Crystal and molecular structures of 1-[3-(3,4-dimethoxyphenyl)-2-propenoyl]pyrrolidine.

The crystal structure of 1-[3-(3,4-dimethoxyphenyl)-2-propenoyl]pyrrolidine (C15H19NO3) (I) has been determined by X-ray analysis. It crystallizes orthorhombic space group Pbca with a = 24.295(3), b = 15.086(3), c = 7.552(3)A, V = 2768(1)A3, Z = 8, Dcalc = 1.254 g/cm3, mu = (Mo K(alpha)) = 0.87 cm(-1). The title compound has analgesic activity of cycloaliphatic amine part. The molecule is deviated from planar configuration.     

Corner spontaneous magnetization

Details are given of a new method allowing an exact calculation of the spontaneous magnetization in the corner as well as along the edge at an arbitrary distance of the corner for a rectangular planar Ising ferromagnet.     

Rotational temperature and density measurements in a hypersonic flow by dual-line CARS

Rotational temperature and nitrogen number density are measured in the shock wave/boundary layer interaction region in the vicinity of a two-dimensional compression corner disposed in a low pressure, 55 K, Mach 10 hypersonic air flow. Spatially-resolved data are recorded using a nonlinear optical technique named dual-line coherent anti-Stokes Raman scattering (DLCARS). Averaged temperature and density profiles are compared with those predicted by a Navier-Stokes solver. Good agreement is found.     

A Note on an Input Control Model of a Predictive Regression Interval

A well-known problem of prediction in linear regression models is to find a confidence interval for the random value of the dependent variable when the values of the independent variables are given. Such a situation may arise in economic quality control models when the independent variables are costly inputs and the dependent variable is some measure of quality or production. In such a circumstance, an important control objective may be to find values for the inputs that will maximize the lower limit of the prediction confidence interval for a fixed budget, or alternatively, to minimize the cost of the inputs for a fixed lower limit of the confidence interval. In this paper, we shall show that global optima can be found using known algorithms. The special case of simple linear regression is discussed and an illustrative example is provided.     

Synthesis and polymerization of o-hexylaniline: Characterization of the corresponding polyaniline

In the field of research on soluble conducting polymers, the poly(o-alkylanilines) are very interesting because we can expect them to give more soluble polymers and new properties. Like poly(o-propylaniline) (POP), which is more soluble than polyaniline (PANi), poly(o-hexylaniline) (POH) appears to be more soluble in organic solvents than POP because of the longer alkyl groups in the 2-position. The higher solubility confers better processability on this new polymer, and because of this solubility, an NMR study in solution became possible.The nitration of hexylbenzene and the reduction of the resulting product to o-hexylaniline were performed according to the literature. The chemical polymerization was easy and it is possible to produce this polymer in large quantities.The polymerization carried out in anhydrous NH₄F, 2.35 HF medium and in 5 M perchloric acid gave a polymer with almost quantitative yield. The electrochemical behaviour of POH displayed faster electron transfers than PANi in organic solvents, depending on the acido-basicity level of the aqueous solutions. Unlike PANi, fractal growth was not observed.     

A Partial Differential Inequality in Geological Models

Sedimentation and erosion processes in sedimentary basins can be modeled by a parabolic equation with a limiter on the fluxes and a constraint on the time variation.This limiter happens to satisfy a stationary scalar hyperbolic inequality,within a constraint,for which the authors prove the existence and the uniqueness of the solution.Actually,this solution is shown to be the maximal element of a convenient convex set of functions.The existence proof is obtained thanks to the use of a numerical scheme.     

On almost-sure versions of classical limit theorems for dynamical systems

The purpose of this article is to support the idea that “whenever we can prove a limit theorem in the classical sense for a dynamical system, we can prove a suitable almost-sure version based on an empirical measure with log-average”. We follow three different approaches: martingale methods, spectral methods and induction arguments. Our results apply, among others, to Axiom A maps or flows, to systems inducing a Gibbs–Markov map, and to the stadium billiard.     

Stereoselective synthesis of trifluoromethyl-substituted 1,2-diamines by aza-Michael reaction with trans-3,3,3-trifluoro-1-nitropropene

Aza-Michael addition of optically pure 4-phenyl-2-oxazolidinone to 3,3,3-trifluoro-1-nitropropene proceeds smoothly at low temperature with a high yield. Diastereoselectivity of the addition depends on the base used and lithiated species proved to be highly efficient affording 92% de. Optically pure 1,2-diamino-3,3,3-trifluoropropane is prepared in 58% yield from the aza-Michael addition product through a three-step procedure.