve NO, sulfhydryl groups or prostaglandins.     

Quasistatic Thermoviscoelastic Frictional Contact Problem with Damped Response

We analyze a problem which describes the frictional contact between a thermoviscoelastic body and a rigid foundation. The process is assumed to be quasistatic and the contact is modeled by a general normal damped response condition with friction law and heat exchange. Then we present a variational formulation of the problem, which is set in an abstract form as a system of evolution equations for the displacements and temperature. We establish the existence and uniqueness of the weak solution, using general results on evolution equations with monotone operators and fixed point arguments. Finally, we study the continuous dependence of the solution with respect to the initial data and contact conditions.     

A quadratic convergence scheme for determining families of periodic solutions

Global and local boundedness results for the solutions of a certain class of A₂-degenerate parabolic equations are proved.