Hermite type ladders in q-Weyl algebras

In this paper we show that the q-deformed commutator for a ladder is related to the usual commutator of the modified ladder. In addition, we consider a family of ladders in the (q, h)-Weyl algebra, which gives a factorization of certain second order difference equations.     

Solutions in Hölder spaces of boundary-value problems for parabolic equations with nonconjugate initial and boundary data

The first and second one-dimensional boundary-value problems for parabolic equations are investigated in the case where the conjugation conditions for all required orders are not satisfied. The existence and uniqueness are proved. Estimates of solutions in classical and weighted Hölder spaces are obtained. We prove that the violation of conjugation for the given functions on the boundary of the domain at the initial-time moment causes the appearance of singular solutions. The order of singularity (as a power of t) is found for the singular solutions for t = 0.     

Exploring the performance of small- and medium-sized enterprises through the credit crunch

Small- and medium-sized enterprises (SMEs) are major contributors to most western economies. They are often supported by government policies, and in the UK the government encourages banks to lend to them. It is generally believed that the credit crunch has had an impact on the performance of SMEs. This study looks at the impact of the crunch using large samples from 2007 through to 2010. It looks at performance by region, age and industrial sector (SIC code). It then proceeds to explore the modelling of default over the years, with a focus on young businesses. It was found that there is a degree of stability within the models, though the level of default varies across years. Young businesses, as has been found before, are shown to be more vulnerable.     

Synchronous ultrasonic Doppler imaging of magnetic microparticles in biological tissues

We considered applicability of acoustic imaging technology for the detection of magnetic microparticles and nanoparticles inside soft biological tissues. Such particles are widely used for magnetically targeted drug delivery and magnetic hyperthermia. We developed a new method of ultrasonic synchronous tissue Doppler imaging with magnetic modulation for in vitro and in vivo detection and visualization of magnetic ultradisperse objects in soft tissues. Prototype hardware with appropriate software was produced and the method was successfully tested on magnetic microparticles injected into an excised pig liver.     

Regioselective silylation of sugars through palladium nanoparticle-catalyzed silane alcoholysis

Palladium(0)-catalyzed silane alcoholysis was applied to sugars for the first time using tert-butyldimethylsilane (TBDMS-H) and Ph(3)SiH as the silanes. The catalyst is a colloidal solution of Pd(0) generated in situ from PdX(2) (X = Cl(-), OAc(-)) and TBDMS-H in N,N-dimethylacetamide. The colloid has been characterized by dynamic light scattering and transmission electron microscopy and consists of catalytically highly active nanoparticles of approximately 2 nm diameter. The silane alcoholysis reaction is an effective method for the regioselective silylation of methyl and phenyl glycosides and generates hydrogen gas as the only side product. For many of the sugar substrates investigated, the distribution of regioisomers obtained is complementary to that of the traditional R(3)SiCl/base (base = pyridine, imidazole) methodology and gives convenient access to the 3,6- rather than the 2,6-silylated pyranosides, obtained as the main product by the silyl chloride method. The method also allows a selective axial silylation of levoglucosan and 1,3,5-O-methylidene-myo-inositol. In an attempt to rationalize the observed regioselectivities, ab initio predictions (HF/3-21G) have been made on the relative energies of some of the silylated products. They suggest that the observed regioselectivities do not reflect a kinetic vs thermodynamic product distribution but are induced by the silylation agent employed. Models for the possible origin of the observed regioselectivity in both silylation methods (silane- and silyl chloride-based) are discussed.     

Phase studies of surfactant–water systems

Significant advances have been made in establishing phase behavior of a number of nonionic, cationic, anionic, catanionic and fluorinated surfactants in water. An interest in phase equilibria existing at sub-ambient temperatures is developing. The study of cubic, intermediate, defective lamellar and sponge phases is an active field of research at present. Further work is needed in exploring thermodynamic stability of rigid nanodisks and densely packed vesicles. Colloidal aspects, thermodynamic and volumetric properties of the surfactant-containing systems deserve special attention.     

Growth and fire resistance of colloidal silica-polyelectrolyte thin film assemblies

Thin films of colloidal silica were deposited on cotton fibers via layer-by-layer (LbL) assembly in an effort to reduce the flammability of cotton fabric. Negatively charged silica nanoparticles of two different sizes (8 and 27 nm) were paired with either positively charged silica (12 nm) or cationic polyethylenimine (PEI). PEI/silica films were thicker due to better (more uniform) deposition of silica particles that contributed to more than 90% of the film weight. Each coating was evaluated at 10 and 20 bilayers (BL). All coated fabrics retained their weave structure after being exposed to a vertical flame test, while uncoated cotton was completely destroyed. Micro combustion calorimetry confirmed that coated fabrics exhibited a reduced peak heat release rate, by as much as 20% relative to the uncoated control. The 10 BL PEI-8 nm silica recipe was the most effective because the coating is relatively thick and uniform relative to the other systems. Soaking cotton in basic water (pH 10) prior to deposition resulted in better assembly adhesion and flame-retardant behavior. These results demonstrate that LbL assembly is a useful technique for imparting flame retardant properties through conformal coating of complex substrates like cotton fabric.     

Selective hydrodechlorination of fluorinated arylamines

Chlorine-containing polyfluorinated anilines and meta-phenylenediamines undergo selective hydrodechlorination easily upon reduction by zinc in aqueous ammonia. A new approach is thus provided to synthetically valuable, partially fluorinated arylamines based on utilizing polyfluorochloroarenes, which are available as intermediates of perfluoroarene production from perchloroarenes. When chlorine atoms are present in positions both ortho and para to the amino group, para chlorine is initially eliminated. Based on this reaction, a one-pot synthesis of partially fluorinated 4-aminopyridines from 3,5-dichlorotrifluoro- and 3-chlorotetrafluoropyridine has been realized.