关于广导算子的零空间

本文讨论了两类广义导算子δＡＢ（ｘ）＝Ａｘ－ｘＢ和τＡＢ（ｘ）ＡｘＢ－Ｘ，并给出了一些成立的充分必要条件     

Heisenberg群上热核及Green核的渐近性

本文讨论Heisenberg群上热核及Green核的渐近性，给出了当群中元素靠近中心和远离中心时的渐近行为     

关于素环的导子

设Ｒ是一个中心为Ｃ的素环，Ｎ是Ｒ的一个非零理想。本文我们将证明下列结果：假设ｄ是Ｒ的一个非零导子使得ｄ＾２（ａ＾２）∈Ｃ对一切ａ∈Ｎ或者〔ｄ（ａ），ａ＾２〕∈Ｃ对一切ａ∈Ｎ，那么当Ｒ的特征不等于２时，Ｒ是一个交换环。我们的结果推广了文献〔２，〔４〕，〔８〕中有关素环导子的某些已知结果。     

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.     

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.     

关于回归函数核估计的叠对数律

讨论了非参数回归函数的核估计，用核估计误差分解方法，较弱条件下，到了回归函数核估计的叠对数值。     

基于次序统计量的ES核估计

本文考虑期望损失ES(Expected Shortfall)的一个新的估计基于次序统计量的核估计,在α-混合序列条件下,给出它的Bahadur表达式和均方误差,并且证明该估计量的渐进正态性.     

ON CERTAIN SUBGROUPS OF PRIME RINGS WITH DERIVATIONS

Let R be a noncommutative prime ring and let d be a nonzero derivation on R. A classical theorem of Posner asserts that the subset {[x ^d , x]|x ∈ R} is not contained in the center of R. Under the additional assumption that char R ≠ 2 and d ³ ≠ 0, we show that the additive subgroup of R generated by the subset {[x ^d , x] | x ∈ R} contains a noncentral Lie ideal of R.     

ON A BRESAR-SEMRL CONJECTURE AND DERIVATIONS OF BANACH ALGEBRAS

In this paper, we answer a question on derivations of densealgebras of linear operators posed by Brear and emrl. Our theoremimplies the following result: let be a complex Banach algebra,and let d and g be continuous derivations of . If dg(x) is quasi-nilpotentfor every x , then dg(x)³ lies in the radical of for everyx . This result was proved by Brear and emrl with the additionalassumption gd = dg.     

THE HEAT KERNEL ON THE CAYLEY HEISENBERG GROUP

1IntroductionThe aim of the present paper is to construct an explicit expression of an heat kernel forthe Cayley Heisenberg group of order n.Hulanicki[1]and Gaveau[2]constructed the explicit expression of the heat kernel for theHeisenberg group by using p…     

ON THE PROBLEM OF NECESSARY CONDITIONS ENSURING UNIFORM CONVERGENCE OF KERNEL DENSITY ESTIMATES

Let X_1,…,X,be a sequence of p-dimensional iid.random vectors with a commondistribution F(x).Denote the kernel estimate of the probability density of F(if it exists)by_n(x)=n~(-1)h~_n(-p)K((x-X_i)/h_n)Suppose that there exists a measurable function g(x)and h_n>0,h_n→0 such thatlim sup丨f_n(x)-g(x)丨=0 a.s.Does F(x)have a uniformly continuous density function f(x)and f(x)=g(x)?This paperdeals with the problem and gives a sufficient and necessary condition for generalp-dimensional case.     

关于几类矩阵的Kronecker和

本讨论了M矩阵、H矩阵、对角占优矩阵及α－对角占优矩阵的Kronecker和的一些重要性质。     

ON THE CONVEXITY OF SOME BANACH SPACES

51. IntroductionThe convexity of Banach spaces is an important topic in functional analysis and playsan importals role in indnite dimensional holomorphy. In order to study the geometricproperties of a Banach spacet Clarksonl3] and Krein (independently) introduced the veryimportallt class of strict convex spaces. In the same paper [3], Clarkson also introduced thestronger notion of uniform convexity. Since Clarkson's paper many authors have definedand studied the classes of Banach spaces lyi…     

若干图的强染色

图 G(V,E)的一正常 k-染色 σ称为 G(V,E)的 - k-强染色当且仅当对任何两个不同顶点 u和 v,只要d(u,v)≤ 2 ,则 u、v染不同颜色 (这里 d(u,v)表示 u,v之间的距离 ) ,并称 xs(G) =min{ k|存在 G的 - k-强染色 }为 G的强色数 ,本文得到 θ-图 ,Cm,n图 ,Halin图的强色数 xs(G)     

一族解析函數的模數

<正> §1.設函數f(ζ)在單位圓|ζ|<1中是正則的,f(0)=0,當|ζ_1|<1,|ζ_2|<1時f(ζ_1)·f(ζ_2)≠1.這種函數的全體記做C.首先研究這種函數的是比巴霸赫,其後有愛倫貝格.洛各淨司基證明:對於C中任一函數f(ζ),必從屬於C中某一單葉函數g(ζ).