α-Phosphoryl Cyclopentanones as Possible Intermediates in the Total Synthesis of Sarkomycin

Abstract

In an effort to synthesize sarkomycin 1 trans-2-diphenylphosphinoyl-3-tris (methylthio) methyl-cyclopentanone 7 and trans-2-diphenylphosphinoyl-3-carbo-methoxy-cyclopentanone 8 were prepared. The Horner-Wittig reaction of the latter with formaldehyde failed. (±)-Sarkonycin 1 was prepared by a sequence of reactions starting from diethyl 2-oxopropanephosphonate. The key steps in this synthesis involve the intramolecular carbenoid cyclization of 1-diazo-2-oxopropanephosphonate 10 and the Horner-Wittig reaction of 2-diethoxyphosphoryl-3-carboxy-cyclopentanone 12 with formaldehyde.     

Boundary Behavior of Large Solutions to the Monge-Ampère Equation in a Borderline Case

This paper is concerned with the boundary behavior of strictly convex large solutions to the Monge-Ampère equation detD²u(x)=b(x)f(u(x)), u > 0, x ∈ Ω, where Ω is a strictly convex and bounded smooth domain in R^N with N ≥ 2, f is normalized regularly varying at infinity with the critical index N and has a lower term, and b ∈ C^∞(Ω) is positive in Ω, but may be appropriate singular on the boundary.     

Physico-chemical properties and healing capacity of potentially bioactive titanium surface

The aim of this study was to evaluate physico-chemical properties and the healing capacity of surface treated titanium. Surface treatment combining sand-blasting, acid etching and alkaline etching (BIO surface) was evaluated together with machined titanium as a reference surface. Hydration, wetting angle, surface area and roughness parameters were evaluated for both surfaces. Stability of dental implants with both surfaces implanted in the tibia of dog was measured during the healing of twelve weeks. BIO surface exhibited lower wetting angle, larger surface area, higher degree of hydration and higher average roughness compared to machined titanium. Implants with the BIO surface maintained their stability during the whole healing period in contrast to those with machined titanium surface, which showed a statistically significant decrease in stability three and nine weeks after implantation.     

Large-eddy simulation of transition to turbulence in a heated annular channel

One carries out three-dimensional large-eddy simulations of natural convection in a horizontal annulus using Smagorinsky's dynamic subgrid model. The onset of transition to turbulence and turbulent regimes are analyzed. The characteristics of unstable flows and their influence on the heat-transfer process are studied. To cite this article: E.L.M. Padilla, A. Silveira-Neto, C. R. Mecanique 333 (2005).     

First order models and closure of the mass conservation equation in the mathematical theory of vehicular traffic flow

This article deals with a review and critical analysis of first order hydrodynamic models of vehicular traffic flow obtained by the closure of the mass conservation equation. The closure is obtained by phenomenological models suitable to relate the local mean velocity to local density profiles. Various models are described and critically analyzed in the deterministic and stochastic case. The analysis is developed in view of applications of the models to traffic flow simulations for networks of roads. Some research perspectives are derived from the above analysis and proposed in the last part of the paper. To cite this article: N. Bellomo, V. Coscia, C. R. Mecanique 333 (2005).     

Generalized genus sequences for misère octal games

Two approaches have been used to solve impartial games with misère play; genus theory, which has resulted in a number of results summarized in [2], and Sibert-Conway decomposition [9], which has been used to solve the octal game 0.77 (known as Kayles). The main aim of this paper is to publish (for the first time) the results archived in [1], extending genus theory beyond the applications to which it has previously been applied. In addition, we extend a result from [6] to misère play by adapting it to use the extended genus theory. The resulting theorems require extensive calculations to verify that their preconditions hold for any particular games. These calculations have been carried out by computer for all two-digit octal games. For many of these games, this has resulted in complete solutions. Complete solutions are presented for four games listed in [8] as unsolved. Received: September 2001     

Quelques Résultats sur les Algèbres Flexibles Préhilbertiennes sans Diviseurs de Zéro Vérifiant ∥a 2∥ = ∥a∥2

Résumé. Soit A une algèbre réelle. On suppose que l’espace vectoriel A est muni d’une norme ∥.∥ préhilbertienne vérifiant ∥a ²∥ = ∥a∥² pour tout . Si A est flexible, sans diviseurs de zéro et de dimension ≤ 4, alors A est isomorphe à ou , ce qui généralise un théorème d’El-Mallah [1]. Si A est flexible, sans diviseurs de zéro, contenant un idempotent central et vérifiant la propriété d’Osborn, alors A est de dimension finie et isomorphe à , ou . Enfin nous montrons qu’une algèbre normée préhilbertienne unitaire d’unité e telle que ∥e∥ = 1 est flexible et vérifie ∥a ²∥ = ∥ a∥².

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Let A be a real algebra. Assuming that a vector space A is endowed with a pre-Hilbert norm ∥.∥ satisfying ∥a ²∥ = ∥a∥² for all . If A is flexible, without divisor of zero and of a dimension ≤ 4, then A is isomorphic to or , which generalize El-Mallah’s theorem [1]. If A is flexible, without divisor of zero, containing a central idempotent and satisfying Osborn’s properties, then A is finite dimensional and isomorphic to , or . Finally we prove that a normed pre-Hilbert algebra with unit e such that ∥e∥ = 1 is flexible and satisfies ∥a ²∥ = ∥a∥².