面积比较与上调和函数及其应用

本文研究了无穷远处具非负截曲率的完备非紧流形的几何和解析性质,并将 它应用于调和映照.     

Benson真有效意义下集值优化的广义最优性条件

本文引入了关于集值映射的α-阶Clarke切导数、α-阶邻接切导数及α-阶 伴随切导数的概念,借此建立了约束向量集值优化Benson真有效解导数型的Kuhn- Tucker条件.     

Remarks on a Noble''''s Theorem

Noble proved the following Theorem: If A (?) X with a nonisolated point and B (?) Y, then A × B is bounded in X×Y if and only if the projection map π : X × Y → X is a z-map with respect to A × B and A, A is bounded in X and B is bounded in Y. In this note, we give two examples showing the necessary and sufficient conditions of Noble's theorem are not right.     

Connecting orbits among Denjoy minimal sets for monotone twist map

In a Birkhoff region of instability for an exact area-preserving twist map, we construct some orbits connecting distinct Denjoy minimal sets. These sets correspond to the local, instead of global minimum of the Lagrangian action. In the earlier work, Mather constructed connecting orbits among Aubry-Mather sets and the global minimizer of the Lagrangian action.     

Compact Kähler Surfaces with Trivial Canonical Bundle

The classical conjectures of Weil on K3 surfaces – that the set of suchsurfaces is connected; that a version of the Torelli theorem holds; thateach such surface is Kähler; and that the period map issurjective – are reconsidered in the light of a generalisation of theNakai–Moishezon criterion, and short proofs of all the conjectures aregiven. Most of the proofs apply equally or with minor variation tocomplex 2-tori, the only other compact Kähler surfaces with trivialcanonical bundle.     

New Component of the Moduli Space M(2;0,3) of Stable Vector Bundles on the Double Space P 3 of Index Two

We study the moduli scheme M(2;0,n) of rank-2 stable vector bundles with Chern classes c ₁=0, c ₂=n, on the Fano threefold X – the double space P ³ of index two. New component of this scheme is produced via the Serre construction using certain families of curves on X. In particular, we show that the Abel–Jacobi map :HJ(X) of any irreducible component H of the Hilbert scheme of X containing smooth elliptic quintics on X into the intermediate Jacobian J(X) of X factors by Stein through the quasi-finite (probably birational) map g:M of (an open part of) a component M of the scheme M(2;0,3) to a translate of the theta-divisor of J(X).     

Spaces of Densely Continuous Forms, USCO and Minimal USCO Maps

Our paper studies the topology of uniform convergence on compact sets on the space of densely continuous forms (introduced by Hammer and McCoy (1997)), usco and minimal usco maps. We generalize and complete results from Hammer and McCoy (1997) concerning the space D(X,Y) of densely continuous forms from X to Y. Let X be a Hausdorff topological space, (Y,d) be a metric space and D _k (X,Y) the topology of uniform convergence on compact sets on D(X,Y). We prove the following main results: D _k (X,Y) is metrizable iff D _k (X,Y) is first countable iff X is hemicompact. This result gives also a positive answer to question 4.1 of McCoy (1998). If moreover X is a locally compact hemicompact space and (Y,d) is a locally compact complete metric space, then D _k (X,Y) is completely metrizable, thus improving a result from McCoy (1998). We study also the question, suggested by Hammer and McCoy (1998), when two compatible metrics on Y generate the same topologies of uniform convergence on compact sets on D(X,Y). The completeness of the topology of uniform convergence on compact sets on the space of set-valued maps with closed graphs, usco and minimal usco maps is also discussed.     

基于0-1编码空间的谱系数图与bj图的互换

从函数最小项系数与基于（0,1）空间的谱系数以及bj系数的关系出发,引进了n-bj系数,进而提出了（0,1）空间的谱系数与bj系数的互换算法并给出了相应的图形转换方法和一种改进的跨图聚合圈法．实例表明,图形转换法具有简单、直接、方便等特点．     

BIFURCATIONS OF ROUGH 3—POINT—LOOP WITH HIGHER DIMENSIONS

The authors study the bifurcation problems of rough heteroclinic loop connecting three saddle points for the case β1 > 1, β2 > 1, β3 < 1 and β1β2β3 < 1. The existence, number, coexistence and incoexistence of 2-point-loop, 1-homoclinic orbit and 1-periodic orbit are studied. Meanwhile, the bifurcation surfaces and existence regions are given.