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.

     

Separation of Monovinyl and Divinyl Protochlorophyllides Using C30 Reverse Phase High Performance Liquid Chromatography Column: Analytical and Preparative Applications

A new, high performance liquid chromatography method has been developed for the separation of monovinyl- and divinyl-protochlorophyllides, using commercially available, C₃₀ reverse phase column and isocratic elution. This method can be used both for analytical applications and preparative scale purification of monovinyl- and divinyl-protochlorophyllides using the same column where submilimolar concentrations of the crude protochlorophyllide extract can be separated in one run. The purity of the obtained protochlorophyllides was demonstrated by spectroscopic methods, as well by the formation of aggregates in toluene.     

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.     

Gas-phase derivatization of [C3H5]+ ions using tandem mass spectrometry methods A13C labelling study

The study of specifically ¹³C-labelled precursors sheds further light on the gas-phase chemistry of allyl and 2-propenyl cations. It is demonstrated that both species are formed from allyl and 2-propenyl bromide upon 70 eV electron impact ionization without skeletal reorganization. Gas-phase derivatization of the [C₃ H₅]⁺ ions with benzene facilitates, as suggested and observed earlier, the distinction of the two isomers using collision-induced dissociation of the Wheland complexes (or isomers thereof). The ¹³C labelling data clearly demonstrate that 64% of allyl cations survive the derivatization while 36% isomerize to 2-phenylpropyl cations; the latter are also formed via the reaction of 2-propenyl cation with benzene, protonation of α-methylstyrene and water loss from protonated 2-phenyl-2-propanol, respectively. Unimolecular loss of C₂H₄ from protonated allylbenzene proceeds via two competing reaction channels: one involves heterolysis of 1-phenylpropyl cations (～30%); the major pathway (～70%), however, involves decomposition via propylene benzenium ions.     

Aerobic oxidation of methyl p-tolyl sulfide catalyzed by a remarkably labile heteroscorpionate RuII-aqua complex,fac-[RuII(H2O)(dpp)(tppm)]2+

fac-[RuII(Cl)(dpp)(L3)]+ (L3 = tris(pyrid-2-yl)methoxymethane (tpmm) = [1A]+ and tris(pyrid-2-yl)pentoxymethane (tppm) = [1B]+ and dpp = di(pyrazol-1-yl)propane) rapidly undergo ligand substitution with water to form fac-[RuII(H2O)(dpp)(L3)]2+ (L3 = tpmm = [2A]2+ and tppm = [2B]2+). In the structure of [2A]2+, the distorted octahedral arrangement of ligands around Ru is evident by a long Ru(1)-O(40) of 2.172(3) A and a large angle O(40)-Ru(1)-N(51) of 96.95(14) degrees . The remarkably short distance between O(40) of H2O and H(45a) of dpp confirms the heteroscorpionate ligand effect of dpp on H2O. [2B]2+ aerobically catalyzes methyl p-tolyl sulfide to methyl p-tolyl sulfoxide in 1,2-dichlorobenzene at 25.0 +/- 0.1 degrees C under 11.4 psi of O2. Experimental facts in support of this aerobic sulfide oxidation are the absence of H2O2 and the oxidative reactivity of the putative Ru(IV)-oxo intermediate toward methyl p-tolyl sulfide, 2-propanol, and allyl alcohol. This study provides the first documented example of aerobic-sulfide oxidation catalyzed by the remarkably labile heteroscorpionate Ru(II)-aqua complex without the formation of a highly reactive peroxide as an intermediate.     

EFFICACY OF PHOTODYNAMIC THERAPY ON ORIGINAL AND RECURRENT RAT MAMMARY TUMORS

Abstract— Photodynamic therapy has demonstrated efficacy toward primary, metastatic and recurrent human tumors. Here, we investigated the ability of photodynamic therapy, using Photofrin, to inhibit growth of R3230AC mammary adenocarcinomas when tumors were treated as original implants and again as lesions recurring at the initial treatment site. The results demonstrate that both initial implants and lesions recurring after the first photodynamic treatment respond similarly to the same photodynamic therapy protocol, with mean tumor volume doubling times of ˜ 11 days in both cases. Cells cultured from original tumor implants or tumors that recurred after photodynamic treatment accumulate equivalent amounts of [¹⁴C]polyhematoporphyrin. Single cell suspensions prepared from either original or recurrent tumors from animals administered 5 mg/kg Photofrin and exposed to light in vitro displayed comparable phototoxicity. Additionally, examination of tumors by light microscopy revealed no morphological differences between the original tumor implants and the recurrent lesions. Taken together, these data indicate that lesions which recurred at the site of the initial photodynamic treatment were not resistant to a second identical course of photodynamic therapy.     

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.