Stereoselective synthesis of 3,4-diaryl β-lactams

Novel 3,4-diaryl β-lactams were prepared with high stereoselectivity in an efficient manner by a palladium-catalyzed [2+2] carbonylative cycloaddition of benzyl halides with heteroarylidene amines. The type of alkyl group linked to the nitrogen atom influences the reaction’s stereoselectivity. Moreover, using chiral imines, separable diastereomeric mixtures of chiral 3,4-diaryl-β-lactams were isolated with good yields and high trans diastereoselections.     

Adhesion of oriented nematic droplets

We propose and analyze a two-dimensional model for the equilibrium of oriented droplets of nematic liquid crystals that may adhere to a rigid substrate, while surrounded by an isotropic environment. We obtain the contact condition at the edge where the liquid crystal, the substrate, and the environment come together. We further develop a fairly general method to arrive at the equilibrium shapes of a drop, which is then applied to the case where the surface tension at the liquid crystal interface is given by Rapini and Papoular's expression. In this case, we also predict the existence of concave equilibrium shapes. Here is indeed the main difference between this method and Wulff's construction, which always yields convex equilibrium shapes for a drop free from adhesion. Received February 22, 2000     

The algebra of reversible Markov chains

For a Markov chain, both the detailed balance condition and the cycle Kolmogorov condition are algebraic binomials. This remark suggests to study reversible Markov chains with the tool of Algebraic Statistics, such as toric statistical models. One of the results of this study is an algebraic parameterization of reversible Markov transitions and their invariant probability.     

Existence and characterization of product-form invariant distributions for state-dependent stochastic networks in the heavy-traffic diffusion limit

We consider state-dependent stochastic networks in the heavy-traffic diffusion limit represented by reflected jump-diffusions in the orthant ℝ₊ ⁿ with state-dependent reflection directions upon hitting boundary faces. Jumps are allowed in each coordinate by means of independent Poisson random measures with jump amplitudes depending on the state of the process immediately before each jump. For this class of reflected jump-diffusion processes sufficient conditions for the existence of a product-form stationary density and an ergodic characterization of the stationary distribution are provided. Moreover, such stationary density is characterized in terms of semi-martingale local times at the boundaries and it is shown to be continuous and bounded. A central role is played by a previously established semi-martingale local time representation of the regulator processes. F.J. Piera’s research supported in part by CONICYT, Chile, FONDECYT Project 1070797. R.R. Mazumdar’s research supported in part by NSF, USA, Grant 0087404 through Networking Research Program, and a Discovery Grant from NSERC, Canada.     

Noise-sensitive hysteresis loops around period-doubling bifurcation points

Summary The noise-sensitive hysteresis loops observed in the bouncing-ball model are described. The phenomenon is analysed within the formalisms of the square map and the dissipative standard mapping. The notion of steady-state paths is introduced. A linear approximation of the simplest steady-state path is found.

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Riassunto Si descrivono gli anelli d’isteresi sensibili al rumore osservati nel modello della palla che rimbalza. Il fenomeno è analizzato nell’ambito dei formalismi della mappa quadrata e della funzione dissipativa standard. S’introduce la nozione di percorsi dello stato stazionario. Si trova un’approssimazione lineare del percorso piú semplice dello stato stazionario.

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Резюме Описываются петли гистерезиса, чувствительные к шуму, которые наблюдаются в модели подскакивающего мяча. Это явление анализируется в рамках формализма отображения квадрата и формализма диссипативного стандартного отображения. Вводится понятие установившихся траекторий. Получается линейная аппроксимация для простейших установившихся траекторий.

     

Quasi-quantization of writhe in ideal knots

The values of writhe of the tightest conformations, found by the SONO algorithm, of all alternating prime knots with up to 10 crossings are analysed. The distribution of the writhe values is shown to be concentrated around the equally spaced levels. The “writhe quantum” is shown to be close to the rational 4/7 value. The deviation of the writhe values from the n(4/7) writhe levels scheme is analysed quantitatively. Received 29 February 2001 and Received in final form 17 August 2001     

An efficient synthesis of new fluorinated uracil derivatives

A series of potentially biologically active fluorinated uracil derivatives has been prepared in three steps from oxazolines and fluorinated nitriles with good chemical yields.     

[4+2]-cycloadditions of thiones with nitrosoalkenes: synthesis of derivatives of 4H-1,5,2-oxathiazine,a new heterocyclic system.

Conjugated nitrosoalkenes, generated $\text{in situ}$$\text{via}$ dehydrobromination of α-bromoketoximes, undergo an easy [4+2]-cycloaddition with thiocarbonyl compounds to give very high yields of the new heterocycles 4H-1,5,2-oxathiazines. The thermolysis and the behaviour to oxidation of these adducts were tested.