Sommes D'Exponentielles et Entiers Sans Grand Facteur Premier

Let S(x,y) be the set S(x,y)= 1 n x : P(n) y, where P(n) denotesthe largest prime factor of n. We study , where f is a multiplicative function. When f=1and when f=µ, we widen the domain of uniform approximationusing the method of Fouvry and Tenenbaum and making explicitthe contribution of the Siegel zero. Soit S(x,y) l'ensemble S(x,y)= 1 n x : P(n) y, désigne le plus grand facteur premier den. Nous étudions , lorsque f est une fonction multiplicative. Quand f=1 et quand f=µ,nous élargissons le domaine d'approximation uniformeenutilisant la méthode développée par Fouvryet Tenenbaum et en explicitant la contribution du zérode Siegel. 1991 Mathematics Subject Classification: 11N25, 11N99.     

A Generic Global Optimization Algorithm for the Chemical and Phase Equilibrium Problem

This paper addresses the problem of finding the number, K, of phases present at equilibrium and their composition, in a chemical mixture of n _s substances. This corresponds to the global minimum of the Gibbs free energy of the system, subject to constraints representing m _b independent conserved quantities, where m _b=n _s when no reaction is possible and m _b n _e +1 when reaction is possible and n _e is the number of elements present. After surveying previous work in the field and pointing out the main issues, we extend the necessary and sufficient condition for global optimality based on the reaction tangent-plane criterion, to the case involving different thermodynamical models (multiple phase classes). We then present an algorithmic approach that reduces this global optimization problem (involving a search space of m _b(n _s-1) dimensions) to a finite sequence of local optimization steps inK(n _s-1) -space, K m _b, and global optimization steps in (n _s-1)-space. The global step uses the tangent-plane criterion to determine whether the current solution is optimal, and, if it is not, it finds an improved feasible solution either with the same number of phases or with one added phase. The global step also determines what class of phase (e.g. liquid or vapour) is to be added, if any phase is to be added. Given a local minimization procedure returning a Kuhn–Tucker point and a global optimization procedure (for a lower-dimensional search space) returning a global minimum, the algorithm is proved to converge to a global minimum in a finite number of the above local and global steps. The theory is supported by encouraging computational results.     

Recent Advances in the Study of High‐Temperature Free Radical Acrylic Solution Copolymerization

Semibatch starved‐feed solution copolymerization is used to produce acrylic resins for coatings formulations. Mechanisms and rate coefficients for polymerization of methacrylates, acrylates, and styrene (ST) under these high‐temperature conditions are reviewed. An extended set of experimental results at 138 °C is used to refine a model describing the solution copolymerization of ST and methacrylates. The data suggest that both changing initiator efficiency and transfer reactions of oxygen‐centered radicals to polymer affect the development of polymer molecular weight. A penultimate model is used to describe the variation in termination rate coefficient with copolymer composition. Significant progress has been made to develop an extended model capable of representing multicomponent high‐temperature acrylic polymerizations.

     

Free convection boundary layers on a vertical surface in a heat-generating porous medium

The natural convection boundary-layer flow on a solid verticalsurface with heat generated within the boundary layer at a rateproportional to (T – T)^p (p 1) is considered. The surfaceis held at the ambient temperature T except near the leadingedge where it is held at a temperature above ambient. The behaviourof the flow as it develops from the leading edge is examinedand is seen to become independent of the initial heat input;however, it does depend strongly on the exponent p. For 1 p 2, the local heating eventually dominates at large distancesand there is a convective flow driven by this mechanism. Forp 4, the local heating does not have a significant effect,the fluid temperature remains relatively small throughout andthe heat transfer dies out through a wall jet flow. For 2 <p < 4, the local heating has a significant effect at relativelysmall distances, with a thermal runaway developing at a finitedistance along the surface.     

Aspects of free analysis

We survey the analysis around the free difference quotient derivation, which is the natural derivation for variables with the highest degree of noncommutativity. The analogue of the Fourier transform is then bialgebra duality for the bialgebra with derivation-comultiplication to which the free difference quotient gives rise and which involves fully matricial analytic functions. Some of the motivation from free probability, especially free entropy and random matrices are also discussed. Dan-Virgil Voiculescu; Research supported in part by NSF Grant DMS 0501178.     

Associative Versus Dissociative Mechanisms of Phosphate Monoester Hydrolysis: On the Interpretation of Activation Entropies

Phosphate monoester and anhydride hydrolysis is ubiquitous in biology, being involved in, amongst other things, signal transduction, energy production, and the regulation of protein function. Therefore, this reaction has understandably been the focus of intensive research. Nevertheless, the precise mechanism by which phosphate monoester hydrolysis proceeds remains controversial. Traditionally, it has been assumed and frequently implied that a near‐zero activation entropy is indicative of a dissociative pathway. Herein, we examine free‐energy surfaces for the hydrolysis of the methyl phosphate dianion and the methyl pyrophosphate trianion in aqueous solution. In both cases, the reaction can proceed through either compact or expansive concerted (A_ND_N) transition states, with fairly similar barriers. We have evaluated the activation entropies for each transition state and demonstrate that both associative and dissociative transition states have near‐zero entropies of activation that are in good agreement with experimental values. Therefore, we believe that the activation entropy alone is not a useful diagnostic tool, as it depends not only on bond orders at the transition state, but also on other issues that include (but are not limited to) steric factors determining the configurational volumes available to reactants during the reaction, solvation and desolvation effects that may be associated with charge redistribution upon approaching the transition state and entropy changes associated with intramolecular degrees of freedom as the transition state is approached.     

Generation of Nanopores Down to 10 nm for Use in Deep‐Nulling Interferometry

Scanning electron microscope images show that it is easy to generate nanopores on polycarbonate membranes with well‐defined pore diameters by ion‐track perforation and subsequent magnetron sputtering with metal. The size reduction of the nanopores during sputtering with gold is a linear function of time. Images of different angles and from the bottom side of the membrane show that the channels are the smallest very close to the surface of the metal layer, have a conelike shape, and reach about half as much into the polymer membranes as the metal‐layer thickness. This topographical pore shape is ideal for use as optically coherent near‐field sources in deep‐nulling microscopy. We present the first results of significantly improved nulling stabilization in the presence (<2 nm optical pathway difference) and the absence (<0.6 nm optical pathway difference) of the nanoapertures in the focal region of a deep‐nulling microscope.     

SYNTHESIS OF HETEROARM STAR-SHAPED POLYMER BY THE USE OF POLYFUNCTIONAL CHAIN-TRANSFER AGENT via CONVENTIONAL FREE RADICAL POLYMERIZATION

Heteroarm star-shaped polymers were synthesized by conventional free radical polymerization in two steps by the use of polyfunctional chain transfer agent.In the first step,free radical polymerization of methyl methacrylate was carried out in the presence of a polyfunctional chain transfer agent,pentaerythritol tetrakis(3-mercaptopropinate).At appropriate monomer conversions,two-arm PMMA having two residual thiol groups at the chain center or three-arm PMMA having one residual thiol group at the core wer...