Lotka-Volterra-type equations and their explicit integration

In this Letter, we give an explicit integration of some two-dimensionalised Lotka-Volterra-type equations associated with simple Lie algebras possessing a representation without branching.     

Determination of the enantiomeric excess of α-hydroxy acids

This work describes a convenient and accurate method for optical purity determination of α-hydroxy acids. Their derivatization with commercially available valine methyl ester affords diastereoisomers easily separable by HPLC using achiral C₁₈ columns.     

Tl2Te and its relationship with Tl5Te3

The crystal structure of Tl₂Te, dithallium telluride, has been determined by single‐crystal X‐ray diffraction. The analysis of the structure shows that this compound is the first known representative of a new crystal structure type. The structural relationship with the related Tl₅Te₃ phase is discussed.     

A long-wavelength biolabeling reagent based on the oxonol fluorophore

A red fluorescent dye of the oxonol class, bis-[1-(carboxymethyl)barbituric acid-(5)]-pentamethinoxonol, has been synthesized and, in the form of the succinimidyl active ester, has been applied to antibody labeling for application to flow cytometry and to imaging of tissue sections. The new dye, named CMOX (for carboxymethyloxonol), shows maximum excitation at 583 nm and emission at 611 nm, with a quantum yield of 0.2 in aqueous buffer and methanol. Antibodies labeled with the new dye show favorable brightness, photostability, and low levels of nonspecific binding.     

Molecular organization of DHP membrane fragments

The phase transition of dihexadecyl phosphate (DHP) bilayered disks has been studied using EPR spectroscopy. In the acid form of DHP, a phase transition temperature exists, that we have monitored through the spin-spin interaction between the nitroxide molecules at high concentration (8%) in DHP bilayers. This spin-spin interaction is due to the gathering of solutes in a fluid defect of the membrane: the border. The fluorescence quenching of two probes by the nitroxide stearic acids in DHP bilayers has been studied by stationary and time-resolved fluorescence measurements. The quenching process is mainly static. Both magnetic and fluorescent probes are localized in the periphery of the bilayered disks. An erratum to this article is available at .     

KVTeO5 and a redetermination of the Na homologue

A single crystal of KVTeO₅, potassium vanadium tellurite, has been grown. The present structure determination has been conducted together with the refinement of the NaVTeO₅ homologue, sodium vanadium tellurite, for the sake of precise comparison. The network consists of [VTeO₅]_n ribbons built up by VO₄ tetrahedra linking centrosymmetric Te₂O₆ groups and stacked along the [010] direction; the alkali cations are intercalated in between. The Te^IV atom exhibits a typical one‐sided coordination number (CN) of 4, completed by a lone pair, which forms a distorted triangular bipyramid with the four O atoms.     

Gradient estimates for some diffusion semigroups

 Consider the semigroup $P_t$ of an elliptic diffusion; we describe a simple stochastic method providing gradient estimates on $P_tf$. If $N$ is a manifold endowed with a connection, the method can also be applied to the associated nonlinear semigroup $Q_t$ acting on $N$-valued maps. With a localization technique, we deduce gradient estimates for real harmonic functions or $N$-valued harmonic maps. Moreover, the results are extended to a class of hypoelliptic diffusions. Received: 31 July 2000 / Revised version: 20 September 2001 / Published online: 15 March 2002