Symbolic derivation of finite difference approximations for the three-dimensional Poisson equation

A symbolic procedure for deriving various finite difference approximations for the three-dimensional Poisson equation is described. Based on the software package Mathematica, we utilize for the formulation local solutions of the differential equation and obtain the standard second-order scheme (7-point), three fourth-order finite difference schemes (15-point, 19-point, 21-point), and one sixth-order scheme (27-point). The symbolic method is simple and can be used to obtain the finite difference approximations for other partial differential equations. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 593–606, 1998     

Highly branched radial block copolymers via dendritic initiation of aliphatic polyesters

Living ring opening polymerization of ε-caprolactone initiated from the numerous chain-end hydroxymethyl groups of the analogous dendrimeric and hyperbranched polyesters derived from 2,2-bis(hydroxymethyl) propionic acid is described. By controlling the size of the dendritic macromolecule and the molar ratio of ε-caprolactone, a variety of highly branched radial block copolymers are obtained. Comparison of the results obtained for the dendrimeric and hyperbranched initiators demonstrates that the reactivity of the chain-end hydroxymethyl groups in the dendrimer are significantly greater than in the isomeric hyperbranched case. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 2793–2798, 1998     

Conserving algorithms for the dynamics of Hamiltonian systems on lie groups

Summary Three conservation laws are associated with the dynamics of Hamiltonian systems with symmetry: The total energy, the momentum map associated with the symmetry group, and the symplectic structure are invariant under the flow. Discrete time approximations of Hamiltonian flows typically do not share these properties unless specifically designed to do so. We develop explicit conservation conditions for a general class of algorithms on Lie groups. For the rigid body these conditions lead to a single-step algorithm that exactly preserves the energy, spatial momentum, and symplectic form. For homogeneous nonlinear elasticity, we find algorithms that conserve angular momentum and either the energy or the symplectic form.     

Breast cancer detection by Fourier transform infrared spectrometry

Fourier transform infrared spectra of 75 biopsies from 55 cases of breast carcinoma were studied in comparison with histo-morphometry. The spectra of carcinomatous tissues are very different from those of normal tissues. There are evident correlations between the intensity of some infrared absorption bands and the volume density of malignant cells measured by optical microscopy [7]. Very high correlation coefficients are observed for phosphate monoester and phosphodiester bands; significant correlation coefficients are also observed for amide I and II bands.     

The thermal decomposition of Mg-Al hydrotalcites: effects of interlayer anions and characteristics of the final structure

The thermal decomposition of hydrotalcites (HTs) with different interlayer anions in the 298-523 K region has been investigated by using transmission electron microscopy (TEM), thermogravimetric analysis (TGA), X-ray diffraction (XRD), and IR, 27Al MAS-NMR and X-ray absorption near-edge structure (XANES) spectroscopy. The thermal stability of the HT with interlayer oxalate was remarkably higher than that of HTs with interlayer carbonate; the onset temperatures for decomposition were 523 K and 473 K, respectively. It is proposed that the basicity of the interlayer anion is the key factor in the onset of dehydroxylation of the brucite-like layers: the lower the basicity, the more thermally stable the HT compound. After heat treatment at 723 K, small Mg(Al)O domains (approximately 5 nm) within the HT crystallites cause broadening of the XRD reflections. The electron diffraction pattern consists of spots and rings, due to nonrandomly oriented crystalline material. Formation of disordered bonds, caused by nonideal packing between the decomposing adjacent cation layers in the (111) direction, could explain the expanded d value in the resulting MgO-like phase observed with XRD and electron diffraction. The orientation of the Mg(Al)O domains in the heat-treated material may be crucial for the so-called "memory effect" of HTs.     

Analyte and system eigenpeaks in nonaqueous capillary zone electrophoresis: theoretical description and experimental confirmation with methanol as solvent

A mathematical model developed for aqueous solutions and adapted to methanol as solvent was applied to predict the electromigration characteristics of analytes and background electrolytes in capillary zone electrophoresis. These characteristics are the effective mobility, and the tendency of the analyte to undergo peak-broadening due to electromigration dispersion. The input parameters for calculation like limiting mobilities and dissociation constants were experimentally determined or taken from the literature. By the aid of the model, the molar response for conductivity detection was calculated as well as the transfer ratio when indirect UV detection was used. They allow depicting the electropherogram by computer simulation. An additional important program output is the prediction of the occurrence of system- or eigenpeaks that mimic peaks of analytes or electroosmotic flow markers. The measured electropherograms were in agreement with those theoretically predicted. Deviations were attributed to ion pairing in methanolic solutions, which was not implemented in the model.     

Nonaqueous capillary electrophoresis with alcoholic background electrolytes: separation efficiency under high electrical field strengths

The effect of high voltage on capillary electrophoresis (CE) separations of anionic analytes in nonaqueous separation media was investigated. Methanol, ethanol, 1-propanol, and 1-butanol were tested as background electrolyte (BGE) solvents. Experiments were carried out with a laboratory-built CE instrument suitable for high-voltage separations. Potentials up to 60 kV were applied with reversed polarity to generate unusually high field strengths (e.g. 2000 Vcm-1) and so achieve fast and efficient separations. Highest separation efficiencies were obtained with propanol as BGE solvent, and the dependency of the efficiency on the separation voltage was more or less linear. With the other alcohols, separation efficiency decreased or remained roughly constant with increasing absolute voltage. The separation efficiencies are discussed in terms of longitudinal diffusion, Joule heating, and analyte interaction with the capillary wall. Capillary preconditioning had a varied effect on the separations in the different BGEs as the BGE and the conditioning process affected the electroosmotic flow (EOF) velocity and direction.     

Influence of solvent on temperature and thermal peak broadening in capillary zone electrophoresis

The present paper deals with the role of the solvent on thermal peak broadening. One main solvent property that determines the magnitude of the temperature gradient due to the generation of Joule heat in capillary zone electrophoresis is the thermal conductivity. As organic solvents have lower thermal conductivity than water (methanol and acetonitrile, e.g., nearly by a factor of 3) it can be hypothesized that the temperature gradient inside the capillary is more pronounced in organic solvents compared to an aqueous solution. On the other hand, the temperature dependence of the ion mobility (which is responsible for the velocity profile and thus for thermal peak broadening) is smaller in organic solvents. To get insight into the thermal effect of the solvent, first the temperature of a solution in a cylindrical tube was calculated utilizing the heat balance equation. It was shown that the two theoretical models most common in the literature (based on the analytical solution or on an assumption of the parabolic temperature profile in the tube, respectively) give the same results. The latter model was chosen for the further calculations, adding a quadratic term to express the electric conductivity as a function of the temperature. The temperature at the inner capillary wall and center as function of the capillary dimensions and the electric power was computed for electrolytes with a given conductivity at 25.0 degrees C with water, methanol, and acetonitrile as solvents. Capillary cooling systems used were circulating liquid cooling, enforced air-cooling, and natural convection in still air. The mean temperature (averaged over the cross section) resulting from Joule heating was compared with experimentally determined temperatures established upon application of an electric field; the latter temperature was derived from the measurement of the electric conductance of the background electrolyte solution and its (measured) temperature dependence. All investigations were carried out with solutions of the same initial electric conductivity (about 0.5 S.m(-1) at 25.0 degrees C). Agreement is found for natural convection conditions, and the deviation between theoretical and experimental results for the forced air and circulated liquid cooling systems can be related to the poorly defined thermal conditions of the capillaries in commercial instrumentation (with a part in a thermostated cassette and a part outside). For given conditions the temperature gradients in the organic solvents exceed largely those in water, independent of the type of cooling. As a consequence, the thermal plate height is significantly larger in organic solvents, at least under conditions where the deviation from the Nernst-Einstein limiting case is not too high. However, even for the maximum applicable field strengths the thermal plate height contributions are negligible compared to longitudinal diffusion in all solvents.     

A new alkylbenzoquinone from Embelia rowlandii Gilg. (Myrsinaceae)

A new alkylbenzoquinone named embeliquinone (1) together with five known compounds, lupeol (2), 3-O-[6′-O-palmitoyl-β-d-glucosyl]-spinasta-7,22(23)-diene (3), quercetin (4), (2S,3S,4R,8E)-2-[(2′R)-2′-hydroxy-heneicosanoylamino]-heneicosane-1,3,4-triol-8-ene (5), and β-sitosterol-3-O-β-d-glucopyranoside (6) were isolated from the MeOH leaf extract of Embelia rowlandii by using repeated open column chromatography techniques. The structure of the new compound was characterized by analyses of 1D- and 2D-NMR, and MS data. Embeliquinone (1) had moderate anti-cell proliferation activity against A549 cell line with the IC₅₀ value of 21.8 μM. In addition, 1 exhibited weak antibacterial activities against Klebsiella pneumoniae and Staphylococcus aureus with an MIC value of 206.0 μM in both cases.     

Comparison of methanol and acetonitrile as solvents for the separation of sertindole and its major metabolites by capillary zone electrophoresis

Sertindole (1-[2-[4-[5-chloro-1-(4-fluorophenyl)-1H-indol-3-yl]-1-piperidinyl]ethyl]-2-imidazolidinone), an atypical antipsychotic drug, was separated by capillary electrophoresis from its two main metabolites norsertindole and dehydrosertindole. The low solubility of the analytes in water (octanol-water partition coefficient is about 10(5)) is overcome by the use of methanol (MeOH) and acetonitrile (ACN) as solvents for the background electrolyte (BGE). Mobilities were measured in BGEs with defined pH in a broad range. It was found that in MeOH the mobility of the analytes is mainly governed by acid-base equilibria, whereas in ACN other reactions like ion pairing and homo-conjugation play a pronounced role and lead to a complex pattern of the mobility as function of the pH. However, separation can be obtained in less than 10 min in both solvent systems.