Machine learning-based direct solver for one-to-many problems on temporal shaping of relativistic electron beams

To control the temporal profile of a relativistic electron beam to meet requirements of various advanced scientific applications like free-electron-laser and plasma wakefield acceleration, a widely-used technique is to manipulate the dispersion terms which turns out to be one-to-many problems. Due to their intrinsic one-to-many property, current popular stochastic optimization approaches on temporal shaping may face the problems of long computing time or sometimes suggesting only one solution. Here we propose a real-time solver for one-to-many problems of temporal shaping, with the aid of a semi-supervised machine learning method, the conditional generative adversarial network (CGAN). We demonstrate that the CGAN solver can learn the one-to-many dynamics and is able to accurately and quickly predict the required dispersion terms for different custom temporal profiles. This machine learning-based solver is expected to have the potential for wide applications to one-to-many problems in other scientific fields.     

子带t分布的快速独立向量分析在语声盲源 分离中的应用*

为了提高独立向量分析算法在盲语声分离任务中的分离性能,降低算法计算复杂度,并改善目前尚未完全解决的顺序模糊性的问题,该文提出一种基于子带t分布的快速独立向量分析算法。在声源模型方面,该算法首先利用语声信号重尾分布的特性,假设声源概率密度函数服从t分布,同时采用子带建模的方法来增强同一声源相邻频点的高阶依赖性,进而减轻频点间的顺序不一致问题。在空间模型方面,该算法采用秩1更新的方式估计声源信号,避免矩阵求逆操作和分离矩阵的估计,从而降低计算复杂度。实验结果表明,与现有的基于独立向量分析的盲源分离算法相比,该算法能够在相同的迭代次数下取得更优的语声分离性能。     

互感系数M12=M21的证明

从定义、磁能、磁矢势、磁偶极子、自由能5个方面出发分别证明了互感系数M12=M21,并对几种证明方法进行了分析对比,提出了自己的看法.     

离散式任意充磁角度Halbach永磁电机解析模型研究

Halbach电机因其自身优势在新型船舶推进、海洋洋流发电等方面受到广泛关注. 本文在假设铁磁材料线性和定子内表面光滑的条件下, 通过将任意充磁角度Halbach阵列等效为两组90° Halbach(或180° Halbach)阵列的矢量合成, 提出了一种分析离散式任意充磁角度Halbach永磁电机气隙磁场的解析方法; 通过对电机中磁标量势的傅里叶级数进行计算, 推导出了最简单的90° Halbach永磁电机在极坐标系下的气隙磁密表达式, 并在此基础上, 给出了任意充磁角度Halbach电机永磁体磁化强度在一个极下的表达式, 进而得出任意充磁角度Halbach电机气隙磁密的分布, 并分析了气隙磁密与电机极对数、永磁体厚度和充磁角度间的关系. 最后通过有限元和试验结果验证了本文方法的正确性. 关键词： 离散式Halbach电机 任意充磁角度 矢量等效 解析模型     

AEIV结合AHSI用于饱和脂肪酮类物质的13C NMR谱模拟

应用一种反映分子局部微环境描述子--原子电性相互作用矢量（vector of atomic electronegative interaction,AEIV）和原子杂化状态指数（Atomic Hybridation State Index, AHSI）对饱和脂肪酮类化合物的55种分子中的153个¹³C NMR谱建模模拟,应用多元线性回归方法得到定量结构波谱关系(QSSR)模型的复相关系数R_MM=0.997, 标准偏差为SD_MM=7.155. 采用留一法交互检验的结果是R_CV=0.993,SD_CV=10.195. 并随机抽出三部分分子进行检验,得到的相关系数分别是R_MM1=0.996,R_MM2=0.996,R_MM3=0.999. 研究结果表明使用AEIV和AHSI所建模型预测能力是相当稳定的.     

基于RBC模型的动态随机一般均衡的数值解

以一般均衡为框架,引入随机变量的动态随机一般均衡系统,由于模型的庞大和函数形式的复杂,往往不能给出明确的数值解.本文给出几种操作性强的、有效的寻求一般化模型数值解的方法,并通过介绍模型参数确定的办法,使得理论的模型有了现实的含义.     

Prediction of the Frontier Electronic States in a Finite Single-wall Carbon Nanotube

A theoretical model is summarized into the shorter vector principle. It is used to predict the topological structure of wave function and the oscillation rule of energy gap in various types of finite carbon nanotubes (CNTs). The theoretical model indicates that the characteristics of the electronic states only depend on the nanotube size and its symmetry along the shorter vector direction. In this direction, the wave functions of the original 3m (or 3m/2) periodicity are also suitable for armchair, chiral and zigzag finite CNTs with the C2 (Cs), C1 and Cn point groups, respectively. Energy gaps present the oscillation with 3m (or 3m/2) or odd-even n. The first principle calculations for some prototype systems are performed. The results are consistent with the theoretical model.     

Inverse Scattering Problem for the Schrödinger Operator with External Yang–Mills Potentials in Two Dimensions at Fixed Energy

ABSTRACT

We consider the Schrödinger equation in ?², with external Yang–Mills potentials that decay exponentially as |x| → ∞. We prove that the scattering amplitude at fixed positive energy determines the potentials uniquely modulo a gauge transformation, assuming that potentials are small.     

A note on spectrum distribution of constraint preconditioned generalized saddle point matrices

In this note, results concerning the eigenvalue distribution and form of the eigenvectors of the constraint preconditioned generalized saddle point matrix and its minimal polynomial are given. These results extend previous ones that appeared in the literature. Copyright © 2009 John Wiley & Sons, Ltd.     

Central configurations of the collinear three-body problem and singular surfaces in the mass space

This Letter is to provide a new approach to study the phenomena of degeneracy of the number of the collinear central configurations under geometric equivalence. A direct and simple explicit parametric expression of the singular surface H₃ is constructed in the mass space (m₁,m₂,m₃)∈³(R⁺). The construction of H₃ is from an inverse respective, that is, by specifying positions for the bodies and then determining the masses that are possible to yield a central configuration. It reveals the relationship between the phenomena of degeneracy and the inverse problem of central configurations. We prove that the number of central configurations is decreased to 3!/2−1=2, m₁, m₂, and m₃ are mutually distinct if m∈H₃. Moreover, we know not only the number of central configurations but also what the nonequivalent central configurations are.