查询词典 periodic function

The existence of periodic solutions for a class of impulsive differential equations of mixed type is studied by constructing periodic sequence solutions of difference equations.

通过构造差分方程的周期序列解，研究了一类混合型脉冲微分方程周期解的存在性。

What differ from that of the researchers in the past is the consideration of the direction of Hopf bifurcation with Dirichlet boundary condition , that is, the conditions when the Hopf bifurcation periodic solutions are orbitally asymptotically stable with asymptotic phase.Our basic idea come from the results given by Tang[30]. We adopt the method used by Hassard in the Hopf bifurcation theorem in [24], which is to judge the existence and the direction of Hopf bifurcation, and the stability of the Hopf bifurcation periodic solutions.

与以前的研究者不同的是，本文不仅讨论了在Dirichlet边界条件下系统的Hopf分支在以扩散系数为分支参数的情况下的存在性和分支周期解的空间非齐次性，而且更多的关注了系统在Dirichlet边界条件下Hopf分支解的稳定性及Hopf分支的方向，也即系统定态解在何种条件下，当分支参数如何变化时产生Hopf分支且分支周期解是带渐近位相轨道渐近稳定的。

In Chapter 1, we use the upper and lower solutions method, the bootstrap technique and the Schauder fixed point theorem to investigate the existence of periodic solutions and the asymptotic behavior of general time-dependent solutions for periodic reaction-diffusion systems of the following three types:(1) Quasimonotone nondecreasing system;(2) Mixed quasimonotone system;(3) A nonquasimonotone 2-system. The boundary conditions are assumed to be either the Dirichlet condition or linear Robin conditions.

在第一章，我们应用上、下解方法，bootstrap技巧和Schauder不动点定理考察如下三类周期反应扩散方程组的周期稳态解的存在性和一般的时变解的渐近性态：（1）拟单增系统；（2）混拟单调系统；（3）一个非拟单调2-系统，其边界条件是Dirichlet条件或线性Robin条件。

For a monotone twist map the well-known Birkhoff fixed point theoremsays that the circles with rational rotation number will break up whence a finitenumber of pairs of periodic points arise,half of which are elliptic and the othershyperbolic.Moreover,around each elliptic periodic point a few of new invariantcurves will appear and make a picture of phase space with a self-similar structure.Again one may ask is there a similar picture for higher dimensional Hamiltoniansystems?

对于单调扭转映射，著名的Birkhoff不动点定理指出，在通有情况下旋转数为有理数的不变曲线一般会破裂，在原来的不变曲线附近会产生有限多对周期点，其中一半是双曲的，一半是椭圆的，而在椭圆型周期点的周围又会产生一圈圈的不变曲线，使得椭圆周期点附近的动力学行为和整个相空间的动力学行为十分相象，换句话说，整个相空间具有无限嵌套的自相似结构，自然又产生了一个问题：对于自由度数目大于2的高维哈密顿系统，其相空间是否有类似的图象？

According to the analytical expression, the phase grating of periodic and non-periodic system is calculated and the result keeps good agreement with that by fast Fourier transform, and the computation time is reduced up to 7 times comparing with fast Fourier transformation which is important to realize monitoring in situ in modern high-resolution technique.

3由以上解析式计算得到的晶体和非晶体的相光栅结果与快速傅立叶变换的结果一致，且能有效地缩短计算时间，这对于实现现代高分辨象的实时监测是很有意义的。

At first, based on the results of the field tests and studies, this paper indicates that there are two kinds of low frequency power oscillations on the weak tie line: one is caused by negative damping, and belongs to the free oscillation; the other is caused by periodic load disturbances and periodic adjustments, and belongs to the forced oscillation.

首先，本文根据现场试验和研究结果指出，互联系统的弱联络线上存在两类性质不同的低频功率振荡：一类是由负阻尼引起的，属于自由振荡；另一类是由于系统周期性负荷扰动或振荡调节等引起的，属于强迫振荡。

The results show that the periodic average yield of acrylonitrile under any forced periodic oscillation of oxygen concentration among this experimental conditions,thus obtained could higher than that under the steady-state condition.

而为完成整个氧化还原循环过程，气相氧分子就必须在不同丙烯吸附中心的再氧化中心上吸附，获得电子，解离后扩散进入催化剂中的阴离子孔穴，如图1所示。从该机理可知，反应气氛中的氧烯比大小对催化剂表面的氧化还原反应过程的循环有重大影响。

First of all, the method of Fredholm alternative is used to obtain the approximate solution of the first order for the bifurcating periodic solutions of a nonlinear system with delayed velocity feedback. The bifurcation direction and the stability of the bifurcating periodic solution are also determined.

首先，用Fredholm择一方法分析了一具有时滞速度反馈的非线性振动系统的Hopf分叉，得到了局部分叉周期解的近似表达式，确定了分叉解的分叉方向及稳定性。

In Chapters 3 and 4, we investigate the existence of periodic solutions of a class of second order functional differential equation and a class of third order functional differential equation, respectively, and obtain new sufficient conditions of their existence result of periodic solutions under growth conditions and linear growth condition, respectively.

第三章与第四章分别研究了一类二阶泛函微分方程及一类三阶泛函微分方程的周期解存在性，分别在增长条件及线性增长条件下，获得了这两类方程周期解存在性的新的充分条件，与文献中已知结果比较，我们所讨论的方程更为一般，所得结果较简洁且易于验证。

In Chapters 3 and 4, we investigate the existence of periodic solutions of a class of second order functional differential equation and a class of third order functional differential equation, respectively, and obtain new sufficient conditions of their existence result of periodic solutions under growth conditions and linear growth condition, respectively. Compared with some known results in the literature, the equations discussed by us are more general, and our results are concise and easy to be verified.

第三章与第四章分别研究了一类二阶泛函微分方程及一类三阶泛函微分方程的周期解存在性，分别在增长条件及线性增长条件下，获得了这两类方程周期解存在性的新的充分条件，与文献中已知结果比较，我们所讨论的方程更为一般，所得结果较简洁且易于验证。

Summary In copyright infringement cases,if the alleged infringer uses or even plagiarizes the copyrighted works or parts thereof,which causes no substantially adverse effect on the normal exploitation of the work,nor does it inflict any substantial damages to the right owner,the de minis doctrine should be applied to exempt the liabilities of the defendant and seek the balance of interests between the right owner and the general public embodied by the copyright law.

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This new product will become our best seller.

这个新产品会成为我们最畅销的产品。