Random perturbations of transformations of an interval

Let μ^ε be invariant measures of the Markov chainsx _n ^F which are small random perturbations of an endomorphismf of the interval [0,1] satisfying the conditions of Misiurewicz [6]. It is shown here that in the ergodic case μ^ε converges as ε→0 to the smoothf-invariant measure which exists according to [6]. This result exhibits the first example of stability with respect to random perturbations while stability with respect to deterministic perturbations does not take place.     

Heterocyclic Analogs of Prostaglandins: I. Synthesis of 3-Alkyl(Aralkyl)-2,5-dihydrofuran-2-ones as Synthons for 11-Deoxy-10-oxaprostanoids

3-Acyl(arylmethyleneacyl)tetronic acids were synthesized. Selective hydrogenation of the carbonyl group in the acyl fragment and reduction of the conjugated double bond afforded in high yield the corresponding 3-alkyl(aralkyl) derivatives possessing either natural or modified prostaglandin -chain. Reduction of the conjugated double bond in vinylogous 3-alkyl(aralkyl)tetronic acid amides with sodium cyanotrihydridoborate gave a mixture of stereoisomeric -amino lactones which underwent retro-Michael elimination of the amine residue, leading to 3-alkyl(aralkyl)-2,5-dihydrofuran-2-ones. The latter can be regarded as synthons for 11-deoxy-10-oxaprostanoids.     

Perturbation des produits infinis et applications

Sans résumé Les auteurs remercient l'Institut de recherche d'été de la Société Mathématiques du Canada, le CNR, DIGES du Québec et la Fondation Fleischer pour leur appui. An erratum to this article is available at .     

Electrochemical polymerization of aromatic amines: IR,XPS and PMT study of thin film formation on a Pt electrode

Films resulting from the anodic oxidation of various monosubstituted aromatic amines have been grafted on Pt electrodes in a CH₃CN?NaClO₄-pyridine medium. An in situ polaromicrotribometric study of changes occurring on the electrode surface during polarization indicates that these deposits have a stable friction coefficient of 1.3f_o. Their analysis by multiple-reflection IR spectroscopy and by X-ray photoelectron spectroscopy shows that these films are organic polymers of emeraldine basic structure and that they probably result from the coupling of electrochemically formed NH^. radicals with the monomer. These films are homogeneous, very adherent, thermally stable and free of ionic impurities. In the dry state they display a conductivity of 5×10^?13 Ω^?1 cm^?1 which is characteristic of insulators.     

More on the linear search problem

The linear search problem concerns a search made in the real line for a point selected according to a given probability distribution. The search begins at zero and is made by continuous motion with constant speed along the line, first in one direction and then the other. The problem is to search in such a manner that the expected time required for finding the point according to the chosen plan of search is a minimum. This plan of search is usually conceived of as having a first step, a second,etc., and in that case, this author has previously shown a necessary and sufficient condition on the probability distribution for the existence of a search plan which minimizes the expected searching time. In this paper, we define a notion of search in which there is no first step, but the steps are instead numbered from negative to positive infinity. These new rules change the problem, and under them, there is always a minimizing search procedure. In those cases which satisfy the earlier criterion, the solutions obtained are essentially the same as those obtained previously. The research work for this paper was supported by the National Science Foundation under grant No. GP 2559 to the University of Wisconsin.     

Synthesis of 4,4′-Oxydibenzoic Acid Amides and Sulfonamides Containing 2-Arylaminopyrimidine Moieties

Russian Journal of Organic Chemistry - New 4,4′-oxydibenzamides and sulfamoyl derivatives of 4,4′-oxydibenzoic acid containing pharmacophoric 2-arylaminopyrimidine fragments in the...     

First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity

This is the first in a series of papers exploring rigidity properties of hyperbolic actions ofZ ^k orR ^k fork ≥ 2. We show that for all known irreducible examples, the cohomology of smooth cocycles over these actions is trivial. We also obtain similar Hölder and C¹ results via a generalization of the Livshitz theorem for Anosov flows. As a consequence, there are only trivial smooth or Hölder time changes for these actions (up to an automorphism). Furthermore, small perturbations of these actions are Hölder conjugate and preserve a smooth volume.     

Reaction of 3,5-Disubstituted 4,5-Dihydroisoxazoles with Hexacarbonylmolybdenum

Depending on the reaction conditions and structure of the 5-substituent, reactions of substituted 4,5-dihydroisoxazoles with hexacarbonylmolybdenum involve cleavage of the heteroring at the N-O bond, its aromatization, or/and 1,3-decyclization.     

Practical aziridinations II: electronic modifications to poly(pyrazolyl)borate-copper catalysts

A significant influence of the electronic features of poly(pyrazolyl)borate ligands on the efficiency of the copper-catalyzed aziridination reaction has been noted. Electron-deficient, bidentate di(pyrazolyl)borates in conjunction with copper(II) chloride generated the most effective catalyst system for the aziridination of a variety of olefins.