Finsler几何中Cartan联络的存在性

用纤维丛理论证明Ｃａｒｔａｎ联络的存在性。先利用对偶原理，指出Ｆｉｎｓｌｅｒ联络（Ｔ，Ｎ）可改由一次微分式ω＾ａ ｂ，（θ＾ｕ）＾ａ确定，然后提出ω＾ａ ｂ（θ＾ｖ）＾ａ的系数Γ＾ｉ ｊｋ，Ｃ＾ｉ ｊｋ及Ｎ＾ｉ ｊ应满足的充要条件，最后验证了由Ｃａｒｔａｎ联络的５条公理得出的函数组Γ＾ｉ ｊｋ，Ｃ＾ｉ ｊｋ，Ｎ＾ｉ ｊ满足这些条件，从而证明了Ｃａｒｔａｎ联络的存在性。     

软件演化过程的度量数据采集策略研究

度量数据的采集是度量软件过程的重要环节,讨论了度量数据的采集过程中遇到的问题,以及有效数据采集应遵循的原则,并针对软件演化过程的特点及不同的应用提出了2种数据采集的策略．     

连续函数超空间

基于空间X到空间Y的连续函数族作为乘积空间X×Y的闭子集组成的超空间CL(X×Y)的子空间 ,在限制Y为Hilbert方体Q时 ,得到连续函数超空间C(X ,Q)同胚于Q的伪内部s;在限制X为单位闭区间I时 ,考虑连续函数超空间C(I,Y)在CL(I×Y)中的闭包 ,得到其元素到Y的投影是连续统 ,且投影随I中的点连续变化 ,并举例说明了即使X为单位圆盘 ,上述第二个结论也不能成立 .     

超球上关于不变度量的（0，q）-Green式的性质

证明了：对任一（0,q)式g(z)=1/q!g_Aq(z)dz^Aq,其系数gAq-(z)满足:gAq(z)/1-|z|^2在B^n-连续，则有□w∫Bng(z)∧*N(z,w)=g(w)。     

lonApollonian度量及其应用(英文)

利用变换和模给出了Apollonian度量的解析表达式 ,建立了Apollonian度量与双曲度量的联系 ,得到了拟圆的一个充分条件。最后 ,作为应用给出了著名的Koebe’s 14 定理的一个新证明     

完备凸度量空间中Ishikawa迭代序列强收敛到两个映射的公共不动点定理

在完备凸度量空间(X,ρ)中,设S、T是满足条件(A)或(B)的闭凸子集上的两个自映射,从两方面研究了映射S、T的公共不动点问题:1.如果映射S、T生成的Ishikawa迭代序列强收敛,则收敛点为S、T的公共不动点;2.如果S、T的公共不动点非空,则映射S、T生成的Ishikawa迭代序列强收敛到S、T的公共不动点.结论改善并推广了部分作者的相关结果[1~5],[7~8].     

拟双曲一致域与弱拟对称映射

根据拟双曲一致域和拟对称映射的基本性质,利用拟双曲度量作为研究的重要工具,主要讨论了度量空间中拟双曲一致域的几何性质,同时刻画了拟双曲一致域在弱拟对称映射下仍然是保持不变的.     

Some classes of Kenmotsu manifolds with respect to semi-symmetric metric connection

In this paper, we study conharmonic curvature tensor in Kenmotsu manifolds with respect to semi-symmetric metric connection and also characterize conharmonically flat, conharmonically semi-symmetric and φ-conharmonically flat Kenmotsu manifolds with respect to semi-symmetric metric connection.     

Privacy Quantification Model Based on the Bayes Conditional Risk in Location-Based Services

The widespread use of Location-Based Services(LBSs),which allows untrusted service providers to collect large quantities of information regarding users’locations,has raised serious privacy concerns.In response to these issues,a variety of LBS Privacy Protection Mechanisms(LPPMs)have been recently proposed.However,evaluating these LPPMs remains problematic because of the absence of a generic adversarial model for most existing privacy metrics.In particular,the relationships between these metrics have not been examined in depth under a common adversarial model,leading to a possible selection of the inappropriate metric,which runs the risk of wrongly evaluating LPPMs.In this paper,we address these issues by proposing a privacy quantification model,which is based on Bayes conditional privacy,to specify a general adversarial model.This model employs a general definition of conditional privacy regarding the adversary’s estimation error to compare the different LBS privacy metrics.Moreover,we present a theoretical analysis for specifying how to connect our metric with other popular LBS privacy metrics.We show that our privacy quantification model permits interpretation and comparison of various popular LBS privacy metrics under a common perspective.Our results contribute to a better understanding of how privacy properties can be measured,as well as to the better selection of the most appropriate metric for any given LBS application.     

Sobolev H1 geometry of the symplectomorphism group

For a closed symplectic manifold $(M,\omega )$ with compatible Riemannian metric g we study the Sobolev $H^1$ geometry of the group of all $H^s$ diffeomorphisms on M which preserve the symplectic structure. We show that, for sufficiently large s, the $H^1$ metric admits globally defined geodesics and the corresponding exponential map is a non-linear Fredholm map of index zero. Finally, we show that the $H^1$ metric carries conjugate points via some simple examples.