两类广义Petersen 图的Euler亏格

广义 Petersen 图 P(n, m) 是这样的一个图:它的顶点集是{u_i, v_i | i=0,1, ^… , n-1}, 边集是 {u_iu_i+1, v_iv_i+m, u_iv_i | i=0,1, ^…, n-1}, 这里 m, n 是正整数、加法是在模n 下且 m<|n/2| . 这篇文章证明了P(2m+1, m)(m≥ 2) 的 Euler 亏格是1, 并且 P(2m+2, m)(m≥ 5) 的 Euler 亏格是2.     

级联型高压重复频率微秒脉冲源的研制

针对等离子体的应用,基于级联型电压叠加技术研制了一种最高输出电压为20 kV的高压微秒脉冲源,该电源由40个相同的电源模块组成,其单个模块电压等级为500 V,降低了对器件的绝缘耐压要求。电源的输出电压值在0~20 kV之间可调;重复频率在0~10 kHz之间、脉宽在0~30 μs之间可调;该电源的上升沿和下降沿均在1 μs以内。模块化的设计提高了电源的冗余容错能力。将该电源作为产生等离子体的激励源时,其输出的高压脉冲波形稳定,且根据负载对输出高压波形的要求不同,该电源可以方便地进行调节。     

Numerical solution of one‐dimensional Burgers' equation

In this article, an iterative method for the approximate solution of a class of Burgers' equation is obtained in reproducing kernel space . It is proved the approximation converges uniformly to the exact solution u(x, t) for any initial function under trivial conditions, the derivatives of are also convergent to the derivatives of u(x, t), and the approximate solution is the best approximation under the system © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1251–1264, 2015     

Dilations and Completions for Gabor Systems

Let be a full rank time-frequency lattice in ℝ ^d ×ℝ ^d . In this note we first prove that any dual Gabor frame pair for a Λ-shift invariant subspace M can be dilated to a dual Gabor frame pair for the whole space L ²(ℝ ^d ) when the volume v(Λ) of the lattice Λ satisfies the condition v(Λ)≤1, and to a dual Gabor Riesz basis pair for a Λ-shift invariant subspace containing M when v(Λ)>1. This generalizes the dilation result in Gabardo and Han (J. Fourier Anal. Appl. 7:419–433, [2001]) to both higher dimensions and dual subspace Gabor frame pairs. Secondly, for any fixed positive integer N, we investigate the problem whether any Bessel–Gabor family G(g,Λ) can be completed to a tight Gabor (multi-)frame G(g,Λ)∪(∪ _j=1 ^N G(g _j ,Λ)) for L ²(ℝ ^d ). We show that this is true whenever v(Λ)≤N. In particular, when v(Λ)≤1, any Bessel–Gabor system is a subset of a tight Gabor frame G(g,Λ)∪G(h,Λ) for L ²(ℝ ^d ). Related results for affine systems are also discussed. Communicated by Chris Heil.     

First-principles study of electron dynamics with explicit treatment of momentum dispersion on Si nanowires along different directions

ABSTRACT

In this research, ground-state electronic structure and optical properties along with photoinduced electron dynamics of Si nanowires oriented in various directions are reviewed. These nanowires are significant functional units of future nano-electronic devices. All observables are computed for a distribution of wave vectors at ambient temperature. Optical properties are computed under the approximation of momentum conservation. The total absorption is composed of partial contributions from fixed values of momentum. The on-the-fly non-adiabatic couplings obtained along the ab initio molecular dynamics nuclear trajectories are used as parameters for Redfield density matrix equation of motion. The main outcomes of this study are transition energies, light absorption spectra, electron and hole relaxation rates, and electron transport properties. The results of these calculations would contribute to the understanding of the mechanism of electron transfer process on the Si nanowires for optoelectronic applications.     

共形Mikaelian声透镜设计*

该文研究了利用共形变换设计声学器件的一般方法,在此基础上根据普通Mikaelian透镜的折射率分布规律,利用指数映射设计出了弧形的Mikaelian透镜,分析并讨论了弧形透镜的密度、模量和折射率分布规律。对160 k Hz的声波进行了仿真实验,仿真结果表明,在弧形透镜的理论预测焦点处出现能量汇聚的现象,即实现了弧形聚焦的效果。同时,声波在经过该透镜后传播方向产生了一定角度的偏转。该工作为实现弧形声学器件提供了理论方法,在水下声探测及水下声通讯等方面有着潜在的应用。     

基于变换声学的角反射器的设计*

基于超材料的新型声学器件是近年来的研究热点,变换声学为这些新型声学器件的实现带来了可能。该文提出了一种基于变换声学的声反射器模型的设计方法。通过简单的线性映射,该声反射器具有均匀而各向异性的参数。利用Biot流体等效介质理论,通过周期分层结构可以对该反射器进行实现。仿真结果显示,在一定角度范围内,该反射器可以将声波按照入射方向进行反射,同时也验证了该结构的宽频有效性。     

NO2分子里德堡态的光学-光学双共振多光子离化谱

采用光学-光学双共振多光子离化（Optical-optical double-resonant multiphoton ionization，简称OODR-MPI）技术详细研究了NO2分子里德堡态的能级结构。结果显示，用不同强度的激光作抽运光，尽管NO2分子的OODR-MPI谱均由规则的光谱序列组成，但NO2分子的离化通道存在很大区别，当抽运光强度较高时，NO2分子通过(3+1+1)双共振多光子过程离化；而当抽运光强度较低时，NO2分子通过(1+2+1)双共振多光子过程离化，两种离化机制的最终共振能级属于不同的里德堡态。     

Characteristics of rogue waves on a soliton background in a coupled nonlinear Schrödinger equation

In this paper, a coupled nonlinear Schrödinger (CNLS) equation, which can describe evolution of localized waves in a two‐mode nonlinear fiber, is under investigation. By using the Darboux‐dressing transformation, the new localized wave solutions of the equation are well constructed with a detailed derivation. These solutions reveal rogue waves on a soliton background. Moreover, the main characteristics of the solutions are discussed with some graphics. Our results would be of much importance in predicting and enriching rogue wave phenomena in nonlinear wave fields.     

Nonlinear propagation of ultraslow pulses in media with electromagnetically induced transparency

The nonlinear behavior of a probe pulse propagating in a medium with electromagnetically induced transparency is studied both numerically and analytically. A new type of nonlinear wave equation is proposed in which the noninstantaneous response of nonlinear polarization is treated properly. The resulting nonlinear behavior of the propagating probe pulse is shown to be fundamentally different from that predicted by the simple nonlinear Schr?dinger-like wave equation that considers only instantaneous Kerr nonlinearity.