Spatial behavior for solutions in heat conduction with two delays

In this note, we investigate the spatial behavior of the solutions of the equation proposed to describe a theory for the heat conduction with two delay terms. We obtain an alternative of the Phragmén-Lindelöf type, which means that the solutions either decay or blow-up at infinity, both options in an exponential way. We also describe how to obtain an upper bound for the amplitude term. This is the first contribution on spatial behavior for partial differential equations involving two delay terms. We use energy arguments. The main point of the contribution is the use of an exponentially weighted energy function.     

Trapping organic molecules in sol–gel aluminosilicate matrices

Inorganic materials may be tailored to obtain specific pore size distributions and surface structures. In this work we present the synthesis of faujasite type amorphous aluminosilicate matrices by the sol–gel process. One of the preparations included the use of mesitylene as a template to create additional porosity. The powders were used to encapsulate the dyes methylene blue (MB) and malachite green (MG). Several analysis were performed, including X-ray diffraction (XRD), small angle X-ray scattering (SAXS), nitrogen adsorption/desorption, scanning electron microscopy (SEM), UV–vis, and diffuse reflectance spectroscopy. According to the results, MB and MG were effectively trapped in the aluminosilicate matrix.     

Exponentially Small Splitting for the Pendulum: A Classical Problem Revisited

In this paper, we study the classical problem of the exponentially small splitting of separatrices of the rapidly forced pendulum. Firstly, we give an asymptotic formula for the distance between the perturbed invariant manifolds in the so-called singular case and we compare it with the prediction of Melnikov theory. Secondly, we give exponentially small upper bounds in some cases in which the perturbation is bigger than in the singular case and we give some heuristic ideas how to obtain an asymptotic formula for these cases. Finally, we study how the splitting of separatrices behaves when the parameters are close to a codimension-2 bifurcation point.     

Dielectronic recombination of lithium-like gold: Towards QED tests

Dielectronic recombination (DR) and radiative recombination (RR) of lithium-like gold in the energy range of 0 to 225 eV have been studied at the Experimental Storage Ring (ESR) of the GSI in Darmstadt. Main objective of the measurements is the precise determination of the 2s_1/2−2p_1/2 energy splitting as an additional QED test. This novel method, developed at the ESR [1], is based on the extrapolation of a multitude of measured resonances Au⁷⁵⁺ (1s²2p_1/2 nl_j) up to the series limit (n = ∞). Furthermore experimental data for the Au⁷⁵⁺ (1s²2p_3/26l_j) resonance manifold are presented. This revised version was published online in July 2006 with corrections to the Cover Date.     

Experimental Determination of the Useful Reflection Coefficient of Non-Cooperative Targets for a Time-of-Flight Laser Rangefinderx

An experimental verification of the reflection properties of non-cooperative targets for a time-of-flight laser rangefinder is proposed. Indeed, knowing the light scattering physical properties of usual targets is necessary to determine the optical power budget of such a device. The useful reflection coefficient (RC) is contained at between 0.6 and 0.7 at the wavelength λlD (=820 nm), polar diagrams presenting almost a lambertian shape for incident angles lower than 60°. The useful RC thus corresponds to the value of the lambertian RC increased by the contribution of the specular RC.Presented at the 7th International Workshop on Multiple Scattering Lidar/Light Experiments (MUSCLE7). July 21–23 1994, Chiba, Japan.     

Axisymmetric configurations of bipolar liquid crystal droplets

Received July 4, 2001 / Published online April 10, 2002     

Critical validation of a new simpler approach to estimate aqueous pKa of drugs sparingly soluble in water

A simple linear approach to estimate the aqueous pK_a of compounds sparingly soluble in water, mainly drugs, from solely one pK_a value determined in any methanol/water mixture is evaluated. The parameters (slope and intercept) of the linear relationships are related to the solvent composition and can be easily calculated according to the acidic or basic functional group of the compound. The method has been tested using the available literature data for phenols, aliphatic carboxylic acids, benzoic acid derivatives, both ortho and non-ortho substituted, amines and imidazole derivatives. The study involves the whole range of solvent composition and about one hundred compounds which show a wide variety of aqueous pK_a, from 1.3 to 12.4. The differences between calculated and previously published aqueous pK_a values are less of 0.2 pK units. Consistent values are obtained whatever the composition of methanol/water mixture employed in the experimental measurements. The results support the usefulness of the tested method as a very simple approach to get reliable aqueous pK_a values for sparingly soluble drugs.     

1,2-Naphthoquinone-2-thiosemicarbazone as a new acid-base indicator in isopropyl and tert-butyl alcohol media

1,2-Naphthoquinone-2-thiosemicarbazone is proposed as an acid-base indicator for use in isopropyl and tert-butyl alcohol media. The dissociation constants have been determined in both media and the colour transition, sensitivity and sharpness of the indicator are described by means of chromatic parameters. The indicator has been used for determination of some organic acids, with errors of less than 1%.