双线性

Near the bifurcation point, the linear stability of difference differential equation which describes acoustooptic bistable systems is analyzed, the expression of resonance frequency and amplification multiple are given.

在分岔点附近，通过对描述布拉格型声光双稳系统的差分－微分方程进行线性稳定性分析，得到了系统对小信号放大时的共振频率，给出了放大倍数的表达式。

Finally, we study the eventual differentiability of a C_0-semigroup associated to a waveequation with boundary dissipation.

最后，我们讨论了一类具边界耗散的线性双曲型方程生成的算子半群的最终可微性，并利用这个结果得到了方程的解具有最终正则性以及半群满足谱决定增长条件。

In the case of Dirichlet boundary conditions,these estimates were improved by Baker[1]who used a technique that can be interpreted as a nonstandard energy argument.

Dupont[15]使用标准能量方法给出了一类线性双曲方程Galerkin解的L2误差估计，对于Dirichlet型边值问题，Baker[1]对其结果作了改进，用的是一种可谓"非标准的能量不等式"方法。

In the second chapter the experiment technique and approaches are discussed,including laser induce fluorescence spectroscopy which the comprehensive adopted for liner laser spectroscopic study,and high resolution two-photon laser spectroscopy without Doppler broadening which belonged to nonlinear laser spectroscopic ,and the theory about the fluorescence rate equation .

第二章实验技术和研究方法中，讨论了在线性激光光谱中最为常用的激光感应荧光光谱、非线性激光光谱学可使谱线的多普勒宽度得以消除无多普勒双光子吸收光谱学和碰撞分析中使用的荧光的速率方程理论。

The one-dimensional time-dependent Schrdinger equation was numerically solved with the symmetric splitting of the short-time exponential propagator and the fast Fourier transformation, and influence of intensity and pulse with on ionization of linear multi-ation molecular ion in two-color laser fields was researched.

利用短时指数传播子对称分割法和快速傅里叶变换技术，数值求解了一维含时Schrodinger方程，探讨了双色激光场中激光的基波和谐波强度之间的不同配比以及脉宽对线性多原子分子离子电离的影响。

On the basis of direct modelling method by using extended Kalman filter, a new method combining extended Kalman filter with adaptive extended Kalman filter is presented to model gyro drift directly from rotate angle of turntable. Extended Kalman filter has great estimation error, what is more, may be divergent if the model and noise statistic are not accurate or wrong. The new method solves the problem of general extended Kalman filter by using fictious noise with timevarying statistic to compensate the linearized model error of extended Kalman filter. The parameter estimators of single-axis and double-axis servo test are designed from it.

本文深入研究了根据伺服试验数据进行陀螺仪漂移误差模型建模的方法，在应用广义Kalman滤波器直接建模的方法基础上，针对广义Kalman滤波器对于不精确或错误的模型和噪声统计，估计误差较大，甚至滤波发散的缺陷，借助于用带时变噪声统计的虚拟噪声补偿广义Kalman滤波的线性化模型误差的新思想，提出了用广义Kalman滤波和自适应广义Kalman滤波算法相结合的方法由转台的转角数据直接建模陀螺仪漂移误差模型，并设计了陀螺仪单轴伺服和双轴伺服测试时参数估计的滤波器。

The grey scale of the pixels in image is expressed by quantum bit and the relation between two pixels is described by means of the superposition of two quantum bit in this paper.Based on this,the average of linear hermitian operator in this superposition can be used for judging the edge of image and a new method for edge detection of image is so created.The rationality of the method is interpreted by probability theory here.

利用量子比特表示图像像素的灰度，用双量子位叠加态来描述两像素之间的关联，通过线性厄米算符在该量子叠加态中的平均值来判断像素的边缘特征，由此建立了一种新的图像边缘检测方法，并从概率论的角度对该方法的合理性给予解释。

In this paper, we consider neutral functional differential equations and study the global existence of their solutions, stable subspaces and unstable subspaces of linear autonomous dynamical systems, local stable manifolds and local unstable manifolds of near hyperbolic equilibrium point of nonlinear autonomous dynamical systems, periodic solutions and oscillation of the neutral equations.

本文主要研究中立型泛函微分方程解的整体存在性，自治线性动力系统的稳定子空间与不稳定子空间、自治非线性动力系统在双曲平衡点的局部稳定流与局部不稳定流，周期解与解的振动性。

Numerical experiments show that because Navier-Stokes equations at highReynolds number are a hyperbolic system,the boundary conditions are appli-cable to prescribe their boundary problems.

数值实验表明，在高Reynolds数下，由于Navier-Stokes方程呈现出很强的双曲型方程的性质，上述经过某些线性化处理得到的无反射边界条件是可以用来指定其边界值问题的。

A L(superscript ∞) bound estimate is provided on the solutions of a semi-linear parabolic system by the theory of phase transitions. The existence of solutions of corresponding hyperbolic system of conservation laws is studied by viscosity methods and compensated compactness framework.

讨论来源于物理相变理论的一类半线性抛物型方程组解的一致L估计，该结果是利用粘性法和补偿列紧框架研究相应的双曲型守恒律解的存在性的重要内容。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新