Structure-activity relationship between the 3D distribution of the electrophilicity of sugar derivatives and their cytotoxic and antiviral properties

Summary The cytotoxic activities of a series of sugar derivatives bearing electrophilic groups (1-cyanovinyl, 4-cyanochromen-2-yl and 3-nitrochromen-2-yl) have been correlated with their electrophilic properties. To this end, an electrophilic index was defined as an isovalue surface where the interaction energy with an incoming model nucelophile (H^–) was equal to a predefined value. This index, calculated from extended Hückel wave functions, allows one to quantify the electrophilic character of the substrates and to describe its spatial localization within the molecular volume (at Michael acceptor sites or on other parts of the molecules). Only sugars for which Michael acceptor reactivity was predicted were retained, and they were subdivided into two groups: those showing antiviral activity against a retrovirus and those devoid of such activity. Under these conditions, good correlations between cytotoxic activity and electrophilic reactivity-positive for the first group, negative for the second-were found. In addition, the ratio electrophilicity/sum of the absolute value of the dipole plus its projection along the principal axis of inertia, Z, of the molecule allows one to predict to which of these groups a sugar derivative belongs.     

Controlled radical polymerization of styrene mediated by the C‐phenyl‐N‐tert‐butylnitrone/AIBN pair: Kinetics and electron spin resonance analysis

Kinetics of the free radical polymerization of styrene at 110 °C has been investigated in the presence of C‐phenyl‐N‐tert‐butylnitrone (PBN) and 2,2′‐azobis(isobutyronitrile) (AIBN) after prereaction in toluene at 85 °C. The effect of the prereaction time and the PBN/AIBN molar ratio on the in situ formation of nitroxides and alkoxyamines (at 85 °C), and ultimately on the control of the styrene polymerization at 110 °C, has been investigated. As a rule, the styrene radical polymerization is controlled, and the mechanism is one of the classical nitroxide‐mediated polymerization. Only one type of nitroxide (low‐molecular‐mass nitroxide) is formed whatever the prereaction conditions at 85 °C, and the equilibrium constant (K) between active and dormant species is 8.7 × 10^?10 mol L^?1 at 110 °C. At this temperature, the dissociation rate constant (k_d) is 3.7 × 10^?3 s^?1, the recombination rate constant (k_c) is 4.3 × 10⁶ L mol^?1 s^?1, whereas the activation energy (E_a,diss.), for the dissociation of the alkoxyamine at the chain‐end is ～125 kJ mol^?1. Importantly, the propagation rate at 110 °C, which does not change significantly with the prereaction time and the PBN/AIBN molar ratio at 85 °C, is higher than that for the thermal polymerization at 110 °C. This propagation rate directly depends on the equilibrium constant K and on the alkoxyamine and nitroxide concentrations, as well. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1219–1235, 2007     

A Theorem of the Alternative in Banach Lattices

We consider a linear sytem in a Banach lattice and provide a simple theorem of the alternative (or Farkas lemma) without the usual closure condition.

     

Self-Attracting Poisson Clouds in an Expanding Universe

 We consider the following elementary model for clustering by ballistic aggregation in an expanding universe. At the initial time, there is a doubly infinite sequence of particles lying in a one-dimensional universe that is expanding at constant rate. We suppose that each particle p attracts points at a certain rate a(p)/2 depending only on p, and when two particles, say p and q, collide by the effect of attraction, they merge as a single particle p*q. The main purpose of this work is to point at the following remarkable property of Poisson clouds in these dynamics. Under certain technical conditions, if at the initial time the system is distributed according to a spatially stationary Poisson cloud with intensity μ ₀ , then at any time t > 0, the system will again have a Poissonian distribution, now with intensity μ _t , where the family solves a generalization of Smoluchowski's coagulation equation. Received: 15 February 2002 / Accepted: 8 July 2002 Published online: 7 November 2002     

A new system of boundary integral equations for plates with free edges

We present a new system of boundary integral equations for the free-edge plate. This system expresses an abstract symmetric variational problem posed on the boundary of the plate. In order to obtain this abstract problem, we must set the exterior boundary value problem corresponding to the free-edge plate in a framework of weighted Sobolev spaces. Finally, we take care of the hypersingular kernels appearing in our system of BIEs, by using an abstract technique of integration by parts.     

Unification of basic and composite nondifferentiable optimization

There are two main classes of iterative methods in nondifferentiable optimization (NDO). In thebasic NDO, the information is limited to the objective function and at least one element of its subdifferential, while in thecomposite NDO, the objective function is split into a sum of a smooth and a nonsmooth function. Our work unifies these two approaches for benefiting of their respective advantages.     

Convexity estimates for nonlinear elliptic equations and application to free boundary problems

We prove the convexity of the set which is delimited by the free boundary corresponding to a quasi-linear elliptic equation in a 2-dimensional convex domain. The method relies on the study of the curvature of the level lines at the points which realize the maximum of the normal derivative at a given level, for analytic solutions of fully nonlinear elliptic equations. The method also provides an estimate of the gradient in terms of the minimum of the (signed) curvature of the boundary of the domain, which is not necessarily assumed to be convex.