具有周期外力场Dirac方程的基态解

本文研究非线性Dirac方程-i∑_k=1³α_k?_ku+aβu+M(x)u=g(x,|u|)u基态解的存在性,其中位势函数M(x)是周期的.当非线性项g在无穷远处分别满足超二次与局部超二次增长条件时,利用非Nehari流形方法,在非线性项没有严格单调条件的情形下,证明Nehari-Pankov型基态解的存在性.主要克服了两个困难:(1)相关能量泛函是强不定的,即工作空间分解成的正负子空间的维数都是无穷大,这导致经典的临界点定理不能直接应用;(2)当非线性项不是全局超二次时,验证Cerami序列的环绕结构并证明其有界性.     

关于紧致广义凯莱流形上的希格斯场的一些注记

在本文中,我们首先解决在紧致广义凯莱流形上的$I_{+-}$-希格斯丛上的阿尔法-厄米特-杨-米尔斯-希格斯方程的狄利克雷边值问题.然后我们证明了在闭的广义凯莱流形上的$I_{+-}$-希格斯丛,它的阿尔法半稳定性蕴含了渐进$\alpha$-厄米特-杨-米尔斯-希格斯结构的存在性.     

Lower-Dimensional Volumes and Kastler-Kalau-Walze Type Theorem for Manifolds with Boundary

In this paper, we define lower-dimensional volumes of spin manifolds with boundary. We compute the lower-dimensional volume Vol（2＇2） for 5-dimensional and 6-dimensional spin manifolds with boundary and we also get the Kastler-Kalau-Walze type theorem in this case.     

Phantom-Like Effects on Warped DGP Brane

We study phantom-like effect on the DGP brane embedded in a five-dimensional AdS bulk. We show that this effect can be realized without phantom matter on this warped DGP brahe. We investigate the role played by the bulk cosmological constant on the phantom-like effect on the brane and we show that it tends to reduce this effect. Also, warped compactification of the bulk manifold increases the values of the effective and total equation of state parameters of the model relative to the case with Minkowski bulk. We extend our study to the ease that induced curvature on the brahe is modified in the spirit of the f（R）-gravity.     

A New （2＋1）-Dimensional KdV Equation and Its Localized Structures

A new （2＋1）-dimensional KdV equation is constructed by using Lax pair generating technique. Exact solutions of the new equation are studied by means of the singular manifold method. Bgcklund transformation in terms of the singular manifold is obtained. And localized structures are also investigated.     

基于Stiefel流形的粒子滤波器研究

为了解决粒子滤波的粒子退化和粒子多样性丧失问题,提出了一种基于Stiefel流形的粒子滤波算法.该算法将系统模型置于Stiefel流形上,用朗之万分布描述过程转移概率分布,用矩阵正态分布表示似然函数分布,在流形分布上进行粒子采样.在计算加权粒子的均值时,将流形嵌入到欧氏空间中,先计算欧氏空间中的粒子均值,再将计算结果投影到嵌套流形上,这就排除了噪声统计特性对粒子权重方差的影响,得到了一种受系统状态模型限制较少的重要性概率密度函数通用选择方案.仿真时选取单变量非静态增长模型,仿真结果验证了该算法的实时性、鲁棒性,滤波精度和滤波效率均比无味粒子滤波算法更好.     

On the Uniqueness of Heat Flow of Harmonic Maps and Hydrodynamic Flow of Nematic Liquid Crystals

For any n-dimensional compact Riemannian manifold (M,g) without boundary and another compact Riemannian manifold (N,h), the authors establish the uniqueness of the heat flow of harmonic maps from M to N in the class C([0,T),W1,n). For the hydrodynamic flow (u,d) of nematic liquid crystals in dimensions n = 2 or 3, it is shown that the uniqueness holds for the class of weak solutions provided either (i) for n = 2, u ∈ Lt∞ L2x∩L2tHx1, ▽P∈ Lt4/3 Lx4/3 , and ▽d∈ L∞t Lx2∩Lt2Hx2; or (ii) for n = 3, u ∈ Lt∞ Lx2∩L2tHx1∩ C([0,T),Ln), P ∈ Ltn/2 Lxn/2 , and ▽d∈ L2tLx2 ∩ C([0,T),Ln). This answers affirmatively the uniqueness question posed by Lin-Lin-Wang. The proofs are very elementary.     

The Riemannian Manifolds with Boundary and Large Symmetry

Seventy years ago, Myers and Steenrod showed that the isometry group of a Riemannian manifold without boundary has a structure of Lie group. In 2007, Bagaev and Zhukova proved the same result for a Riemannian orbifold. In this paper, the authors first show that the isometry group of a Riemannian manifold M with boundary has dimension at most 1/2 dim M（dim M - 1）. Then such Riemannian manifolds with boundary that their isometry groups attain the preceding maximal dimension are completely classified.     

GENERIC WARPED PRODUCT SUBMANIFOLDS OF LOCALLY CONFORMAL KEAHLER MANIFOLDS

Warped product manifolds are known to have applications in physics. For instance, they provide an excellent setting to model space-time near a black hole or a massive star （cf. [9]）. The studies on warped product manifolds with extrinsic geometric point of view were intensified after the B.Y. Chen＇s work on CR-warped product submanifolds of Kaehler manifolds （cf. [6], [7]）. Later on, similar studies were carried out in the setting of 1.c.K. manifolds and nearly Kaehler manifolds （el. [3], [11]）. In the present article, we investigate a larger class of warped product submanifolds of 1.c.K. manifolds, ensure their existence by constructing an example of such manifolds and obtain some important properties of these submanifolds. With regard to the CR-warped product submanifold, a special case of generic warped product submanifolds, we obtain a characterization under which a CR-submanifold is reducesd to a CR-warped product submanifold.     

SHARED VALUE IN A FINITE-DIMENSIONAL BANACH MANIFOLD

Sufficient conditions are given to assert that two C1-mappings share only one value in a connected compact Banach manifold modelled over Rn. The proof of the result, which is based upon continuation methods, is constructive.