von Neumann代数中套子代数上的Lie导子

本文对因子von Neumann代数中套子代数上的线性映射L:alg_Mβ→M满足L(AB—BA)=L(A)B-BL(A)+AL(B)-L(B)A( A,B∈alg_Mβ)进行了刻划,证明了存在线性函数h:alg_Mβ→C;且对任意A,B∈alg_Mβ,有h(AB—BA)=0和算子T∈M,使得对任意X∈alg_Mβ,都有L(X)=XT-TX+h(X)I.     

Pontrjagin空间上J.V.N代数的导子

本文证明Pontrjagin空间上非退化的J.V.N代数的导子是内的等价于它在该代数的奇异部分上 的限制为零.对退化的J.V.N代数,证明了Ⅱ1空间第0,Ⅱa和Ⅲa类J.V.N代数上的导子是内 的.通过构造例子说明了第Ⅰ,Ⅱb和Ⅲb类对称代数上的导子一般不是内的.     

On the Derivations of Filiform Leibniz Algebras

The algebras of derivations of naturally graded Leibniz algebras are described. The existence of characteristically nilpotent Leibniz algebras in any dimension greater than 4 is proved.__________Translated from Matematicheskie Zametki, vol. 77, no. 5, 2005, pp. 733–742.Original Russian Text Copyright ©2005 by B. A. Omirov.     

A Class of Non-degenerate Solvable Lie Algebras and Their Derivations

The author constructs a class of indecomposable non-degenerate solvable Lie Algebras corresponding to a Cartan matrix A over the field of complex numbers and we determine all their derivations.     

On the Boltzmann-Grad limit for the Broadwell model of the Boltzmann equation

An example is given of a model dynamics for which the Broadwell model of the Boltzmann equation seems to appear in the formal stage of the Boltzmann-Grad limit, but actually does not.     

Non-Abelian Cohomology of Groups

Following Guin's approach to non-abelian cohomology [4] and, using the notion of a crossed bimodule, a second pointed set of cohomology is defined with coefficients in a crossed module, and Guin's six-term exact cohomology sequence is extended to a nine-term exact sequence of cohomology up to dimension 2     

Transfer processes in fractal media

An irreversible process in fractal media involves coupling relation between the space and the time. The present note displays how the fractional derivation has to be introduced to describe this effect. As a result the law of the chemical diffusion to a fractal is given.     

Computer derivation of algebraic equations associated with runge-kutta formulas

The derivation of algebraic non-linear equations associated with Runge-Kutta formulas increases in complexity as the order of these formulas increases. To overcome this difficulty various operational methods have been devised. But these methods are quite involved and there also exists the possibility of human errors which may be difficult to detect. The aim of this paper is the derivation of these algebraic equations through a digital computer, the IBM 7094, using Fortran IV. The technique employed is based upon a mathematical method established by the first author. With the advent of the space age there arose a continuous need for Runge-Kutta formulas of higher and higher orders. It seems that the computer offers the best, if not the only, hope in keeping up with these needs.     

A perturbation of ring derivations on Banach algebras

Suppose A is a Banach algebra and suppose is an approximate ring derivation in the sense of Hyers-Ulam-Rassias. This stability phenomenon was introduced for the first time in the subject of functional equations by Th.M. Rassias [Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978) 297-300]. If A has an approximate identity, or if A is semisimple and commutative, then we prove that f is an exact ring derivation.