Sinc-Collection Methods for Two-Point Boundary Value Problems

A collocation method is developed for the approximate solutionof two-point boundary-value problems with mixed boundary conditions.The method is based on replacing the exact solution by a linearcombination of Sinc functions. No integrals need to be evaluatedapproximately when setting up the resulting system of linearequations. The error of the method converges to zero like O(exp(-cN²)),as N, where N is the number of collocation points used, andwhere c is a positive constant independent of N. It is claimedthat the method is superior to the Sinc-Galerkin method dueto its simple implementation and possible extensions to moregeneral boundary-value problems.     

Key properties of monohalogen substituted phenols: interpretation in terms of the electron localization function

This paper is an attempt to bridge the key properties of monohalogen substituted phenols with the electronic localization function, which has a vivid 3D topological pattern and the vector gradient field of which is determined by the electron transition current density. A primary goal is to interpret the ‘anomalous’ strength of the intramolecular hydrogen bond O—H···X formed in cis ortho-X substituted phenols, depending upon the halogen atom (X = F, Cl, and Br) in terms of the populations of the electronic localization function basins and a so-called core valence bifurcation index. A theoretical model is considered aiming to explain convincingly the cis-trans conversion in ortho-X phenols occurring in some solvents and resulting in the experimentally observed splitting of the ν_OH stretch and based on the Pauling model. Characteristic harmonic vibrational modes of all monohalogen substituted phenols are discussed thoroughly. The order of stability of monohalogen substituted phenols is established at a high level of computational performance, showing the ‘anomalous’ order of stability of fluorophenols, the result being that, in contrast to Cl and Br, the F atom favours the trans meta position over the cis ortho with formation of the intramolecular hydrogen bond.     

Charged hard dumbbell in the binding mean-spherical approximation

A simple model for charged hard dumbbell is proposed in the binding mean-spherical approximation (BIMSA). The thermodynamic properties are analytical solutions of the unique screening parameter Γ^B with full association. Critical point and vapour-liquid coexistence curve are identical to those of Kalyuzhnyi, Yu. V., 1998, Molec. Phys., 94, 735, where a site-site integral equation has to be solved. Substituting Γ without association for Γ^B, the BIMSA reduces to the simple interpolation scheme (SIS). A simple interpolation between the SIS and the BIMSA is proposed: this gives the critical point (T_c? = 0.0525, p?_c = 0.0640) which, for the time being, is the closest to the computer simulation results. Similarity between the charged hard dumbbell and the restricted primitive model of electrolyte is also addressed.     

An ultrastructural study of the interaction of a fungal endoglucanase from Humicola insolens with cotton fibres

Because cellulases are finding more applications in the textile and detergent industries, their effect on cotton fibres must be evaluated. For this purpose, the action of a recombinant cellulase, endoglucanase V from the fungus Humicola insolens, has been followed by scanning electron microscopy (SEM) in classical longitudinal views as well as in cross-sections of cotton fibres. The experiments were conducted at large enzyme dilution typical of conditions where cellulases are used for biopolishing, i.e. for the removal of defects created by mechanical abrasion. Endoglucanase V appears to restrict its action to the hydrolysis of the loose fibrils created at the surface of the fibres and no indication of extensive enzyme penetration and damage to the interior of the fibres could be detected by SEM. The adsorption sites for endoglucanase V on cotton fibres were examined by transmission electron microscopy (TEM) on ultrathin cross-sections after immuno-gold labeling of the enzyme. This approach showed that the enzymes did not penetrate the fibres but remained at their surface. The use of an immuno-gold labeled cellulase provides a new way to probe the surface features of cotton fibres This revised version was published online in August 2006 with corrections to the Cover Date.     

Flag Varieties and the Yang-Baxter Equation

We investigate certain bases of Hecke algebras defined by means of theYang–Baxter equation, which we call Yang–Baxter bases. These bases areessentially self-adjoint with respect to a canonical bilinear form. In thecase of the degenerate Hecke algebra, we identify the coefficients in theexpansion of the Yang–Baxter basis on the usual basis of the algebra withspecializations of double Schubert polynomials. We also describe theexpansions associated to other specializations of the generic Heckealgebra.     

PHOTOREACTIVITY OF 5-GERANOXYPSORALEN AND LACK OF PHOTOREACTION WITH DNA

5-Geranoxypsoralen, commonly called bergamottin, a major furocoumarin contained in bergamot oil, is reported in vitro as a highly photoreactive psoralen. In ethanol, it exhibits quite a high triplet state quantum yield (approximately 0.37). The triplet state is involved in subsequent photochemistry which depends on the initial concentration and on the presence of oxygen. In contrast to most psoralens, absorption and fluorescence data suggest that 5-geranoxypsoralen does not interact with DNA in the dark. No UVA-induced interstrand cross-links in DNA were shown.     

Thermodynamic properties and phase equilibria of charged hard sphere chain model for polyelectrolyte solutions

A recent thermodynamic perturbation theory for flexible polyelectrolyte solutions is extended to study thermodynamic properties and phase equilibria for polyelectrolyte solutions with different polyion, chain lengths. Osmotic pressure, activity coefficient of an individual ion (polyion or counterion) and average activity coefficient are calculated. Except for the activity coefficient of the polyion, the chain length dependence of the properties is small. Also presented are vapour-liquid equilibrium coexisting curves, vapour pressures and critical points. As the polyion chain length approaches infinity the critical properties (temperature, pressure and density) become constants.     

The perpendicular fundamental v5 of chloroform 12CH35Cl3: high resolution infrared study of the v5 band together with the millimetre-wave rotational spectrum

The infrared spectrum of the perpendicular fundamental v₅ of chloroform around 776 cm^?1 has been studied by applying two high resolution methods. A short range from the central part of the spectrum was measured with a diode laser by using a cold jet sample including chloroform in natural isotopic abundancies. More than 100 rotational lines of ¹²CH³⁵Cl₃ could be assigned. The whole band region was measured by a Fourier transform spectrometer at a resolution of 0.0010cm^?1. In this case an isotopically pure sample of ¹²CH³⁵Cl₃ was used. Starting from the results of the diode laser investigation more than 2000 lines could be assigned with J_max = 91 and K_max = 58. In addition to the infrared spectra, millimetre-wave lines also were measured. A total of 58 lines corresponding to J values 22, 23 and 35 at the excited vibration state v₅ = 1 were assigned and analysed. All the data from three different spectra were simultaneously fitted and, for example, the results v₀ = 775.961 50(3) cm^?1, 98, B₅-B₀ = ?0.180171(22) × 10^?3cm^?1, C₅ ? C₀ = ?0.170 57(15) × 10^?3cm^?1, and (Cζ)₅ = 0.047 5294(11) cm^?1 were obtained.     

Density Results in Sobolev Spaces Whose Elements Vanish on a Part of the Boundary

This paper is devoted to the study of the subspace ofW ^m,r of functions that vanish on a part γ ₀ of the boundary. The author gives a crucial estimate of the Poincaré constant in balls centered on the boundary of γ ₀. Then, the convolution-translation method, a variant of the standard mollifier technique, can be used to prove the density of smooth functions that vanish in a neighborhood of γ ₀, in this subspace. The result is first proved for m = 1, then generalized to the case where m ≥ 1, in any dimension, in the framework of Lipschitz-continuous domain. However, as may be expected, it is needed to make additional assumptions on the boundary of γ ₀, namely that it is locally the graph of some Lipschitz-continuous function.