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.     

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.     

Gauge group,degeneration, and degrees of freedom in the ECSK theory of gravity. II. The Moncrief decomposition

It is shown that in the ECSK theory (coupled to an arbitrary tensor matter field) the degeneration distribution of the symplectic 2-form is closely connected with the action of the gauge groupG in the space of solutions to the field equations.     

Voltammetry at the mercury film electrodes: Comparison of theoretical and experimental results obtained for indium in thiocyanate medium

The voltammetric behaviour of the In(III)-In(Hg) system was studied at the silver-, graphite-, and glassy carbon-based mercury film electrodes under cyclic and stripping conditions in thiocyanate media. The reversible curves obtained at high thiocyanate ion concentration showed a good agreement with theoretical predictions, particularly for the cathodic process. The anodic curves obtained at thin silver-based mercury film electrodes deviated from theoretical predictions due to the interactions between indium, dissolved in mercury, and the silver substrate of the film electrode. At low thiocyanate ion concentrations, where the current was controlled partly by the rate of the preceding chemical step and partly by diffusion, the variations in the film thickness affected the position of the curve as predicted theoretically for the reversible diffusion controlled case.     

Application of Discrete Wavelet Transform in the Analysis of Nonlinear Chemical System

Oscillations of species concentration are phenomena accompanying several types of electrochemical and purely chemical processes. Importance of analyzing of such processes results from both scientific and practical reasons. In the paper the authors deal with investigation of time dependent spectra of various stages of Belousov-Zhabotinsky type chemical oscillations. As the analytical tool the discrete wavelet transform is proposed.