Synthesis of 2- and 4-substituted 5,12-dihydroxy-6,11-dioxo-1-azanaphthacenes from 2-aminoquinizarine

The reaction of 2-aminoquinizarine with α,β-unsaturated carbonyl compounds in presence of 10N-hydrochloric acid gives 2- and 4-substituted 5,12-dihydroxy-6,11-dioxo-1-azanaphthacenes.     

Sesquiterpenes produced by Pestalotiopsis microspora HF 12440 isolated from Artocarpus heterophyllus

Abstract

A drimane-type sesquiterpene, (+)-dendocarbin L (1) together with two bisabolane-type sesquiterpenes, (+)-sydonic acid (2) and (+)-sydowic acid (3) were isolated from the mycelium of Pestalotiopsis microspora HF 12440, an endophytic fungus from the stem of Artocarpus heterophyllus. The structures of all compounds were elucidated using spectroscopic methods and by comparison with the literature. Compound 1 was isolated from the fungi for the first time, compounds 2 and 3 were firstly obtained from this endophytic fungus. Compound 3 showed cytotoxicity (IC₅₀ 2.56?μg/mL) against murine leukemia P-388 cells.     

Radial Dunkl processes: Existence,uniqueness and hitting time

We give shorter proofs of the following known results: the radial Dunkl process associated with a reduced system and a strictly positive multiplicity function is the unique strong solution for all times t of a stochastic differential equation with a singular drift, the first hitting time of the Weyl chamber by a radial Dunkl process is finite almost surely for small values of the multiplicity function. The proof of the first result allows one to give a positive answer to a conjecture announced by Gallardo–Yor while that of the second shows that the process hits almost surely the wall corresponding to the simple root with a small multiplicity value. To cite this article: N. Demni, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Modeling of the mode dynamics generated by Madison Symmetric Torus machine utilizing a modified sine-Gordon equation

In this paper, a new dynamic model is presented for the experimental data generated by the Madison Symmetric Torus (MST) machine. The model is based on a modified sine-Gordon (SG) dynamic equation. The modified sine-Gordon equation model effectively captures the behavior of the slinky mode in reversed-field pinch experiments. In addition, this paper demonstrates how the derived model accurately describes the behavior of the localized magnetohydrodynamic mode (slinky mode) that appears in reversed-field pinch toroidal magnetic confinement systems. The modified SG equation model is solved analytically by using the perturbation method. The resulting model is fit to match a variety of experimental results in the MST reversed-field pinch experiment. The efficacy of the newly developed model in effectively representing the slinky mode is verified by comparing obtained analytical solution to experimentally measured data.     

Interaction soliton–sable dans un canal en eau peu profonde

Interaction between solitons and a sandy bed in shallow water is investigated. In our experiments, solitons are generated on the background of a harmonic wave, in a wave flume used in resonant mode. It is found that the sand ripples formed by the solitons propagation induce a significant decrease of solitons amplitude and of the phase shift between the soliton and the harmonic wave. However, the amplitude of the harmonic wave is approximately constant. The possible physical processes of such behaviour for the soliton amplitude and for the harmonic wave amplitude are discussed. To cite this article: F. Marin et al., C. R. Mecanique 333 (2005).     

Quaternionic Brownian Windings

Journal of Theoretical Probability - We define and study the three-dimensional windings along Brownian paths in the quaternionic Euclidean, projective and hyperbolic spaces. In particular, the...     

Moments of the Hermitian Matrix Jacobi Process

In this paper, we compute the expectation of traces of powers of the Hermitian matrix Jacobi process for a large enough but fixed size. To proceed, we first derive the semi-group density of its eigenvalues process as a bilinear series of symmetric Jacobi polynomials. Next, we use the expansion of power sums in the Schur polynomial basis and the integral Cauchy–Binet formula in order to determine the partitions having nonzero contributions after integration. It turns out that these are hooks of bounded weight and the sought expectation results from the integral of a product of two Schur functions with respect to a generalized beta distribution. For special values of the parameters on which the matrix Jacobi process depends, the last integral reduces to the Cauchy determinant and we close the paper with the investigation of the asymptotic behavior of the resulting formula as the matrix size tends to infinity.     

The design of TOPK inhibitors using structure-based pharmacophore modeling and molecular docking based on an MD-refined homology model

Molecular Diversity - The TOPK enzyme (also known as PBK) is a serine-threonine protein kinase that is rarely detected in normal tissues yet is found to be overexpressed and activated in a variety...