1－N－（苯并咪唑－1－乙酰基）－4－苯基－3－氨基硫脲金属配合物的合成及结构表征

合成了新配体１－Ｎ－（苯并咪唑－１－乙酰基）－４－苯基－３－氨基硫脲（ＢＰＭＳ），将其与Ｍｎ（Ⅱ）、Ｃｏ（Ⅱ）、Ｎｉ（Ⅱ）、Ｃｕ（Ⅱ）、Ｃｄ（Ⅱ）、Ｚｎ（Ⅱ）、ＵＯ２（Ⅱ）等金属的醋酸盐反应，合成了７个新配合物。所有化合物均经元素分析、ＩＲ、１ＨＮＭＲ和热重分析等表征。红外光谱表明，配体以四齿方式通过烯醇式羰基氧原子、烯醇式硫羰基硫原子以及Ｃ＝Ｎ１和Ｃ＝Ｎ２的氮原子与金属配位     

Calculs de complexité relatifs à une méthode de dissection emboîtée

Résumé Nous présentons une numérotation de type Nested Dissection des inconnues d'un système linéaireAX=B pour des ensembles de matricescreuses symétriques définies positives correspondant à des famille de graphes non orientés,à degré borné, et admettant un -thérème de séparation. Comparativement aux méthodes et résultats de Rose [9], l'algorithme présenté est plus simple, mais les théorèmes de complexité moins généraux, en raison de l'hypothèse restrictive de degré borné. En outre, les démonstrations font appel en permanence à la structure d'arbre sur la famille des séparateurs qui constitue, par ailleurs, une partition de l'ensemble des sommets du graphe initial. Nous présentons ensuite le schéma général d'implémentation dans le cadre du code d'éléments finis MODULEF pourdes problèmes plans d'éléments finis, et nous donnons quelques mesures comparatives avec la numérotation plus classique qui tend à minimiser le profil de la matrice.

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Complexity bounds for a nested dissection method

Summary A nested dissection ordering is given for solving any system of linear equationsAX=B, for the family ofsparse symmetric positive definite matrices corresponding to the class of undirected graphs withbounded degree, and satisfyinga -separator theorem. If we compare the methods and results presented by Rose [9], our algorithm is more simple, but the complexity results are less general because of the restriction of bounded degree. Besides, our proofs use continually the arborescent structure on the family of separators, which is, by another way, a partition of the set of vertices for the initial graph. Then, the general implementation scheme in the finite element package MODULEF, fortwo-dimensional finite element problems, is presented, and numerical comparisons between our ordering and the standard envelope method are given.

     

Two families of mixed finite elements for second order elliptic problems

Summary Two families of mixed finite elements, one based on triangles and the other on rectangles, are introduced as alternatives to the usual Raviart-Thomas-Nedelec spaces. Error estimates inL ² () andH ^–5 () are derived for these elements. A hybrid version of the mixed method is also considered, and some superconvergence phenomena are discussed.     

Is Gauss quadrature optimal for analytic functions?

Summary We consider the problem of optimal quadratures for integrandsf: [–1,1] which have an analytic extension to an open diskD _r of radiusr about the origin such that 1 on . Ifr=1, we show that the penalty for sampling the integrand at zeros of the Legendre polynomial of degreen rather than at optimal points, tends to infinity withn. In particular there is an infinite penalty for using Gauss quadrature. On the other hand, ifr>1, Gauss quadrature is almost optimal. These results hold for both the worst-case and asymptotic settings.This research was supported in part by the National Science Foundation under Grants MCS-8203271 and MCS-8303111This research was supported in part by the National Science Foundation under Grant MCS-8923676     

The convergence of spline collocation for strongly elliptic equations on curves

Summary Most boundary element methods for two-dimensional boundary value problems are based on point collocation on the boundary and the use of splines as trial functions. Here we present a unified asymptotic error analysis for even as well as for odd degree splines subordinate to uniform or smoothly graded meshes and prove asymptotic convergence of optimal order. The equations are collocated at the breakpoints for odd degree and the internodal midpoints for even degree splines. The crucial assumption for the generalized boundary integral and integro-differential operators is strong ellipticity. Our analysis is based on simple Fourier expansions. In particular, we extend results by J. Saranen and W.L. Wendland from constant to variable coefficient equations. Our results include the first convergence proof of midpoint collocation with piecewise constant functions, i.e., the panel method for solving systems of Cauchy singular integral equations.Dedicated to Prof. Dr. Dr. h.c. mult. Lothar Collatz on the occasion of his 75th birthdayThis work was begun at the Technische Hochschule Darmstadt where Professor Arnold was supported by a North Atlantic Treaty Organization Postdoctoral Fellowship. The work of Professor Arnold is supported by NSF grant BMS-8313247. The work of Professor Wendland was supported by the Stiftung Volkswagenwerk     

Numerical solution of delay differential equations by uniform corrections to an implicit Runge-Kutta method

Summary In this paper we develop a class of numerical methods to approximate the solutions of delay differential equations. They are essentially based on a modified version, in a predictor-corrector mode, of the one-step collocation method atn Gaussian points. These methods, applied to ODE's, provide a continuous approximate solution which is accurate of order 2n at the nodes and of ordern+1 uniformly in the whole interval. In order to extend the methods to delay differential equations, the uniform accuracy is raised to the order 2n by some a posteriori corrections. Numerical tests and comparisons with other methods are made on real-life problems.This work was supported by CNR within the Progetto Finalizzato Informatica-Sottopr. P1-SOFMAT     

A three-dimensional quadratic nonconforming element

Summary We define a second-degree nonconforming element on tetrahedra. We build a basis for the opproximation space derived from this element. We prove a discrete regularity property similar to the one that holds for the corresponding two-dimensional element.This work was partly supported by NSERC and by the Ministère de l'Education du Québec     

Pt4(OCOCH3)4(OCOCH=CH2)4的合成及其在n型单晶硅表面的嫁接与组装

利用羧基取代法, 通过化合物Pt4(OCOCH3)8与过量的丙烯酸作用合成了配合物Pt4(OCOCH3)4(OCOCH=CH2)4. 晶体结构研究结果表明, 化合物Pt4(OCOCH3)8中的4个乙羧基能够被烯丙羧基有规律地选择性替换, 从而形成一个含双键的对称铂配合物. 利用Si—H与不饱和键的加成性质将该配合物嫁接到氢化n型单晶硅(111)表面, 发现配合物Pt4(OCOCH3)4(OCOCH=CH2)4除了能嫁接到单晶硅表面外, 还能在n型单晶硅表面进行自组装而形成许多岛状纳米粒子, 这种组装体系具有良好的热稳定性和一定的抗酸性.     

SYNTHESIS AND CHARACTERIZATION OF A NEW POLYSILOXANE CONTAINING N,N’-BIS(DIPHENYLSILYL)TETRAPHENYLCYCLODISILAZANE

A new kind of polysiloxane containing N,N'-bis(diphenylsilyl)tetraphenylcyclodisilazane was prepared by anionicnon-equilibrium polymerization with a "seed solution" as initiator. The monomer, N,N'-bis(hydroxydiphenylsilyl)-tetraphenyl-cyclodisilazane (BHPTPC), was synthesized via the hydrolysis of N,N'-bis(chlorodiphenylsilyl)tetraphenyl-cyclodisilazane (BCPTPC). A new method for the preparation of BCPTPC is also reported here with high yield and simplermanipulation. The synthesized polysiloxane containing N,N'-bis(diphenylsilyl)tetraphenylcyclodisilazane was characterized by ~1H-NMR, ~(29)Si-NMR, gel permeation chromatography (GPC) and intrinsic viscosity.     

Synthesis,Crystal Structure and Calculated β Value of a Tetrahedral Zinc (II) Complex——Zn(2-NH_2py)_2Br_2

1 INTRODUCTION Coordination chemistry has been playing an important role in nonlinear optical (NLO) materi- als [1~3] in recent years. It has been found that tetrahedral or square pyramidal molecular configurations are useful for designing transparent second-harmonic generation (SHG) materials from coordination compounds[4]. It has also been reported that the pyridyl-based metal complexes can exhibit SHG effects[5]. Recently, we have successfully synthesized a new coordination compoun…