An asymptotic finite element method for improvement of solutions of boundary layer problems

Summary A scheme that uses singular perturbation theory to improve the performance of existing finite element methods is presented. The proposed scheme improves the error bounds of the standard Galerkin finite element scheme by a factor of O(ⁿ⁺¹) (where is the small parameter andn is the order of the asymptotic approximation). Numerical results for linear second order O.D.E.'s are given and are compared with several other schemes.     

Finite element approximation on incompressible Navier-Stokes equations with slip boundary condition

Summary We consider a mixed finite element approximation of the stationary, incompressible Navier-Stokes equations with slip boundary condition, which plays an important rôle in the simulation of flows with free surfaces and incompressible viscous flows at high angles of attack and high Reynold's numbers. The central point is a saddle-point formulation of the boundary conditions which avoids the well-known Babuka paradox when approximating smooth domains by polyhedrons. We prove that for the new formulation one can use any stable mixed finite element for the Navier-Stokes equations with no-slip boundary condition provided suitable bubble functions on the boundary are added to the velocity space. We obtain optimal error estimates under minimal regularity assumptions for the solution of the continous problem. The techniques apply as well to the more general Navier boundary condition.     

A priori-Schranken für diskrete Lösungen monotoner Operatorgleichungen und Anwendungen

Summary Operator equationsTu=f are approximated by Galerkin's method, whereT is a monotone operator in the sense of Browder and Minty, so that existence results are available in a reflexive Banach spaceX. In a normed spaceY error estimates are established, which require a priori bounds for the discrete solutionsu _h in the norm of a suitable space . Sufficient conditions for the uniform boundedness u _{h Z} =O(1) ash0 are proved. Well-known error estimates in [3] for the special caseX=Y=Z are generalized by this. The theory is applied to quasilinear elliptic boundary value problems of order 2m in a bounded domain . The approximating subspaces are finite element spaces. Especially the caseX=W ₀ ^{m, p} (), 1<p<,Y=W ₀ ^{m. 2} (),Z=W ₀ ^{m. max (2,p)} ()W^m, () is treated. Some examples for 1<p<2 are considered. Forp2 a refined technique is introduced in the author's paper [7].

     

GEOENVIRONMENTAL CHARACTERS OF YELLOW (HUANGHE) RIVER SUSPENDED LOAD

Three important characters of the suspended load of the Yellow (Huanghe) River are discussed, i.e. its temporal fluctuation as a function of solar activity, its uneven spatial distribution along the main course and the inevitability of these phenomena as a natural earth process rather than a result of disturbed ecological system caused by human activity. Implications of this understanding with regard to the control of the Yellow River are also discussed.     

Synthesis, crystal structure and magnetic properties of a novel complex [Cu(NIT2Py)(PDA)(H2O)]·(CH3OH)(H2O)

A novel complex [Cu(NIT2Py)(PDA)(H₂O)]·(CH₃OH)(H₂O) has been synthesized and structurally characterized by X-ray diffraction methods. It crystallizes in the monoclinic space group P2(1)/c. The structure consists of [Cu(NIT2Py)(PDA)(H₂O)] moiety, one solvent methanol molecule and one water molecule. The copper(II) ion is in a distorted octahedral environment: one nitrogen atom and one oxygen atom from the NIT2Py, one nitrogen atom from the PDA (2,6-pyridine dicarboxylic acid) and one oxygen atom from the aqueous in the basal plane; two oxygen atoms from the PDA in the axial position. The units of [Cu(NIT2Py)(PDA)(H₂O)] were connected as one dimension chain by the intermolecular hydrogen bonds. The complex exhibits intramolecular antiferromagnetic interactions between the Cu(II) ion and the NIT2Py.     

相变温度低且宽的含有胆甾烯基和反式-4-烷基环己基苯氧基的二介晶化合物

Unsymmetrical dimesogenic compounds with cholesteryl and 4-（trans-4-n-alkylcyclohexyl）phenoxy parts were synthesized by condensation of cholester-3-yl 6-bromohexanoate with appropriate 4-（trans-4-n-alkylcyclohexyl）- phenols. Structures and thermal phase behaviour of these dimesogenic compounds have been confirmed by IR, IH NMR, elemental analysis, DSC, polarity microscopy and XRD measurements. Their thermal phase behaviour was significantly different with that of other cholesterol-based dimesogens while they exhibited low and wide phase transition temperature.     

Cu(OTf)2-catalyzed Et3SiH-reductive etherification of various carbonyl compounds with trimethylsilyl ethers

A triethylsilane-reductive etherification of the trimethylsilyl ethers with a variety of carbonyl compounds in good yields at room temperature employing 0.5 mol% Cu(OTf)₂ as an extremely efficient catalyst is described here.     

含氰基侧基聚芳醚砜的合成与表征

汉２，６－二卤苯甲腈、４，４′－二氯二苯砜、４，４′－二羟基二苯砜、间苯二酚、对苯二酚、酚酞及双酚Ａ为主要原料，合成了含不同结构单元和不同氰基含量的含氰基侧基的聚芳醚砜，并采用ＩＲ、＾１３ＣＮＭＲ等分析手段对其结构进行了表征，同时研究了结构单元和氰基含量对聚芳醚砜性能的影响。     

荧光钙探针试剂及其在生物分析中的应用

本文评论了荧光钙探针试剂合成、性质、结构和生物分析应用方面的进展。各种典型的荧光钙探针试剂均已分别加以讨论。