On Polynomial Solutions of Generalized Moisil-Théodoresco Systems and Hodge-de Rham Systems

The aim of the paper is to study relations between polynomial solutions of generalized Moisil-Théodoresco (GMT) systems and polynomial solutions of Hodge-de Rham systems and, using these relations, to describe polynomial solutions of GMT systems. We decompose the space of homogeneous solutions of GMT system of a given homogeneity into irreducible pieces under the action of the group O(m) and we characterize individual pieces by their highest weights and we compute their dimensions.     

Graph 3-coloring with a hybrid self-adaptive evolutionary algorithm

This paper proposes a hybrid self-adaptive evolutionary algorithm for graph coloring that is hybridized with the following novel elements: heuristic genotype-phenotype mapping, a swap local search heuristic, and a neutral survivor selection operator. This algorithm was compared with the evolutionary algorithm with the SAW method of Eiben et al., the Tabucol algorithm of Hertz and de Werra, and the hybrid evolutionary algorithm of Galinier and Hao. The performance of these algorithms were tested on a test suite consisting of randomly generated 3-colorable graphs of various structural features, such as graph size, type, edge density, and variability in sizes of color classes. Furthermore, the test graphs were generated including the phase transition where the graphs are hard to color. The purpose of the extensive experimental work was threefold: to investigate the behavior of the tested algorithms in the phase transition, to identify what impact hybridization with the DSatur traditional heuristic has on the evolutionary algorithm, and to show how graph structural features influence the performance of the graph-coloring algorithms. The results indicate that the performance of the hybrid self-adaptive evolutionary algorithm is comparable with, or better than, the performance of the hybrid evolutionary algorithm which is one of the best graph-coloring algorithms today. Moreover, the fact that all the considered algorithms performed poorly on flat graphs confirms that graphs of this type are really the hardest to color.     

Characterization of three saponins from a fraction using 1D DOSY as a solvent signal suppression tool. Agabrittonosides E–F. Furostane Saponins from Agave brittoniana Trel. spp. Brachypus

A careful NMR analysis, especially by 1D TOCSY and 1D ROESY, of a refined saponin fraction allowed us to determine the structure of three saponins from a polar extract of Agave brittoniana Trel. spp. Brachypus leaves. The use of 1D DOSY for the suppression of the solvent signal was useful to obtain the chemical shifts of anomeric signals. A full assignment of the ¹H and ¹³C spectral data for the new saponins, agabrittonosides E–F (1–2) and the well‐known Karatavioside C (3) and their methoxyl derivatives, is reported. The structures were established using a combination of 1D and 2D (¹H, ¹H‐COSY, TOCSY, ROESY, g‐HSQC, g‐HMBC and g‐HSQC‐TOCSY) NMR techniques and ESI–MS. In addition, the methoxylation of these furostane saponins in the presence of MeOH was studied. Copyright © 2010 John Wiley & Sons, Ltd.     

Regularity and uniqueness in quasilinear parabolic systems

Inspired by a problem in steel metallurgy, we prove the existence, regularity, uniqueness, and continuous data dependence of solutions to a coupled parabolic system in a smooth bounded 3D domain, with nonlinear and nonhomogeneous boundary conditions. The nonlinear coupling takes place in the diffusion coefficient. The proofs are based on anisotropic estimates in tangential and normal directions, and on a refined variant of the Gronwall lemma.     

Thermodynamics of shape-memory alloys under electric current

Phase transformation in shape-memory alloys is known to cause electric resistivity variation that, under electric current, may conversely influence Joule heat production and thus eventually the martensitic transformation itself. A thermodynamically consistent general continuum-mechanical model at large strains is presented. In special cases, a proof of the existence of a weak solution is outlined, using a semidiscretization in time.     

Effectiveness and design of surface texturing for different lubrication regimes

The aim of the present research work was to investigate the possibilities of designing surface texturing for different lubrication regimes and to evaluate its effectiveness, especially under starved, boundary and mixed lubrication regimes. This was achieved by combining an experimental tribological investigation with a surface-roughness analysis, a 2D FEM simulation and fluid dynamic modelling. The tribological investigation under unidirectional and reciprocating sliding was focused on the effect of the laser-texturing parameters—including the dimple depth and size, the dimple area density and the contact size—on the coefficient of friction under different lubrication regimes, achieved by varying the sliding speed, the normal load and the lubricant viscosity.     

On Possible Singular Solutions to the Navier — Stokes Equations

In this paper, we exclude the possibility of existence of a singular solution of the selfsimilar type proposed by Jean Leray More precisely, using a slightly stronger hypothesis we give a simpler proof to the analogous result established by J. Ne?as, M. Rú?i?ka and V. ?verák. We also discuss the possible existence of a singular solution of pseudo-selfsimilar type.