Global Classical Solutions of the Relativistic Vlasov–Darwin System with Small Cauchy Data: The Generalized Variables Approach

We show that a smooth, small enough Cauchy datum launches a unique classical solution of the relativistic Vlasov–Darwin (RVD) system globally in time. A similar result is claimed in Seehafer (Commun Math Sci 6:749–769, 2008) following the work in Pallard (Int Mat Res Not 57191:1–31, 2006). Our proof does not require estimates derived from the conservation of the total energy, nor those previously given on the transversal component of the electric field. These estimates are crucial in the references cited above. Instead, we exploit the formulation of the RVD system in terms of the generalized space and momentum variables. By doing so, we produce a simple a priori estimate on the transversal component of the electric field. We widen the functional space required for the Cauchy datum to extend the solution globally in time, and we improve decay estimates given in Seehafer (2008) on the electromagnetic field and its space derivatives. Our method extends the constructive proof presented in Rein (Handbook of differential equations: evolutionary equations, vol 3. Elsevier, Amsterdam, 2007) to solve the Cauchy problem for the Vlasov–Poisson system with a small initial datum.     

Inference for the invariance of canonical analysis under linear transformations

Using a recent result about the invariance problem in linear canonical analysis (LCA), we introduce a criterion by means of which one can see if this invariance holds when the related random vectors are transformed by linear maps. Then, the estimation of this criterion is considered as well as the problem of testing for invariance of LCA. Particularly, a new test for additional information in canonical analysis is proposed and simulations are used to gain understanding of the finite sample performance of this test and to compare it with the likelihood ratio test.     

Linear relative canonical analysis of Euclidean random variables,asymptotic study and some applications

We introduce the Linear Relative Canonical Analysis (LRCA) of Euclidean random variables. Then similar properties than for usual linear Canonical Analysis are obtained. Furthermore, we develop an asymptotic study of LRCA and apply the obtained results to tests for lack of relative linear association, dimensionality and invariance.     

Recombinant human estrogen, androgen and progesterone receptors for detection of potential endocrine disruptors

This work reports the binding capacity of various chemicals (so-called endocrine disruptors) to recombinant human steroid receptors (hER, hPR and hAR). The tested chemicals are organochlorine insecticides (DDT and its metabolites, methoxychlor, aldrin, dieldrin, chlordecone, lindane, trichlorobenzene), estrogenic insecticides (endosulfan, toxaphene, nonachlor), herbicides (alachlor and atrazine), fungicides (benomyl and vinclozolin), industrial chemicals (nonylphenol, bisphenol A, diphenylphtalate), antioxidants (butylated hydroxyanisol) and some phytoestrogens. Except for phytoestrogens, most of the tested chemicals (DDT and its metabolites, aldrin, - and -endosulfan, toxaphen, trans-nonachlor) show higher affinities for hPR than for hER, indicating that the interaction with the progesterone receptor could contribute to the endocrine-disrupting effects imputed to these chemicals. We propose to use binding assays using recombinant human steroid receptors as screening tools for the detection of endocrine disruptors in various samples.     

One-Dimensional Numerical Algorithms for Gradient Flows in the p-Wasserstein Spaces

We numerically approximate, on the real line, solutions to a large class of parabolic partial differential equations which are “gradient flows” of some energy functionals with respect to the L ^p -Wasserstein metrics for all p>1. Our method relies on variational principles involving the optimal transport problem with general strictly convex cost functions.     

Early Relaxation Dynamics in the Photoswitchable Complex trans-[RuCl(NO)(py)4]2+

The design of photoswitchable transition metal complexes with tailored properties is one of the most important challenges in chemistry. Studies explaining the underlying mechanisms are, however, scarce. Herein, the early relaxation dynamics towards NO photoisomerization in trans-[RuCl(NO)(py)₄]²⁺ is elucidated by means of non-adiabatic dynamics, which provided time-resolved information and branching ratios. Three deactivation mechanisms (I, II, III) in the ratio 3:2:4 were identified. Pathways I and III involve ultrafast intersystem crossing and internal conversion, whereas pathway II involves only internal conversion.     

New class of chiral ligands derived from isosorbide: first application in asymmetric transfer hydrogenation

A new class of β-amino alcohol and diamine ligands was prepared from isosorbide as a chiral renewable resource. The original wedge-shaped structure of isosorbide offers an interesting chiral pocket to promote the metal-catalyzed enantioselective reduction of ketones by transfer hydrogenation.     

Excited states of conjugated hydrocarbon radicals using the molecular mechanics – valence bond (MMVB) method

By using a parameterised Heisenberg Hamiltonian coupled to a molecular mechanics force field, excited-state geometries were optimised for three conjugated hydrocarbon radicals: cyclopentadienyl, phenalenyl (perinaphthenyl), and triphenylmethyl. The results are compared with ab initio calculations, and with recent spectroscopic measurements. Electronic Supplementary Material is available in the online version of this article at http://dx.doi.org/10.1007/s00214-003-0461-3     

Water‐soluble pH‐sensitive 2,6‐bis(substituted ethylidene)‐cyclohexanone/hydroxy cyanine dyes that absorb in the visible/near‐infrared regions

Three methods were used to synthesize a series of the title compounds. The ketones absorb in the visible region, and upon protonation (pH<6) they are converted to hydroxy‐substituted heptamethine cyanines that show an intense absorption in the near‐infrared region (>700 nm). The conversion is reversible and depends solely on pH conditions.