Dual gradient method for linearly constrained,strongly convex,separable mathematical programming problems

A new dual gradient method is given to solve linearly constrained, strongly convex, separable mathematical programming problems. The dual problem can be decomposed into one-dimensional problems whose solutions can be computed extremely easily. The dual objective function is shown to have a Lipschitz continuous gradient, and therefore a gradient-type algorithm can be used for solving the dual problem. The primal optimal solution can be obtained from the dual optimal solution in a straightforward way. Convergence proofs and computational results are given.     

具有σ点有限cfp网的空间

本文研究了度量空间的象,引进诱导紧覆盖弱紧映射,建立了具有σ点有限cfp网的空间与度量空间之间的联系,将完善"映射与空间"理论.     

The Cauchy Problems and Global Solutions to the Deybe System and Burgers＇ Equations in Pseudomeasure Spaces

In this paper we consider the Cauchy problems of Burgers＇ equations and the Deybe system. Their existence and uniqueness of the time-global solutions for small initial data in some pseudomeasure spaces are obtained. The asymptotic stability of small solutions is proved. As an immediate result the existence and uniqueness of the self-similar solutions are also obtained provided the initial data satisfy the self-similar structures.     

The Poisson problem with mixed boundary conditions in Sobolev and Besov spaces in non-smooth domains

We introduce certain Sobolev-Besov spaces which are particularly well adapted for measuring the smoothness of data and solutions of mixed boundary value problems in Lipschitz domains. In particular, these are used to obtain sharp well-posedness results for the Poisson problem for the Laplacian with mixed boundary conditions on bounded Lipschitz domains which satisfy a suitable geometric condition introduced by R.Brown in (1994). In this context, we obtain results which generalize those by D.Jerison and C.Kenig (1995) as well as E.Fabes, O.Mendez and M.Mitrea (1998). Applications to Hodge theory and the regularity of Green operators are also presented.

     

Well-bounded operators on nonreflexive Banach spaces

Every well-bounded operator on a reflexive Banach space is of type (B), and hence has a nice integral representation with respect to a spectral family of projections. A longstanding open question in the theory of well-bounded operators is whether there are any nonreflexive Banach spaces with this property. In this paper we extend the known results to show that on a very large class of nonreflexive spaces, one can always find a well-bounded operator which is not of type (B). We also prove that on any Banach space, compact well-bounded operators have a simple representation as a combination of disjoint projections.

     

含间断项的非线性积分、微分方程极解的存在性

在不涉及紧型条件和耗散型条件的情形下，证明了Ｂａｎａｃｈ空间中含间断项的非线性积分、微分方程极解的存在性，推广了文［１］、［２］和［３］中的结果．     

On Minimal Annuli with a Straight Line Boundary

Shiffman proved that if a minimal annulus A in a slab is bounded by two convex Jordan curves contained respectively in the two boundary planes P and Q of the slab, then A intersects all parallel planes between P and Q in strictly convex curves. We generalize Shiffman's result to the case that A is bounded by a strictly convex C² Jordan curve and a straight line. We show that in this case Shiffman's result is still true.     

Neighborhood assignments and cardinal functions: a unified approach to metrization and uniformity

We use neighborhood assignments and cardinal functions to give a unified approach to metrizability and uniformity. This leads to a number of characterizations of m(X), the metrizability degree of X, u(X), the uniform weight of X, and w(X), the weight of X. For X normal (and regular), m(X) = u(X); it is unknown whether this result extends to completely regular spaces.     

区间判断的凸锥模型与排序方法

本文用凸锥模型对层次分析法中区间判断条件下的排序问题进行研究，给出了权重向量的合理算法．并对区间判断下权重向量的合理位置，产生逆序的可能性等重要问题进行了探讨和研究，给出了计算实例．     

The Order Properties of r-compact Operators on Banach Lattices

We present here that F（E,F）, the space of all r-compact operators from E into F, is a generalised sublattice of L^r（E, F） for arbitary Banach lattices E and F, and that the characterization of the regular norm on F（E, F） is order continuous. Some conditions for F（E, F） to be a KB-space or a band in .L（E, F） are also provided.