Identification of a source factor in a control problem for the heat equation with a boundary memory term

We consider a material with thermal memory occupying a bounded region Ω with boundary Γ. The evolution of the temperature u(t,x) is described by an integrodifferential parabolic equation containing a heat source of the form f(t)z₀(x). We formulate an initial and boundary value control problem based on a feedback device located on Γ and prescribed by means of a quite general memory operator. Assuming both u and the source factor f are unknown, we study the corresponding inverse and control problem on account of an additional information. We prove a result of existence and uniqueness of the solution (u,f). Copyright © 2015 John Wiley & Sons, Ltd.     

Stereoselective cyclopropanation by cyclocopolymerization of butadiene

An unprecedented cyclopropanation by cyclopolymerization reaction is presented. In particular, catalytic copolymerization processes of ethene and butadiene lead with high trans selectivity to a complete cyclocopolymerization of butadiene units. Ethene-based copolymers including cyclopropane and cyclopentane rings, which can be relevant to polyolefin applications, are obtained with high yields. Several aspects relative to the mechanism of this cyclocopolymerization reaction, including the high stereoselectivity, are discussed.     

Reactivity of a cyclic α-bromoiminium bromide towards nucleophiles

Piperidine-pyrrolidine ring contraction of 1-piperideinium bromide ( 1 ) was observed by reaction with aqueous bases, sodium methoxide, phenylhydrazine, (S)-1-phenylethylamine and sodium borohydride, whereas diazomethane addition mainly gave pyrrolo[3,4-b]pyridine derivative 8. Some stereochemical features of these reactions have been investigated. 1 gave back bromine under suitable conditions.     

Asymmetric addition of ethyl azidoformate to optically active enamines. Reversal of facial selectivity compared with (ethoxycarbonyl)nitrene

Thermal reaction of ethyl azidoformate with proline-derived optically active enamines of cyclohexanone, followed by photolysis, proceeds with opposite facial selectivity to that observed using (ethoxycarbonyl)nitrene. A tentative explanation is proposed. The absolute configuration of the main product, 2-(ethoxycarbonylamino)cyclohexanone (6), was deduced by chemical correlation.     

Convergence Analysis of an Inexact Infeasible Interior Point Method for Semidefinite Programming

In this paper we present an extension to SDP of the well known infeasible Interior Point method for linear programming of Kojima, Megiddo and Mizuno (A primal-dual infeasible-interior-point algorithm for Linear Programming, Math. Progr., 1993). The extension developed here allows the use of inexact search directions; i.e., the linear systems defining the search directions can be solved with an accuracy that increases as the solution is approached. A convergence analysis is carried out and the global convergence of the method is proved.     

Experimental evidence of above-threshold photoemission in solids

Nonlinear photoemission from a silver single crystal is investigated by femtosecond laser pulses in a perturbative regime. A clear observation of above-threshold photoemission in solids is reported for the first time. The ratio between the three-photon above-threshold and the two-photon Fermi edges is found to be 10(-4). This value constitutes the only available benchmark for theories aimed at understanding the mechanism responsible for above-threshold photoemission in solids.     

Totally stereoselective synthesis of 1,3-disaccharides through Diels-Alder reactions

A nonclassical, totally stereoselective synthesis of orthogonally protected 1,3-disaccharides is reported. Enantiomerically pure beta-keto-delta-lactones, efficiently obtained from glucal and galactal, are transformed into electron-poor heterodienes and chemo-, regio-, and stereoselectively cycloadded to glycals as electron-rich dienophiles, to directly afford 2-thiodisaccharides. The reductive desulfurization of the latter smoothly gave the corresponding 2,2'-dideoxydisaccharides.     

Una classe di algebre rigide

Riassunto Si prova la rigidità di una certa classe di algebre integre di Cohen-Macaulay.

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Summary We prove the rigidity of a certain class of algebras which are Cohen-Macaulay integral domains.

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Lavoro svolto nell'ambito del G.N.S.A.G.A., sez. n. 3, del C.N.R.     

On the reactivity of isoxazoles with Mo(CO)6

Ring opening with molybdenum hexacarbonyl of functionalized isoxazoles is a valuable synthetic process. Tetrazolopyridine 4 and pyrazolopyridine 9 were obtained from isoxazolopyridines 3 and 6 , respectively, whereas the isoxazole 14 gave ketone 16 through the intermediate 17.