特殊二阶微分方程的线性自治系统的辛多步法

１．引言１９世纪Ｈａｍｉｌｔｏｎ提出经典力学的一种基本的方程形式．记Ｐ＝Ｍｑ表示动量,ｑ表示位移,于是动能Ｔ＝１／２（ｐ,Ｍ－１　ｐ）,并将总能量Ｈ＝Ｔ＋Ｖ位能）表示为ｐ,ｑ的函数：于是经典力学的标准形式－Ｎｅｗｔｏｎ形式称为Ｈａｍｉｌｔｏｎ正则方程．（１．１）是ＺＩ维相空间或称辛空间中的相变量（ＰＩ,...,Ｐ。,ｑｌ;...,ｑｎ）'的一阶微分方程组．其中ｑ-（ｑｌ,...;ｑｒｔ）'是位置向量,ｄｑ,、Ｉ。。。。。ｑ＝ｉ＝（ｑｌ,...,ｑｈ）'是速度向量,ｄｔ'"""。'。'。。。ｌ、。。ｄ"ｑ,...．、,-,-…     

关于Fuzzy Drazin子半群

本文引进了ＦｕｚｚｙＤｒａｚｉｎ子半群的概念,并讨论了它们的一些代数性质,改进并推广了［５］、［６］、［８］、［１０］及［１１］中的许多重要结果     

Construction of Symmetric and Symplectic Bilinear Forms

Let V be a finite-dimensional vector-space. A linear mapping on V is called simple if V( - 1) is 1-dimensional. Let S be a set of simple bijections on V. We discuss conditions entraining that each element of S is orthogonal (respectively symplectic) under an appropriate symmetric (respectively symplectic) bilinear form on V.     

S~1 × S~1-Borsuk-Ulam Theorem on Product Spaces

Ｓ~１×Ｓ~１－Ｂｏｒｓｕｋ－ＵｌａｍＴｈｅｏｒｅｍｏｎＰｒｏｄｕｃｔＳｐａｃｅｓＺｈｏｎｇＣｈｅｎｇｋｕｉ（钟承奎）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＬａｎｚｈｏｕＵｎｉｖｅｒｓｉｔｙ，Ｌａｎｚｈｏｕ，７３００００）Ａｂｓｔｒａｃｔ：...     

Energy Conservation with Non-Symplectic Methods: Examples and Counter-Examples

Energy conservation of numerical integrators is well understood for symplectic one-step methods. This article provides new insight into energy conservation with non-symplectic methods. Sufficient conditions and counter-examples are presented. AMS subject classification (2000) 65L06, 65P10, 37J99.Submitted June 2004. Accepted October 2004. Communicated by Syvert Nørsett.     

Folded 2,5-diazapent-3-ene metallacycle in ene-diamido group 4 metal compounds: DFT and AIM analyses

Mononuclear complexes, which contain a dianionic ene-diamido ligand bound to a group 4 metal atom in the formal d⁰ configuration, are analyzed by the DFT method to interpret the electronic origin of the folding at the five-membered 2,5-diazapent-3-ene metallacycle moiety. Geometry optimizations were carried out for the following models, TiCl₂[o-(Me₃SiN)₂C₆H₄], Ti(OPh)₂(DAD), CpTiCl(DAD), CpTiMe(DAD) and Cp₂Zr(DAD) (DAD = HNCHCHNH). They show some common electronic features, the nature of the HOMO, in particular. In all cases, the latter results from the donation of a filled ene-diamido level into an empty σ metal orbital, this being maximized upon the folding of the metallacycle. Such a geometric rearrangement involves the filled nitrogen p_π lobes, while the CC π bond remains essentially uninvolved. The feature is confirmed by the application of the atom in molecules (AIM) theory, that provides no evidence of critical points between the metal center and the pair of two carbon atoms.     

tBuP(NH2)2--a reactive synthon for the synthesis of molecular imidophosphinates of group 13 metals

Reactions of tBuP(NH(2))(2) with Group 13 trialkyls MR(3) (M=Al, Ga, In; R=Me, tBu) were investigated in detail. According to variable-temperature (VT) NMR investigations, the reaction proceeds stepwise with the initial formation of aminophosphane adducts, which subsequently react to give iminophosphorane adducts and finally the heterocyclic metallonitridophosphinates. BP86/TZVPP (DFT) calculations were performed to verify this reaction pathway, to elucidate the influence of the central Group 13 element on the stability of the reaction intermediates and the heterocycles, as well as to assess the thermodynamics of their formation. The relative stability of free and complexed aminophosphane RP(NH(2))(2) and iminophosphorane R(H(2)N)(H)P=NH (adducts) with P(III) and P(V) centers was studied in more detail with DFT and MP2 methods. In addition, the influence of the substituent R was investigated by variation of R from H to Me, tBu, F, and NH(2). In general, the aminophosphane form was found to be favored for the free ligand, however, upon complexation with MR(3) (M=Al, Ga; R=alkyl) both forms are almost equal in energy.     

On perturbations of the group of shifts on the line by unitary cocycles

It is shown that the class of perturbations of the semigroup of shifts on by unitary cocycles with the property (where is the Hilbert-Schmidt class) contains strongly continuous semigroups of isometric operators, whose unitary parts possess spectral decompositions with the measure being singular with respect to the Lebesgue measure. Thus, we describe also the subclass of strongly continuous groups of unitary operators that are perturbations of the group of shifts on by Markovian cocycles with the property .