A Note on Free Groups in the Ring of Fractions of Skew Polynomial Rings

Let L be a function field over the rationals and let D denote the skew field of fractions of L[t;σ], the skew polynomial ring in t, over L, with automorphism σ. We prove that the multiplicative group D ^× of D contains a free noncyclic subgroup.     

A novel approach for strong S-Box generation algorithm design based on chaotic scaled Zhongtang system

Nonlinear Dynamics - Substitution Box (S-Box) is one of the most significant structures used to create an encryption which is strong and resistant against attacks in block encryption algorithms....     

A Short Note on the History of Chromatography at the University of Tartu, Estonia

Some historical notes on the activities of Teodor Lippmaa and Mikhail S. Tswett at the University of Tartu.     

Immobilized ruthenium complexes and aspects of their reactivity

Methodologies for the immobilization and characterization of ruthenium complexes into/onto functionalized silica gel, zeolites, polymers, dendrimers, sol–gel, nano and microparticles are described. The corresponding spectroscopic, electrochemical, and photochemical properties as well as chemical reactivities are used for their characterization and study. Comparison between the reactivities of immobilized and in solution species is presented. Some biological applications are also described.     

Characterization of polyether‐poly(methyl methacrylate)‐lithium perchlorate blend electrolytes

Solid polymer electrolyte (SPE) systems based on interpenetrating blends of poly(ethylene oxide‐co‐propylene oxide) and poly(methyl methacrylate) host matrices, with lithium perchlorate as guest salt, were prepared. These electrolytes were presented as free‐standing films, and their thermal and electrochemical properties were characterized by conductivity and electrochemical stability measurements. The properties of the interpenetrating blends of poly(ethylene oxide‐co‐propylene oxide) and poly(methyl methacrylate) host matrices as the electrolyte component of a solid‐state electrochromic device are reported and the results obtained suggest that this electrolyte provides an encouraging performance in this application. The most conducting electrolyte composition of this SPE system is the formulation designated as SPE2‐0PC (5.01 × 10^?4 S cm^?1 at about 57°C). The lowest decomposition temperature was registered with the SPE6‐15PC composition (233°C). The average transmittance in the visible region of the spectrum was above 41% for all the samples analyzed. After coloration the device assembled with 71 wt% PC presented an average transmittance of 15.71% and an optical density at 550 nm of 0.61. Copyright © 2010 John Wiley & Sons, Ltd.     

Conformational Study of Glycal-Type Neuraminidase Inhibitors

The conformational flexibility of two glycal-type neuraminidase inhibitors has been studied, using several molecular modeling techniques. In agreement with the experimental data available, an intramolecular hydrogen bond, representing a key structural feature that controls the conformer distribution in solution, has been identified. The contribution of each substituent to the overall equilibrium was evaluated using simplified derivatives. Additionally, four methods for estimating NMR coupling constants from dihedral angles were evaluated and the Haasnoot method was found to be appropriate for this class of sugars. These results should allow a better understanding of the structural parameters governing physico-chemical properties of glycal-like compounds. Supplemental materials are available for this article. Go to the publisher's online edition of Journal of Carbohydrate Chemistry to view the free supplemental file.     

Density estimates for a random noise propagating through a chain of differential equations

We here provide two sided bounds for the density of the solution of a system of n differential equations of dimension d, the first one being forced by a non-degenerate random noise and the n−1 other ones being degenerate. The system formed by the n equations satisfies a suitable Hörmander condition: the second equation feels the noise plugged into the first equation, the third equation feels the noise transmitted from the first to the second equation and so on … , so that the noise propagates one way through the system. When the coefficients of the system are Lipschitz continuous, we show that the density of the solution satisfies Gaussian bounds with non-diffusive time scales. The proof relies on the interpretation of the density of the solution as the value function of some optimal stochastic control problem.     

Effect of amine catalysts on preparation of nanometric SiO<Subscript>2</Subscript> particles and antireflective films via sol–gel method

SiO₂ sols were prepared by hydrolysis and condensation reactions of tetraethyl orthosilicate through a one step acid or a two step acid + base catalysis process, in the presence of nitric acid and four different base catalyzers, namely trimethylamine, triethylamine, tripropylamine and tributylamine. Hydrolysis of TEOS was followed by FT-IR analyses. Particle size distributions of the sols were evaluated after predetermined durations in 1–22 days. Particle growth was seen to be faster in amine catalyzed systems than in one step acid catalyzed system. The highest rate of growth was in triethylamine catalyzed system. Glass substrates were dip coated with the prepared SiO₂ sols. Effect of sol aging duration on film thickness and on light transmittance properties of the films was investigated with respect to type of base catalyst. Thicknesses of the films which were measured to be in the range of 100–400 nm, were seen to increase with aging duration of the sols. Triethylamine catalyzed system presented the highest film thickness. Films obtained from one step acid catalyzed system presented an increase of 4.8%; whereas acid + base catalyzed films provided an increase in the light transmittance of 5.7% in the first 4 days of aging. Surfaces of films were examined by FESEM and AFM. The antireflective character of the films was verified by diffuse reflectance analyses.