振荡方程

According to coherent population oscillation and gain theory, the analytic expression of the group index from rate equation is obtained.

根据布居振荡效应及增益理论，由速率方程出发，得到了探测光的群折射率的理论解析表达式。

In this paper, we verify some existed results of oscillating asymptotic of Painlev equation, and also get a few new results by asymptotic of the numerical solution.

本文通过对数值解的渐近表示，验证了Painlevé方程振荡渐近解的一些现有结果，并得出一些新的结果。

According to the Navier-Stokes' equations and using themethod of Bessel function of imaginary argument,a system of foimulas is obxained.

从基本的Navier－Stokes方程出发，进行线性化之后采用虚宗量Bessel函数的方法求解，得出了一组描述血管振荡状态下发展流动的速度分布、压力分布公式。

The entanglement of the system is calculated by making use of concurrence. we discuss the variation of the concurrence with time.

在Milburn方程的支配下，通过concurrence计算了系统的纠缠，我们讨论了concurrence随时间的振荡情况。

To accelerate the widespread of Synchronous Chip Seal and improve the operation quality of Synchronous Chipsealer, key techniques which influence the operation quality is studied detailedly, including the control of distributing quality, the dynamics characteristics of hydraulic system and the spray characteristics of asphalt nozzle of Synchronous Chipsealer.1 The factors which influence Synchronous Chip Seal quality are studied. Fiducial probability of simultaneous distribution density is advised to be used in evaluating the distribution bias and standard deviation of asphalt and aggregates simultaneously, which is more advanced than the single index evaluation method used before.2 The volume efficiency formula of asphalt pump is revised after analyzing the data of volume efficiency with mathematical statistics, which is helpful to match the asphalt spray system and control the flow out of asphalt pump accurately. With equation deduction and experiment, dynamic of hydraulic system used in Synchronous Chipsealer is studied, which lay the theory foundation on improving the stability and efficiency from design and controlling.4 Simulation on hydraulic system used in Synchronous Chipsealer is done with AMESim; the results indicate that multi-circle parallel connected hydraulic system with constant pressure power is better than that with load-sensing pressure power at present, because the latter will oscillate when the multi circles work at the same time. This conclusion has been proved during the debug of Synchronous Chipsealer.5 Asphalt nozzle characteristics, such as flat jet shape, flow distribution, are studied with experiment, the results indicate that cross quality of asphalt distributing is not increased linearly follow the increase of fan overlap level, the best point usually exists between two whole overlap level, asphalt distributing quality is better than±4% at the 2.5 overlap level, meets the superior specified in standard; The distribution quality of Synchronous Chipsealer can be increased by spray asphalt of different flow rang with nozzle of different diameter

为了加快同步碎石封层技术的推广，提高同步碎石封层设备的作业质量，本文对同步碎石封层设备作业质量的影响因素与控制方法、液压系统的动力学特性和沥青喷嘴的喷洒特性等关键技术进行了深入细致的研究：1研究了影响同步碎石封层作业质量的因素，提出了采用联合密度分布置信概率对同步碎石封层中沥青洒布量和碎石撒布量的系统偏差和标准差指标进行综合评价的方法，克服了传统评价方法只能对单一指标进行评价的缺陷；2采用数理统计的方法，研究了沥青泵的容积效率特性，修正了沥青泵容积效率公式，为沥青喷洒系统的匹配和沥青泵出口流量的精确控制提供了依据；采用数理方程推导与试验相结合的方法，研究了同步碎石封层设备液压系统的动力学特性，为从设计和控制的角度提高同步碎石封层设备液压系统的稳定性和效率奠定了理论基础；3运用AMESim软件对采用负载敏感控制和恒压控制的两种同步碎石封层设备液压系统进行仿真，结果表明：负载敏感控制的并联液压系统在多回路同时工作时，由于液压泵排量控制参考压力不稳定，容易引发液压系统振荡，恒压控制的并联液压系统是目前技术条件下比较理想的同步碎石封层设备工作装置驱动方案；该结论亦通过同步碎石封层设备装机试验得到了验证。4采用试验的方法对沥青喷嘴的喷洒特性进行了研究，结果表明：沥青洒布的横向精度并不是随着喷洒扇面重叠度的增加线性增加，其最高点通常出现在二个重叠度之间的"半重叠位置"，"2.5重叠"洒布时，沥青的横向洒布精度≤±4%，可以达到国家相关标准中的优级标准；同步碎石封层设备还可以根据不同洒布量情况下的流量需求，采用不同通径的喷嘴进行喷洒，提高沥青洒布精度。

A series of theoretical and experimental studies on the microstrip patch antennas with dielectric superstrates is carried out systematically. Firstly, a comprehensive survey of the microstrip antenna technology and its theories are presented. Then, two analysis techniques, named as the spectral domain Green's function method and the spectral domain integral equation method are developed. The SDGF method is a simplified analysis technique, which takes advantage of the spectral domain immittance approach to find the dyadic Green's function for the stratified media, and obtains the complete closed-form formulas for radiation patterns, directivity, efficiency, gain etc. Some interesting calculated results are presented. The SDIE method is capable of determining resonant frequency, radiation characteristics, input impedance etc, for the covered microstrip patch antennas. Comparing with other full-wave analyses it reduced computation and mathematical labour remarkably. The singularities near the pole location of the surface-wave modes and the difficulty of the integral computation over infinite range of oscillating integrands are dealt with actively and documented well. Results predicted by the SDIE method agree extremely well with our experimental results for resonant frequencies of various superstrates. The superstrate effects on impedance and radiation characteristics also have been investigated experimentally so that the gap due to lack of measured data and computed results for multi-layered superstrate has been filled to some degrees and two useful observations have been achieved for weakening the resonant frequency shift and optimizing the microstrip antenna gain. As a meaningful application, the design and analysis of a 4×4 patch array are introduced.

实用微带天线普遍加介质覆盖层来防护热，物理损伤和环境影响，也可能在飞行或严酷气候条件下自然形成覆盖层本论文对带介质覆盖层的微带贴片天线系统地作了一系列理论和实验研究首先，对微带天线技术和理论作了全面的综述然后，发展了两种分析方法，称为谱域格林函数法和谱域积分方程法SDGF法是一种简化的分析技术，它利用谱域导抗法来求得分层媒质的并矢格林函数，并得出方向图、方向性系数、增益等参数的完整的闭式公式，给出了一些令人感兴趣的计算结果SDIE法能确定介质覆盖微带天线的谐振频率、辐射特性和输入阻抗等与其它全波分析方法相比，它明显减小了计算量和数学工作量已有效地处理了表面波模极点附近的奇异性和对振荡的被积函数的无限区间积分计算的困难对于不同覆盖层情况下的谐振频率，由SDIE法所预示的结果与我们的实验结果吻合得很好对于覆盖层对阻抗和辐射特性的影响也已作了实验研究这在某种程度上填补了缺少实验数据和计算结果之间的间隙，并得出了缓解谐振频率偏移和优化天线增益的两点有用的结论作为有意义的应用，介绍了一个4×4元矩形贴片天线阵的设计和分析。

Based on this, a new WENO difference scheme which based on Dispersion-Relation-Preserving relation is developed, and representative test cases with this scheme for computational aeroacoustics problems has been implemented and compared in order to test capability of wave capturing; In addition, WENO schemes generally do not converge at high order in the presence of contact discontinuity of Euler equations, so a conservative front tracking technique coupling WENO schemes and Level Set method to simulate the translating density profile is presented here, and numerical simulation with this technique for representative test case has been implemented and results show the desired accuracy.

本文研究了高阶精度加权基本无振荡格式及其在双曲守恒律方程中的应用，在此基础上作了两个方面的工作：一是针对高频声波问题构造出一种基于保色散关系的WENO有限差分格式，并对计算气动声学问题的代表性算例进行了大量数值实验，比较了该格式捕捉波数的能力；另外，针对高阶WENO格式在处理Euler方程的接触间断时精度有所降低的问题，研究了利用界面追踪技术Level Set方法和高阶激波捕捉WENO格式相结合的一种守恒追踪方法，并且给出有代表性的密度滑移面问题的算例，得到一致高阶精度的数值模拟结果。

For diffusive Predator-Prey model with Holling-Ⅲ functional response without time delay, shooting argument together with LaSalle's Invariance Principle and the Hopf bifurcation theorem are applied to prove the existence of traveling wave solutions and small amplitude traveling wave train solutions.

在数学理论的研究中，行波解可以揭示方程本身的许多重要性质；在实际应用中，行波解可以很好的表现自然世界中的振荡现象。因此，对反应扩散方程行波解的研究具有非常重要的意义。

The article first theoretically analyzes the principle that microcavity reduces threshold 、changes resonant modes of output light and enhances unidirection of the random laser.Then study the structure parameters of different microcavity by transfer matrix.Based on the theory of Maxwell equations and the rate equations, analyze the principle that microcavity reduces the threshold by FDTD method: Changing the confined position,reducing relaxation time and increasing reversing particles, also simultaneously study the influences of the threshold and output light modes by different microcavities and random intensity of random medium.

首先从理论上分析了利用微腔降低随机激光器阈值、改变出射光振荡模式、提高出射光准直性的原理，然后利用传输矩阵法模拟研究了不同的微腔应具有的结构参数，最后以麦克斯韦方程和速率方程理论为基础，利用时域有限差分法分析了利用微腔降低阈值的原理：改变局域化位置、缩短弛豫时间及增大粒子数反转，同时也模拟研究了微腔、随机介质的随机强度对阈值及出射光波模式的影响。

The unsteady flow and heat transfer in pressure wave refrigerator is investigated numerically in the present paper. The Godunov scheme and control volume method are used to solve the 1D Euler integral equations and heat transfer equation respectively.

建立了振荡管内非定常流动与传热的数学模型，分别采用Godunov格式和控制容积法对气动方程及传热方程进行离散，得到了管内压力波形、气流速度及温度随时间的变化历程。

I am accused of being overreligious," she said in her quiet, frank manner,"but that does not prevent me thinking the children very cruel who obstinately commit such suicide.""

客人们在卡罗利娜·埃凯家里，举止就文雅一些，因为卡罗利娜的母亲治家很严厉。

Designed by French fashion house Herm è s, this elegant uniform was manufactured in our home, Hong Kong, and was the first without a hat.

由著名品牌 Herm è s 设计，这件高贵的制服是香港本土制造，是我们第一套不配帽子的制服。