Kinetic and NMR spectroscopic studies of chiral mixed sodium/lithium amides used for the deprotonation of cyclohexene oxide

The mixed-metal complex formed from n-butylsodium, n-butyllithium, and a chiral amino ether has been studied by NMR spectroscopy. Three different mixed-metal amides were used as chiral bases for the deprotonation of cyclohexene oxide. The selectivity and initial rate of reaction were compared for sodium-amido ethers, lithium-amido ethers, and mixtures of sodium and lithiumamido ethers in diethyl ether and tetrahydrofuran, respectively. The mixed sodium/lithium amides are more reactive than the single sodium and lithium amides, whereas the stereoselectivities are higher when lithium amides are used. The alkali-metal/gamma-amido ethers exhibit both higher initial reaction rates and stereoselectivities than their beta-amido ether analogues. NMR spectroscopic studies of mixtures of n-butylsodium (nBuNa), n-butyllithium (nBuLi), and the gamma-amino ethers in diethyl ether show the exclusive formation of dimeric mixed-metal amides. In diethyl ether, the lithium atom of the mixed-metal amide is internally coordinated and the sodium atom is exposed to solvent; however, in tetrahydrofuran, both metals are internally coordinated.     

多孔介质中两相不可压缩可混溶驱动问题的动态混合元方法及其特征修正格式

许多依赖时间的问题涉及到局部化现象,如突出的前沿位置、激波、边界层等, 其位置随时间而变动.多孔介质中两相不可压缩可混溶驱动问题是一典型的、有代表性 的"局部化现象"问题,其数学模型为耦合非线性偏微分方程组的初边值问题.为减轻数 值解在局部前沿位置的数值振荡,提高解的精确性,本文给出了该问题的动态混合元格 式和沿特征线修正的动态混合元格式,证明了其收敛性,并给出了误差估计.     

Recursive equations for compound distribution with the severity distribution of the mixed type

In this paper, recursive equations are obtained for compound distribution with the number of claims belonging to (a, b)-family and the severity distribution of the mixed type. Numerical methods to solve these equations are presented, and some numerical results are given.     

A new method of spectral decomposition of covariance matrix in mixed effects models and its applications

For the mixed effects models with balanced data, a new ordering of design matrices of random effects is defined, and then a simple formula of the spectral decomposition of covariance matrix is obtained. To compare with the two methods in literature, the decomposition can not only give the actual number of all distinct eigenvalues and their expression, but also show clearly the relationship between the design matrices of random effects and the decomposition. These results can be applied to the problems for testifying the analysis of the variance estimate being a minimum variance unbiased under all random effects models and some mixed effects models with balanced data, for finding the explicit solution of maximum likelihood equations for the general mixed effects model and for showing the relationship between the spectral decomposition estimate and the analysis of variance estimate.     

Some results for non-linear elliptic problems with mixed boundary conditions

We prove existence and uniqueness results for non-linear elliptic equations with lower order terms, L¹ data, and mixed boundary conditions that include as particular cases the Dirichlet and the Neumann problems. Mathematics Subject Classification (2000) 35J25, 35D05, 35J70, 35J60