条件方程

On the basis of the 1 degree girded data of the seasonal mean temperature and salinity at standard levels in the South China Sea, mean Brunt-Visl frequency profiles were derived in order to compute numerically the vertical normal-mode for different seasons in various part of the South China Sea, and the associate linearized equation for horizontal large-scale waves is solved numerically with a improved thompson-Haskell algorithm.

根据南海1°×1°网格的标准层季节平均温、盐度资料，在未引入Boussinesq近似条件下，采用改进的Thompson-Haskell算法求解线性化斜压海洋水平大尺度波的垂直结构方程，从而得到了南海各网格点的第一斜压重力波相速度和相应的罗斯贝变形半径，并探讨其地理分布和季节变化特征，以期有助于南海环流和中尺度涡旋以及有关海洋侧边界效应的研究。

This paper was concerned with a one-dimensional linear wave equation associated with nonlinear boundary conditions.

文章里证明了一类一维线性波动方程，在非线性边界条件下，存在唯一的局部解。

The distribution of the associated characteristic equation roots is given according to the polynomial theorem, and the conditions for ensuring the existence of Hopf bifurcation are obtained. The obtained result is applied to chaotic control.

利用多项式理论给出了其特征方程根的分布，得到了Hopf分岔产生的条件，并将结果应用到混沌神经网络的控制中。

In this thesis, we take the delay r as a bifurcation parameter to investigate the Hopf bifurcation phenomenon in system (1). By analyzing the associated characteristic transcendental equation of system (2), and using the Hopf bifurcation theorem, we obtain one condition for the existence of Hopf bifurcation in system (1). Furthermore, based on the center manifold theorem and the method of normal form, some interesting results about the properties of Hopf bifurcation are obtained, including the direction of Hopf bifurcation and stability of Hopf bifurcating periodic solutions.

我们以时滞T作为分支参数，研究了系统(1)的Hopf分支现象：通过分析系统(2)的特征超越方程，结合利用Hopf分支定理获得了系统(1)的Hopf分支存在的一个条件；利用中心流形定理和正规形方法分析了系统(1)的Hopf分支的性质，包括分支的方向和分支周期解的稳定性。

Then the delay is used in circadian model. Using the delay as a argument, the distribution of the roots of the characteristic equation associated with the model under light is analyzed. Then the stable and Hopf bifurcation condition of the circadian model with delay is obtained.

然后，将时滞引入到昼夜节律系统模型后，以滞量为参数，讨论光照昼夜节律模型线性部分特征方程根的分布情况，得到该系统的稳定性和Hopf分支产生的条件。

By analyzing the distribution of the zeros to the transcendental characteristic equation associated with the trivial.solution,we obtain some- sufficient conditions on the stability and instability of the trivial solution.These results are generalized to n-unit neural networks by means of space decomposition in this Chapter.

在第二章中，我们讨论了不带自反馈与带自反馈的3元环状神经网络系统平凡解所对应超越特征方程的根的分布情况，确定了系统平凡解稳定与不稳定的充分条件，并利用空间分解的方法把相应的结果推广到n元环状神经网络系统。

Where h and k are the Love numbers appropriate for the satellite, Me is the mass of the Earth, Rm is the radius of the satellite and P20 is the l = 2, m = 0 associated Legendre polynomial.

Me是地球质量，Rm是卫星半径，P20是勒让德多项式在L=2，m=0时的解（相关内容参考这个链接： http：//en.wikipedia.org/wiki/Legendre_polynomials ，它是球对称条件下的常见的微分方程的解——gohomeman1注）。

First, under certain detectability that the system satisfies, the sufficient conditions are presented for the asymptotic convergence of the observer error by using the singular value theory. The method of solving gain matrix is presented based on the Riccati equation.

首先， 当系统满足某种可检测性时，利用奇异值理论得到了使得观测误差渐近收敛的增益矩阵需满足的充分性条件，并基于Riccati方程给出了计算增益矩阵的方法。

Some known results are generalized.Second,the global asymptotic stability for a higher order rational difference equation was investigated by using "Subsequence Analysis Method " in Chapter 3,and the "Semi-cycle Analysis Method" is a extension and supplement of "Semi-cycle Analysis Method".

因此，本文第三章应用"子序列分析法"研究了一类高阶的有理差分方程解的全局动力行为，进一步得到了此类高阶有理差分程解得全局渐近稳定的一些充分条件，一些已知的结果被推广。

Moreover, the criterion of asymptotic stability of the zero solution are established for the SDDE with a general form.

同时，还建立了一般形式下的随机延迟微分方程零解渐近稳定的判别条件。

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