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.     

A Continuation Method of Parameter Inversion for Non-Equilibrium Convection-Dispersion Equation

Based on the homotopy mapping, a globally convergent method of parameter inversion for non-equilibrium convection-dispersion equations （CDEs） is developed. Moreover, in order to further improve the computational efficiency of the algorithm, a properly smooth function, which is derived from the sigmoid function, is employed to update the homotopy parameter during iteration. Numerical results show the feature of global convergence and high performance of this method. In addition, even the measurement quantities are heavily contaminated by noises, and a good solution can be found.     

Orthonormal polynomial bases in function spaces

We construct polynomial orthonormal bases in various function spaces. Our bases have linear order of growth of degrees of polynomials. We show that this order is optimal.     

On the Neighbour-Distinguishing Index of a Graph

A proper edge colouring of a graph G is neighbour-distinguishing provided that it distinguishes adjacent vertices by sets of colours of their incident edges. It is proved that for any planar bipartite graph G with Δ(G)≥12 there is a neighbour-distinguishing edge colouring of G using at most Δ(G)+1 colours. Colourings distinguishing pairs of vertices that satisfy other requirements are also considered.     

Multinuclear magnetic resonance study of some mesoionic oxatriazoles containing nitrogenous exocyclic groups

¹H,¹³C,¹⁴N and¹⁵N NMR measurements are reported for four mesoionic 1-oxa-2, 3, 4-triazoles containing exocyclic nitrogenous groups. The NMR signal assignments are discussed and compared with those previously published for some corresponding oxatriazoles. The results obtained support the proposed cyclic mesoionic structures for the compounds studied. The questions of possible charge delocalization and valence tautomerism are addressed. Compound with N^– H as a exocyclic group (Fig. 1) is found to be relatively unstable, this is attributed to proton migration in the corresponding non-cyclic form of this molecule.Published in Khimiya Geterotsikiicheskikh Soedinenii, No. 9, pp. 1260–1263, September, 1995.     

Spectrochemical Properties of Noncubical Transition Metal Complexes in Solutions. XIV. Angular Overlap Studies of bis(Salicylidene-2-aminothiazole)Copper(II) in Various Solvents

The copper(II) complex [Cu(sat)], where Hsat is salicylidene-2-aminothiazole (bidentate Schiff - base), was studied in variety of solvents. In the solid state, the complex is black. It has been characterized by elemental analysis, solubility in common solvents, molar conductivity, and ultraviolet (UV) and visible (Vis) spectroscopy. The complex is easily soluble in common solvents such as chloroform, dimethylformamide, dimethyl sulfoxide, and 1,4-dioxane. The known crystal structure of similar compounds shows planar coordination geometry for the copper center. Combined multitechnique experiments have been applied to confirm the structure of the complex in solutions. The molar conductivities indicate their nonelectrolyte properties in all these solvents. The spectroscopic measurements were used to study the coordination properties of donoratoms and their bonding abilities.     

Spectral and Thermal Studies of Rare Earth Element 3-methylglutarates

Conditions for the formation of rare earth element (Y, La–Lu) 3-methylglutarates were studied and their quantitative composition and solubilities in water at 293 K were determined (10^–2 mol dm^–3). The IR spectra of the prepared complexes with general formula Ln₂(C₆H₈O₄)₃ nH₂O (n=3–8) were recorded and their thermal decomposition in the air were investigated. During heating the hydrated 3-methylglutarates are dehydrated in one step and next anhydrous complexes decompose to oxides Ln₂O₃ with intermediate formation Ln₂O₂CO₃ (Y, La, Nd–Gd) or directly to the oxides, Ln₂O₃, CeO₂, Pr₆O₁₁ and Tb₄O₇ (Ce, Pr, Tb–Lu). This revised version was published online in August 2006 with corrections to the Cover Date.