Convergence estimates of Galerkin-wavelet solutions to a Cauchy problem for a class of periodic pseudodifferential equations

A class of Cauchy problems for interesting complicated periodic pseudodifferential equations is considered. By the Galerkin-wavelet method and with weak solutions one can find sufficient conditions to establish convergence estimates of weak Galerkin-wavelet solutions to a Cauchy problem for this class of equations.

     

Structure and catalytic activity of some soluble polyethylene glycol-peptide conjugates

Soluble catalysts for the Juliá-Colonna asymmetric epoxidation reaction have been constructed in three different ways, using NH₂-PEG-OMe as the support system: suitable solvents have been identified and it is shown that the degree of helicity of the conjugates correlates with the extent of conversion and (to a lesser extent) the enantioselectivity of epoxidation.     

On non-stationary Navier-Stokes flows with vanishing viscosity associated with a variational inequality

Let g is a positive increasing function with 1?g(0). The existence of a unique solution of the Navier-Stokes flow associated with K_ε,γ and the convergence of the solution to that of the Euler equations as the viscosity goes to zero are established.     

Graph bisection algorithms with good average case behavior

In the paper, we describe a polynomial time algorithm that, for every input graph, either outputs the minimum bisection of the graph or halts without output. More importantly, we show that the algorithm chooses the former course with high probability for many natural classes of graphs. In particular, for every fixedd≧3, all sufficiently largen and allb=o(n ^{1?1/[(d+1)/2]}), the algorithm finds the minimum bisection for almost alld-regular labelled simple graphs with 2n nodes and bisection widthb. For example, the algorithm succeeds for almost all 5-regular graphs with 2n nodes and bisection widtho(n ^2/3). The algorithm differs from other graph bisection heuristics (as well as from many heuristics for other NP-complete problems) in several respects. Most notably:

1. the algorithm provides exactly the minimum bisection for almost all input graphs with the specified form, instead of only an approximation of the minimum bisection,
2. whenever the algorithm produces a bisection, it is guaranteed to be optimal (i.e., the algorithm also produces a proof that the bisection it outputs is an optimal bisection),
3. the algorithm works well both theoretically and experimentally,
4. the algorithm employs global methods such as network flow instead of local operations such as 2-changes, and
5. the algorithm works well for graphs with small bisections (as opposed to graphs with large bisections, for which arbitrary bisections are nearly optimal).

     

1,4-Addition of benzene to a dihydrocyclopent[a]indene diradical: synthesis and DFT study

Photochemical cyclization of compound 1, a homoenediyne (-CCC=CCH2CC-) bearing two ethynylanthracene chromophores, yields two isomeric dihydrocyclopent[a]indene ring systems, spiro-fused to the 9-position of a 9,10-dihydroanthracene moiety. Evidence of a photochemically initiated diradical cyclization pathway is proposed on the basis of (i) hydrogen abstraction from reaction with 1,4-cyclohexadiene (1,4-CHD) and (ii) the observation of 1,4-addition of benzene (solvent). The reaction was further analyzed by a complete density functional theory (DFT) study, using an unrestricted approach (UBLYP) with a 6-31G* basis set for the open-shell triplet states of the reactants, products, and diradical intermediates to model the photochemical nature of observed transformation. A mechanism detailing the observed cyclization/addition reaction is proposed.     

Selective reduction of aldehydes by a formic acid- trialkylamine- RuCl2(PPh3)3 system

In the presence of trialkylamine and formic acid RuCl₂(PPh₃)₃ selectively reduces aldehydes to the corresponding alcohols at room temperature. Other reducible groups are unaffected.     

SENSITIZED PHOTOOXYGENATION ACCORDING TO TYPE I MECHANISM (RADICAL MECHANISM) — PART III. EXPERIMENTS WITH CONTINUOUS ILLUMINATION

Abstract— The photochemical reaction in the system thionine (sensitizer), allylthiourea (ATU, acceptor), and oxygen was studied with continuous illumination. In oxygen-free aqueous solution thionine is photoreduced to leucothionine. With oxygen, however, a photooxygenation of the acceptor takes place. At the same time the quantum yield of the bleaching reaction of thionine decreases markedly in comparison with that of the oxygen-free solution. At about 100 sec after the beginning of illumination, the overall quantum yield of the bleaching reaction diminishes further because the leucothionine formed during the reaction now becomes transformed into thionine. The quantum yields do not change significantly over the range of oxygen concentrations studied (initial concentration 1 × 10^-5 to 5 × 10^-5 M ). In addition they are independent of the light intensity. The influence of the pH and the acceptor concentration were also investigated.
The sensitizer is not only bleached reductively, but is also partly destroyed by oxidation. The results are in agreement with the reaction scheme elucidated by flash photolysis measurements.
In accordance with this reaction scheme, the primary reaction (a) of the reductive bleaching of the sensitizer, (b) of the photooxygenation of the acceptor and (c) of the oxidative destruction of the sensitizer, is identical in all cases. This process is the redox reaction between the sensitizer triplet and the acceptor, where a semithionine and an ATU-radical are formed. The reaction represents an example of a Type I photooxygenation according to the notation of Gollnick.     

Capillary gas chromatographic-mass spectrometric study of the effect of solvents on metoprolol and other aryloxypropanolamines

When metoprolol in methanol was analysed by capillary gas chromatography (GC), an additional peak was observed; mass spectrometry (MS) showed this additional peak to have a molecular weight 12 dalton higher than that of the parent compound. A similar phenomenon was observed with other beta-adrenergic blocking aryloxypropanolamines in methanol or dichloromethane. Capillary GC-MS using deuterated solvents as isotopic markers showed that a methylene group from the solvents was incorporated into the parent molecule. The structure of the observed products and the mechanism of their formation are proposed.     

Recherches dans la série des cyclitols XXXVII Etude par spectrométrie de masse

Low resolution mass spectra of cyclohexane-triols, -tetrols, -pentols and -hexols and of some of their deuterium labelled derivatives have been measured. The results indicate that for some geometrical isomers quantitative differences between ion intensities are significant, allowing to deduce the stereochemistry of the molecule from its mass spectrum. In all these compounds the electron impact induced elimination of water occurs mainly by interaction between OH groups. There is a correlation between the relative abundance of (M – H₂O)⁺ and (M ?2 H₂O)⁺ ions and the number of axial hydroxyls in the more stable conformation of the molecule. Difficulties encountered in deducing fragmentation patterns, and determination of number and position of deuterium atoms in the molecule of ms-inositol are discussed.