广义凸集的支撑函数

本文讨论了笔者在[1]中提出的伪凸集,拟凸集的支撑函数与障碍锥的性质,并通过这些性质得出了二个闭性准则。     

凸度量空间中非扩张映象的不动点定理

设X是一凸度量空间,并且它的每一直径趋于零的非空闭子集的逆减序列具有非空交的性质.本文证明了,如果X的非空闭子集K的自映象T满足不等式:d(Tx,Ty)≤ad(x,y) b{d(x,Tx) d(y,Ty)} c{d(x,Ty) d(y,Tx)},(?)x,y∈K其中0≤a<1,b≥0,c≥0,使得a c≠0且a 2b 3c≤1.则T在K中存在唯一不动点.     

Fractional-Linear Transformations of Operator Balls; Applications to Dynamical Systems

The operator sets, which are the subject of this paper, have been studied in many papers where, under different restrictions on the generating operators, convexity, compactness in the weak operator topology, and nonemptiness were proved for sets of different classes under study. Then the results obtained were used in these papers to solve several applied problems. Namely, they played the key role in establishing the dichotomy of nonautonomous dynamical systems, with either continuous or discrete time. In the present paper, we generalize and sharpen the already known criteria and obtain several new criteria for convexity, compactness, and nonemptiness of several special operator sets. Then, using the assertions obtained, we construct examples of sets of the form under study which are nonconvex, noncompact in the weak operator topology, as well as empty, and are generated by ＂smooth＂ operators of a special class. The existence problem for such sets remained open until the authors of this paper announced some of its results.     

部分变量带非负约束的严格凸二次规划问题的新算法

本将正交校正共轭梯度法推广来解只有部分变量带非负约束而其它变量无约束的严格凸二次规划，所建立的新算法的优点是：在迭代过程中，不用求逆矩阵，这样能保持矩阵的稀疏性，数值结果表明，算法对大规模稀疏二次规划问题是可行和有效的。     

多目标分数变分问题的对偶性

本文利用参数逼近在函数广义（F，ρ）－凸的条件下，建立了一类多目标式变分问题关于有效解的对偶理论。     

赋范空间中的相对Chebyshev中心

在本文中,我们得到了下列结论: 定理1 设F是赋范空间E的有界子集,Y是E的凸子集,0∈Y则     

双全纯映照的一些偏微分不等式

该文在有界星形圆型域上建立一些与双全纯星形映照有关的偏微分不等式．作为应用，给出有界星形圆型域上ε星形映照以及近似星形映照的一些充分判别条件．     

一种基于预测分类的小波图像编码

对于小波较像编码，如何有效地组织小波域系数是提高图像压缩效果的关键。本文在研究小波域系数统计特性的基础上，提出一种用于图像压缩的预测分类模式，与基于零树结构的编码不同的是它充分利用了小波域中“重要”系数的各种相关性，并通过结合提出的种子膨胀算法实现系数的分类输出，实验结果表明该方法所取得的压缩效果要优于基于零树结构的图像编码，同时又具有较强的鲁棒性。     

Backlund transformation and variable separation solutions for the generalized Nozhnik—Novikov—Veselov equation

Using the extended homogeneous balance method, the B?cklund transformation for a (2+1)-dimensional integrable model, the generalized Nizhnik－Novikov－Veselov (GNNV) equation, is first obtained. Also, making use of the B?cklund transformation, the GNNV equation is changed into three equations: linear, bilinear and trilinear form equations. Starting from these three equations, a rather general variable separation solution of the model is constructed. The abundant localized coherent structures of the model can be induced by the entrance of two variable-separated arbitrary functions.     

双－全氟烷基氮氧自由基从取代苯甲醛的攫氢反应──用EPR方法建立取代基自旋离域参数σ的新尝试

Ｒ_ＦＮ（Ｏ　）Ｒ_Ｆ和Ｒ_ＦＮＯ的Ｆ１１３溶液在室温下与一系列的对位取代苯甲醛反应，得到稳定的对位取代苯甲酰基全氟烷基氮氧自由基。由△ａ_Ｎ和△ａ_Ｆ~β的σ单参数相关以及△ａ_Ｎ与σ和σ　双参数相关表明：极性效应是影响氟烷基酰基氮氧自由基中氮原子自旋密度变化的主要因素，而自旋离域效应的影响是很小的。