Sasakia空间型的C—全实伪脐子流形

本文讨论了Ｓａｓａｋｉａｎ空间型的Ｃ－全实伪脐子流形，给出关于第二基本形式长度的一个Ｐｉｎｃｈｉｎｇ定理。     

关于S^n＋p和CP^n＋p中的极小子流形

本文改进了分别由Ｓ．Ｔ．Ｙａｕ，Ａ．Ｒｏｓ及沈一兵给出的关于单位球面Ｓｎ＋ｐ的极小流形和复射影空间ＣＰ＾ｎ＋ｐ的Ｋａｅｈｌｅｒ子流形及全实极小子流形的截面曲率的Ｐｉｎｃｈｉｎｇ常数。     

随机抽样情况下CSP—3方案的流向图方法

本文将转移概率流向衅及转移概率母函数等方法引入到在的抽样检查阶段使用随机抽样方法的连续抽样方案ＣＳＰ－３的平均检出质量ＡＯＱ，平均检查比率ＡＦＩ和操作特性函数Ｌ（Ｐ）等三个指标的讨论中，为探讨ＣＳＰ－３方案提供新途径。     

η—Einstein—Sasaki子流形和它们的谱

本文证明了Ｓａｓａｋｉ空间形式中具有η－平形第二基本形式的η－Ｅｉｎｓｔｅｉｎ－Ｓａｓａｋｉ子流形在某些假定下由它的谱所决定；并给出了复Ｑｕａｄｒｉｃ上的圆周丛的谱特征。     

广义Rudin—Shaprio函数及其性质

为获得动力系统的高阶谱数「１２」，Ｑｕｅｆｆｅｌｅｃ引入了广义（ｑ阶，ｑ≥３）Ｒｕｄｉｎ－Ｓｈａｐｉｒｏ序列｛ｒｋ｝起关键作用的指数和的不等式为：ｍａｘθ│∑ｎ－１ｋ＝０ｒｋｅ＾ｉｋθ│≤Ｃｎ，（ｎ≥１）其中常数Ｃ取值为ｑ＋ｑｑ，本文对广义Ｒｕｄｉｎ－Ｓｈａｐｉｒｏ序列进行了进一步研究，引入了广义Ｒｕｄｉｎ－Ｓｈａｐｉｒｏ函数ψ，将以上系数Ｃ改进为（１＋２）ｑ，并证明了ψ是Ｒ上一个连续但几乎处处不     

CSP—3—R方案的动态平均检出质量

本文引用８中方法和结果，通过对未检产品数等变量的讨论，首次导出了ＣＰＳ－３－Ｒ方案的动态平均检出质量。     

投影寻踪型Cramer—von Mises—Smirnov统计量

为了检验一个总体分布是否服从所给定的分布Ｆ（ｘ），Ｃｒａｍｅｒ－ｖｏｎ Ｍｉｓｅｓ－Ｓｍｉｒｎｏｖ统计量是一种常用的重要工具，对于一维分布，计算表明确切分布很快趋于极限分布。当样本量大于３时，确切分布与极限分布之差就很小，当总体分布是连续分布方法建立Ｃｒａｍｅｒ－ｖｏｎ Ｍｉｓｅｓ－Ｓｍｉｒｎｏｖ统计量，对此统计量尾部概率上界及极限分布，包括当样本很大，维数很高时的极限性质，自助法是否能逼近极限分     

带有中止检查规划（n—i）的CSP—1方案

本文引人转移概率母函数及幂级数等方法讨论带有中止规划（ｎ－ｉ）的连续抽样方案ＣＳＰ－１的中止概率Ｐ，得到了Ｐ作为ＣＳＰ－１方案的度量的理论特性，证明了Ｄｏｄｇｅ型，ＣＳＰ－１方案与带有中止规划的ＣＳＰ－１方案具有相同的ＡＯＱ，ＡＦＩ，ＯＣ函数，文末还给出了一些数值结果。     

USING FINITE GEOMETRIES TO CONSTRUCT 3-PBIB(2) DESIGNS AND 3-DESIGNS

ＵＳＩＮＧＦＩＮＩＴＥＧＥＯＭＥＴＲＩＥＳＴＯＣＯＮＳＴＲＵＣＴ３－ＰＢＩＢ（２）ＤＥＳＩＧＮＳＡＮＤ３－ＤＥＳＩＧＮＳ￥ＹＡＮＧＢＥＮＦＵ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＣｈｅｎｇｄｕＴｅａｃｈｅｒｓＣｏｌｌｅｇｅ，Ｃｈｅｎｇｄｕ...     

关于｛P2,Ci│i≥3｝—覆盖图

设Ｇ是一个图,若对于Ｇ的任意一边Ｇ都有｛Ｐ２,Ｃｉ│ｉ≥３｝－因子含有这条边,则称Ｇ是｛Ｐ２,Ｃｉ│ｉ≥３｝－覆盖图。本文给出连通非二分图Ｇ是｛Ｐ２,Ｃｉ│ｉ≥３｝－覆盖图的充要条件为任给Ｓ包含于Ｖ（Ｇ）,Ｖ（Ｇ）≠Ｓ≠ф有ｉ（Ｇ－Ｓ）≤│Ｓ│－１成立。     

关于复射影空间的三维全实极小子流形

本文给出复射影空间中三维紧致全实极小子流形的Ricci曲率和数量曲率的鞭些拼挤定理.特别是证得:若M³是CP³的紧致全实极小子流形且它的Ricci曲率大于1/6,则M³是全测地的.     

3-Quasi-Sasakian manifolds

In the present article we carry on a systematic study of 3-quasi-Sasakian manifolds. In particular, we prove that the three Reeb vector fields generate an involutive distribution determining a canonical totally geodesic and Riemannian foliation. Locally, the leaves of this foliation turn out to be Lie groups: either the orthogonal group or an abelian one. We show that 3-quasi-Sasakian manifolds have a well-defined rank, obtaining a rank-based classification. Furthermore, we prove a splitting theorem for these manifolds assuming the integrability of one of the almost product structures. Finally, we show that the vertical distribution is a minimum of the corrected energy.      

Anti-Invariant Submanifolds in a.Bochner-Kaehler Manifold

The Properties of submanifolds in a Bochner-Kaehler manifold have been studied mainly in the cases that the submanifolds are totally real by Yano, K., Houh, 0. S. and others. The main purpose of the present paper is to study whether the condition for the submanifold to be totolly real in their theorems is necessary, and to prove some theorems which are analogous to those mentioned above. A submanifold M^n of Kaehlerian manifold M^2m is called totally real or antiinvariant,if each tangent space of M^n is mapped into the normal space by the complex structure $\[{F_{\nu \mu }}\]$ of M^2m. Similarly, a submanifold M^n of Kaehlerian manifold M^2m is called anti-in variant with respect to L', if each tangent space of M^n is mapped into the normal space by the operator L' of M^2m. We obtain: (1) A necessary and sufficient condition for a totally umbilical submanifold M^n, n>3, in a Boohner-Kaehler manifold M^2m to be conformally flat is that the submanifold M^n is either a totally real submanifold or an anti-invariant submanifold with respect to L'. (2) Let M^n be the submanifold immersed in a Boohner-Kaehler manifold M^2m. If each tangent vector of M^n is Ricci principal direction and Ricci principal curvature $\[{\rho _h}\]$ does not equal $[\frac{{\tilde K}}{{4(m + 1)}}\]$ , then the anti-invariant submanifold with respect to L^' coincides with the totally real submanifold. (3) Let M^n be a totally umbilical submanifold immersed in a Boohner-Kaehler manifold M^2m If M^n is a totally real submanifold or an anti-invariant submanifold,then the sectional curvature of Mn is given by $[\rho (u,v) = \frac{1}{8}(\tilde K(u) + \tilde K(v)) + \sum\limits_{x = n + 1}^{2m} {{H^2}} ({e_x})\]$(A) where H(e_x) =H_x. Conversely, if the sectional curvature of M^n satisfying the condition mentioned in (2) is given by (A) for any two orthonormal tangent vectors u^\alpha and $v^\alpha$ then M^n is a totally real submanifold.     

Some remarks on pseudo-umbilical totally real submanifolds in a complex projective space

This paper studies the relationship between the pseudo-umbilical totally real submanifolds and the minimal totally real submanifolds in a complex projective space. Two theo- rems which claim that some types of pseudo-umbilical totally real submanifolds must be minimal submanifolds are proved.     

Topological parallelisms of the real projective 3-space

A parallelism of a projective 3-space Π is a family P of spreads such that each line of Π is contained in exactly one spread of P. A parallelism is said to be totally regular, if all its members are regular spreads. By a generalized line star with respect to an elliptic quadric Q of a classical projective 3-space we understand a set $\cal A$ of 2-secants of Q such that each non-interior point of Q is incident with exactly one line of $\cal A$ . From each generalized line star we can construct a totally regular parallelism which we do in essential by the Thas-Walker construction. A parallelisms of the real projective 3-space PG(3, ?) is called topological, if the operation of drawing a line parallel to a given line through a given point is continuous. Clifford parallelisms are topological. Using generalized line stars we exhibit examples of non-Clifford topological parallelisms and of non-topological parallelisms.     

TOTALLY REAL MINIMAL SUBMANIFOLDS IN A QUATERNION PROJECTIVE SPACE

Some curvature pinching theorems for compact totally real minimal submanifolds in a quaternion projective space axe given, so that the corresponding results due to B. Y. Chen and C. S. Houh in [1] are improved.     

具有半对称度量联络的复空间型中全实子流形的Chen型不等式

In this paper, we obtain Chen＇s inequalities for totally real submanifolds in complex space forms with a semi-symmetric metric connection. Also, some results of A. Mihai and C. Ozgiir＇s paper have been modified.     

Totally Real Minimal Submanifolds in a Quaternion Projective Space

51.IntroductionAquaternionKaehlermanifoldisdefinedasa4m-dimensionalRiemannianmanifoldwhoseholonomygroupiscontainedinSp(m).Sp(1)withtheadditionalconditionform=lthatitisaself-dualEinsteinspace.AquaternionprojectivespaceQP:)isaquaternionKeahlermanifoldwithconstantquaternionsectionalcurvaturec>O.AcomplexprojectivespaceCP2)withconstantholomorphicsectionalcurvatureccanbeisometricallyimbeddedinQP:)asatthtallygeodesicsubmanifold.LetMbeannsidimensionalRiemannianmanifoldander:M-Qer).-.'an1sometr1…     

复射影空间CPn+p中的全实2-调和子流形

本文研究了复射影空间中的全实2 -调和子流形问题.利用活动标架法,获得了这类子流形成为极小子流形的关于第二基本形式模长的Pinching定理及一个积分不等式.此外还得到关于全实2-调和伪脐子流形的一些刚性定理,推广了CPn中全实2-调和子流形的一些相应结果.     

Local C~k──boundary Regularity of Integral Solution Operators of the ──equations on Open Set with Piecewise C~1──boundary

ＬｏｃａｌＣ~ｋ──ｂｏｕｎｄａｒｙＲｅｇｕｌａｒｉｔｙｏｆＩｎｔｅｇｒａｌＳｏｌｕｔｉｏｎＯｐｅｒａｔｏｒｓｏｆｔｈｅ ──ｅｑｕａｔｉｏｎｓｏｎＯｐｅｎＳｅｔｗｉｔｈＰｉｅｃｅｗｉｓｅＣ~１──ｂｏｕｎｄａｒｙ￥ＭａＺｈｏｎｇｔａｉ（Ｄｅｐｔ．Ｏ?..