An analytic approach to the ergodic theory of a stochastic variational inequality

In an earlier work made by the first author with J. Turi (Degenerate Dirichlet Problems Related to the Invariant Measure of Elasto-Plastic Oscillators, AMO, 2008), the solution of a stochastic variational inequality modeling an elasto-perfectly-plastic oscillator has been studied. The existence and uniqueness of an invariant measure have been proven. Nonlocal problems have been introduced in this context. In this work, we present a new characterization of the invariant measure. The key finding is the connection between nonlocal PDEs and local PDEs which can be interpreted with short cycles of the Markov process solution of the stochastic variational inequality.     

Exaltone® (=Cyclopentadecanone) from Isomuscone® (=Cyclohexadecanone), a One‐C‐Atom Ring‐Contraction Methodology via a Stereospecific Favorskii Rearrangement: Regioselective Application to (−)‐(R)‐Muscone

Treatment of cyclohexadecanone ( 1g ; with I₂ (2.2 mol‐euqiv.) and KOH in MeOH) furnished the unsaturated (Z)‐ester 2g in 83% yield, via a stereospecific Favorskii rearrangement (Scheme 1). Further treatment with 3‐chloroperbenzoic acid (m‐CPBA) afforded the unreported epoxy ester 3g (88% yield), which was cleaved in 33% yield to Exaltone^® (=cyclopentadecanone; 1f ) with NaOH in MeOH/H₂O and then HCl at 65°. This methodology was similarly extended to higher (C₁₇) and lower (C₁₅ to C₁₁) cyclic ketone analogues, as well as regioselectively to (?)‐(R)‐muscone ( 5c ) and homomuscone ( 5f ) (Scheme 2). Olfactive properties of the corresponding macrocyclic 1‐oxaspiro[2,n]alkanes and ‐alkenes 4 and 8 , resulting from a Corey? Chaykovsky oxiranylation, are also presented.     

MRI investigation of granular interface rheology using a new cylinder shear apparatus

The rheology of granular materials near an interface is investigated through proton magnetic resonance imaging. A new cylinder shear apparatus has been inserted in the magnetic resonance imaging device, which allows the control of the radial confining pressure exerted by the outer wall on the grains and the measurement of the torque on the inner shearing cylinder. A multi-layer velocimetry sequence has been developed for the simultaneous measurement of velocity profiles in different sample zones, while the measurement of the solid fraction profile is based on static imaging of the sample. This study describes the influence of the roughness of the shearing interface and of the transverse confining walls on the granular interface rheology.     

Syntheses,Structures and Photoelectron Spectra of Phospha-Alkenes and Phospha-Alkynes and Their Transition Metal Complexes

Abstract

The chemistry of the novel phospha-alkenes RP[dbnd]CR'₂, and phospha-alkynes, RC[tbnd]P, containing 2pπ-3pπ bonds is of current interest.^1,2 Recent molecular orbital calculations,^3,4 suggest that the highest occupied molecular orbital in CH₂[dbnd]PH is of the π-type with the phosphorus lone pair ó-orbital only slightly more stable while the π? lumo orbital is relatively low lying. We now report He (I) photoelectron spectroscopic studies on a variety of RC[tbnd]P molecules^5,6 which indicate that the homo is also of the π-type and the π-σ separation is much greater than that found in the analogous RC[tbnd]N systems.     

Synthesis of a New C-15 Phosphorus Ylide Used for the Preparation of Some β-End-Group Retinoid Derivatives

A synthesis of a new C-15 phosphorus ylide from a C-14 enaminone is reported. This reagent, which undergoes selective 1,2- or 1,4-additions with saturated and unsaturated aldehydes, may find some synthetic use for the preparation of β-end-group retinoid derivatives.