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According to Sarkovskii's theorem, if the continuous self-map f of the closed interval has a 3-periodic orbit, then f must has an n-periodic orbit for any positive integer n But f can not has all n-periodic orbits for some n.

但f不可能有所有类型的n-周期轨。例如：则f仅有两种类型的3-周期轨中的一类。这表明Sarkovskii定理远远没有给出周期轨之间的关系的全部信息。

In this paper, we will discuss the existing condition of the periodic solution of Duffing type equation with damping term. We use homeomorphism and fixed point method to prove the periodic solutions existence. We try to loose its condition, analysis and then get the existing condition of periodic solution according to defining atmospheric dynamics equation.

本文中，我们探讨带阻尼项的Duffing型方程周期解的存在性条件，运用不动点方法和Leray-Schauder度理论来证明其存在周期解，尽可能放宽其约束条件，并针对具体的大气动力学方程，分析并求取其周期解的存在性条件。

We develop and apply the Hirota bilinear-θfunction method,Jacobi elliptic function expansion method,linear superposition method and F-expansion method respectively to solve many 2+1 dimensional nonlinear wave models including 2+1 dimensional 2DsG equation,the coupled ZK equation,2+1 dimensional KdV equation,2+1 dimensional long wave short wave resonance interaction equation and 2+1 dimensional dispersive long wave equation,abundant Jacobi elliptic function doubly periodic solutions are derived.These solutions show various periodic wave shapes and special periodic characters.

发展和应用Hirota双线性-θ函数方法，雅克比椭圆函数展开法，线性叠加法，F-函数展开法等分别求解2+1维2DsG方程，耦合ZK方程，2+1维KdV方程，2+1维长波短波共振相互作用方程，2+1维色散长波方程，获得丰富的雅克比椭圆函数双周期波解，描述了一些周期波形态及周期特性。

Using algebraic methods which include extended Tanh-method,some new solitary solutions to the DBM and Log-DBM equation,such as singular solitary solutions,double singular peakon solitary wave solutions,double solitary wave solution with peakon and singular periodic solitary wave solutions are obtained..With the aid of an auxilitary function combined with the elliptic integral of the first kind,periodic solitary solution,singular and periodic singular solitary solutions can be obtained.

第三章利用扩展的Jacobi椭圆函数展开法研究了方程，并给出ZK-MEW方程的Jacobi椭圆函数解，特别的，当模数m→0和m→1时，其中一部分解退化为三角函数解和孤立波解；其次使用sn-cn拟设法，研究了K(k，s，1)方程，得到了k=s=3时的新的精确解，并在模数m→0和m→1时得到了丰富的三角函数和孤立波解。

By using theories of almost type functions,the theorem about relation of asymptotically periodic functions and asymptotically periodic sequences ,as well as the equipollence of vector-valued asymptotically periodic functions and almost periodic functions on R+ are obtained.

利用概周期型函数的理论，得出了渐近周期函数和渐近周期序列二者的关系定理，以及R+上的向量值渐近周期函数与概周期函数的等价关系。研究了渐近强周期函数空间、渐近周期序列空间的可分性质

We calculated the main effective second order nonlinear optical coefficients of the 〓 quasperiodic superlattice, analyzed the relationship between them and the quasi-periodic structure parameters, studied the extinction phenomenon and the extinction rules in quasi-periodic structure, standardized the expression of frequency conversion in homogenous crystal, periodic and quasi periodic superlattice crystal.

计算了〓准周期超晶格的有效二阶非线性系数，研究了它与准周期各结构参数之间的关系，分析了准周期结构中的消光规律，统一了频率转移效应在均匀材料、周期超晶格和准周期超晶格中的表述。

A fire\|new theory for periodic or quasi\|periodic signal sampling is proposed,w hich is especially for sampling high\|frequency wideband periodic or quasi\|peri odic signal by low sampling rate system.

涉及一种周期或准周期信号的采样技术，特别适用于低频采样系统采集高频宽带周期或准周期信号。

By Ensemble-averaged Method, the mean field was got to show the 3D structure of flow. By Phase-locked Averaged Technique, the periodic mean field was got to reflect the periodic unsteady characteristic. The 3D structure and the periodic unsteady characteristic of the unsteady flow within the vaneless and vaned diffuser were discussed through analyzing the mean field and the periodic mean field.

离心风机扩压器内非定常流动的实验研究本文完成了离心风机两种结构条件下无叶扩压器、有叶扩压器内部的非定常流动瞬态全流场的实验测量，获得了不同运行工况下PIV的瞬态流谱，为研究扩压器内部非定常流动提供了基础实验资料。

A high-speed digital-to-analog converter measurement method acquires and quantizes an analog ramp output by the DAC corresponding to a digital ramp input to produce a quantized ramp, determines a start and end of the quantized ramp, obtains a difference between the quantized ramp and an ideal ramp to produce a quantized periodic signal, determines a frequency for a qualified peak from an FFT of the quantized periodic signal, produces a mask filtered periodic signal from an iFFT around the qualified peak, and determines a sample window spanning a local maximum and minimum for each period of the quantized periodic signal.

一种高速模拟数字转换器测量方法，采集和量化由DAC输出的相应于数字斜坡输入的模拟斜坡以产生量化的斜坡，确定量化的斜坡的开始和结束，获得量化的斜坡和理想的斜坡之间的差值以产生量化的周期信号，从量化的周期信号的FFT中确定合格峰值的频率，从合格峰值周围的iFFT中产生屏蔽过滤的周期信号，并且在量化的周期信号的每一周期内确定跨越局部最大值和最小值的采样窗口。

Based on the return map and the principle of closed vectors, a new method is proposed to extract unstable periodic orbits embedded in chaotic attractors. As examples, the UPOs embedded in chaotic attractors of Logistic, Hénon and Lorenz are extracted respectively by this method. And our results of Skewed Hénon map also be compared with Nusse's. These results suggest that this method is valid for unstable periodic orbits from period one to period infinite of arbitrary dimension chaotic system. The dynamic considerations of spiking and UPO coding for individual neuron and neural system under external periodic and chaotic exciting stimulus also be studied in this dissertation. A lot of spiking phenomena, such as synchronization, period, and chaos appear alternatively with the changing of the stimulus frequency. For the small stimulus frequency the neuron could completely convey the periodic signal in synchronous anti-phase into interspike intervals sequences. For the slow time–scale chaotic input, the output two ISI sequences are reciprocally related to input signals, and their oscillation wave shape in time course can be derived from that of the input signals variation, furthermore, the similar input sequence and order of UPOs, distribution of LES and value of KYD remain in attractors reconstructed from ISI sequences.

发现周期信号在单个神经元传递过程中，随着激励频率的改变，神经元输出的峰峰间期interspike interval时间序列呈现出周期、混沌和准周期的交错变化，特别当外加激励信号频率较低时，周期信号可以通过神经元ISI序列以反相同步的周期运动形式传递下去；同时无论是周期还是混沌激励信号，在神经系统中的传递均与其自身强度和神经元之间的耦合强度的大小密切相关；快变时间尺度的混沌激励信号在耦合的神经系统传递过程中，会造成大量基本信息的丢失；而慢变时间尺度的混沌激励信号在神经系统传递中，它的非线性特征信息，如混沌吸引子、不稳定周期轨道、Lyapunov指数谱和分形维数，会通过系统输出的ISI序列部分地重现出来，如与输入慢变时间尺度的混沌激励信号相比，神经系统输出的ISI序列具有：相似几何形状的混沌吸引子、相近的Lyapunov指数谱和分形维数、局部结构相同的不稳定周期轨道的排列方式。

I'll try to bring the conversation around to the subject of money.

我想把谈话引到钱的问题上。

Only from a superior source of goats can an exceptional chevon product be made.

羊源 有优良的羊源才能生产出好品质的羊肉。