Two novel steroids from Euphorbia officinarum latex

Two novel steroids, 3beta,7alpha-dihydroxy-4alpha,14alpha-dimethyl-5alpha-cholest-8-en-11-one (2) and 3beta,7beta-dihydroxy-4alpha,14alpha-dimethyl-5alpha-cholest-8-en-11-one (3) were isolated from the latex of Euphorbia officinarum. Their structures were established on the basis of NMR and MS studies.     

Spectral properties of several fluorene derivatives with potential as two-photon fluorescent dyes

Investigations of the absorption, steady-state fluorescence, excitation and excitation anisotropy properties of several fluorene derivatives, (7-benzothiazol-2-yl-9,9-didecylfluoren-2-yl)-diphenylamine, 9,9-didecyl-2,7-bis-(N,N-diphenylamino)fluorene and {4-[2-(7-diphenylamino-9,9-diethylfluoren-2-yl)vinyl]phenyl}phosphoric acid diethyl ester, in liquid solutions have been conducted. Spectral characteristics of these compounds, including fluorescence quantum yields, were measured in acetonitrile, methylene chloride, tetrahydrofuran and hexane at room temperature. Excitation anisotropy spectra provided a means to determine the nature of the short wavelength absorption bands as an electronic transition into a higher excited singlet state. It was found that excitation spectra in the short wavelength region do not correspond to the absorption bands that are correlated with the wavelength dependence of the fluorescence quantum yields. Major reasons of such spectral behavior are discussed.     

The influence of the periodic disturbance on the local heat transfer in separated and reattached flow

A numerical study based on the large eddy simulation methodology was made of heat transfer in locally disturbed turbulent separated and reattached flow over a backward facing step. The local disturbance was given to the flow by a sinusoidally blowing/suction of the fluid into a separated shear layer. The Reynolds number was fixed at 33,000 and Richardson number at 0.5. The disturbance frequency was varied in the range 0 ≤ St ≤ 2, where St is the Strouhal number of disturbance. The obtained results revealed the existence of an optimum perturbation frequency value, St = 0.25, in terms of the reduced reattachment length. At this frequency the heat transfer is significantly enhanced in the recirculation zone. The influence of the frequency and the amplitude of disturbance, in the maximum heat transfer positions and the maximum local Nusselt number, is analysed.     

Critère de régularité directionnelle

We characterize pointwise directional regularity by highly oriented multi-scaled wavelet coefficients.     

Directional and Anisotropic Regularity and Irregularity Criteria in Triebel Wavelet Bases

Many natural mathematical objects, as well as many multi-dimensional signals and images from real physical problems, need to distinguish local directional behaviors (for tracking contours in image processing for example). Using some results of Jaffard and Triebel, we obtain criteria of directional and anisotropic regularities by decay conditions on Triebel anisotropic wavelet coefficients (resp. wavelet leaders).     

Spectral analysis of two doubly infinite Jacobi matrices with exponential entries

We provide a complete spectral analysis of all self-adjoint operators acting on ${?}^2(\mathbb{Z})$ which are associated with two doubly infinite Jacobi matrices with entries given by

$q^{?n+1}{\delta }_{m,n?1}+q^{?n}{\delta }_{m,n+1}$

and

${\delta }_{m,n?1}+\alpha q^{?n}{\delta }_{m,n}+{\delta }_{m,n+1},$

respectively, where $q\in (0,1)$ and $\alpha \in \mathbb{R}$. As an application, we derive orthogonality relations for the Ramanujan entire function and the third Jackson q-Bessel function.