一阶

Thirdly, the Hopf bifurcation of the self-excited vibration model with moving boundaries is considered.

研究了具有运动边界的自激振动模型的Hopf分叉问题，从系统自激振动的极限环生成和消亡的过程可发现：系统在边界的运动速率变化时能够发生一阶超临界Hopf分叉。

Two intuitionistic systems of firstorder sentential calculus, Hilbert s type and natural deduction t ype, were introduced.

介绍了一阶命题演算的两个直觉主义系统：希尔伯特型及自然演绎型，并证明了这两个系统的等价性，揭示了直觉主义逻辑的内涵及与其他非经典逻辑的关

Be able to solve some first-order differential equations which have separable variables.

能解决可分离变量的一阶常微分方程。

When r is positive and large, first differencing can eliminate most of the serial correlation.

当r 为正而且很大时，一阶差分可以消除大部分的序列相关性。

Consumption: first differencing can take away large part of serial correlation.

消费：一阶差分可以去掉大部分序列相关。

Using the perturbation method and Stroh's formula, a nonideal crack, which is mathematically sharp and the opposing crack faces still have a gap in which a stiffless dielectric fills, the two-field problem is reduced to a standard Riemann-Hilbert problem. The internal electric field distribution is obtained by solving a singular integral equation, and then the full field both inside and outside the crack is obtained and the electro-mechanical intensity factors to the first order of accuracy are given.

采用摄动方法对裂尖理想尖锐而裂纹面又具有一定张开的非理想裂纹进行分析，裂隙内含有无刚度的各向同性电介质，利用Stroh公式，将二域问题化为标准的Riemann-Hilbert问题，裂隙内电场分布通过解一个奇异积分方程获得，从而得到裂纹内外的力电全场分布，进而给出一阶精度下的力电强度因子的表达式。

In chapter 2, we consider the direct method of solution for singular integral equations with solutions having singularities of order one.

第二章讨论了具有一阶奇异性解的完全奇异积分方程的直接解法，这是本文的关键所在。

In this paper, we study the direct method of solution for a class of singular integral equations with solutions having singularities of order one.

本文研究了一类具有一阶奇异性解的完全奇异积分方程的直接解法。

1It is the first time to study the direct method of solution for singular integral equations with solutions having singularities of order one. The necessary and sufficient condition for the solvability and the close form of the solution are obtained.

本文主要在以下几个方面有所创新：第一，首次研究了具有一阶奇异性解的完全奇异积分方程的直接求解，并得到其可解的充要条件和解的封闭形式。

Its discretization is based on spectral elements in space and central differences method in time. The numerical result, shows that this approximation has spectral accuracy in space and up to second-order in time.

该解法引入一阶Clayton-Engquist-Majda吸收边界条件，在空间上利用谱元方法，在时间上利用中心差分的积分方法得到波动方程的离散形式，并给出具体算例进行了验证。

The labia have now been sutured together almost completely.The drains and the Foley catheter come out at the top.

此刻阴唇已经几乎完全的缝在一起了，排除多余淤血体液的管子和Foley导管从顶端冒出来。

To get the business done, I suggest we split the difference in price.

为了做成这笔生意，我建议我们在价格上大家各让一半。