Effective dissipation and turbulence in spectrally truncated euler flows

A new transient regime in the relaxation towards absolute equilibrium of the conservative and time-reversible 3D Euler equation with a high-wave-number spectral truncation is characterized. Large-scale dissipative effects, caused by the thermalized modes that spontaneously appear between a transition wave number and the maximum wave number, are calculated using fluctuation dissipation relations. The large-scale dynamics is found to be similar to that of high-Reynolds number Navier-Stokes equations and thus obeys (at least approximately) Kolmogorov scaling.     

Investigation of the rh-catalyzed asymmetric reductive aldol reaction. Expanded scope based on reaction analysis

[reaction: see text] A series of experiments are described that suggest that the Rh-catalyzed reductive aldol reaction proceeds by addition of a Rh(I) hydride, generated in situ, to the reacting acrylate followed by a stereochemistry-controlling aldol addition reaction. On the basis of this hypothesis, reaction conditions are engineered that allow for increased substrate scope.     

Zero-temperature equation of state of two-dimensional 3He

The equation of state of two-dimensional 3He at zero temperature has been calculated using the diffusion Monte Carlo method. By means of a combination of the fixed-node and released-node techniques, it is shown that backflow correlations provide a very accurate equation of state. The results prove unambiguously the non-self-bound character of two-dimensional 3He due to its Fermi statistics. We present solid evidence that the gas phase, predicted for the two-dimensional system, can be extrapolated to the case of 3He adsorbed on a strong substrate such as graphite.     

Using the 1,2‐dihydro‐1,2‐diphosphinine ring as a template for the synthesis of new bicyclic structures and new trans‐chelating bis‐phosphines

The 1,2‐dihydro‐1,2‐diphosphinine decacarbonylditungsten complex 1 has been used as a synthetic equivalent of the corresponding 1,2‐dianion 2 . These two 1,2‐positions can be linked by a (CH₂)₄ bridge to yield a [4.4.0] bicyclic structure 6 whose identity has been confirmed by X‐ray crystal structure analysis. Alternatively, two ω‐iodohexyl chains can be grafted onto these positions and the resulting diiodo derivative 9 transformed into a long‐chain bis‐phosphine 10 by reaction with lithium diphenylphosphide. This bis‐phosphine gives a chelate complex with PdCl₂ whose trans‐stereochemistry was established by X‐ray crystal structure analysis. © 2005 Wiley Periodicals, Inc. Heteroatom Chem 16:44–48, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/hc.20073     

On a variant of Giuga numbers

In this paper, we characterize the odd positive integers n satisfying the congruence∑n -1 j=1 j n-1/2 ≡ 0 (mod n). We show that the set of such positive integers has an asymptotic density which turns out to be slightly larger than 3/8.     

On new computational local orders of convergence

Four new variants of the Computational Order of Convergence (COC) of a one-point iterative method with memory for solving nonlinear equations are presented. Furthermore, the way to approximate the new variants to the local order of convergence is analyzed. Three of the new definitions given here do not involve the unknown root. Numerical experiments using adaptive arithmetic with multiple precision and a stopping criteria are implemented without using any known root.