Identification of new catalysts for the asymmetric reduction of imines into chiral amines with polymethylhydrosiloxane using high-throughput screening

The use of high-throughput techniques allowed the rapid identification of new catalysts for the enantioselective reduction of imines using polymethylhydrosiloxane (PMHS) as a reducing agent. By a simple modification of the chiral ligand structure that came out of the screening, the enantioselectivity of the reduction was increased from 40% ee to 60% ee.     

Des équations de Dirac et de Schrödinger pour la transformation de Fourier

Dyson has associated with the Fredholm determinants of the even (resp. odd) Dirichlet kernels a Schrödinger equation on the half-axis and has used, in tandem, the Gel'fand–Levitan and Marchenko methods of inverse scattering theory to study the asymptotics of these determinants. We have proposed following our unearthing of the conductor operator to seek to realize the Fourier transform itself as a scattering, and we obtain here to this end two Dirac systems on the entire real axis which are intrinsically associated, respectively, to the cosine and to the sine transforms. To cite this article: J.-F. Burnol, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Conversations on mind, matter, and mathematics

Conclusion  The debate between Jean-Pierre Changeux and Alain Connes is one of the most, interesting to take place in recent years. It re-frames in a very up-to-date context a whole series of traditional and difficult questions from the standpoint of the knowledge and experience of two of the leading protagonists of contemporary science. To the choice presented by the neurobiologist between a Platonist ontology and a neurocognitive psychology of mathematical activity, the mathematician replies with a conception that is objective (neither ontological nor psychological) of the thoroughly consistent universe of mathematical idealities. It is indeed in this three-sided arena that the major difficulties play themselves out. One of the great virtues of the book is to cast a spotlight on this confrontation.     

Speed of adaptation in structured populations

Adaptation of populations takes place with the occurrence and subsequent fixation of mutations that confer some selective advantage to the individuals which acquire it. For this reason, the study of the process of fixation of advantageous mutations has a long history in the population genetics literature. Particularly, the previous investigations aimed to find out the main evolutionary forces affecting the strength of natural selection in the populations. In the current work, we investigate the dynamics of fixation of beneficial mutations in a subdivided population. The subpopulations (demes) can exchange migrants among their neighbors, in a migration network which is assumed to have either a random graph or a scale-free topology. We have observed that the migration rate drastically affects the dynamics of mutation fixation, despite of the fact that the probability of fixation is invariant on the migration rate, accordingly to Maruyama's conjecture. In addition, we have noticed a topological dependence of the adaptive evolution of the population when clonal interference becomes effective.     

On the global structure of crystalline surfaces

We bound the number of plane segments in a crystalline minimal surface S in terms of its Euler characteristic, the number of line segments in its boundary, and a factor determined by the Wulff shapeW of its surface energy function. A major technique in the proofs is to quantize the Gauss map ofS based on the Gauss map ofW. One thereby bounds the number of positive-curvature corners and the interior complexity ofS. The support of the National Science Foundation and the Air Force Office of Scientific Research and the hospitality of Stanford University, where this paper was extensively rewritten, are gratefully acknowledged.     

Inherited LU-factorizations of matrices

Various types of LU-factorizations for nonsingular matrices, where L is a lower triangular matrix and U is an upper triangular matrix, are defined and characterized. These types of LU-factorizations are extended to the general m × n case. The more general conditions are considered in the light of the structures of [C.R. Johnson, D.D. Olesky, P. Van den Driessche, Inherited matrix entries: LU factorizations, SIAM J. Matrix Anal. Appl. 10 (1989) 99-104]. Applications to graphs and adjacency matrices are investigated. Conditions for the product of a lower and an upper triangular matrix to be the zero matrix are also obtained.     

Diagramme polythermique du systeme ternaire H2O—Al(NO3)3—Mg(NO3)2

The solid—liquid equilibria of the ternary system H₂O—Al(NO₃)₃—Mg(NO₃)₂ were studied at –30, –20, –10 and 0°C by using a synthetic method which allows to detemine all the characteristic points of isothermal sections. The stable solid phases which appear are respectively: ice, Al(NO₃)₃·9H₂O, Mg(NO₃)₂·9H₂O and Mg(NO₃)₂·6H₂O. Neither double salts nor mixed crystals are observed in the temperature and composition field studied. Polytherm diagram layout show two invariant transformations correspond with an eutectic point and a peritectic point.This revised version was published online in November 2005 with corrections to the Cover Date.     

Multipole-Bound Molecular Negative Ions

 Within the framework of a simple electrostatic model, as compared to recent experimental results, we here discuss the stability of very weakly bound molecular negative ions. In contrast with the case of conventional valence anions, the excess electron is then located in a very diffuse orbital and is mainly bound by electrostatic dipolar, quadrupolar, and polarization forces, at large distances from the neutral molecular core. By fitting a single repulsion parameter of the model to the available experimental data, it is possible to make quantitative predictions of the excess-electron binding energies in these species. Critical values of the dipole moment, quadrupole moment or polarizability required for the observation of stable multipole-bound negative ions are predicted and compared to available experimental data and ab initio calculations. Received October 24, 2001; accepted for publication November 16, 2001     

A diffusion approximation result for two parameter processes

Summary We consider a one-dimensional linear wave equation with a small mean zero dissipative field and with the boundary condition imposed by the so-called Goursat problem. In order to observe the effect of the randomness on the solution we perform a space-time rescaling and we rewrite the problem in a diffusion approximation form for two parameter processes. We prove that the solution converges in distribution toward the solution of a two-parameter stochastic differential equation which we identify. The diffusion approximation results for oneparameter processes are well known and well understood. In fact, the solution of the one-parameter analog of the problem we consider here is immediate. Unfortunately, the situation is much more complicated for two-parameter processes and we believe that our result is the first one of its kind.Partially supported by ONR N00014-91-J-1010