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.     

Polymerization of styrene started by free radicals,generated by external force action-chemical potential gradient of the swelling agent — on the PVC/solvent optical phase boundary

Summary There were studied the process of styrene polymerization in PVC swollen surface layer initiated by free radicals generated under the action of chemical potential gradient as an external force. It was found that conversion of styrene into the block copolymer is an diffusion controlled process.

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Zusammenfassung Die Initiation des Prozesses der Polymerization von Styrol in den Oberflächenquellungsschichten von PVC wurde untersucht.Dabei wurde festgestellt, daß die freien Radikale, welche bei Zerreißung von spannungsbeanspruchten Bindungen, wie sie durch Einfluß von äußeren Kräften auf den Gradienten des chemischen Potentials des Quellungsmittels an Oberflächenquell bildungsmittel Polymer entstehen können, Polymerizationsprozesse des olefinischen Quellungsmittels initiieren können.

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Dedicated to ProfessorV. Kellö in celebration of his 60th birthday.     

Hyaluronic acid-copper(II) complexes: Spectroscopic characterization

Hyaluronic acid-copper(II) complexes were studied by ultraviolet and electron spin resonance spectroscopy (ESR), as well as by rheological measurements. Spin-Hamiltonian parameters were obtained from experimental spectra measured at 200 K by non-linear optimization method. These showg _x g _y <g _z and indicate the ground electronic state of copper ion, which is characteristic for carboxylato-copper(II) complexes. The non-axial symmetry of theg-tensor suggest rhombic crystal field symmetry. Formation of HA-Cu(II) complex is realized through the interaction of copper ions with carboxyl groups of the HA macromolecule. This complex is characteristic of the network-like rheological properties of its aqueous solution.     

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.