含k-次增生算子的Ishikawa迭代的收敛性问题

主要研究了非线性方程x Tx=f的Ishikawa迭代解．其中T为k-次增生的或增生的，并在一致光滑和任意的实Banach空间分别研究了上述方程的带误差的Ishikawa迭代解，从而推广了已知的一些结果。     

Non-compact generalized variational inequalities for quasi-monotone and hemi-continuous operators with applications

Some results are obtained for non-compact cases in topological vector spaces for the existence problem of solutions for some set-valued variational inequalities with quasi-monotone and lower hemi-continuous operators, and with quasi-semi-monotone and upper hemi-continuous operators. Some applications are given in non-reflexive Banach spaces for these existence problems of solutions and for perturbation problems for these set-valued variational inequalities with quasi-monotone and quasi-semi-monotone operators. This revised version was published online in June 2006 with corrections to the Cover Date.     

狄拉克方程的单旋量解法以及由此引起的认识上的差异

把狄拉克方程分解成了两个单旋量的联立方程组．指出现行的自旋理论仅考虑了其中的一个方程，是以一个单旋量代替双旋量来描述状态而建立起来的．笔者在认同现行自旋理论可以作为狄拉克方程的一种求解方法，因而同意其中的某些提法外，对于其主要的物理观念：微观粒子存在着独立于现实的位形空间之外的一个自旋空间，在这个自旋空间内禀着角动量S和磁矩μ；这个自旋理论是相对论性量子力学导出的必然结论等等看法予以否定．笔者认为，只有同时考虑两个单旋量的方程，同时计及两个单旋量，才能准确地描述状态，从而正确地描述客观规律．     

Banach空间中二阶积分-微分方程的初值问题

使用锥理论及单调迭代技术，首先讨论了Banach空间中一阶积分-微分方程初值问题的最小最大解的存在性，并在此基础上讨论了带有一阶微分项的二阶积分-微分方程初值问题的最小最大解的存在性。     

Back Reaction in Static Einstein Spaces—Change of Entropy

Using the thermodynamical approach and the method of York, the back-reaction of anti-de Sitter Schwarzschild black hole in thermal equilibrium with conformal spin-2 field is studied. It is found that both approaches give identical results.     

Optimally Dense Packings of Hyperbolic Space

In previous work, a probabilistic approach to controlling difficulties of density in hyperbolic space led to a workable notion of optimal density for packings of bodies. In this paper we extend an ergodic theorem of Nevo to provide an appropriate definition of those packings to be considered optimally dense. Examples are given to illustrate various aspects of the density problem, in particular the shift in emphasis from the analysis of individual packings to spaces of packings.     

A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space

We provide a local as well as a semilocal convergence analysis for two-point Newton-like methods in a Banach space setting under very general Lipschitz type conditions. Our equation contains a Fréchet differentiable operator F and another operator G whose differentiability is not assumed. Using more precise majorizing sequences than before we provide sufficient convergence conditions for Newton-like methods to a locally unique solution of equation F(x)+G(x)=0. In the semilocal case we show under weaker conditions that our error estimates on the distances involved are finer and the information on the location of the solution at least as precise as in earlier results. In the local case a larger radius of convergence is obtained. Several numerical examples are provided to show that our results compare favorably with earlier ones. As a special case we show that the famous Newton-Kantorovich hypothesis is weakened under the same hypotheses as the ones contained in the Newton-Kantorovich theorem.     

Variation Preserving Extensions and Generalized Essential Variation

A mapping from a subset of the real axis to a metric space with finite generalized variation is shown to admit extension to a mapping of the whole real axis with the same variation. This result leads to characterization of the generalized essential variation of a mapping.     

Extended Cesàro operators on Bergman spaces

We define an extended Cesàro operator T_g with holomorphic symbol g in the unit ball B of Cⁿ. For a large class of weights w we characterize those g for which T_g is bounded (or compact) from Bergman space L^p_a,w(B) to L^q_a,w(B), 0<p,q<∞. In addition, we obtain some results about equivalent norms, the norm of point evaluation functionals, and the interpolation sequences on L^p_a,w(B).     

On the Image Regularity Condition

In this paper, we continue the analysis of the image regularity condition (IRC) as introduced in a previous paper where we have proved that IRC implies the existence of generalized Lagrange-John multipliers with first component equal to 1. The term generalized is connected with the fact that the separation (in the image space) is not necessarily linear (when we have classic Lagrange-John multipliers), but it can be also nonlinear. Here, we prove that the IRC guarantees, also in the nondifferentiable case, the fact that 0 is a solution of the first-order homogeneized (linearized) problem obtained by means of the Dini-Hadamard derivatives.