A new generalization of the KMOV cryptosystem

The KMOV scheme is a public key cryptosystem based on an RSA modulus \(n=pq\) where p and q are large prime numbers with \(p\equiv q\equiv 2\pmod 3\). It uses the points of an elliptic curve with equation \(y^2\equiv x^3+b\pmod n\). In this paper, we propose a generalization of the KMOV cryptosystem with a prime power modulus of the form \(n=p^{r}q^{s}\) and study its resistance to the known attacks.     

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     

Synthesis,spectroscopic and structural studies of 2,2,2-trifluoroethyl phosphorodiamidate complexes with tin(IV) chloride

The two octahedral complexes SnCl₄ · 2(O)P(NR₂)₂OCH₂CF₃ (R = Me (1) or Et (2)) have been prepared from SnCl₄ and the ligands (R₂N)₂P(O)OCH₂CF₃ in chloroform solution. Both adducts have been characterised by (³¹P and ¹¹⁹Sn) NMR, IR spectroscopy and elemental analysis. The NMR data show that the complexes exist as mixtures of cis and trans isomers in solution with the latter isomer being the predominant species. The structure of 1 has been determined by X-ray crystallography. Accordingly, the structure is centrosymmetric and the two ligands are bound trans to each other in the octahedral tin complex. DFT/B3LYP calculations show that trans configuration does indeed lead to the lowest energy species. Comparison of the structural, NMR and theoretical data of both complexes with those related to SnCl₄ · 2L (L = (Me₂N)₃P(O) and (Me₂N)₂P(O)F) further supports the important effects of the nature of the substituents in the ligand on the stereochemistry of the complex formed.     

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.