Characterization of v-sufficiency from the Newton filtration

The aim of this paper is to study the germ mappings : (ⁿ, 0)(^p, 0), more precisely, we formulate certain criteria for the v-sufficiency related to the Newton polyhedron. Our result implies in particular the criteria for v-sufficiency due to Kuo and Paunescu.This research was supported by the Japan Society for the Promotion of Science.Mathematics Subject Classification (2000): 14B05;58A35     

Reactivity of Gold Complexes towards Elementary Organometallic Reactions

For a while, the reactivity of gold complexes was largely dominated by their Lewis acid behavior. In contrast to the other transition metals, the elementary steps of organometallic chemistry—oxidative addition, reductive elimination, transmetallation, migratory insertion—have scarcely been studied in the case of gold or even remained unprecedented until recently. However, within the last few years, the ability of gold complexes to undergo these fundamental reactions has been unambiguously demonstrated, and the reactivity of gold complexes was shown to extend well beyond π‐activation. In this Review, the main achievements described in this area are presented in a historical context. Particular emphasis is set on mechanistic studies and structure determination of key intermediates. The electronic and structural parameters delineating the reactivity of gold complexes are discussed, as well as the remaining challenges.     

σ-Acceptor, Z-type ligands for transition metals

The ability of Lewis acids to coordinate to transition metals as σ-acceptor ligands was recognized as early as in the 1970's, but so-called Z-type ligands remained curiosities until the early 2000's. Over the last decade, significant progress has been made in this area, especially via the incorporation of Lewis acid moieties into multidentate, ambiphilic ligands. Our understanding of the nature and influence of TM → Z interactions has considerably improved and the scope of Lewis acids susceptible to behave as σ-acceptor ligands has been significantly extended. This feature article summarizes these recent achievements.     

A dual organic/organometallic approach for catalytic ring-opening polymerization

A dual catalytic system combining an original cationic zinc complex and a tertiary amine is shown to promote efficiently the polymerization of lactide under mild conditions.     

ELASTIC MEMBRANE EQUATION WITH MEMORY TERM AND NONLINEAR BOUNDARY DAMPING:GLOBAL EXISTENCE,DECAY AND BLOWUP OF THE SOLUTION

In this paper we consider the Elastic membrane equation with memory term and nonlinear boundary damping.Under some appropriate assumptions on the relaxation function h and with certain initial data,the global existence of solutions and a general decay for the energy are established using the multiplier technique.Also,we show that a nonlinear source of polynomial type is able to force solutions to blow up in finite time even in presence of a nonlinear damping.     

Robust and high-order effective boundary conditions for perfectly conducting scatterers coated by a thin dielectric layer

A new approach is considered to construct effective boundaryconditions for the solution of problems related to the scatteringof electromagnetic waves by perfectly conducting cylinders coatedby a thin dielectric shell. These boundary conditions aim tobe both robust and of high order while remaining set in termsof surface differential operators involving at most second-orderderivatives. Error estimates yield a theoretical basis for theuse of these boundary conditions in practical computations.Some numerical experiments at frequencies beyond the range ofvalidity of the usual impedance boundary conditions validatethe efficiency of the approach.