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.
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. 相似文献
Let g is a positive increasing function with 1?g(0). The existence of a unique solution of the Navier-Stokes flow associated with Kε,γ and the convergence of the solution to that of the Euler equations as the viscosity goes to zero are established. 相似文献
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(n1?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(n2/3). The algorithm differs from other graph bisection heuristics (as well as from many heuristics for other NP-complete problems) in several respects. Most notably:
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,
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),
the algorithm works well both theoretically and experimentally,
the algorithm employs global methods such as network flow instead of local operations such as 2-changes, and
the algorithm works well for graphs with small bisections (as opposed to graphs with large bisections, for which arbitrary bisections are nearly optimal).
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. 相似文献
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. 相似文献
Solutions are presented herein of some contact problems connected with the torsion of a composite half-space. In the general case the problem of the torsion of a composite elastic half-space is examined by means of the rotation of a stiff finite cylinder welded into a vertical recess of this half-space. Moreover, the following particular problems on the torsion of such a half-space are considered.
1. 1) A composite half-space with a vertical elastic infinite core, twisted by means of the rotation of a stiff stamp affixed to the upper endplate of the elastic core.
2. 2) A half-space with a vertical cylindrical infinite hole, twisted by means of the rotation of a stiff finite cylinder welded into the upper part of this hole.
In the general case the solution of the problem reduces to the solution of an integral equation of the second kind on a half-line. The question of the solvability of this fundamental integral equation is investigated, and it is shown that its solution may be constructed by successive approximations.
Let us note that the problem of the torsion of a homogeneous half space and of an elastic layer by means of rotation of a stiff stamp has been considered by Rostovtsev [1], Reissner and Sagoci [2], Ufliand [3], Florence [4], Grilitskii [5] and others.
The problem of the torsion of a circular cylindrical rod and the half-space welded to it which are subject to a torque applied to the free endface of the rod has been considered by Grilitskii and Kizyma[6].
The torsion of an elastic half-space with a vertical cylindrical inclusion of some other material by the rotation of a stiff stamp on the surface of this half-space has been considered in [7], wherein it has been assumed that the stamp is symmetrically disposed relative to the axis of the inclusion and lies simultaneously on both materials. 相似文献
The crystal structures of hydrate (1) and anhydrate (2) forms of 2,3-pentamethylene-3,4-dihydroquinazolin-4-one hydrochloride have been determined by X-ray structure analysis. Crystal data of 1 are 2(C13H14N2O)*3(HCl)*4.5 (H2O), triclinic P?1, Z=2, a=8.004(5), b=13.129(7), c=15.725(7) Å, α=106.45(4), β=92.61(4), γ=97.98(5), R=0.0652 and 2 are C13H14N2O*HCl, monoclinic C2/c, Z=8, a=21.360(4), b=5.954(1), c=21.263(4), β=117.89(3), R=0.0556. The crystal of the hydrate form 1is unstable. This form collapses easily with evaporation of H2O and part of HCl molecules from crystals. By recrystallizing destroyed form has been obtained stable crystal form 2. 相似文献
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. 相似文献