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991.
3,5-Dimethoxybenzoic acid 3 has been transformed into olivetol dimethyl ether 6 in three steps in 79% yield. Directed ortho-metallation-alkylation of 6, followed by boron tribromide demethylation resulted in a simple and inexpensive synthesis of resorstatin, in 70% overall yield from 3. 相似文献
992.
Triarylbismuthanes react with sodium perborate in acetic acid under mild conditions to afford triarylbismuth diacetates in good yields. This method is fast, efficient and environmentally friendly. 相似文献
993.
Sym-phthaloyl chloride under controlled cathodic reduction is converted into trans-[1(3H)-isobenzofuranone, 3-(3-oxo-1(3H)-isobenzofuranylidene)]: trans-biphthalyl in 65% yield. 相似文献
994.
Reaction of 4-trifluoromethanesulfonyloxycoumarin derivatives with benzyloxyphenylboronic acid derivatives under modified Suzuki reaction conditions afforded the corresponding neoflavones. Selective debenzylation took place in high yields when the palladium-catalysed hydrogenolysis was performed in the presence of acetic acid. 相似文献
995.
方乐 Wouter J.T. Bos Xiaozhou Zhou Liang Shao Jean-Pierre Bertoglio 《Acta Mechanica Sinica》2010,26(2):151-157
The approach of Obukhov assuming a constant skewness was used to obtain analytical corrections to the scaling of the second order structure function, starting from Kolmogorov's 4/5 law. These corrections can be used in model applications in which explicit expressions, rather than numerical solutions are needed. The comparison with an interpolation formula proposed by Batchelor, showed that the latter gives surprisingly precise results. The modification of the same method to obtain analytical corrections to the scaling law, taking into account the possible corrections induced by intermittency, is also proposed. 相似文献
996.
Jean-Pierre Barthélemy 《Discrete Applied Mathematics》2008,156(8):1237-1250
In many clustering systems (hierarchies, pyramids and more generally weak hierarchies) clusters are generated by two elements only.This paper is devoted to such clustering systems (called binary clustering systems). It provides some basic properties, links with (closed) weak hierarchies and some qualitative versions of bijection theorems that occur in Numerical Taxonomy. Moreover, a way to associate a binary clustering system to every clustering system is discussed.Finally, introducing the notion of weak ultrametrics, a bijection between indexed weak hierarchies and weak ultrametrics is obtained (the standard theorem involves closed weak hierarchies and quasi-ultrametrics). 相似文献
997.
A mixture of iso-amyl nitrite/HBr is shown to be a mild and efficient reagent for electrophilic aromatic bromination. The reaction succeeds with slightly activated arenes and heterocyclic compounds. By using HCl instead of HBr, chlorination can also be performed in few cases. The i-amONO2/HBr mixture can also be utilized for bromination in the α-position of electron withdrawing groups. A possible mechanism is briefly discussed. 相似文献
998.
999.
Jean-Pierre Magnot 《Bulletin des Sciences Mathématiques》2008,132(2):112-127
In this article, we describe a class of algebras with unbounded operators on which the Schwinger cocycle extends. For this, we replace a space of bounded operators commonly used in the literature by some space of (maybe unbounded) tame operators, in particular by spaces of pseudo-differential operators, acting on the space of sections of a vector bundle E→M. We study some particular examples which we hope interesting or instructive. The case of classical and log-polyhomogeneous pseudo-differential operators is studied, because it carries other cocycles, defined with renormalized traces of pseudo-differential operators, that are some generalizations of the Khesin-Kravchenko-Radul cocycle. The present construction furnishes a simple proof of an expected result: The cohomology class of these cocycles are the same as cohomology class of the Schwinger cocycle. When M=S1, we show that the Schwinger cocycle is non-trivial on many algebras of pseudo-differential operators (these operators need not to be classical or bounded). These two results complete the work and extend the results of a previous work [J.-P. Magnot, Renormalized traces and cocycles on the algebra of S1-pseudo-differential operators, Lett. Math. Phys. 75 (2) (2006) 111-127]. When dim(M)>1, we furnish a new example of sign operator which could suggest that the framework of pseudo-differential operators is not adapted to all the cases. On this example, we have to work on some algebras of tame operators, in order to show that the Schwinger cocycle has a non-vanishing cohomology class. 相似文献
1000.
We have discussed the approximate methods which are used for obtaining scalar guided modes of optical waveguides. The methods include the perturbation method, the variational method including the Rayleigh-Ritz method, and the Galerkin and the collocation method. The main purpose of this paper is to discuss the inter-relationships and equivalences of these methods, and to bring out the fact that these relationships have, in fact, not been recognized in the guided wave optics literature, although in the numerical electromagnetics and applied mathematics literature some of these relationships are well known. We have also pointed out specific examples where, due to this lack of recognition of relationships, there are repetitions in the literature. In particular, we have noted that the Rayleigh-Ritz method and the Galerkin method have been used using the same set of basis functions for the same kind of waveguides without recognizing the existing literature. We have also reported for the first time an explicit relationship between the Galerkin method and the collocation method. This relationship also points out in which cases one method is more accurate and/or numerically efficient than the other. Another interesting relationship explored is that between the perturbation method and the variational method. 相似文献