Global stability and the Hopf bifurcation for some class of delay differential equation

In this paper, we present an analysis for the class of delay differential equations with one discrete delay and the right‐hand side depending only on the past. We extend the results from paper by U. Fory? (Appl. Math. Lett. 2004; 17 (5):581–584), where the right‐hand side is a unimodal function. In the performed analysis, we state more general conditions for global stability of the positive steady state and propose some conditions for the stable Hopf bifurcation occurring when this steady state looses stability. We illustrate the analysis by biological examples coming from the population dynamics. Copyright © 2007 John Wiley & Sons, Ltd.     

Crystallographic evidence of Gly‐d,l‐Met oxidation to its sulfoxide in the presence of gold(III): solid solution of the racemic mixture of two diastereoisomers

Crystallographic analysis of a solid solution of two diastereoisomers, i.e. ({(1S,R)‐1‐carboxy‐3‐[(R,S)‐methylsulfinyl]propyl}aminocarbonyl)methanaminium tetrachloridoaurate(III) and ({(1S,R)‐1‐carboxy‐3‐[(S,R)‐methylsulfinyl]propyl}aminocarbonyl)methanaminium tetrachloridoaurate(III), (C₇H₁₅N₂O₄S)[AuCl₄], has shown that in the presence of gold(III), the methionine part of the Gly‐d ,l ‐Met dipeptide is oxidized to sulfoxide, and no coordination to the Au^III cation through the S atom of the sulfoxide is observed. In view of our observation, literature reports that methionine acts as an N,S‐bidentate donor ligand forming stable gold(III) complexes require verification. Moreover, it has been demonstrated that crystallization of the oxidation product leads to a substantial 77:23 excess of both S‐methionine/R‐sulfoxide and R‐methionine/S‐sulfoxide over S‐methionine/S‐sulfoxide and R‐methionine/R‐sulfoxide. The presence of two different diastereoisomers at the same crystallographic site is a source of static disorder at this site.     

Comparison of protein precipitation methods for various rat brain structures prior to proteomic analysis

Sample preparation is a fundamental step in proteomic methodologies. The quality of the results from a proteomic experiment is dependent on the nature of the sample and the properties of the proteins. In this study, various pre-treatment methods were compared by proteomic analysis; we analysed various rat brain structures after chloroform/methanol, acetone, TCA/acetone and TCA protein precipitation procedures. The protein content of the supernatant was also examined by 2-DE. We found that for four of the rat brain structures, precipitation with chloroform/methanol and acetone delivered the highest protein recovery for top-down proteomic analysis; however, TCA precipitation resulted in good protein separation and the highest number of protein spots in 2-DE. Moreover, TCA precipitation also gave high efficiency of protein recovery if prior sonication procedure was performed.     

Cramér transform and t-entropy

t-entropy is the convex conjugate of the logarithm of the spectral radius of a weighted composition operator (WCO). Let \(X\) be a nonnegative random variable. We show how the Cramér transform with respect to the spectral radius of WCO is expressed by the t-entropy and the Cramér transform of the given random variable \(X\) .     

Effect of Temperature and Composition on the Density and Viscosity of Binary Mixtures of Ionic Liquid with Alcohols

Density and viscosity were determined for the binary mixtures containing the ionic liquid 1-butyl-3-methylimidazolium thiocyanate ([BMIM][SCN]) and 1-alcohols (1-butanol, 1-pentanol and 1-hexanol) at six temperatures (298.15, 308.15, 318.15, 328.15, 338.15 and 348.15) K and ambient pressure. The density and viscosity correlation for these systems was tested by an empirical second-order polynomial and by the Vogel-Fucher-Tammann equation in wide ranges of temperatures. Excess molar volumes were described by the Redlich-Kister polynomial expansions. The density and viscosity variations with composition were described by polynomials. A qualitative analysis of the trend of the properties with solvent and temperature was performed. The obtained results indicate that ionic liquid interactions with 1-alcohols are strongly dependent on the special trend of packing of this ionic liquid into hydroxylic solvents. As previously observed, an increase of the 1-alcohol carbon-chain length leads to lower interactions on mixing. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.     

Influence of rhodium additive on hydrogen electrosorption in palladium-rich Pd–Rh alloys

Hydrogen electrosorption into Pd-rich (>80 at.% Pd in the bulk) Pd–Rh alloys has been studied in acidic solutions (0.5 M H₂SO₄) using cyclic voltammetry and chronoamperometry. The influence of temperature (in the range between 283 and 328 K), electrode potential and alloy bulk composition on hydrogen electrosorption properties of Pd–Rh alloys is presented. It has been found that the additive of Rh to Pd–Rh alloys increases the maximum hydrogen solubility (for Rh bulk content below 10 at.%), decreases the potential of absorbed hydrogen oxidation peak and decreases the potential of the α → β phase transition. Increasing temperature decreases the potential of absorbed hydrogen oxidation peak, the maximum hydrogen solubility, and the potential of the α → β phase transition. The amounts of electrosorbed hydrogen for α- and β-phase boundaries, i.e., α_max and β_min, have been determined from the integration of the initial parts of current–time responses in hydrogen absorption and desorption processes. The H/M ratio corresponding to α_max increases with increasing Rh content, while for β_min a maximum of H/M ratio is observed for the alloys containing ca. 95% Rh.

     

(Liquid + liquid) equilibria of binary systems containing hyperbranched polymer Boltorn® H2004 – Experimental study and modelling in terms of lattice-cluster theory

(Liquid + liquid) phase equilibria (LLE) of binary mixtures containing hyperbranched polymer Boltorn® H2004 and n-alkanes (n-hexane, n-heptane, n-octane, and n-decane) were studied over the temperature range from about (260 up to 360) K. The polymer is partially miscible with n-alkanes and the solubility decreases with an increase of the chain length of the solvent. Corresponding LLE phase diagrams including spinodal and binodal (liquid + liquid) coexistence curves were calculated in terms of the statistical mechanics – based on the lattice-cluster theory, based only on the upper critical solution temperature, and the polymer chain architecture. The results show semi-qualitative agreement of predicted and experimental equilibrium compositions and temperatures. Boltorn® H2004 reveals complete miscibility in the liquid phase with alcohols (C₁–C₈), aromatic hydrocarbons (benzene, toluene, and thiophene), and ethers (methyl tetra-butyl ether, ethyl tetra-butyl ether, and tetrahydrofurane).     

Liquid phase hydrogen transfer to cyclopentanone over MgO-I2 and MgO-RI catalysts

Instead of cyclopentanol, 2-cyclopentylidene-cyclopentanone is the main product of liquid phase hydrogen transfer from secondary alcohols to cyclopentanone in the presence of pure MgO [1]. In the present work it has been shown that a significant increase in the selectivity towards cyclopentanol has been observed for MgO treated with I₂ or alkyl iodides.