Electrochemistry of platinum single crystal surfaces: Part II. Structural effect on formic acid oxidation and poison formation on Pt (111), (100) and (110)

The geometrical arrangement of sites favourable for formic acid oxidation and the poison formation reaction is determined using low index platinum single crystal planes. For this determination, the least number of sites required for the reactions to occur, which was obtained in the study of electrocatalysis by adatoms, was used, that is three adjacent sites are required for formic acid oxidation and four adjacent sites are required for poison formation.The triplet of sites on a unit lattice of Pt (111) and that on a unit lattice of Pt (100) plane are equally very favourable for the main oxidation reaction, but that on a unit lattice of Pt (110) is not so favourable as those on the former two planes. The oxidation rate is more than one order of magnitude lower on the latter than on the former triplets.The poison formation reaction proceeds at a very high rate on the (100) and the (110) planes. The geometrical arrangement of four sites on a square unit lattice of the (100) plane and on a rectangular unit lattice of the (110) plane are favourable for the poison formation reaction, but that on a hexagonal unit lattice of the (111) plane is not so favourable as the former two.     

Some new Triebel-Lizorkin spaces on spaces of homogeneous type and their frame characterizations

Let(X,p,μ)d,θ be a space of homogeneous type,(?) ∈(0,θ],|s|＜(?) andmax{d/(d＋(?)),d/(d＋s＋(?))}＜q≤∞.The author introduces the new Triebel-Lizorkin spaces (?)_∞q~s(X) and establishes the framecharacterizations of these spaces by first establishing a Plancherel-P(?)lya-type inequalityrelated to the norm of the spaces (?)_∞q~s(X).The frame characterizations of the Besovspace (?)_pq~s(X) with|s|＜(?),max{d/(d＋(?)),d/(d＋s＋(?))}＜p≤∞ and 0＜q≤∞and the Triebel-Lizorkin space (?)_pq~s(X)with|s|＜(?),max{d/(d＋(?)),d/(d＋s＋(?))}＜p＜∞ and max{d/(d＋(?)),d/(d＋s＋(?))}＜q≤∞ are also presented.Moreover,the au-thor introduces the new TriebeI-Lizorkin spaces b(?)_∞q~s(X) and H(?)_∞q~s(X) associated to agiven para-accretive function b.The relation between the space b(?)_∞q~s(X) and the spaceH(?)_∞q~s(X) is also presented.The author further proves that if s＝0 and q＝2,thenH(?)_∞q~s(X)＝(?)_∞q~s(X),which also gives a new characterization of the space BMO(X),since (?)_∞q~s(X)＝BMO(X).     

Instabilité d'une nappe de vorticité étirée instationnaireInstability of an unsteady stretched vortex layer

We consider how the Kelvin–Helmholtz instability is affected by an external hyperbolic strain flow. The basic flow being unsteady, the inviscid evolution of perturbations is studied within the framework of a non-normal analysis in which the maximum amplification is computed for any given time. A positive or negative stretching is shown to enhance or reduce, respectively, the instability even for weak stretching rates. To cite this article: T. Gomez, M. Rossi, C. R. Mecanique 331 (2003).     

Characterization of a class of polycrystals whose effective elastic bulk moduli can be exactly determinedCaractérisation d'une classe de polycristaux dont les modules de compression isotrope effectifs peuvent exactement être déterminés

Necessary and sufficient conditions are established for the stress response of a linearly elastic material to an isotropic stain to be hydrostatic. In the 3D case, these conditions are satisfied not only by the isotropic and cubic materials but also by all other anisotropic materials provided appropriate restrictions are imposed. In the 2D case, only the isotropic and square materials have an isotropic stress response to an isotropic strain. Using a uniform field argument, the elastic bulk modulus of a polycrystal consisting of monocrystals compatible with the established conditions is shown to equal that of any constituent monocrystal. Thus, Hill's relevant result about a polycrystal composed of cubic monocrystals is generalized. To cite this article: Q.-C. He, C. R. Mecanique 331 (2003).     

Three-Convex Approximation by Free Knot Splines in C [0, 1]

A Jackson-type estimate is obtained for the approximation of 3 -convex functions by 3 -convex splines with free knots. The order of approximation is the same as for the Jackson-type estimate for unconstrained approximation by splines with free knots. Shape-preserving free knot spline approximation of k -convex functions, k > 3 , is also considered. January 15, 1996. Date revised: December 9, 1996.     

关于Ma(n)é集与Aubry集的研究

J. Mather and A. Fathi defined Ma(n)ié set and Aubry set, which are the important invariant sets in positive definite Lagrangian system, in different ways.They use variational principle and Weak KAM theory respectively. In this paper we provide a proof of the equivalence between the two kinds of definitions, and generalize A. Fathi's definition. In the end of the paper, we calculate the Ma(n)é set and Aubry set for a single pendulum system.     

Seismic response of a set of blocks partially imbedded in soft soilRéponse sismique d'un ensemble de blocs partiellement encastrés dans un terrain mou

The seismic response of a set of ten non-equally spaced, non-equally sized, homogeneous blocks partially imbedded in a soft soil layer overlying a hard halfspace is studied numerically and shown to be generally larger, in terms of amplitude, duration and spatial variability than that of the ground in the presence of one block or in the absence of blocks. This is qualitatively similar to observed seismic response in the past at sites such as Mexico City and suggests that the built portion of cities may, under certain conditions, play a significant role in the global seismic response of a city. To cite this article: C. Tsogka, A. Wirgin, C. R. Mecanique 331 (2003).     

Unusual atomic arrangements in amorphous silicon

The existence of small bond angles (like those of triangles and squares) in amorphous silicon networks were studied by the tight-binding molecular dynamics method, by analyzing the statistical data of Si-Si-Si fragments inside large molecules, and also by the Reverse Monte-Carlo simulation method. The influence of small bond angles on the electronic density of states was revealed.     

Lobachevsky triangle altitudes theorem as the Jacobi identity in the Lie algebra of quadratic forms on symplectic plane

An isomorphism between the Lobachevsky and de Sitter’s world geometries with the symplectic geometry and the Lie algebra of binary quadratic forms is used to derive the altitudes concurrence for the Lobachevsky and de Sitter triangles.