正交表的乘法

该文根据投影矩阵的正交分解定义了一种正交表的乘法运算, 利用这种乘法可以从小的正交表构造新的大的正交表.     

A Note on the Construction of Orthogonal Latin Hypercube Designs

Latin hypercube designs have been found very useful for designing computer experiments. In recent years, several methods of constructing orthogonal Latin hypercube designs have been proposed in the literature. In this article, we report some more results on the construction of orthogonal Latin hypercubes which result in several new designs.     

A Note on the Graded K-Theory of Certain Graded Rings

Following ideas of Quillen we prove that the graded K-theory of a ? ⁿ -graded ring with support contained in a pointed cone is entirely determined by the K-theory of the subring of degree 0 elements.     

Generalized Topological Index

This paper deals with an index which is different in general from the topological index defined by Atiyah and Singer because we loosen the normalization property. The intrinsic relation of this new index with operations in K-theory is explained. It is also shown that if we change the normalization axiom, the corresponding index is well-defined and may be expressed in terms of the topological index.     

局部凸代数L(E)的乘法连续性

本文讨论了(E,σ(E,E′))上连续自同态代数L(E)上在几种常见拓扑下的乘法连续性,得到相应的等价条件．     

有关正交随机测度的一些结果

本文给出正交随机测度和数值测度的零一律及拓扑群成为局部紧的充分条件.     

Vitali定理的一个注记

证明了Vitali定理的部分逆定理成立,从而给出了函数列依测度收敛的一个充分必要条件。     

Multiplication operators on sobolev disk algebra

In this paper,we study the algebra consisting of analytic functions in the Sobolev space W~(2,2) (D) (D is the unit disk),called the Sobolev disk algebra,explore the properties of the multiplication operators M_f on it and give the characterization of the corn- mutant algebra A′(M_f) of M_f.We show that A′(M_f) is commutative if and only if M_f~* is a Cowen-Douglas operator of index 1.     

Multiplication Modules and a Theorem of P. F. Smith

P. F. Smith [7, Theorem 8] gave sufficient conditions on a finite set of modules for their sum and intersection to be multiplication modules. We give sufficient conditions on an arbitrary set of multiplication modules for the intersection to be a multiplication module. We generalize Smith"s theorem, and we prove conditions on sums and intersections of sets of modules sufficient for them to be multiplication modules. This revised version was published online in June 2006 with corrections to the Cover Date.     

On Associative Ring Multiplication on Abelian Mixed Groups

An abelian group is called a mixed one if it is neither torsion nor torsion-free. It is to be proved that every mixed group can be provided with a nonzero associative ring structure. Our methods of proofs are straightforward and elementary.     

A Note on the Place Topology of Projective Planes

It is shown that the place topology induced by a proper epimorphism of a projective plane , which is known to make a Lenz-topological plane, makes even a topological projective plane, if the extended radical of some underlying ternary field is bounded.     

Fock空间上的乘法算子

Fock空间是由整函数组成的具有再生核的Hilbert空间.Fock空间上的乘法算子的定义域不是整个Fock空间,它在Fock空间上是稠定的.研究了Fock空间上的乘法算子的性质,对其值域进行了刻画,并得出了乘法算子作用在Fock空间的拟不变子空间上值域余一维的充要条件.     

关于Sturm定理的一点注记

经典的S turm定理用于判定多项式在给定区间上不同的实根个数,但是并不能刻画重根的情况.在这里定义了推广的S turm序列,将S turm定理进行一定地延拓,给出区间上多项式的所有实根均是偶重根或奇重根的充要条件.作为应用,讨论了多项式正(负)半定的判定问题.     

递推序列的一个注记

我们给出变系数线性递推序列的一个算术性质，它类似于常系数线性递推序列的情形。     

Weak Multiplication Modules

In this paper we characterize weak multiplication modules.     

关于几乎拓扑群的注记

In this paper, we mainly discuss some generalized metric properties and the cardinal invariants of almost topological groups. We give a characterization for an almost topological group to be a topological group and show that:(1) Each almost topological group that is of countable π-character is submetrizable;(2) Each left λ-narrow almost topological group isλ-narrow;(3) Each separable almost topological group is ω-narrow. Some questions are posed.     

关于Misuirewing一个定理的注记

本文改进了Misuirewing的一个定理，并给出小熵猜测的一个新的证明。     

关于勒让德多项式的一个注记

本文利用勒让德多项式的性质证明了其导数多项式是［－１，１］上关于权１－ｘ２的正交多项式．     

Hilbert空间H上正交射影对的一个注记

本文研究了Hilbert空间H上正则射影对的性质和结构，证明了酉算子V与正交射影对（P，Q）交织（i．e．，VP=QV，PV=VQ）的充分必要条件是dim（R（P）∩N（Q））=dim（N（P）∩R（Q）），给出了满足上述条件均酉算子V均一般形式．