Theoretical Studies on Adsorption Sites and States of O and N on Ni（311）

The adsorption of O and N atoms on the Ni(311) surface was investigated by the 5-parameter Morse potential(5-MP) method in detail. For the O-Ni(311) system, there are three surface adsorption states and thefcc-3-fold site is metastable; the frequency of 75 meV[67 meV in high resolution electron energy loss spectroscopy(HREELS) experiment] is attributed to the vibration at the hcp-3-fold site. For the N-Ni(311) system, however, there are only two surface adsorption states(no surface adsorption state was calculated at fcc-3-fold site). In addition, subsurface states were predicted and all critical characteris-tics were obtained for the two systems.     

Improved bounds for interatomic distance in Morse clusters

We improve the best known lower bounds on the distance between two points of an optimal Morse cluster, with ρ[4.967,15]. We develop a generalization of a method previously applied to the Lennard-Jones potential, that also leads to improvements of lower bounds for the Morse potential.     

Hypersurfaces in ℝn and critical points in their external region

In this paper we study the hypersurfaces given as connected compact regular fibers of a differentiable map , in the cases in which has finitely many nondegenerate critical points in the unbounded component of .     

Existence and multiplicity results for classes of elliptic resonant problems

In this paper we prove some new existence results of nontrivial solutions for classes of elliptic resonant problems. We also establish several multiplicity results. The methods used here are based on combining the minimax methods and the Morse theory especially some new observations on the critical groups of a local linking-type degenerate critical point.     

几何分析中的基本概念与原理

本文是根据作者在中国科学院“中德几何分析伙伴小组”成立仪式上的演讲整理而成，主要目的在于通过回顾几何分析中的基本概念及基本定理，了解现阶段的研究情况和将来的研究线路，主要描述黎曼几何与量子场论中的思想，特别特别是极化物理量与几何量产生的变分问题。     

Focal sets of hypersurfaces

Let M ? R ⁿ⁺¹ be a compact connected smooth hypersurface, and let W ? R ⁿ⁺¹ be the area bounded by M. We study the question: Does W contain a principal centre of curvature for some point of M?     

On the differentiability of optimal values for bounded nonlinear programs with equality constraints

We consider a parametrized family of nonlinear programs where the feasible region is defined by equality constraints in a ball. The global optimal value is shown to be twice continuously differentiable over an open and dense set in the perturbation parameter space.     

Singular limit laminations, Morse index, and positive scalar curvature

For any 3-manifold M³ and any nonnegative integer g, we give here examples of metrics on M each of which has a sequence of embedded minimal surfaces of genus g and without Morse index bounds. On any spherical space form we construct such a metric with positive scalar curvature. More generally, we construct such a metric with Scal>0 (and such surfaces) on any 3-manifold which carries a metric with Scal>0.     

The stability theorem for smooth pseudoisotopies

The stability theorem states that the suspension map C(M) C(M X I) defined on the pseudoisotopy space C(M)=Diff(M X I rel M X O U M X I) of a compact smooth n-manifold M is n/3-connected. This implies that C(M) has the R~ n/3-homotopy type of the stable pseudoisotopy space P(M) which is related to Waldhausen's algebraic K-theory of spaces by Waldhausen's formula A(X) S(X₊) X B2P(X). This paper gives a detailed proof of the smooth stability theorem following ideas by Hatcher for the proof of a PL stability theorem.Supported by NSF Grant No. MCS-85-02317.