ON THE INVARIANT SUBMANIFOLDS OF RIEMANNIAN PRODUCT MANIFOLD

In this paper, the vertical and horizontal distributions of an invariant submanifold of a Riemannian product manifold are discussed. An invariant real space form in a Riemannian product manifold is researched. Finally, necessary and sufficient conditions are given on an invariant submanifold of a Riemannian product manifold to be a locally symmetric and real space form.     

ON SELF-ADJOINTNESS OF THE PRODUCT OF TWO n-ORDER DIFFERENTIAL OPERATORS ON[a,b]

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ON THE PRODUCT OF GATEAUX DIFFERENTIABILITY LOCALLY CONVEX SPACES

A locally convex space is said to be a Gateaux differentiability space (GDS)provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gateaux differentiable in D.This paper shows that the product of a GDS and a family of separable Frechet spaces is a GDS,and that the product of a GDS and an arbitrary locally convex space endowed with the weak topology is a GDS.     

序列的一种无组合系数的根表示

本文在讨论了组合数C_x~k等在GF(q)上的多元多项式表示的基础上,给出了序列的一种避免组合系数的根表示法,并利用它对两个有重根的反馈多项式生成序列之积的线性复杂性进行了讨论.     

A NOTE ON PRODUCTS OF THE WHITEHEAD TYPE

Abstract

A survey is given of various generalizations of the Whitehead product. Carrying the procedure a step further, a generalization is given that specialized in one wry relates to the “Whitehead elements” in the (mod p) kernel of the double suspension (p an odd prime, p > 4). Specialized in another way the product relates to the action of the Q-homomorphism (in the EHQ sequence) on elements that are not double suspensions.     

ON NONABELIAN TENSOR PRODUCT MODULO q OF GROUPS

The nonabelian tensor product modulo q of two crossed modules of groups is investigated, where q is a positive integer. It is obtained a six term exact sequence of groups connecting the nonabelian tensor product modulo q with algebraic K-functor K ₂ with Z _q coefficients for (noncommutative) local rings. The notion of q-homology groups of a group G with coefficients in a G-module A is introduced, some its properties and calculations are given. The relationship between q-homology groups and derived functors of tensor product modulo q is studied.     

ON A THEOREM OF BRADEN

We give a new proof of Braden’s theorem ([Br]) about hyperbolic restrictions of constructible sheaves/D-modules. The main geometric ingredient in the proof is a 1-parameter family that degenerates a given scheme Z equipped with a $ {\mathbb G} $ _m -action to the product of the attractor and repeller loci.     

ON THE EXISTENCE OF MAXIMAL LIKELIHOOD ESTMATORS

In this paper, we give necessary and sufficient for the existence of maximal likelihood estimators when the density functions of probability distributions are product measurable. We also show that when we adopt the generalized definition of maximal likelihood estimators, the generalized maximal likelihood estimators always exist,provide the denesity functions are product measurable.     

REPRESENTATION OF GENERALIZED TRANSLATIONS OF THE PRODUCT OF TWO FUNCTIONS ON SIGNED HYPERGROUPS ON THE REAL LINE

In this paper,we consider the generalized translations associated with the Dunkl and the Jacobi-Dunkl differential-difference operators on the real line which provide the structure of signed hrpergroups on R.Especially,we study the representation of the generalized translations of the product of two functions for these signed hypergroups.     

一些积图的点可区别均匀边色数

本文研究了积图的点可区别均匀边染色问题.利用构造法得到了积图G×G的点可区别均匀边染色的一个结论,并且获得了等阶的完全图与完全图、星与星、轮与轮的积图的点可区别均匀边色数,验证了它们满足点可区别均匀边染色猜想(VDEECC).     

ON THE PRODUCT OF GATEAUX DIFFERENTIABILITY LOCALLY CONVEX SPACES

A locally convex space is said to be a Gâteaux differentiability space (GDS) provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gâteaux differentiable in D. This paper shows that the product of a GDS and a family of separable Fréchet spaces is a GDS, and that the product of a GDS and an arbitrary locally convex space endowed with the weak topology is a GDS.     

三类笛卡尔积图的关联色数

图的关联色数的概念是 Brualdi和 Massey于 1 993年引入的 ,它同图的强色指数有密切的关系 .Guiduli[2 ] 说明关联色数是有向星萌度的一个特殊情况 ,迄今仅确定了某些特殊图类的关联色数 .本文给出了完全图与完全图、圈与完全图、圈与圈的笛卡尔积图的关联色数。     

表大偶數為一個不超過三個素數的乘積及一個不超過四個素數的乘積之和

<正> V.Brun最初在1920年證明了:每一充分大的偶數可表為兩個各不超過9個素數的乘積之和.簡記之為(9,9).後來,不少數學家改進與簡化了Brun方法,因此,Brun的結果也得到相應的改進,     

关于体上分块矩阵的群逆

本文利用分块矩阵方法．研究了体上两个矩阵乘积的群逆的存在性及表示形式，给出了体上两个矩阵乘积群逆存在的充分必要条件和表示形式．并且在一定条件下．给出了体上分块矩阵的群逆存在性及表示形式．     

HARMONIC FUNCTIONS ON PRODUCT OF CERTAIN KAHLER MANIFOLDS WITH A POLE

In the paper [1], adn Y. L. Proved that any abate energy haxmonic map from classicalbounded symmetric domains (except Wy(2) = H: x H') into any comPlete gem~anm~d has to be const8Dt. And he asked if there easts a hannoulc map of able energy~ Rzv(2) = Ha x Ha into a melnannha m~ld. In this short note, we will partiallyanswer this question. Actually, we will ProveTheorem. Let MP, Ma be complete noncofnpoct Keeled manifolds oj comalys dimenaions m and n reSPeCtiveig. Assume all of the ge…     

对称性对Schrodinger算子特征向量存在性的影响

讨论了sl2（C）中矩阵乘积的迹的性质；证明了离散Schrodinger算子H在其势Vn为Thue－Morse序列或准对称序列时，在空间Co（Z）内不存在特征向量．     

REGULAR FUNCTIONS ON A PRODUCT OF AFFINE VARIETIES

ABSTRACT

Assume that f:X×Y→Z is a map from the product of two affine varieties into another affine variety such that f is a regular map when one variable is fixed. We show that f is a regular map if the underlying field is not countably infinite. The condition is indispensable.     

几类高阶微分方程解的复振荡

本文研究了几类高阶线性微分方程解的增长性,零点,以及构成基础解的一组线形无关解的乘积的增长性.得到了5个定理,推广了陈宗煊,S.Bank和J.Langley给出的结果.     

COMPLETE CONVERGENCE THEORY OF THE CONTACT PROCESS ON Td × Z

The author considers the contact process on a branching plane Td× Z, which is the product of a regular tree Td and the line Z. It is shown that above the second critical point, the complete convergence theory holds.     

論矩陣的一種變換

<正> 在本文中,數域限定為複數域.我們要來研究如下的變換:(1)(它將方陣A變成方陣B),式中P表示任意正則陣,P表示P的元素的共軛救構成的陣.所有的變换(1)顯然成羣.這種變換現在姑稱之為種變換.如果二方陣A與B可由一個種變換變此成彼,我們就說,A與B是對相似的.