凸子

Let X be a reflexive Banach space with both X and X locally uniformly convex. D is a bounded, open, convex subset of X. T∶D→X is a pseudo-monotone operator; C∶D→X is a compact or strongly continuous operator.

何震设X是自反Banach空间且X和X均为局部一致凸空间，D是X的开、有界、凸子集， T∶D→X是伪单调算子(pseudo-monotone)， C∶D→X是紧算子或全连续算子。

We prove an extension of the representation theorem of the convex pricing rule. We also give the corresponding probabilistic repre-sentation theorem of the convex pricing rule in a financial market with convex constraints.

我们证明了凸价格算子相应的表示定理，并给出了在凸约束的金融市场下凸价格算子的一个概率表达式。

The contents are the following:In chapter two, the existence and multiplicity results for the following equation of p-Laplacian type are obtained.For the elliptic quasilinear hemivariational inequality involving the p-Laplacian operator,in order to use the mountain pass theorem proving the existence result, the authors usually need to use the uniform convexity of the Sobolev space to prove the energy function satisfies the PS condition. But for the p-Laplacian type equation mentioned above, this method is no use. To overcome this difficulty, the potential function is assumed to be convex, then I prove the existence result and by using the extension of the Ricceri theorem, the multiplicity result for the problem is obtained.

在第二章我们首先考虑关于以下p-Laplacian型(p-Laplacian type)方程非平凡解及多解的存在性对于带有p-Laplacian算子的椭圆拟线性半边分不等式问题，为应用非光滑的山路引理证明解的存在性，在证明方程所对应的能量泛函满足非光滑的PS条件时，需利用Sobolev空间的一致凸性，但是对于具有更一般形式的算子的p-Laplacian型方程，不具备上述性质，在文中为克服这一困难，本人对位势泛函做了一致凸的假设，从而证明了解的存在性，并应用推广的Ricceri定理，证明了方程三个解的存在性。

Systems of inqualities,the minimum or maximum of a convex function over a convex set,Lagrange multipliers,and minimax theorems are among the topic treated,as well as basic results about the structure of convex sets and continuity and differentiability of convex functions and saddle-functions.

其中对不等式系统、凸集上的凸函数的极小或极大、拉格朗日乘子和极小极大定理做了专题论述，同时对凸集的结构和连续性以及凸函数的可微性和鞍点函数的基本结果做了介绍。

A theorem of the alternative for the generalized subconvexlike set-valued maps is established using the separation theorem of convex sets in a Banach spaces, the concept of weak Benson proper efficient elements for a vector optimization problem is introduced, and the optimality necessary and sufficient Lagrange conditions for a vector set-valued map constrained optimization problem with the weak Benson proper efficiency is developed, with which the optimality Lagrange conditions for a nonconvex vector top-base constrained optimization of set-valued maps with the Benson proper efficiency are obtained.

刘莹 ，刘三阳，盛宝怀运用凸集分离定理对广义锥次类凸集值映射建立了一种择一性定理。引入向量优化弱Benson真有效元的概念，对带约束的非凸向量集值优化问题建立了在弱Benson真有效意义下有效元应满足Lagrange乘子型的必要及充分条件，并用这一结果建立了多目标主从非凸向量集值优化在弱Benson真有效意义下最优解的Lagrange乘子型充要条件。

Chapter 4 -rotundity and nearly strict convexity of quotient spaces. It is proved that ifis a -rotund or nearly strict convex Banach space andis a closed and proximinal subspace of, then the quotient spaceis also -rotund or nearly strict convex.

第四章 商空间的-严格凸性和近严格凸性：本章证明了若是Banach空间的任意可逼近子空间，则商空间对原空间的-严格凸性和近严格凸性都具有遗传性。

An example of these maximal monotone operators is the subdifferential of a closed convex function.

这种多值极大单调算子的一个特殊例子是闭凸函数的下微分算子，所以本文考虑的多值随机微分方程包含了在凸区域内具有反射边界的随机微分方程。

That the cam-bore to valve/tappet dimensions are gauged with the head bolted to the block.

校对凸轮孔到气阀/凸子的距离时，顶盖已被螺钉固定在机体。

This chapter is dedicated to the study of the properties of close-to-convex univalent harmonic mappings.

在这一章中，我们主要研究了单叶调和映照的近于凸子族，首先给出了近于凸单叶调和映照与正实部解析函数之间的一个关系。

NC-products roller bearings, roller Outer Ring Road crown ultra-precision machine; NC roller bearings inside and outside circle Raceway crown grinder; NC roller bearings inside and outside circle Ribs grinder; NC car wheels first, Second and third generation, the outer ring-channel grinder, and other equipment in the domestic series with industry leading level.

主导产品数控滚子轴承内、外圈滚道凸度超精机；数控滚子轴承内外圈滚道凸度磨床；数控滚子轴承内外圈挡边磨床；数控汽车轮毂第一、二、三代内、外圈沟道磨床等系列设备在国内同行业中处于领先水平。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。