Determination of microtacticity of poly(vinylketones) and their derivatives by NMR spectroscopies of carbon-13 and proton

Sequence distribution of atactic poly(phenylvinylketone) (PPVK) has been determined by [¹³C]-[¹H]NMR spectroscopy. Quantitative analysis of the carbonyl pattern allows resolution into pentads with intensities fitting a first order Markov process. The carbonyl pattern of highly isotactic PPVK, initiated by diethylzinc, deviates strongly from Bernoullian statistics, as in the case of highly isotactic polymethylvinylketone (PMVK). For n-butyl-lithium initiated poly(isopropenylphenylvinylketone) (PIPK), the carbonyl pattern practically agrees with a Bernoullian distribution. Atactic PMVK, analyzed from the methylene and the carbonyl pattern in [¹³C] or [¹H]NMR, shows that the polymerization process is purely Bernoullian and quite different from that for poly(isopropenylmethylketone). Except for poly(methylallylalcohol) for which the tacticity can be determined, the resolution is too poor to allow a quantitative sequence distribution of poly(allylalcohols) or poly(allyltrifluoroacetates). [¹H] and [¹⁹F]NMR spectroscopies of these compounds do not give better results.     

On Improvements to the Analytic Center Cutting Plane Method

In this paper, we explore a weakness of a specific implementation of the analytic center cutting plane method applied to convex optimization problems, which may lead to weaker results than Kelley's cutting plane method. Improvements to the analytic center cutting plane method are suggested, and tested on some example problems.     

Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity

We consider the nonlinear Schrödinger equation: (1) $${{i\partial u} \mathord{\left/ {\vphantom {{i\partial u} {\partial t}}} \right. \kern-\nulldelimiterspace} {\partial t}} = - \Delta u - \left| u \right|^{{4 \mathord{\left/ {\vphantom {4 N}} \right. \kern-\nulldelimiterspace} N}} uandu\left( {0,.} \right) = \varphi \left( . \right),$$ whereu:[0,T)×? ^N →?. For any given pointsx ₁,x ₂,...,x _k in ? ^N , we construct a solution of Eq. (1),u(t), which blows up in a finite timeT at exactlyx ₁,x ₂,...,x _k . In addition, we describe the precise behavior of the solutionu(t) whent→T, at the blow-up points {x ₁,x ₂,...,x _k } and in ? ^N ?{x ₁,x ₂,...,x _k }.     

Polymérisation anionique amorcée par les composés lamellaires du graphite et du lithium

In the present work, we use the binary insertion compound LiC₁₂ to polymerize styrene, methyl methacrylate, butadiene, isoprene, and to copolymerize isoprene and styrene in various hydrocarbon solvents (aromatics and aliphatic) and etheral solvents. We show that the styrene polymerization in aromatic solvents gives better yields than in the etheral solvents, the polymer being atactic. Methyl methacrylate does not polymerize in toluene but does so completely in DME. More generally, the yields of polymerization are better with KC₃₇ than with LiC₁₂ because of the different capacities of the monomer to get into the carbon layers. The polymerization of dienes with LiC₁₂ shows that the microstructures of the polymer obtained in π-or n-donor solvents are similar to the ones obtained by homogenous polymerization with Li cation in such solvents. However, for isoprene in cyclohexane, the results are different. The isoprene styrene copolymers are statistical ones and the mean length of styrene blocks is less than 5. The monomer interaction with the insertion compound and the growing chain geometry between the carbon layers are the facts which control either the stereospecificity of the polymerization or the selectivity of the copolymerization.     

Stereoselective peterson alkoxycarbonylmethylenation reaction of substituted cyclohexanones

In contrast to previous results the Peterson olefination reaction of substituted cyclohexanones with metallotrimethylsilylacetates (1) affords moderate to high stereoselectivity.     

Orbital control of stereochemistry in acid-catalysed addition reactions of endo -tricyclo[3.2.1.02,4]0ct-6-ene

The reaction of endo-tricyclo[3.2.1.0^2,4]oct-6-ene 1 with methanol in the presence of catalytic amounts of toluene-p-sulphonic acid has been shown to give 2-exo- and endo-methoxybicyclo[3.2.1]oct-3-ene (2c) and (2d) and 2-endo-methoxybicyclo[3.2.1]oct-6-ene (13). The formation of 2-exo- methoxybicyclo[3.2.1]oct-3-ene (2c), the major product of reaction, has been probed by deuterium labelling experiments and a series of 6-exo-7-exo- dideuterobicyclo[3.2.1]oct-3-enes synthesised for ²H, ¹H and ¹³C NMR spectral analysis in order unambiguously to determine the stereochemistry of proton attack on endo-tricyclo[3.2.1 0^2,4]oct-6-ene (1). The formation of 2-exo-methoxybicyclo[3.2.1]oct-3-ene (2c) has been determined to involve corner protonation of the cyclopropyl moiety and skeletal rearrangement to an allylic cation with a small but measurable memory effect     

Blow-up results of viriel type for Zakharov equations

We consider the Zakharov equations in ^N (for N=2,N=3). We first establish a viriel identity for such equations and then prove a blow-up result for solutions with a negative energy.     

Superoxide radical anion adduct of 5,5-dimethyl-1-pyrroline N-oxide (DMPO). 2. The thermodynamics of decay and EPR spectral properties

The formation of the superoxide radical anion (O2*-) adduct of the nitrone 5,5-dimethyl-1-pyrroline N-oxide (DMPO) as detected by electron paramagnetic resonance (EPR) spectroscopy is one of the most common techniques for O2*- detection in chemical and biological systems. However, the nature of DMPO-O2H has confounded spin-trapping investigators over the years, since there has been no independently synthesized DMPO-O2H to date. A density functional theory (DFT) approach was used to predict the isotropic hyperfine coupling constants arising from the N, beta-H, and gamma-H nuclei of DMPO-O2H using explicit interactions with water molecules as well as via a bulk dielectric effect employing the polarizable continuum model (PCM). Theoretical calculation on the thermodynamics of DMPO-O2H decay shows favorable intramolecular rearrangement to form a nitrosoaldehyde and a hydroxyl radical as products, consistent with experimental observations. Some pathways for the bimolecular decomposition of DMPO-O2H and DMPO-OH have also been computed.     

Synthèse et réactivité des bromhydrines dérivées de la chromone

Bromohydroxylated derivatives of chromone are obtained by addition of N-bromosuccinimide in dimethylsulfoxide. The configuration and conformation of these compounds are confirmed by NMR spectroscopy. Alkaline alcoholates react with these bromohydrins to give a ring contraction into 2-formyl-3-benzofuranone.