Analytical Determination of Higher Buckling Modes for Unimodal Optimal Columns*

Recent results have revived interest in the problem of determining the optimal shape of clamped-clamped columns. The bimodal behavior of certain cases has drawn particular attention. In this paper a revised formulation of the problem is used. This formulation permits the determination of the optimal design in the unimodal range in a simpler form than was previously available. The equations governing higher buckling modes of unimodal optimal clamped-clamped columns are posed and solved in series form. The onset of bimodal behavior is determined analytically. Earlier numerical results are confirmed and increased in accuracy.     

Advances in synchrotron hard X-ray based imaging

Modern synchrotron radiation (SR) sources have dramatically fostered the use of SR-based X-ray imaging. The relevant information such as density, chemical composition, chemical states, structure, and crystallographic perfection is mapped in two, or, increasingly, in three dimensions. The development of nano-science requires pushing spatial resolution down towards the nanoscale.The present article describes a selection of hard X-ray imaging and microanalysis techniques that emerged over the last few years, by taking advantage of the flux and coherence of the SR beams, as well as exploiting the advances in X-ray optics and detectors, and the increased possibilities of computers (memory, speed). Examples are given to illustrate the opportunities associated with the use of these techniques, and a number of recent references are provided. To cite this article: J. Baruchel et al., C. R. Physique 9 (2008).     

Efficient synthesis of enantiopure conduritols by ring-closing metathesis.

Two short synthetic approaches to enantiopure conduritols are described starting from the chiral pool. In both cases, the cyclohexene ring is assembled via ring-closing olefin metathesis. The terminal diene precursers for the metathesis reaction are prepared either from octitols or from tartaric acids. The former route involves a new method for selective bromination of the primary positions in long-chain carbohydrate polyols. Subsequent reductive elimination with zinc then generates the diene. The latter route uses a highly diastereoselective addition of divinylzinc to tartaric dialdehydes for preparation of the dienes.     

On a common generalization of Koszul duality and tilting equivalence

We propose a new definition of Koszulity for graded algebras where the degree zero part has finite global dimension, but is not necessarily semi-simple. The standard Koszul duality theorems hold in this setting.     

N‐Methyl‐dl‐aspartic acid mono­hydrate

The title compound, C₅H₉NO₄·H₂O, has been synthesized and crystallized. It crystallizes in Cc with one mol­ecule in the asymmetric unit. The compound is found in its zwitterionic form. d and l forms of the compound are linked in the crystal via O—H?O and N—H?O hydrogen bonds, both directly between the aspartic acid‐derivative entities and to the crystal water mol­ecule. A weak intramolecular N—H?O interaction is found. The carbon skeleton is slightly twisted with C—C—C—C = 166.83 (11)°. A comparison with other derivatives of aspartic acid shows only two rotamers – one with a near planar carbon skeleton and one with a significantly twisted carbon skeleton.