Path properties of l_p-valued Gaussian random fields

General limit theorems are established for l~p-valued Gaussian random fields indexed by a multidimensional parameter,which contain both almost sure moduli of continuity and limits of large increments for the l~p-valued Gaussian random fields under(?)explicit conditions.     

Micellar effect in hydroformylation of high olefin catalysed by water-soluble rhodium complexes associated with sulfonated diphosphines

High linear alkenes (1-octene and 1-decene) have been hydroformylated using water-soluble rhodium complexes associated with sulfonated diphosphines in the presence of ionic surfactants or methanol. In all cases, the hydroformylation activities were higher than in experiments without additives. The selectivity in aldehydes was higher when we used cetyltrimethylammonium hydrogensulfate (CTAHSO₄) as the surfactant or methanol as the co-solvent.     

On the approximation of convex functions by Bernstein-type operators

As a consequence of Jensen's inequality, centered operators of probabilistic type (also called Bernstein-type operators) approximate convex functions from above. Starting from this fact, we consider several pairs of classical operators and determine, in each case, which one is better to approximate convex functions. In almost all the discussed examples, the conclusion follows from a simple argument concerning composition of operators. However, when comparing Szász-Mirakyan operators with Bernstein operators over the positive semi-axis, the result is derived from the convex ordering of the involved probability distributions. Analogous results for non-centered operators are also considered.     

Generators of some Ramanujan formulas

In this paper we prove some Ramanujan type formulas for 1/π but without using the theory of modular forms. Instead we use the WZ—method created by H. Wilf and D. Zeilberger and find some hypergeometric functions in two variables which are second components of WZ—pairs than can be certified using Zeilberger's EKHAD package. These certificates have an additional property which allows us to get generalized Ramanujan's type series which are routinely proven by computer. We call these second hypergeometric components of the WZ—pairs generators. Finding generators seems a hard task but using a kind of experimental research (explained below), we have succeeded in finding some of them. Unfortunately we have not found yet generators for the most impressive Ramanujan's formulas. We also prove some interesting binomial sums for the constant 1/π². Finally we rewrite many of the obtained series using pochhammer symbols and study the rate of convergence. 2000 Mathematics Subject Classification Primary—33C20     

Lower bounds for transition probabilities on graphs

The paper presents two results. The first one provides separate conditions for the upper and lower estimates of the distribution of the time of exit from balls of a random walk on a weighted graph. The main result of the paper is that the lower estimate follows from the elliptic Harnack inequality. The second result is an off-diagonal lower bound for the transition probability of the random walk.     

Relation de Rankine Hugoniot faible pour les lois de conservation avec contraintes primitives convexes

We describe a Weak Rankine Hugoniot relation for constrained discontinuous solutions of conservation laws. The constraint is convex in the primitive variable. Various examples show the potential interest of this approach. To cite this article: B. Després, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Growth kinetics of iron boride layers: Dimensional analysis

Dimensional analysis is presented as a powerful tool in the study of the paste boriding process. In particular, a dimensional method is used to study the growth kinetics of the boride layers FeB and Fe₂B. Experiments were performed in AISI 1045 steel and AISI M2 steel, to test the suggested model. Samples of 1045 steel were prepared and treated using boron paste thickness of 3-5 mm, at temperatures of 1193, 1223 and 1273 K, with 2, 4 and 6 h of treatment time. The M2 specimens had boron paste thickness of 3 and 4 mm and temperatures of 1223, 1253 and 1273 K for 2 and 6 h. Results indicate that the growth of boron layers obeys power laws of the form y = αx^β, where α and β constants are a function of the material and the interface of interest. Validation of the model was carried out using experimental data with an average error percentage of 7.6% for Fe₂B in 1045 steel, 15.8% for FeB and 3.4% for Fe₂B in M2 steel.     

AlGaN/GaN HEMTs grown on silicon (001) substrates by molecular beam epitaxy

We report the realization of an AlGaN/GaN HEMT on silicon (001) substrate with noticeably better transport and electrical characteristics than previously reported. The heterostructure has been grown by molecular beam epitaxy. The 2D electron gas formed at the AlGaN/GaN interface exhibits a sheet carrier density of 8×10¹² cm⁻² and a Hall mobility of 1800 cm²/V s at room temperature. High electron mobility transistors with a gate length of 4 μm have been processed and DC characteristics have been achieved. A maximum drain current of more than 500 mA/mm and a transconductance g_m of 120 mS/mm have been obtained. These results are promising and open the way for making efficient AlGaN/GaN HEMT devices on Si(001).     

Observation of hydrogen induced intermediate borides in PrFeB based alloys by Mössbauer effect spectroscopy

In the present work, a quantitative analysis of the phase compositions by Mössbauer effect spectroscopy of solid and conventional hydrogen disproportionated Pr_13.7Fe_80.3B_6.0 and Pr_13.7Fe_63.5Co_16.7Zr_0.1B_6.0 alloys was carried out. Significant amounts of intermediate borides t-Fe₃B and Pr(Fe, Co)₁₂B₆ were detected after solid hydrogen disproportionation treatment in Pr_13.7Fe_80.3B_6.0 and Pr_13.7Fe_63.5Co_16.7Zr_0.1B_6.0 alloys, respectively. After conventional hydrogenation–disproportionation–desorption–recombination treatment these phases were not detected and in no case residual Pr₂Fe₁₄B-phase was found. It was observed that the amount of intermediate borides after disproportionation can be correlated with the degree of texture after recombination at various temperatures.