关于多项式映射自同构恒等集的一个注记

本文给出了判定一个仿射代数集是否是一个自同构恒等集的充分条件.作为一个推论,我们给出了Mckay-Wang的一个问题的一个新证明.我们也给出了一些具体的例子来说明主要的定理.     

LINEAR ISOMETRIC NON-ANTICIPATIVE TRANSFORMATIONS OF WIENER PROCESS

ThispaperisanoutcomeofnumerousdiscusionsandexchangeofideaswithlatePredragPerunicic,whosedeepandprofoundmathematicalknowledgeandhumanvaluesgaveusaninspirationandmotivationtofinalizeourjointideas.1.Wereferto[3,4]forthenotionofspectralmultiplicitytheoryintheseparableHilbertspace.LetHbeacyclicHilbertspacewiththeresolutionoftheidentity{p(t)}ofthemaximalspectraltypelIP(dt)ll'~dt-ordinaryLebesguemeasure.Anon-anticipativelineartransformationsisdefinedbyVolterrakernelg(t,u),uSt,ajsf'g(t)u)p(du),t>0…     

一个二阶方程的振动性质及其应用

本文研究了一个二阶微分方程的解及其振动性质,利用它获得了一般二阶自共轭方程的振动性判别准则,特别对其中一类二阶微分方程的振动性给出了定量的判别方法.推广了E.Hille的工作,使E.Hille的研究结论成为本文结果的极特殊的情形,同时对一类具有“积分小”系数或可化为具有“积分小”系数的二阶微分方程的振动性与非振动性给出了简便、精确的判别方法.     

试探方程法及其在非线性发展方程中的应用

提出了一种比较系统的求解非线性发展方程精确解的新方法, 即试探方程法. 以一个带5阶 导数项的非线性发展方程为例, 利用试探方程法化成初等积分形式，再利用三阶多项式的完 全判别系统求解，由此求得的精确解包括有理函数型解, 孤波解, 三角函数型周期解, 多项 式型Jacobi椭圆函数周期解和分式型Jacobi椭圆函数周期解 关键词： 试探方程法 非线性发展方程 孤波解 Jacobi椭圆函数 周期解     

环上带有广义导子和自同构的恒等式

设R是一个素环,RF是它的左Martindale商环.如果φ(xigik△ij)是环R的某个本质理想I的一个多重线性既约且带有自同构的广义微分恒等式,那么φ(zikj)是环RF的一个广义多项式恒等式.设R是一个具有特征P≥0的半素环,RF是它的左Martindale商环.如果φ(xigik△ijfik)是环R的一个多重线性既约且带有自同构的广义微分恒等式,那么φ(zikjfike(△ij)是环RF的一个广义多项式恒等式,这里fik和e(△ij)是RF中的幂等元.     

for commutative rings with identity

Let , , , , be the usual operators on classes of rings: and for isomorphic and homomorphic images of rings and , , respectively for subrings, direct, and subdirect products of rings. If is a class of commutative rings with identity (and in general of any kind of algebraic structures), then the class is known to be the variety generated by the class . Although the class is in general a proper subclass of the class for many familiar varieties . Our goal is to give an example of a class of commutative rings with identity such that . As a consequence we will describe the structure of two partially ordered monoids of operators.

     

Applications of operator identities to the multiple q-binomial theorem and q-Gauss summation theorem

In this paper, we first give an interesting operator identity. Furthermore, using the q-exponential operator technique to the multiple q-binomial theorem and q-Gauss summation theorem, we obtain some transformation formulae and summation theorems of multiple basic hypergeometric series.     

A new eight-dimensional Lie superalgebra and two corresponding hierarchies of evolution equations

A new eight-dimensional Lie superalgebra is constructed and two isospectral problems with six potentials are designed. Corresponding hierarchies of nonlinear evolution equations, as well as super-AKNS and super-Levi, are derived. Their super-Hamiltonian structures are established by making use of the supertrace identity, and they are integrable in the sense of Liouville.     

Breather Lattice Solutions to Negative mKdV Equation

In this paper, dependent and independent variable transformations are introduced to solve the negative mKdV equation systematically by using the knowledge of elliptic equation and Jacobian elliptic functions. It is shown that different kinds of solutions can be obtained to the negative mKdV equation, including breather lattice solution and periodic wave solution.     

Hyperidentities of some generalizations of lattices

In the paper we present bases and hyperbases of hyperidentities of some generalizations of the variety L of all lattices and the variety D of distributive lattices. We describe the form of hyperidentities of some varieties with two binary operations. Received January 22, 1997; accepted in final form January 7, 1998.