Displacement of rays in a turbulent medium

The Fokker-Planck equation associated with the fluctuation (ray) equation is derived. The resulting equation for an isotropic turbulence is in the form of a diffusion equation. It has been found that the diffusion coefficient is more naturally defined in terms of the logarithmic refractive index. In the limit of weak turbulence, the present definition reduces to the conventional one. For a general and arbitrary "initial" condition, certain moments of the diffusion equation have been obtained. These moments give 1) the probability of finding a ray with a given ray direction and given path length, and 2) the mean and mean-square position of the ray in a given direction and given path length.     

薛定谔方程中包络孤子运动及相互作用的辛算法模拟

给出并证明了薛定谔方程中高斯包络孤子的表达式.针对该高斯包络孤子进一步提出了薛定谔方程中存在高斯包络孤子相互作用的情况;针对薛定谔方程提出其辛算法.通过分离波函数实部和虚部把薛定谔方程变换成标准的哈密顿正则方程组,对正则方程进行欧拉中心差分离散实现辛算法.给出了辛算法的守恒量,并证明了其稳定性.对薛定谔方程中的高斯包络孤子运动及多孤子相互作用过程进行了数值仿真,实验结果证明了所提观点的正确性及辛算法的有效性.     

基于随机微分的相位噪声统计特性

根据随机微分与噪声信号处理的内在联系,对相位噪声信号进行了系统的分析。建立了相位噪声通过滤波器后所满足的福克尔-普朗克方程,利用群移傅里叶变换(MGFT)给出了方程的解,得到了相位噪声幅度和相位的联合概率密度函数。     

非线性协调控制系统状态方程的级数解

针对非线性系统,为了合理利用变量间的有益耦合、消除有害的关联,提出了具有扰动补偿的非线性协调控制原则.根据控制原则,建立了非线性协调控制系统的状态方程,基于该方程导出了对于外界扰动的完全补偿条件,进而给出了完全补偿协调控制系统非线性状态方程.采用直接试探法,求得了该方程的任意阶级数解析解,这是一种有效的非线性系统状态方程的近似求解方法.     

道路约束在Kalman滤波中的应用

研究把道路约束引入Kalman滤波的新方法,分析了道路对过程噪声和目标速度的约束,给出了道路约束条件下目标的运动方程以及过程噪声方差调整的方法;将道路对目标速度的约束以伪测量的形式引入测量方程并给出了对应的滤波方程。两个不同场景的蒙特卡罗仿真结果验证了上述新算法带来的性能改善。     

Analytical and numerical techniques for analyzing an electrically short dipole with a nonlinear load

An electrically short dipole with a nonlinear dipole load is analyzed theoretically using both analytical and numerical techniques. The analytical solution is given in terms of the Anger function of imaginary order and imaginary argument and is derived from the nonlinear differential equation for the Thévenin's equivalent circuit of a dipole with a diode. The numerical technique is to solve the nodal equation using a time-stepping finite difference equation method. The nonlinear resistance of the diode is treated using the Newton-Raphson iteration technique. A comparison between the analytical and numerical solutions is given.     

Principles of the radiosity method versus radiative transfer forcanopy reflectance modeling

The radiosity method is introduced to plant canopy reflectance modeling. The authors review the physics principles of the radiosity method which originates in thermal radiative transfer analysis when hot and cold surfaces are considered within a given enclosure. The radiosity equation, which is an energy balance equation for discrete surfaces, is described and contrasted with the radiative transfer equation, which is a volumetric energy balance equation. Comparing the strengths and weaknesses of the radiosity formulation with those of the radiative transfer formulation for canopy reflectance modeling, it is concluded that both methods are complementary to each other. Results of a sample calculation are given for a simplified canopy model with 4000 leaves     

电子束扫描式扁平显像管偏转系统的电子光学分析

电子束扫描式扁平显像管中，电子束基本要偏转数次后上屏．本文用曲光轴聚焦理论分析了扁平显像管的偏转系统，包括正交场偏转扫描和电极推动扫描方式．文中给出了电子运动所在的电场分布的级数表达式．由变分方程出发，给出了偏转时曲光轴坐标中的高斯轨迹方程，并对方案进行了计算机模拟，分析了各种因素对于偏转电子束的影响．     

基于随机微分的雨衰模型

本文利用随机微分理论研究了卫星通信中雨衰的统计特性,首先利用非线性变换得到了雨衰的随机微分方程,然后利用福克尔一普朗克（Fokker-Planck）方程给出了雨衰的概率密度函数,最后利用办6公式推导出了雨衰的功率谱密度函数,并通过实测数据验证了所提方法的准确性。     

A recursive approach to signal detection

The classical problem of detecting known signals in additive nonstationary nonwhite noise is treated using state-variable methods. The noise is assumed to be generated as the solution of a linear time-varying differential equation driven by white noise. The Markov property of the noise is used to derive a difference equation for the likelihood ratio. The terms in the difference equation are given directly in terms of the coefficients of the differential equation defining the noise. These results, being in recursive form, reduce considerably the computational effort when discrete samples are used. The signal-to-noise ratio is also derived. Explicit expressions for the likelihood ratio are also obtained for continuous processing. These results are given directly in terms of the signals and the noise-generating equation. Thus, there are no integral equations to solve. The signal-to-noise ratio is calculated explicitly for both stationary and nonstationary noise.     

背脊波导双环铁氧体移相器

本文导出双环背脊波导锁式铁氧体移相器的传播常数公式。在典型参数下,计算了该器件的差相移和插入损耗。结果表明,该移相器的优值和差相移比同一条件下的矩形波导的同类移相器的大。为了验证文中所给方程的正确性,对差相移作了实验,其结果与计算值基本相符。     

Pulse response analysis of a complementary MOSFET inverter by the hyperbolic functional description

The characteristic equation of a MOSFET which up to the present has been expressed by two equations is given by a single equation using a hyperbolic function. The pulse response analysis of a complementary MOSFET inverter is carried out with the use of this new characteristic equation, and the results that have been shown by several equations are represented by a single equation.     

Spectral factorization of time-varying covariance functions

The determination of the state-space equations of a time-varying finite-dimensional linear system with a prescribed output covariance matrix is considered when the system is excited by Gaussian white-noise inputs. It is shown that a symmetric state covariance matrix provides the key link between the state-space equations of a system and the system output covariance matrix. Furthermore, such a matrix satisfies a linear matrix differential equation if the state-space equations of the system are known, and a matrix Riccati equation if the output covariance matrix of the system is given. Existence results are given for the Riccati equation solution, and discussion of asymptotic solutions of the differential equations is also included.     

Caudrey–Dodd–Gibbon–Kotera–Sawada方程的对称、精确解和守恒律

应用改进的CK直接方法,得到了（2+1）维Caudrey–Dodd–Gibbon–Kotera–Sawada（CDGKS）方程的对称群定理。利用对称群理论和方程的旧解得到了该方程新的精确解,扩大了解的范围。最后根据对称和共轭方程求出了（2+1）维CDGKS方程的无穷多守恒律。     

The electron beam in a cathode-ray tube

The beam in a cathode-ray tube is described by a "paraxial" Liouville equation. This equation takes into account the thermal spread of the electrons as well as the influence of the space charge of the beam. The solution of this equation is given. An ordinary differential equation is derived for the beam radius. The equation has been solved in the field-free region outside the gun. The result is presented in graphs which can be applied to the determination of the spot size on the screen of a cathode-ray tube.     

轴向流动激光放电管温度场的解析分析

从能量守恒定律出发 ,分析了快速轴向流动激光器放电管中的传热情况。采用微元分析法建立了快速轴向流动激光器放电管的热能平衡方程。根据实际器件放电管的工作气体流场 ,进行了合理的数学物理处理 ,并应用热传导的物理边界条件 ,求出了热能平衡方程的解析解 ,得出了实际器件放电管横截面内的工作气体温度分布公式及温度分布曲线。     

多维声电光效应耦合波方程理论

按照参量互作用的观点推出多维声电光效应的耦合波方程，并给出多维声电光效应衍射效率计算公式。     

空间等离子体鞘层的时域特性研究

空间等离子体环境,是计算机及各类电子设备所面临的新型恶劣环境。通过将设备表面简化为平面,给出了一维粒子层模型。根据静电场理论给出了描述鞘层电位的Poisson方程、等离子体理论和Boltzmann方程,给出了粒子数密度守恒方程。通过牛顿运动定律建立了等离子体的动量方程。基于Poisson方程、粒子数密度守恒方程和等离子体动量方程建立了等离子体鞘层动力学模型。该模型可以给出航天器表面附近等离子体鞘层形成过程的时域特性,如电荷通量、充电电位随时间的变化规律,为电子设备抗空间等离子体防护技术的研究提供理论基础。     

Optimum Finite Duration Nyquist Signals

This paper deals with the design of finite duration signals, which maximize spectral content inside a given band and which avoid intersymbol interference by being orthogonal to discretely delayed versions of itself. The signal is a solution of an integral equation With constraints. Techniques for numerically solving this equation are given. The signals are compared to the classical prolate spheroidal wave functions, for a few cases.     

Interference of Fiber-Coupled Gaussian Beam Multiply Reflected Between Two Planar Interfaces

The interference of a single-mode fiber-coupled Gaussian beam multiply reflected between two tilted planar interfaces is presented. The general equation of such interference is given. Following the guidance of the equation, the design criteria of a diaphragm fiber-optic sensor is discussed.