Lame Function and Its Application to Some Nonlinear Evolution Equations

In this paper, based on the Lame function and Jacobi emptic function, the perturbation method is appliedto some nonlinear evolution equations to derive their multi-order solutions.     

Barrier asymmetry and the mm-wave performance of resonant tunnel diodes

The effects of barrier asymmetry in a resonant tunnel diode (RTD) on the frequency response of the negative dynamical resistance are described for (i) DC biasing in the positive differential resistance (PDR) region and (ii) DC biasing in the negative differential resistance (NDR) region. Collector barriers more transparent than emitter barriers enhance performance for NDR DC-biased devices. Asymmetry has no apparent effect for PDR DC-biased devices operating in transit time mode.     

String Cosmological Solutions with O(d,d) Duality Symmetry and Matter Coupling

The duality properties of string cosmology model with negative energy matter are investigated by means of renormalization group equation,the cosmological solutions with exotic matter coupling are obtained in D=d+1 dimensional space-time.These inflation-power solutions can describe accelerated and decelerated process in the early universe,and the duality solutions can be generated through O(d,d) transformations.     

Novel Wronskian Condition and New Exact Solutions to a （3＋1）-Dimensional Generalized KP Equation

Utilizing the Wronskian technique, a combined Wronskian condition is established for a （3＋1）-dimensional generalized KP equation. The generating functions for matrix entries satisfy a linear system of new partial differential equations. Moreover, as applications, examples of Wronskian determinant solutions, including N-soliton solutions, periodic solutions and rational solutions, are computed.     

Er3＋-Yb3＋-Mo6＋共掺杂ZrO2-Al2 O3固溶体的上转换发光

采用共沉淀法制备了一系列Al2 O3含量由低到高的ZrO2-Al2 O3固溶体,并研究了固溶体的晶相结构以及稀土Er3＋在固溶体中的上转换发光增强机制。XRD结果表明固溶体为四方晶相ZrO2结构,Al2 O3的最高固溶度约为20 mol％。上转换发光光谱分析表明,Er3＋掺杂ZrO2室温下具有绿色上转换荧光发射,通过共掺杂Yb3＋和M o6＋离子,使得Er3＋掺杂ZrO2的绿色上转换发光强度增强了约20倍,获得了明亮的黄绿色上转换发光。基质ZrO2通过与Al2 O3固溶形成复合氧化物,由于产生的大量氧空位缺陷的能级与Er3＋的4 F7/2能级高度相接近,增强了Yb3＋-MoO2-4基团（2 F7/2,3 T2）能级向Er3＋的4 F7/2能级的能量传递。通过形成固溶体复合氧化物基质材料,使得Er3＋的绿色上转换发光在获得20倍增强的基础上又提高了8倍。绿色与红色上转换发光比例的变化也提高了材料的色纯度,上转换发光由黄绿色变为纯绿色。     

Nonlinear resonant tunneling diode (RTD) circuits for microwave A/D conversion

Short-duration electrical pulses play important roles in ultrafast time-domain metrology: they are used to sample rapidly varying signals or as probe signals in ranging radars, time-domain reflectometry and in communication. In this work, we design a nonlinear transmission, which is loaded with resonant tunneling diode to be suitable for microwave A/D conversion. A resonant tunneling diode (RTD) has a negative differential resistance that means when the voltage increases the current decreases. The equivalent circuit of monostable line is given. The simulation is performed by using OrCad program. Results show that a spike is produced and after a charging time constant, another switching occurs. Hence – similar to a relaxation oscillator – the spiking period is determined by the amplitude and frequency of the input current. The transmission line itself ensures the generation and propagation of identical spikes, such as solitons formed after few diodes.     

Existence and Nonlinear Stability of Stationary States of the Schrödinger–Poisson System

We consider the Schrödinger–Poisson system in the repulsive (plasma physics) Coulomb case. Given a stationary state from a certain class we prove its nonlinear stability, using an appropriately defined energy-Casimir functional as Lyapunov function. To obtain such states we start with a given Casimir functional and construct a new functional which is in some sense dual to the corresponding energy-Casimir functional. This dual functional has a unique maximizer which is a stationary state of the Schrödinger–Poisson system and lies in the stability class. The stationary states are parameterized by the equation of state, giving the occupation probabilities of the quantum states as a strictly decreasing function of their energy levels.     

Al原子共振双线跃迁几率实验研究

我们用Nd：YAG脉冲激光烧蚀金属Al靶产生等离子体，利用时间分辨技术摄取Al等离子体辐射时间分辨谱，获得Al原子共振双线辐射谱；通过积分谱线下的面积，计算共振双线强度；根据共振双线强度比，推断Al原子共振双线跃迁几率比，并与理论计算结果比较。结果发现，实验结果与理论计算符合的很好。     

浅水体系中的多孤立波

形式分离变量法被推广应用于寻求不可积模型的多孤立波解.特别地,应用形式分离变量法于三个描述浅水体系的非线性方程:推广WhithamBroerKaup(WBK)方程、2+1维耦合KortewegdeVries(KdV)方程和1+1维耦合KdV方程,给出了这些体系的明显的解析的多孤立波解 关键词： 浅水体系 多孤立波 形式分离变量法 不可积模型     

三层流体界面内波的二阶Stokes解

以小振幅波理论为基础，利用摄动方法研究了三层密度成层状态下的界面内波，求得了三层成层状态下各层速度势的二阶渐近解及界面内波波面位移的二阶Stokes解.结果表明：一阶解为正弦波解，与传统线性理论的结果相一致；二阶解描述了界面波的二阶非线性修正及两界面波之间的非线性相互作用；一阶解及二阶解都依赖于各层流体的厚度及密度.Umeyama导出的理论结果为本文的特殊情形. 关键词： 三层密度成层流体 内波 二阶Stokes解 小振幅波理论