A New Route to Crystalline Salts of the Hydrolytic Dimer of Chromium(III)

Crystalline salts of the hydrolytic dimer of Cr(III), [Cr₂(μ-OH)₂(H₂O)₈]X₄·n H₂O (X = p-toluenesulfonate (tos) or mesitylene-2-sulfonate (dmtos)) have been prepared in good yields via a simple two-step procedure: H⁺ oxidation of Cr metal to give Cr²⁺ (T ≈? 70°) followed by O₂ oxidation, of Cr²⁺ to give the dimer (T ≈? 25°). The mechanism of conversion of Cr²⁺ into the dimer is discussed.     

A regularity result for critical points of conformally invariant functionals

Let be an open set inR ² andI be a conformally invariant functional defined onH ¹(,R ^d ). Letu be a critical point ofI. We show that, ifu is apriori assumed to be bounded, thenu is smooth in , up to (ifu _| is smooth). This is a partial (positive) answer to a conjecture of S. Hildebrandt [13]. As an application, we establish a regularity result for weak solutions to the equation of surfaces of prescribed mean curvature in a three-dimensional compact riemannian manifold.     

Finite strains at the tip of a crack in a sheet of hyperelastic material: I. Homogeneous case

This paper describes an asymptotic analysis of the strain and stress fields at the tip of a crack in a sheet of incompressible hyperelastic material. The investigations are carried out within the framework of finite elastostatics and for the class of Generalized Neo-Hookean materials. Both the symmetric (mode I) and non-symmetric (mixed-mode) cases are considered. It is shown that the latter situation corresponds locally to a rigid body rotation of the symmetric fields. The effect of the hardening parameter on crack tip blunting is investigated analytically and numerically.     

Congresses,conferences, symposia,meetings, and seminars in the field of chemical sciences held in 1995–1996

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Congresses, conferences, symposia, meetings, and seminars in the field of chemical sciences held in 1995–1996     

Optimality of a Threshold Policy in theM/M/ queue with repeated vacations

Consider anM/M/1 queueing system with server vacations where the server is turned off as soon as the queue gets empty. We assume that the vacation durations form a sequence of i.i.d. random variables with exponential distribution. At the end of a vacation period, the server may either be turned on if the queue is non empty or take another vacation. The following costs are incurred: a holding cost ofh per unit of time and per customer in the system and a fixed cost of each time the server is turned on. We show that there exists a threshold policy that minimizes the long-run average cost criterion. The approach we use was first proposed in Blanc et al. (1990) and enables us to determine explicitly the optimal threshold and the optimal long-run average cost in terms of the model parameters.     

CdS nanoclusters stabilized by thiolate ligands: A mini-review

One of the most exciting frontiers in materials chemistry in recent years is the optoelectronics of quantum-confined semiconductor nanoclusters. These nanoclusters are 10–200 A in diameter, and in this size regime exhibit extra-ordinarily interesting quantum mechanical effects. Cadmium sulfide is a popular semiconductor for these studies, and reviewed here is the synthesis and charac-terization of such CdS nanoclusters, with emphasis on how chemical control of the surface by thiolates influences product formation and properties. Also described are the syntheses and structures of true molecular clusters of CdS capped with thiolate ligands.     

Some remarks on R-contact flows

Let (M, ) be an R-contact manifold, then the set of periodic points of the characteristic vector field is a nonempty union of closed, totally geodesic odd-dimensional submanifolds. Moreover, the R-metric cannot have nonpositive sectional curvature. We also prove that no R-contact form can exist on any torus.