Bochner-Kähler metrics

A Kähler metric is said to be Bochner-Kähler if its Bochner curvature vanishes. This is a nontrivial condition when the complex dimension of the underlying manifold is at least . In this article it will be shown that, in a certain well-defined sense, the space of Bochner-Kähler metrics in complex dimension has real dimension and a recipe for an explicit formula for any Bochner-Kähler metric will be given.

It is shown that any Bochner-Kähler metric in complex dimension  has local (real) cohomogeneity at most . The Bochner-Kähler metrics that can be `analytically continued' to a complete metric, free of singularities, are identified. In particular, it is shown that the only compact Bochner-Kähler manifolds are the discrete quotients of the known symmetric examples. However, there are compact Bochner-Kähler orbifolds that are not locally symmetric. In fact, every weighted projective space carries a Bochner-Kähler metric.

The fundamental technique is to construct a canonical infinitesimal torus action on a Bochner-Kähler metric whose associated momentum mapping has the orbits of its symmetry pseudo-groupoid as fibers.

     

Enumerating near-4-regular maps on the sphere and the torus

In this paper rooted near-4-regular maps on the plane and the torus are counted with formulae with respect to four parameters: the root valency, the number of edges, the inner faces, and nonroot-vertex loops. In particular, the number of rooted near-4-regular maps on those surfaces with exactly k nonroot-vertex loops is investigated.     

曲面上构造三次3-连通非Hamiltonian地图的一种方法(英文)

Tutte在1946年构造性证明了并非每个简单的3-凸胞腔都是Hamiltonian的后,人们又陆续提出了多种构造三次3-连通非Hamiltonian平面图的方法,但无一能用于在一般曲面上寻找三次3-连通非Hamiltonian地图.本文提出了一种新的构造方法,可在任一个曲面上构造出三次3-连通非Hamiltonian地图.     

Natural abundance C REDOR coupled to a singly N-labeled nucleus: simultaneous determination of interatomic distances in crystalline ammonium [N] -glutamate monohydrate

REDOR technique was applied to natural abundance ¹³C nuclei coupled to a singly labeled ¹⁵N nucleus to determine the ¹³C, ¹⁵N interatomic distances simultaneously in crystalline ammonium [¹⁵N] -glutamate monohydrate (1). Consequently, the interatomic C–N distances between ¹⁵N and ¹³C=O, ¹³C_α, ¹³C_β, ¹³C_γ, and ¹³C_δ carbon nuclei for 1 were determined with a precision of ±0.15 Å, after the experimental conditions such as the location of samples in the rotor, length of π pulse etc. were carefully optimized. ¹³C-REDOR factors for three spin system, (ΔS/S₀)_CN1N2, and the sum of two isolated 2-spin system, (ΔS/S₀)^*=(ΔS/S₀)_CN1+(ΔS/S₀)_CN2, were further evaluated by the REDOR measurements on isotopically diluted 1 in a controlled manner. Subsequently, the intra- and intermolecular C–N distances were separated by searching the minima in the contour map of root mean square deviation (RMSD) between the theoretically and experimentally obtained (ΔS/S₀)^* values against two interatomic distances, r_C–N1 and r_C–N2. When the intramolecular C–N distance (r_C–N1) of the particular carbon nucleus is substantially shorter than the intermolecular one (r_C–N2), C–N distances within a single molecule were obtained with an accuracy of ±0.06 Å as in the cases of C=O, C_α and C_β carbon nuclei. C–N distances between the molecule in question and the nearest neighboring molecules can be also obtained, although accuracy was lower. On the contrary, it was difficult to determine the interatomic distances in the same molecule when the intermolecular dipolar contribution is larger than the intramolecular one as in the case of C_δ carbon nucleus.     

Strange—Nonchaotic—Attractor—Like Behaviors in Coupled Map SYstems

In a coupled map system,an attractor which seems to be strange nonchaotic attractor(SNA)is discovered for nonzero measure in parameter range,The attractor has nonpositive Lyapunov exponent(LE) and discrete structure.We call it strange-nonchaotic-attractor-like(SNA-like) behavior because the size of its size of its discrete structure decreases with the computing precision increasing and the true SNA does not change.The SNA-like behavior in the autonomous system is born when the truncation error of round-off is amplified to the size of the discrete part of the attractor during the long time interval of positive local LE.The SNA-like behavior is easily mistaken for a true SNA judging merely from the largest LE and the phase portrait in double precision computing.In non-autonomous system an SNA-like attractor is also found.     

基于电子地图的路径最优算法研究

针对车载导航系统和交通监控系统中的最优路径这一关键技术,研究了矢量奄际图数据结构及春用它表示的真实道路网络的特点,探讨了基于电子地图最优路径求解的启发式代价树搜索算法,并提出了不同情形下的求解策略。     

ON HARMONIC MAPS INTO SYMPLECTIC GROUPS Sp（N）

50. IntroductionThe construction and the factorization of harmonic maps from R2 (or its simPlyconnecteddomain) into the uIiltary group U(N) were firstly solved by K.Ulilenbeck in [11, wherethe conception of unitons was iniroduced. Since then various developmenis have beencoatributed[2--5]. Recently, by introducing (singular) Darboux transformations, a purelya1gebraic method to construct harmonic maPs and unitons illto U(N) has been shownin t6'7]. This method can be aIso aPplied to the ca…     

耦合映象格子中时空混沌的控制

采用相同的相空间压缩方法,有效地控制了均匀及非均匀耦合映象格子中的时空混沌.数值模拟结果表明,在一定的相空间压缩参数区域内,控制时空混沌到均匀稳定状态时,控制结果与控制参数之间存在确定的函数关系.利用这个控制方程,选择不同的相空间压缩参数控制耦合映象格子中的时空混沌,获得了各种所需要的稳定斑图 关键词： 时空混沌 耦合映象格子     

直流偏置的与RLC谐振器耦合的约瑟夫森结动力学行为的数值模拟

用数值模拟方法研究一种直流偏置的与RLC电路耦合的约瑟夫森结的动力学行为.数值模拟发现,选择合适的偏置电流,系统表现出周期三与混沌共存的动力学现象.给出了相应吸引子,吸引域的几何结构.对该系统的动力学研究为约瑟夫森器件稳定工作提供了有价值的参考 关键词： 约瑟夫森结 混沌 吸引子 吸引域 庞加莱截面 李雅谱诺夫指数     

实验教学挂图的研制及教学功能

本文提出了研制教学挂图的基本形式 ,并根据教学实践总结出了实验挂图的独到作用