The first stereoselective total synthesis of the Z-isomer of cytospolide E

A convergent and highly stereoselective total synthesis of the Z-isomer of cytospolide E has been achieved via Evan’s aldol reaction, Sharpless kinetic resolution and RCM cyclisation.     

Bit-size estimates for triangular sets in positive dimension

We give bit-size estimates for the coefficients appearing in triangular sets describing positive-dimensional algebraic sets defined over Q. These estimates are worst case upper bounds; they depend only on the degree and height of the underlying algebraic sets. We illustrate the use of these results in the context of a modular algorithm.This extends the results by the first and the last author, which were confined to the case of dimension 0. Our strategy is to get back to dimension 0 by evaluation and interpolation techniques. Even though the main tool (height theory) remains the same, new difficulties arise to control the growth of the coefficients during the interpolation process.     

Spatial properties of Wohlhart symmetric mechanism

The aim of this paper is to present a new analytical resolution to find closure equations of Wohlhart symmetric mechanism and to give some interesting spatial properties of this mechanism. These properties are used to put in evidence possible industrial applications for this type of mechanism. First, it concerns the analytic resolution of the twelve equations system obtained from the closure equation, system particularized for the case of Wohlhart symmetric mechanism. The matrix form of closure equations is written for a single loop overconstrained mechanism composed by six revolute joints, mechanisms called 6R. A kinematical analysis is made, putting in evidence some interesting kinematical and geometrical properties. These properties allow us to consider a new spatial disposition for this mechanism, by imposing three non-successive joints to remain in a determined plan. Thus, we obtain a translator, a possible future industrial application for this type of overconstrained mechanism.     

Compressibility of a zinc single crystal under confining pressure

Abstract

In the present study, the two compressibility moduli of a zinc single crystal were measured at room temperature up to 18 GPa. The results are compared with those obtained by Bridgman from a different experimental method. This study required a gaseous hydrostatic confining pressure, and then it has been necessary to develop an original diamond anvil cell with a large optical aperture allowing the use of sophisticated video imaging and image analysis techniques. A model is proposed for the zinc volume-pressure relation.     

A one-round,two-prover,zero-knowledge protocol for NP

The model of zero-knowledge multi-prover interactive proofs was introduced by Ben-Or, Goldwasser, Kilian and Wigderson in [4]. A major open problem associated with this model is whether NP problems can be proven by one-round, two-prover, zero-knowledge protocols with exponentially small error probability (e.g. via parallel executions). A positive answer was claimed by Fortnow, Rompel and Sipser in [12], but its proof was later shown to be flawed by Fortnow who demonstrated that the probability of cheating inn independent parallel rounds can be much higher than the probability of cheating inn independent sequential rounds (with exponential ratio between them). In this paper we solve this problem: We show a new one-round two-prover interactive proof for Graph Hamiltonicity, we prove that it is complete, sound and perfect zeroknowledge, and thus every problem in NP has a one-round two-prover interactive proof which is perfectly zero knowledge under no cryptographic assumptions. The main difficulty is in proving the soundness of our parallel protocol namely, proving that the probability of cheating in this one-round protocol is upper bounded by some exponentially low threshold. We prove that this probability is at most 1/2 ^n/9 (wheren is the number of parallel rounds), by translating the soundness problem into some extremal combinatorial problem, and then solving this new problem.