Cationic olefin Pd(II) complexes bearing α-iminoketone N,O-ligands: synthesis, intramolecular and interionic characterization and reactivity with olefins and alkynes

Complexes [Pd(η¹, η²-5-OMe-C₈H₁₂)(N,O)]BF₄ (N,O=2,6-(i-Pr)₂(C₆H₃)NC(Ph)-C(Ph)O, 1; 2,6-(i-Pr)₂(C₆H₃)NC(Me)-C(Ph)O, 2; 2-benzoylpyridine, 3) were synthesized by the reactions of [Pd(η¹,η²-5-OMe-C₈H₁₂)Cl]₂ with the suitable N,O-ligand. They were tested as catalysts for olefin or alkyne polymerizations. During such reactions 1-3 quantitatively transformed into their η¹,η²-1-OMe-C₈H₁₂ isomers (1a-3a). The same isomerization occurred in methylene chloride, even in the absence of olefins or alkynes, with a much slower rate. All complexes were fully characterized in solution by multinuclear and multidimensional low temperature NMR spectroscopy. The solid state structures of complexes 1 and 1a were investigated by X-ray single crystal studies. ¹⁹F, ¹H-HOESY NMR experiments carried out in methylene chloride-d₂ at 217 K indicated that the anion prefers to locate on the side of N,O-ligand shifted toward the O-arm in 1-1a and 2-2a while it approaches the N-arm in 3 and 3a compounds.     

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.     

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.

     

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.     

Solution-, solid-phase, and fluorous synthesis of beta,beta-difluorinated cyclic quaternary alpha-amino acid derivatives: a comparative study

The diastereoselective synthesis of cyclic beta,beta-difluorinated alpha-amino acid derivatives bearing a quaternary stereocenter is described. The process relies on the chemo- and diastereoselective addition of allylic organometallic reagents to fluorinated alpha-imino esters and a subsequent ring-closing metathesis reaction (RCM). Complete selectivity in the nucleophilic addition was achieved with (R)-phenylglycinol methyl ether as a chiral auxiliary. The resulting amino acids were introduced into peptide chains, which could facilitate the preparation of potentially bioactive dipeptide derivatives. In addition, the solution synthesis of these cyclic fluorinated alpha-amino acids was successfully adapted to solid-phase and fluorous-phase techniques. The reaction times and final deprotection were clearly more favorable in the latter, in which a fluorous trimethylsilylethanol (TMSE) tag was used. The tag was then easily removed upon treatment with TBAF in a high-yield transesterification process.