Klein-Gordon-Zakharov系统中的交叉强制变分方法

本文我们提出-类交叉强制变分方法来研究二维空间中的Klein-Gordon-Zakharov系统的整体解.首先,通过构造交叉强制变分问题,建立发展流的交叉不变流形,得到所研究系统解爆破和整体存在的-个最佳条件.其次,利用这个结论,我们回答了如下问题:当初值为多小时,所研究系统的整体解存在.     

Energy Spectrum of Helium Confined to a Two-Dimensional Space

Making use of the adiabatic hyperspherical approach, we report a calculation for the energy spectrum of the ground and low-excited states of a two-dimensional helium in a magnetic field. The results show that the ground and low-excited states of helium in low-dimensional space are more stable than those in three-dimensional space and there may exist more bound states.     

含基 Banach 空间中的不动点定理

在 Banach 空间 E 中定义了由其规范基确定的半序,讨论了该半序及由其导出的锥的性质,在此基础上证明了几个新的不动点定理.最后,讨论了有限维空间中 Hammerstein 积分方程解的存在性.     

战斗对策:有约束极小极大途径(Ⅱ)

本文提出几个用集合,测度和积分工具来的极小极大判别准则,用来解有约束极小极大问题．     

A LOWER BOUND FOR FIRST EIGENVALUE WITH MIXED BOUNDARY CONDITIOIN

Let M be an n-dimensional compact Riemannian manifold with or without boundary,and its Ricci curvature RicM≥n- 1. The paper obtains an inequality for the first eigenvalue η1 of M with mixed boundary condition, which is a generalization of the results of Lichnerowicz,Reilly, Escobar and Xia. It is also proved that η1≥ n for certain n-dimensional compact Riemannian manifolds with boundary,which is an extension of the work of Cheng,Li and Yau.     

高维空间中半线性波动方程的Sobolev指数

ＧｕｓｔａｖｏＰｏｎｃｅ与ＴｈｏｍａｓＣ．Ｓｉｄｅｒｉｓ［４］猜测对一些具有特殊非线性项的半线性波动方程，如ｕｔ－△ｕ＝ｕｋ（Ｄｕ）α（ｘ∈Ｒｎ，ｋ∈Ｚ＋，ｌ＝｜α｜２），其中Ｓｏｂｏｌｅｖ指数会在ｎ２与（ｎ２＋１）之间．文［４］中，在ｘ∈Ｒ３时，回答了这一问题．本文在ｎ３维空间中，得到了半线性波动方程ｕｔ－△ｕ＝ｕｋ（Ｄｕ）α（ｘ∈Ｒｎ，ｋ∈Ｚ＋，ｌ＝｜α｜２）的Ｓｏｂｏｌｅｖ指数为ｍａｘ｛ｎ２＋１２，（ｎ２－１）·ｌ－３ｌ－１＋２｝，此数确实在区间［ｎ２＋１２，ｎ２＋１］中．     

Tingley’s problem on symmetric absolute normalized norms on ℝ 2

In this paper,we study Tingley＇s problem on symmetric absolute normalized norms on R^2.We construct new methods for Tingley＇s problem on two-dimensional spaces by using isosceles orthogonality,which does not make use of the notion of natural extension.Furthermore,using our methods,several sufficient conditions for Tingley＇s problem on symmetric absolute normalized norms on R2 are given.As applications,we present various new examples including the two-dimensional Lorentz sequence space d^（2）（ω,q） and its dual d^（2）（ω,q）＊by simple arguments.     

Sharp threshold of global existence for the Klein-Gordon equations with critical nonlinearity

In this paper, we present a cross-constrained variational method to study the Cauchy problem of the nonlinear Klein-Gordon equations with critical nonlinearity in two space dimensions. By constructing a type of cross-constrained variational problem and establishing so-called cross-invariant manifolds of the evolution flow, we establish a sharp threshold of global existence and blowup of it. Furthermore, we answer the question： How small are the initial data if the solution exists globally.     

2维SU(NC)格点规范理论中矢量介子质量

用改进的格点哈密顿量和变分法,研究了2维SU(NC)规范场中矢量介子质量MV与夸克质量m和Wilson参数 的依赖关系．数值结果表明：对于NC =2、3、4、5、6、7, …,在标度窗口 内,MV/g与m的依赖关系近似为直线;但是矢量介子质量MV不明显依赖于Wilson参数 （这与夸克凝聚的情况不同）. 特别是,当 时, 本文的格点结果与Bhattacharya’s的连续理论强耦合相分析结果很好地一致, 而 的值十分接近Schwinger模型中的相应值.