Some heteroclinic solutions of a model of skin pattern formation

In this paper we study travelling wave solutions to a system of four non‐linear partial differential equations, which arise in a tissue interaction model for skin morphogenesis. Under the ‘small‐stress’ assumption we prove the existence and uniqueness (up to a translation) of solutions with the dermis and epidermis cell densities being positive, which are a perturbation of a uniform epidermal cell density. We discuss the problem of the minimal wave‐speed. Copyright © 2004 John Wiley & Sons, Ltd.     

Influence of heat treatment conditions on the porosity changes of sulfonated styrene/divinylbenzene copolymers

Sulfonic cation exchangers with two ion exchange group concentrations (0.5 and 2.4 mmol/g, samples A and B, respectively) were obtained by sulfonation of a porous styrene (S) and divinylbenzene (DVB) copolymer with chlorosulfonic acid. Strong thermal decomposition of the sulfonated copolymer A, accompanied by significant changes in its porous structure, starts at ca. 400°C. The char has no sulfonic groups. After heat treatment at 400°C in steam, a sorbent was obtained (yield 65%) that shows higher phenol sorption than the untreated sample when related to the bed volume. The chlorosulfonic derivatives of the initial copolymer were less thermally resistant than the sulfonic ones obtained by hydrolysis. Pyrolysis of the cation exchanger B, in its H+ and Ca²⁺ forms, was carried out at 900°C (yield of both chars close to 30%). By subsequent steam activation at 800°C to a 50% burn-off of the char, sorbents with well-developed, but distinctly different, porous structures were obtained. The activated char from the sulfonated copolymer in its hydrogen form was highly microporous and indicated an effective surface area of 1180 m²/g. However, because of a low contribution of mesopores, its ability to adsorb phenol from the liquid phase was not very high. The activated char from the calcium-doped copolymer, indicating a smaller surface area (580 m²/g) but characterized by a well-developed mesoporosity, was a better sorbent for phenol. © 1994 John Wiley & Sons, Inc.     

The twisted SU(N) group. On the C *-algebra C(S μ U(N))

It is proved that C(S U(N)) is a type I C ^*-algebra.     

Shear-induced coalescence of emulsified oil drops

Crude oil droplets, when suspended in water, possess negative surface charges which give rise to double-layer repulsive forces between the drops. According to conventional DLVO theory, the magnitude of this repulsion (based on the measured zeta potential) is more than sufficient to prevent coalescence of the droplets. Indeed, when two such droplets were brought together on direct (i.e., "head-on") approach, coalescence was rarely observed. Upon oblique approach, however, the same droplets were seen to coalesce readily. An oblique encounter must necessarily give rise to lateral relative motion-or shearing-between the droplet surfaces. It is speculated that, if the charge distributions at the droplet surfaces were heterogeneous, lateral shearing would facilitate many encounters between surface patches of different zeta potentials across the intervening water film. If the repulsion across any local region were sufficiently weak to allow formation of an oil bridge across the water film, coalescence of the drops would follow inevitably. With the hypothesis of surface heterogeneity, it is not necessary to invoke any additional colloidal interactions (such as "hydrophobic forces") to account for the observed droplet-droplet coalescence. This finding may have important implications for the underlying mechanisms of emulsion stability in general and the commercial extraction of bitumen from oil sands in particular.     

Sandwich structures at oil-water interfaces under alkaline conditions

Equilibrium liquid crystal (LC) layer on an interface between crude oils and water was observed at high pH. This layer is composed mainly of sodium naphthenates produced in situ at the water/oil interface. Transient LC layer was also evolved at the interface of aqueous phase of sodium hydroxide solutions and oleic phase of naphthenic acid (NA) solutions as result of a chemical reaction between NaOH and NA. This chemical reaction causes transport process resulting in a disturbance of the interface. Optical observation of this interface disturbance reviled that the interface covered with LC shows considerably lower flexibility as compared to LC free interface. The LC layer eventually dissolves in the water phase at low oil-to-water ratio, while at high oil-to-water ratio it can form an equilibrium phase, which spreads spontaneously at the oil-water interface.     

Fluorescence lifetimes and spectral properties of protochlorophyllide in organic solvents in relation to the respective parameters in vivo

In this work, absorption and fluorescence spectra of protochlorophyllide (Pchlide), as well as its fluorescence lifetime, were investigated in organic solvents having different physical properties. The obtained Pchlide spectral features are discussed in relation to the parameters describing solvent properties (refractive index and dielectric constant) and taking into account the specific solvent-Pchlide interaction. The correlation of Pchlide Qy and Soret absorption bands with solvent polarizability function ((n2 - 1)/(n2 + 2)) has been found; however, the dispersion of the observed points was rather high. A small Stokes shift of a magnitude between 50 and 300 cm(-1) was found, which indicates low sensitivity of Pchlide to nonspecific solvation. The fluorescence decay of Pchlide was single exponential in all the investigated solvents, with the lifetime value ranging from 5.2 ns for dioxane to 3.5 ns for methanol. Dependence of the obtained fluorescence lifetimes on the solvent orientation polarizability, a parameter being the function of both refractive index and dielectric constant, was discussed. In water-methanol mixtures, a further decrease of the fluorescence lifetime was observed, giving values of 2.9 ns for 25% methanol. Double-exponential decay of Pchlide fluorescence was found for Pchlide in a solution of 15% methanol with the lifetimes of 4.5 +/- 0.5 ns and 1.2 +/- 0.3 ns and in pure water with the lifetimes of 2.5 +/- 0.5 ns and 0.4 +/- 0.1 ns. The obtained results are discussed in relation to spectroscopic properties of Pchlide in vivo.     

Oxidative reactivity of Cu-TESHHK- and its alanine analogues

Redox properties of Cu(II) complexes of the terminally blocked hexapeptide -TESHHK- and a series of its alanine substituted analogs: -TASHHK-, -TEAHHK-, -TESAHK-, -TESHAK-, were investigated in their reactions with hydrogen peroxide in solution and by cyclic voltammetry in a broad range of pH. The formation of reactive oxygen species was followed with the use of spectrophotometric indicators, NDMA and NBT. The results indicate that the ability of these complexes to generate hydroxyl-like radicals correlates with the formation of active Cu(III) complexes resulting from the oxidation of Cu(II) by H2O2, which interact with further H2O2 molecules specifically.     

Identification of selenium species in urine by ion-pairing HPLC–ICP–MS using laboratory-synthesized standards

This study focused on the detection/identification of possible selenium metabolites in human urine. Organoselenium compounds not commercially unavailable were synthesized and characterized by electrospray mass spectrometry. Separation of selenomethionine, methylselenomethionine, trimethylselonium, selenoethionine, and selenoadenosylmethionine was achieved by ion-pairing HPLC with a mobile phase of 2 mmol L^–1 hexanesulfonic acid, 0.4% acetic acid, 0.2% triethanolamine (pH 2.5), and 5% methanol. The column effluent was introduced on-line to inductively coupled plasma–mass spectrometry for selenium-specific detection (⁷⁷Se and ⁷⁸Se). For selenium speciation in urine, solid-phase extraction was carried out using C₁₈ cartridges modified with hexanesulfonic acid. Selective retention of cationic species was observed from acidified urine (perchloric acid, pH 2.0). After elution with methanol, evaporation, and dissolution in the mobile phase, the sample was introduced to the HPLC–ICP–MS system and the chromatographic peaks were assigned by adding standards. The species identified in urine were selenomethionine, trimethylselonium ion, and selenoadenosylmethionine. The last species was detected for the first time and our results suggest that selenomethionine might enter the metabolic pathway of its sulfur analog in the activated methylation cycle.Kazimierz Wrobel and Katarzyna Wrobel are on the leave from the Institute of Scientific Research, University of Guanajuato, L. de Retana No. 5, 36000 Guanajuato, Gto., Mexico     

Iterations of holomorphic maps of infinite dimensional homogeneous domains

In this paper regions of variability are determined and a distortion theorem is proved for iterations of holomorphic maps of bounded symmetric homogeneous domains inJ ^*-algebras.