On the domain dependence of solutions to the compressible Navier–Stokes equations of a barotropic fluid

We prove a general compactness result for the solution set of the compressible Navier–Stokes equations with respect to the variation of the underlying spatial domain. Among various corollaries, we then prove a general existence theorem for the system in question with no restrictions on smoothness of the spatial domain. Copyright © 2002 John Wiley & Sons, Ltd.     

Isometries of the Dirichlet space among the composition operators

We show that every composition operator which is an isometry of the Dirichlet space is induced by a univalent full map of the disk into itself that fixes the origin. This is an analogue of the Hardy space result for inner functions due to Nordgren. The proof relies on the Stone-Weierstrass theorem and the Riesz representation theorem.

     

Scaled-oscillation and regularity

We give sufficient conditions for Sobolev and Lipschitz functions in terms of their lower scaled-oscillation. The sharpness of these conditions is shown by examples. Our examples also show that a Stepanov-type differentiability theorem does not hold under the boundedness assumption of the lower scaled-oscillation.

     

New examples of Osserman metrics with nondiagonalizable Jacobi operators

Explicit examples of Osserman 4-manifolds with exactly two distinct eigenvalues of the Jacobi operators, α and β=4α≠0, are given. The former has multiplicity two and is a double root of the minimal polynomial of the Jacobi operators.     

Complementary regioselective esterification of non-reducing oligosaccharides catalyzed by different hydrolases

The enzymatic transesterification of several tri- and tetrasaccharides with vinyl laurate is described. The lipases from Candida antarctica B (Novozym 435) and Thermomyces lanuginosus (Lipozyme TL IM) and the alkaline protease from Bacillus licheniformis (subtilisin Carlsberg) have been used with each carbohydrate to obtain different regioisomers. By using the sugars in their amorphous form, complete solubility is achieved in the reaction media (tert-butanol/pyridine mixtures for the lipases and pyridine for the protease) and high isolated yields of the corresponding monoesters are obtained. Good to excellent regioselectivity is observed for all the enzymes, showing a final complementary picture respect to the primary hydroxyls of the oligosaccharides studied.     

配送量不定的供应链协调

本文研究供应链管理中配送量不确定时，制造商和分销商之间的协调问题。通过建立惩罚和奖励机制模型来协调供应链各部分的运作，使得分散系统就如一个整体。同时分析供应链的利润分配问题，分别得出各个机制下分销商的最优决策。     

Enantiodiscrimination of racemic electrophiles by diketopiperazine enolates: asymmetric synthesis of methyl 2-amino-3-aryl-butanoates and 3-methyl-aspartates

Enolates of (S)-N,N′-bis-(p-methoxybenzyl)-3-iso-propylpiperazine-2,5-dione exhibit high levels of enantiodiscrimination in alkylations with (RS)-1-aryl-1-bromoethanes and (RS)-2-bromoesters, affording substituted diketopiperazines containing two new stereogenic centres in high de. Deprotection and hydrolysis of the resultant substituted diketopiperazines provides a route to the asymmetric synthesis of homochiral methyl 2-amino-3-aryl-butanoates and 3-methyl-aspartates in high de and ee.     

Some remarks to multivariate regression model

Some remarks to problems of point and interval estimation, testing and problems of outliers are presented in the case of multivariate regression model. This work was supported by the Council of Czech Government J14/98:153100011.