Epidifferentiability of the map of infima in Hilbert spaces

This article deals with derivatives for set-valued maps that take values in ordered vector spaces, in particular it concerns about the relationship between the epiderivatives of a set-valued map and its associated map of infima. When the image space is a real separable Hilbert space ordered by an orthonormal basis, by using a variational technique based on a decoupling of the ordering cone into half-spaces, we show that both epiderivatives coincide under certain hypothesis of compactness and stability. Furthermore we obtain some computation formulas for these derivatives in terms of associated scalar set-valued maps.     

确界原理的一个修正证明

分析了华东师大版《数学分析》（第四版）教材中关于确界原理证明的不足之处,给出更为细致的修正证明.     

FIXED POINTS OF INCREASING OPERATORS IN ORDERED SPACE WITH APPLICATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｖｅｓｔｉｇａｔｉｎｇｔｈｅｆｏｌｌｏｗｉｎｇｂｏｕｎｄａｒｙｐｒｏｂｌｅｍｉｎｏｒｄｉｎａｒｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎ :¨ｘ+ｆ(ｔ,ｘ(ｔ) ) =0 ,ａ<ｔ<ｂ,αｘ(ａ) -β ｘ(ａ) =0 ,γｘ(ｂ) +δ ｘ(ｂ) =0 ,( 1 )ｗｈｅｒｅα ,β,γ ,δ≥ 0 ,Δ=(ｂ-ａ)αγ+αδ+ βγ>0 .ｆ(ｔ,ｓ)ｍａｙｂｅｓｉｎｇｕｌａｒｉｎｔ =ａ ,ｂ.Ｉｔｈａｓｂｅｅｎｄｉｒｅｃｔｌｙｖｅｒｉｆｉｅｄｔｈａｔｘ(ｔ)ｉｓｔｈｅｓｏｌｕｔｉｏｎｏｆ( 1 )ｉｎＣ2 [ａ ,ｂ]ｉｆａｎｄｏｎｌｙｉｆｘ(…     

广义FGM Copula的一个判定定理及应用

研究了形如C_θ(u,v)=uv θu~av~b(1-u~m)~c(1-v~n)~d的一种新型广义FGM copula中参数θ的精确取值范围．所研究的copula含盖了文献中许多特殊类型的FGM copula,具有广泛的代表性．参数θ的计算方法简单易行,改进并完善了文献中相应的结论．     

关于Hardy不等式的加强改进

对 Hardy不等式 ,建立如下结构的加强不等式 :∑∞n=11n∑nk=1akp 1 ,an≥ 0 (n∈ N) ,0 <∑∞n=1apn<∞ ,Cp=1 -(1 -p- 1) p- 1,p≥ 2 ;1 -p- 1,1 相似文献   

暂留Bessel过程的将来极小值及其位置的联合分布

对暂留 Ｂｅｓｓｅｌ过程 Ｘ,令 Ｉ（ｔ）＝ｉｎｆ_s≥tＸ（ｓ）及　ξ（ｔ）＝ｉｎｆ｛ｕ≥ｔ：Ｘ（ｕ）＝Ｉ（ｔ）｝,本文求出了Ｉ（ｔ）,　ξ（ｔ）及Ｘ_t的联合分布。     

Orthogonal partitions in designed experiments

A survey is given of the statistical theory of orthogonal partitions on a finite set. Orthogonality, closure under suprema, and one trivial partition give an orthogonal decomposition of the corresponding vector space into subspaces indexed by the partitions. These conditions plus uniformity, closure under infima and the other trivial partition give association schemes. Examples covered by the theory include Latin squares, orthogonal arrays, semilattices of subgroups, and partitions defined by the ancestral subsets of a partially ordered set (the poset block structures).Isomorphism, equivalence and duality are discussed, and the automorphism groups given in some cases. Finally, the ideas are illustrated by some examples of real experiments.Dedicated to Hanfried Lenz on the occasion of his 80th birthday.     

暂留Brown运动的极大游程与极小游程

对于暂留Ｂｒｏｗｎ运动,我们给出了极大游程与极小游程的若干定义,并且求出了极大游程（极小游程）的分布,以及极大游程（极小游程）与首达极大时（首达极小时）的联合分布．作为推论求出了首达极大时与首达极小时的分布。     

属性粗糙集的新型近似算子

由等价类中元素属性测度的上、下确界定义的属性粗糙集,没有充分反映等价类中其它元素的作用,在信息处理中不免造成元素信息的丢失.为此提出一种新的属性粗糙集近似算子的表示方法,给出了相应的性质并实例说明了这一方法的合理性.