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.     

Thermal analysis of anhydrous and hydrated Cholesterol

Cholesterol constitutes the major component of most gallstones. It was identified and determined, in gallstones, issued from eleven patients, by thermal analysis: differential scanning calorimetry (DSC), with the use of the melting temperature and enthalpy, thermogravimetry (TG), with the mass loss of water. Anhydrous cholesterol (ChA) was characterized by two endothermic peaks (polymorphic, melting) and cholesterol monohydrate (ChH) by two endothermic peaks (dehydration, melting), too. Cha needle and Chh plate crystals were observed under polarizing light microscopy. The numerous stones obtained from nine patients were cholesterol stones: the ChA was higher 45 and lower 96%. ChH was present in stones of three patients. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

Scanning probe microscopic imaging of guanine on a highly oriented pyrolytic graphite electrode.

Guanine adsorbed onto a highly oriented pyrolytic graphite electrode was studied by MAC-Mode Atomic Force Microscopy (AFM), and the electrochemical behaviour of the guanine layer was investigated with Electrochemical AFM. Guanine adsorbs spontaneously, without forming a well-packed structure, into nucleation spots, which are stable with time and cover the surface uniformly and almost completely. The process of guanine adsorption and nucleation can be controlled and the effect of altering the exposure time and varying the potential was investigated.     

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.