Splitting multisymplectic integrators for Maxwell’s equations

In the paper, we describe a novel kind of multisymplectic method for three-dimensional (3-D) Maxwell’s equations. Splitting the 3-D Maxwell’s equations into three local one-dimensional (LOD) equations, then applying a pair of symplectic Runge–Kutta methods to discretize each resulting LOD equation, it leads to splitting multisymplectic integrators. We say this kind of schemes to be LOD multisymplectic scheme (LOD-MS). The discrete conservation laws, convergence, dispersive relation, dissipation and stability are investigated for the schemes. Theoretical analysis shows that the schemes are unconditionally stable, non-dissipative, and of first order accuracy in time and second order accuracy in space. As a reduction, we also consider the application of LOD-MS to 2-D Maxwell’s equations. Numerical experiments match the theoretical results well. They illustrate that LOD-MS is not only efficient and simple in coding, but also has almost all the nature of multisymplectic integrators.     

相量法在交流电桥实验中的应用

相量法是分析正弦交流电路问题的重要方法之一.它的特点是数学模型简单、直观,可操作性强.本文以交流电桥实验中的电感桥和电容桥为例,展示了相量法在交流电桥平衡的分析与求解过程中的优点.该方法用于交流电桥实验不仅有助于学生巩固相量的概念,而且能深刻地理解交流电桥的测量原理.     

A Galerkin boundary element method based on interpolatory Hermite trigonometric wavelets

A Galerkin boundary element method based on interpolatory Hermite trigonometric wavelets is presented for solving 2-D potential problems defined inside or outside of a circular boundary in this paper. In this approach, an equivalent variational form of the corresponding boundary integral equation for the potential problem is used; the trigonometric wavelets are employed as trial and test functions of the variational formulation. The analytical formulae of the matrix entries indicate that most of the matrix entries are naturally zero without any truncation technique and the system matrix is a block diagonal matrix. Each block consists of four circular submatrices. Hence the memory spaces and computational complexity of the system matrix are linear scale. This approach could be easily coupled into domain decomposition method based on variational formulation. Finally, the error estimates of the approximation solutions are given and some test examples are presented.     

广义严格对角占优矩阵判定的新迭代准则

本文给出了广义严格对角占优矩阵判定的几个新迭代准则,改进了近期的一些结果,并给出相应的数值算例来说明结果的有效性.     

稀疏数据非线性降维的CN-Isomap算法

针对经典的流形学习算法Isomap在非线性数据稀疏时降维效果下降甚至失效的问题,提出改进的切近邻等距特征映射算法(Cut-Neighbors Isometric feature mapping,CN-Isomap).该算法在数据稀疏的情况下首先通过有效识别样本点的"流形邻居"来剔除近邻图上的"短路"边,然后再通过最短路径算法拟合测地线距离,使得拟合的测地线距离不会偏离流形区域,从而低维嵌入映射能够正确地反映高维输入空间样本点间的内在拓扑特征,很好地发现蕴含在高维空间里的低维流形,有效地对非线性稀疏数据进行降维.通过对Benchmark数据集的实验表明了算法的有效性.CN-Isomap算法是Isomap算法的推广,不仅能有效地对非线性稀疏数据进行降维,同样也适用于数据非稀疏的情况.     

支付离散红利的交换期权定价

在标的资产支付离散红利的情形下,对交换期权定价问题进行了讨论,并采用Dai和Lyuu（2008）的股票支付离散红利的期权定价方法,给出了支付离散红利的交换期权的闭式解。     

用于光纤光栅制作的监控光源掺Yb3+超荧光光源的研究

根据石英中Yb³⁺发射光谱在1030 nm发射截面比1053 nm附近大得多而导致在1030 nm附近出现荧光峰值的特点,采用抑制1030 nm附近荧光峰值、提高1053 nm附近荧光输出的方法,在装置中使用反射圈对超荧光进行了研究,在82 mW泵浦功率下得到了19 mW的超荧光,其中1053 nm附近荧光输出达到-31.7 dBm. 用这种方法研制的超荧光能监控中心波长从1013 nm到1093 nm范围内、反射率从30 dB到60 dB所有光纤光栅的制作.     

非对称相移分布反馈光纤激光器的双向输出波长特性

为了得到单频输出的光纤激光器，常采用带有相移的分布反馈结构，但当耦合强度比较大时，基模的激光功率将集中在相移区，这时，如果相移区太偏离光纤光栅的中心位置，由于空间烧孔效应，相移分布反馈激光器的两端会出现不同的输出波长特性。在接近于相移区的一端，输出为在布拉格波长的基模，而在另一端，输出为位于布拉格波长两侧的一阶模。给出了理论分析和相应的实验结果。     

用于DC–SC超导光电子枪中的光阴极的研制

DC-SC超导光阴极微波电子枪是一种新型的高平均流强电子源,本文介绍了其中的关键部件—光阴极的研制.在自行研制的光阴极制备室里成功制备了两种光阴极:Cs₂Te和Cs₃Sb光阴极.Cs₂Te光阴极的寿命长,用266nm紫外光激发,量子效率QE>25%,真空中(1×10^－5Pa)寿命50h.Cs₃Sb光阴极是多层膜结构,用532nm激光激发,量子效率2%,真空中(10^－5Pa)寿命只有几个小时.两者都可以满足电子枪的设计要求,但是由于Cs₂Te光阴极更稳定,在目前的DC-SC超导光电子枪调试实验中采用这种光阴极     

KMgF3:Cr3+的EPR参量和K+空位研究

EPR和ENDOR表明:顺磁离子取代KMgF₃中的Mg²⁺离子后,所处的环境具有轴对称。本文研究了KMgF₃:Cr³⁺的Δg=g_∥-g_⊥和零场分裂值D,证实KMgF₃:Cr³⁺中K⁺空位的存在。并且指出:由于K⁺空位,使Cr³⁺的最近邻F^-离子分 关键词：