Führer f在不同环中分解的理论(Ⅱ)

<正> 引言本文目的是把作者在前文[1]中所获得的结果作出更一般的研究.设 o 是合有么元且满足理想约束极小条件的一个整区,(?)是合有与 o 相同么元且包含 o 的一个整区,并且假设(?)是代数整封闭的.记 Q(?)与 Q(o)如前文[1]中那样分别为(?)及 o 的商体,并且满足 Q(?):Q(?)=n<∞ 的条件.因此在(?)中以(?)的非零理想     

平面上Volterra型随机微分方程的弱解

设 B 是(?)上的 Brown 运动,考虑平面上 Volterra—It(?)型随机微分方程(Ⅰ)X_(?)=(?)+(?)a(z,ξ,X_ξ)dξ+∫_(R_z)β(z,ξ,X_(?))dB_(?) z∈R_+~2其中(?)是两参数连续过程,满足:对(?)T>0,(?),则当α(z,ξ,x),β(z,ξ,x)连续,且关于 z 满足 Lip 条件,关于 x 满足增长性条件时,本文用迟滞逼近方法证得方程(Ⅰ)弱解存在。     

ω_μ-可加的拓扑空间(Ⅰ)

<正> 按照 R.Sikorski[1],所谓集(?)是ω_μ-可加拓扑空间,即指对其每个子集 X 都定义了满足下列条件的闭包(?):     

Ω单一化拓扑稳定性

<正> 在微分动力系统稳定性理论研究中,对紧 Riemann 流形上满足公理 A 和无环条件的微分同胚,Smale,S.证明了其(?)稳定性,Nitecki,Z.证明了其(?)拓扑稳定性.对满足公理 A 和无环条件的覆盖映射,[2]证明了其(?)单一化稳定性,本文证明了其(?)单一化拓扑稳定性,部分地解决了 Nitecki,Z.在[1]中对自映射情形所提出的问题.     

椭圆型方程广义解Liouville型定理的一个注

在Ｅⁿ考虑椭圆方程(?)其中Ａ，Ｂ满足如下的结构条件：(?)本文证明如果广义整解ｕ∈W_p,loc¹(Eⁿ)∩ L_α(Eⁿ)，其中(?)那么ｕ≡０．     

退缩椭圆型方程的特征值问题注记

即方程可能退缩,而Σ_3=(?)Q\∑_0其n-1维测度不为零,∑_0为(?)Q上sum from (ij)=1 to n a_ij)n_in_j=0的点集,(n_1,…,n_n)表示(?)Q的内单位法向量。 实数λ称为问题(1)的广义特征值,如存在不为0的函数u∈(?),对任意的ξ∈(?)满足     

带有循环条件的黎曼空间的共圆变换

§1 引言和预备知识带有循环条件的黎曼空间{M~n,g)(n>3)已被不少文献讨论过,下面列举本文将讨论到的一些类型(见[3]):1°若{M~n,g}的黎曼曲率张量满足R_(ijk(?)l)~h=λ_lR_(ijk)~h,则{M~n,g}称为 Ruse 意义下的循环空间.     

向量有理插值的一个行列式公式

<正> 设由不同实数组成的实数序列为x_0,x_1,x_2,…,对应的有限向量序列为(?)_0,(?)_1,(?)_2,…,其中(?)_i=(?)(x_1)∈D~d定义若向量有理函数(?)_n(x)=(?)(x)/q(x),其中(?)(x)是d 维多项式值向量,q(x)是实多项式,满足:     

Führer f在不同环中分解的理论(Ⅰ)

<正> 本文发展了 H.Grell 的工作.H.Grell 曾作过如下的研究:设 o 是含有么元的整区,且满足理想约束极小条件,(?)是含有与 o 相同么元的一个整区,且又设(?)是代数整封闭的,设 Q(?)与 Q(o)分别是(?)及 o 的商体,Grell 限制Q(?)=Q(?),那末在此情况下由 Grell 的一般保持定理知道,任一介于 o 与(?)之间的     

特殊向一般的转化

1.纤维丛积分方法可以将特殊相对性量子场论“积分”而为一般相对性量子场论。根据这个原则,Min-kowski 空间的混合量可以“积分”而为 Einstein 空间的混合量。我们以 x(?)(x~1,…,x~4)(x~4(?)ix~0(?)ict)表示 Minkowski 空间的坐标系,以 X(?)(X~1,…,X~4)(X~4(?)iX~0(?)icT)表示 Einstein 空间的坐标系,取 c=h=1,h(?)h/(2π),以拉丁小字母表示 Minkowski 空间的混合量,以拉丁大字母表示 Einstein 空间的混合量。纤维丛积分以普通积分号“∫”的镜象“(?)”表之。我们有关系式     

Theorems of existence and of vanishing of conformally killing forms

On an n-dimensional compact, orientable, connected Riemannian manifold, we consider the curvature operator acting on the space of covariant traceless symmetric 2-tensors. We prove that, if the curvature operator is negative, then the manifold admits no nonzero conformally Killing p-forms for p = 1, 2, …, n ? 1. On the other hand, we prove that the dimension of the vector space of conformally Killing p-forms on an n-dimensional compact simply-connected conformally flat Riemannian manifold (M,g) is not zero.     

(α, β)- 空间中的Killing 向量场

本文证明了非Riemannian (α, β)- 空间中的Killing 向量场最大维数是n(n - 1)/2 + 1. 并且给出了具有最大维数Killing 向量场的非Riemannian (α, β)- 空间的度量形式. 最后, 若进一步假定α 是一个齐性Riemannian 度量, 则可确定(α, β)- 空间的第二空隙. 最后给出几个低维流形上Killing 场空间维数的例子, 这表明在(α, β) 情形下Killing 场空间维数的空隙被压缩.     

Conformal holonomy of C-spaces, Ricci-flat, and Lorentzian manifolds

The main result of this paper is that a Lorentzian manifold is locally conformally equivalent to a manifold with recurrent lightlike vector field and totally isotropic Ricci tensor if and only if its conformal tractor holonomy admits a 2-dimensional totally isotropic invariant subspace. Furthermore, for semi-Riemannian manifolds of arbitrary signature we prove that the conformal holonomy algebra of a C-space is a Berger algebra. For Ricci-flat spaces we show how the conformal holonomy can be obtained by the holonomy of the ambient metric and get results for Riemannian manifolds and plane waves.     

局部对称共形平坦黎曼流形中的紧致子流形

本文研究局部对称共形平坦黎曼流形中具有平行平均曲率向量的紧致子流形的性质，通过一个代数不等式的证明，改进了已有的结果．     

Lorentzian Clairaut submersions

We investigate a class of semi-Riemannian submersions satisfying a Lorentzian analogue of the classical Clairaut's relation for surfaces of revolution. We show that a Lorentzian submersion with one-dimensional fibers is Clairaut if and only if the fibers are totally umbilic with a gradient field as the normal curvature vector field. We also investigate the behavior of timelike and null geodesics in Lorentzian Clairaut submersions. In particular, every null geodesic of a Lorentzian Clairaut submersion with one-dimensional fibers projects to a pregeodesic in the base space with respect to a conformally related metric on the base space if and only if the integrability tensor of the submersion vanishes.     

n-2型黎曼空间的等距对应

<正> §1.导言一个正则的 n 维黎曼空间,若恰有 p 个函数独立的不变量,便称为 p 型的,这样的空间,我们将用 R(n,p)表之.此定义创自 T.Y.Thomas,他并详尽地研究了特殊情况:n=2,p=0,1,2.本文作者假定两个 R(n,n—2)具有结构相同的两组不变式 I_1,     

论数论函数ψ(n),σ(n)及d(n)的一些性质

<正> 命 f(n)为一数论函数.关于函数比值(?)的分布问题,Soma-yajulu,Sierpi(?)ski 及 Schinzel 曾用算术的方法,对于ω(n),σ(n)及 d(n)加以处理.华罗庚教授首先指出用 Brun 节法处理这一类问题的途径.按这一方向,作者与     

Decomposition of spaces with geodesics contained in compact flats

We prove a decomposition result for analytic spaces all of whose geodesics are contained in compact flats. Namely, we prove that a Riemannian manifold is such a space if and only if it admits a (finite) cover which splits as the product of a flat torus with simply connected factors which are either symmetric (of the compact type) or spaces of closed geodesics.

     

Parallel connections over symmetric spaces

Let M be a simply connected Riemannian symmetric space, with at most one flat direction. We show that every Riemannian (or unitary) vector bundle with parallel curvature over M is an associated vector bundle of a canonical principal bundle, with the connection inherited from the principal bundle. The problem of finding Riemannian (or unitary) vector bundles with parallel curvature then reduces to finding representations of the structure group of the canonical principal bundle.     

Some Results on Contact Metric Manifolds

If the sectional curvatures of plane sections containing the characteristic vector field of a contact metric manifold M are non-vanishing, then we prove that a second order parallel tensor on M is a constant multiple of the associated metric tensor. Next, we prove for a contact metric manifold of dimension greater than 3 and whose Ricci operator commutes with the fundamental collineation that, if its Weyl conformal tensor is harmonic, then it is Einstein. We also prove that, if the Lie derivative of the fundamental collineation along the characteristic vector field on a contact metric 3-manifold M satisfies a cyclic condition, then M is either Sasakian or locally isometric to certain canonical Lie-groups with a left invariant metric. Next, we prove that if a three-dimensional Sasakian manifold admits a non-Killing projective vector field, it is of constant curvature 1. Finally, we prove that a conformally recurrent Sasakian manifold is locally isometric to a unit sphere.