Traveling wave solutions of a model of skin pattern formation in a singular case

We study traveling wave solutions to a system of four non‐linear partial differential equations, which arise in a tissue interaction model for skin morphogenesis. Under the assumption that the strength of attachment of the epidermis to the basal lamina is sufficiently large, we prove the existence and uniqueness (up to a translation) of traveling wave solutions connecting two stationary states of the system with the dermis and epidermis cell densities being positive. We discuss the problem of the minimal wave speed. Copyright © 2010 John Wiley & Sons, Ltd.     

Tame Equivalence and Wild Sets

For semigroups with divisor theory we introduce an equivalence relation that preserves the p-dimensions of divisor class groups. While the approach has been motivated by the results on Hilbert-symbol equivalence in quadratic form theory over algebraic number fields, it is the purpose of the paper to generalize the setup to semigroups with divisor theory and to simplify the proofs by avoiding any ring- or number-theoretical arguments.     

Sensitivity analysis of optimization problems in Hilbert space with application to optimal control

A family of optimization problems in a Hilbert space depending on a vector parameter is considered. It is assumed that the problems have locally isolated local solutions. Both these solutions and the associated Lagrange multipliers are assumed to be locally Lipschitz continuous functions of the parameter. Moreover, the assumption of the type of strong second-order sufficient condition is satisfied.It is shown that the solutions are directionally differentiable functions of the parameter and the directional derivative is characterized. A second-order expansion of the optimal-value function is obtained. The abstract results are applied to state and control constrained optimal control problems for systems described by nonlinear ordinary differential equations with the control appearing linearly.     

Experimental confirmation by galvanomagnetic methods of a complex transport model in In0.53Ga0.47As layers deposited by MBE on SI-InP

At low temperatures In_0.53Ga_0.47As samples show an increase of carrier concentration, which can be explained in terms of a two carriers transport model. This type of problem exists since the beginning of the semiconductor era, dating back to monocrystalline germanium.We propose that in all the investigated layers, there are X atoms or charged dislocations in the region of the first monolayers, which are built in during epitaxial growth. The layers were intentionally undoped. They form an impurity band in which low mobility carriers dominate over the localised electron scattering due to the s-d exchange interaction. These carriers do not freeze out at liquid helium temperature and give rise to two transport media for electrons; a conduction band at higher temperatures and an impurity band at lower temperatures. The electron which fall down onto the previously ionised X atoms, then move by thermally activated hopping. We show that the two carriers model for In_0.53Ga_0.47As epitaxial layers are confirmed by the carrier concentration-temperature, carrier concentration-magnetic field, resistivity-magnetic field behaviour, and also by YKA theory also. The differences between the two transport models are so distinctive that observed phenomena may exist. This paper presents experimental results, which constitute comprehensive evidence for the complicated structure of the semiconductor epitaxial layers on the sample of n-type In_0.53Ga_0.47As/InP layer with n=2.2×10¹⁵/cm³.     

Lower-rim versus upper-rim functionalization in di-ionizable calix[4]arene-crown-5 isomers. Synthesis and divalent metal ion extraction

Two series of di-ionizable calix[4]arene-crown-5 isomers in the cone conformation are synthesized to probe the effect of the pendant acidic group location on their metal ion extraction properties. In one series, the ionizable groups are attached to the lower rim of the calix[4]arene scaffold, which orients them near the crown ether cavity. In the second series, the ionizable groups are connected to the upper rim positioning them away from the crown ether ring, but close to the hydrophobic pocket of the calix[4]arene unit. The metal ion extraction behaviors of the two series of ligands are compared in extractions of alkaline earth metal cations, Hg²⁺, and Pb²⁺.     

K-subadditive and K-superadditive set-valued functions bounded on “large” sets

Aequationes mathematicae - We prove that every K–subadditive set–valued map weakly K–upper bounded on a “large” set (e.g. not null–finite, not...     

Simultaneous determination of uranium(IV) and thorium(IV) ions with Arsenazo III by partial least squares method

A multivariate calibration method, Partial Least Squares Type 1 (PLS-1), is proposed for simultaneous spectrophotometric determination of uranium and thorium ions as their complexes with arsenazo III in hydrochloric acid medium. Several data characteristics are taking into account in order to minimize the optimum number of factors required for the construction of calibration model, while using various statistical criterions of selection. Finally, the evaluated calibration model is satisfactorily applied to determination of these ions in samples that resemble sulfuric acid leach solution obtained from a uranium ore.     

On the thermodynamic equivalence of the Dicke maser model and a certain spin system

We prove the thermodynamic equivalence of the Dicke two-level model and a van der Waals spin system. This serves to show that there are cases where the Wang-Hioe procedure and the Power-Zienau transformation may be applied in any order.     

The influence of thiourea on the electroreduction of Zn2+ ions in various supporting electrolytes in respect to the cap-pair effect

The mechanism of the cap-pair effect was examined with respect to its acceleration of the electro-reduction of Zn²⁺ ions in NaCIO₄, NaCl and NaBr. It was found that the presence of thiourea in the solution increased the rate of the electrode process; a role is played in the acceleration by the composition of zinc complexes formed in the bulk of the solution.