对偶算法的进一步研究

The dual algorithm for minimax problems is further studied in this paper. The resulting theoretical analysis shows that the condition number of the corresponding Hessian of the smooth modified Lagrange function with changing parameter in the dual algorithm is proportional to the reciprocal of the parameter,which is very important for the efficiency of the dual algorithm. At last ,the numerical experiments are reported to validate the analysis results.     

Weak Density of Smooth Maps in W 1, 1(M,N) for Non-Abelian π1(N)

We prove that smooth maps are dense in the sense of biting convergence in W ^{1, 1}(M, N) when M and Nare compact Riemannian manifolds and N is closed.     

Generalized projection and approximation of fixed points of nonself maps

Let K be a nonempty closed convex proper subset of a real uniformly convex and uniformly smooth Banach space E; T:K→E be an asymptotically weakly suppressive, asymptotically weakly contractive or asymptotically nonextensive map with F(T){xK: Tx=x}≠. Using the notion of generalized projection, iterative methods for approximating fixed points of T are studied. Convergence theorems with estimates of convergence rates are proved. Furthermore, the stability of the methods with respect to perturbations of the operators and with respect to perturbations of the constraint sets are also established.     

A SMOOTH C1 INTERPOLATION FOR TWO-DIMENSIONAL CONTACT PROBLEMS USING PARAMETRIC CURVE TECHNIQUE

A smooth C1 interpolation for two-dimensional contact problems using paxametric curve technique was developed and implemented. The parametric curve can ensure C1 continuity of the contact surfaces and provide a unique surface normal vector. Some numerical examples were used to illustrate the advantages of the newly developed representation of contact surface. The results reveal a significant improvement in the prediction of contact stresses and contactarea. The predicted contact stresses are less sensitive to the mismatch in meshes of the different contacting bodies.     

Lipschitz局部严格伪压缩映象的迭代逼近

设Ｋ是一致光滑Ｂａｎａｃｈ空间Ｋ的非空子集，Ｔ：Ｋ→Ｘ是Ｌｉｐｓｃｈｉｔｚ局部严格伪压缩映象。本文给出一个迭代序列强收敛到Ｔ的唯一不动点，并给出一个涉及Ｌｉｐｓｃｈｉｔｚ局部强增殖映象Ｔ的非线性方程Ｔｘ＝ｆ的解的迭代逼近。     

求解单阶段随机规划的一种光滑逼近法

本文借助某种离散方式把单阶段随机规划问题转化为具有多个约束的确定性非线性规划，然后利用极大熵函数方法，把此确定性规划转化为只带简单约束的非线性规划，由此提出了求解这种随机规划的光滑逼近法，同时给出了该法的收敛性分析，较好地克服了因提高离散精度导致约束函数个数迅速增大所带来的求解困难．     

EQUIVARIANT SELF EQUIVALENCES OF PRINCIPAL FIBRE BUNDLES

Let E be a compact Lie group, G a closed subgroup of E, and H a closed normal sub-group of G. For principal fibre bundle (E,p, E,/G;G) tmd (E/H,p‘,E/G;G/H), the relation between auta(E) (resp. autce (E)) and autG/H(E/H) (resp. autGe/H(E/H)) is investigated by using bundle map theory and transformation group theory. It will enable us to compute the group JG(E) (resp. SG(E)) while the group J G/u(E/H) is known.     

The cobordism classification of involution on DOLD manifoldP(1,2l)

Supposing the smooth involution of the DOLD manifoldP(1,2l) satisfies the following condition: the fiberation π:P(1,2l)× _T×(−1)S^∞→RP(∞) is totally nonhomologous to zero (cf. [1, p373]), this paper determines the classification of smooth involution on the DOLD manifoldP(1,2l) totally. Supported by the Foundation of Tian Yuan and the Natural Science Foundation of Hebei province.     

具非线性边界条件的奇异扩散方程

本文讨论具非线性第二边界条件的一端无界的奇异扩散方程的初边值间题,利用先验估计方法得到的主要结果是:存在唯一的整体光滑解,且解连续依赖于初值．     

Three-step iterations for nonlinear accretive operator equations

In this paper, we suggest and analyze a three-step iterative scheme for solving nonlinear strongly accretive operator equation Tx=f without continuous condition in a uniformly smooth Banach space. Our results include the Ishikawa, Mann and Noor iterations as special cases. The results presented in this paper improve and extend almost all the current results in the more general setting.