Unprecedented conversion of triethylamine and disulfur dichloride into a thienopentathiepin and a heptathiocane

[reaction: see text] In a remarkable cascade reaction, triethylamine is converted into the thienopentathiepin 2a and the heptathiocane 3a by a preequilibrated solution of disulfur dichloride and DABCO in chloroform.     

Approximation and Prediction of the Numerical Solution of Some Burgers Problems

The Aitken's ²-prediction of Brezinski has already been used by Morandi Cecchi et al. in order to compute a numerical approximation of the solution of a parabolic initial-boundary value problem. This method consists in two consecutive steps: the first one is the approximation with a finite elements method, where the solution of the involved nonlinear system is computed by Gauss–Seidel method; the second one is a prediction of further terms with Aitken's ²-process. By comparison with this method, we use other methods of prediction in another way. First, we consider a generalization of ²-prediction, the so-called -prediction. In this paper, we only use vector prediction which is more stable than the scalar one. Then, the methods of prediction presented can be used in order to predict the starting vector of the Gauss–Seidel method.     

Contributions of microbial biofilms to ecosystem processes in stream mesocosms

In many aquatic ecosystems, most microbes live in matrix-enclosed biofilms and contribute substantially to energy flow and nutrient cycling. Little is known, however, about the coupling of structure and dynamics of these biofilms to ecosystem function. Here we show that microbial biofilms changed the physical and chemical microhabitat and contributed to ecosystem processes in 30-m-long stream mesocosms. Biofilm growth increased hydrodynamic transient storage-streamwater detained in quiescent zones, which is a major physical template for ecological processes in streams-by 300% and the retention of suspended particles by 120%. In addition, by enhancing the relative uptake of organic molecules of lower bioavailability, the interplay of biofilm microarchitecture and mass transfer changed their downstream linkage. As living zones of transient storage, biofilms bring hydrodynamic retention and biochemical processing into close spatial proximity and influence biogeochemical processes and patterns in streams. Thus, biofilms are highly efficient and successful ecological communities that may also contribute to the influence that headwater streams have on rivers, estuaries and even oceans through longitudinal linkages of local biogeochemical and hydrodynamic processes.     

On the Topology of Fibrations with Section and Free Loop Spaces

We relate the brace products of a fibration with section tothe differentials in its Serre spectral sequence. In the particularcase of free loop fibrations, we establish a link between thesedifferentials and Browder operations in the fiber. Applicationsand several calculations (for the particular cases of spheresand wedges of spheres) are given. 2000 Mathematical SubjectClassification: 55P35, 55Q15, 55R05, 55R20.     

Stationary Flow Past a Semi-Infinite Flat Plate: Analytical and Numerical Evidence for a Symmetry-Breaking Solution

We consider the question of the existence of stationary solutions for the Navier Stokes equations describing the flow of a incompressible fluid past a semi-infinite flat plate at zero incidence angle. By using ideas from the theory of dynamical systems we analyze the vorticity equation for this problem and show that a symmetry-breaking term fits naturally into the downstream asymptotic expansion of a solution. Finally, in order to check that our asymptotic expressions can be completed to a symmetry-breaking solution of the Navier–Stokes equations we solve the problem numerically by using our asymptotic results to prescribe artificial boundary conditions for a sequence of truncated domains. The results of these numerical computations a clearly compatible with the existence of such a solution. Mathematics Subject Classification (2000). 76D05, 76D25, 76M10, 41A60, 35Q35 Supported in part by the Fonds National Suisse.     

Packing and covering with linear programming: A survey

This paper considers the polyhedral results and the min–max results on packing and covering problems of the decade. Since the strong perfect graph theorem (published in 2006), the main such results are available for the packing problem, however there are still important polyhedral questions that remain open. For the covering problem, the main questions are still open, although there has been important progress. We survey some of the main results with emphasis on those where linear programming and graph theory come together. They mainly concern the covering of cycles or dicycles in graphs or signed graphs, either with vertices or edges; this includes the multicut and integral multiflow problems.     

Vertex Operator Solutions of¶2d Dimensionally Reduced Gravity

We apply algebraic and vertex operator techniques to solve two dimensional reduced vacuum Einstein's equations. This leads to explicit expressions for the coefficients of metrics solutions of the vacuum equations as ratios of determinants. No quadratures are left. These formulas rely on the identification of dual pairs of vertex operators corresponding to dual metrics related by the Kramer-Neugebauer symmetry.     

Simple optoelectronic method for analysis of transverse mode structure of lasers

Laser beam quality evaluation is generally carried out through the measurement of the M² second-moment. This standard procedure is time consuming and is difficult to be implemented for checking, for instance, each VCSEL diode moving out of the assembly line of a high volume production factory. In this paper, we propose an alternative fast method allowing to distinguish easily a single transverse mode from a multiple transverse mode behaviour. This method is based on an electronic analysis (locking amplifier) of the local slope of the output laser characteristic, i.e. laser output power versus pumping.     

Chiral sulphonated phosphines : II. Influence of water on the enantioselectivity in the reduction of dehydro-aminoacids

For the reduction of dehydro aminoacids in various media with rhodium complexes containing chiral ligands, a linear correlation of log %S/%R with the solvophobicity parameter S_p has been observed. The decrease in enantioselectivity in water is due to the high interfacial energy of this solvent.