查询词典 parabolic cusp

Firstly, based on the force acting on a single-particle, establish a discriminant formula of the sand threshold, and prove that the sand threshold belongs to the cusp catastrophe. Then establish the basic equation of the cusp catastrophe using coordinate transformation and catastrophe theory. Finally, while particle Reynold number and equivalend diameter are the state variables and Shields parameter is the control variables, we can obtain the model of cusp catastrophe of sand threshold, putting those variables into the basic equations of the cusp catastrophe. The model is derived from the mathematics, which has a certain mathematical theory foundation.

首先从单颗沙粒受力分析出发，建立沙床沙粒起动条件判别公式，进而证明了风沙起动属于尖点型突变；然后通过坐标变换和突变理论建立了尖点突变的基本方程；最后本文选择颗粒雷诺数和等效粒径作为控制变量，希尔兹参数作为状态变量，并把它们代入尖点突变的基本方程，经过拓扑变换得到风沙起动的尖点突变模型，并与前人的公式及实验数据进行比较。

The second part is the controllability of parabolic equation .We study on the controllability of parabolic systems with a nonlinear term involving the state and the gradient ,the null-controllability property of a 1-d parabolic equation involving a fractional power of the Laplace operator ,null controllability of some systems of two parabolic equations with one control force ,and exact controllability of the parabolic system with bilinear control .

第二部分写的是，抛物方程的能控性，我们研究了含有状态和梯度的非线性的项抛物系统的能控性，含有拉普拉斯算子的分数阶的1-d抛物方程的零能控性，带有一个强控制的两个抛物方程的一些系统的零能控性和具有双线性控制抛物系统的精确能控性。

The measuring device is structured by including a He-Ne laser; a beam expander, a soft aperture slot and a off-axis parabolic mirror to be measured are arranged in turn along the direction of the emergent laser beam direction of the He-Ne laser; a standard cross hair and a micro objective are arranged in turn on the direction of the reflected beam of the off-axis parabolic mirror; the micro objective is arranged on the focus of the off-axis parabolic mirror; the focus is imaged on an area array CCD; the output end of the area array CCD is connected with a computer; the off-axis parabolic mirror is fixed on a five-dimensional electric adjusting frame.

一种离轴抛物面镜点聚焦能力测定装置和测定方法，测定装置的构成包括：一台He-Ne激光器，沿该He-Ne激光出射激光束方向依次设置扩束器、软边光阑和待测的离轴抛物面镜，在该离轴抛物面镜的反射光束方向依次设置标准叉丝和显微物镜，该显微物镜位于所述的离轴抛物面镜的焦点，所述的焦点成像于面阵CCD上，该面阵CCD的输出端接计算机，所述的离轴抛物面镜固定在一五维电动调整架上。

Chapter 3 emphasizes on the case that the considered systems contain not only impulse but also time delay. We mainly investigate impulsive parabolic systems with time delay and neutral impulsive parabolic systems. Section 3.1 discusses the oscillation of impulsive parabolic systems with time delay under Robin boundary condition and obtains some useful criteria via first order impulsive differential inequalities with time delay. Section 3.2 studies the oscillation of neutral impulsive parabolic systems under Neumann boundary condition and Robin boundary condition, respectively, and obtains some sufficient conditions for oscillation and strong oscillation via first order neutral impulsive differential inequalities.

第三章针对于"脉冲"与"时滞"共存的复杂情形，仍采用反证法讨论了含时滞的脉冲偏微分系统的振动理论，具体研究了脉冲时滞抛物系统和中立型脉冲时滞抛物系统。3.1节考虑了脉冲时滞抛物系统的振动理论，借助于一阶脉冲时滞微分不等式的解的性质，得到了满足Robin边界条件的脉冲时滞抛物系统的若干振动准则；3.2节考虑了中立型脉冲时滞抛物系统的振动理论，借助于一阶中立型脉冲时滞微分不等式的解的性质，分别给出了满足Neumann边界条件和Robin边界条件的中立型脉冲时滞抛物系统的若干振动和强振动准则。

We study on the controllability of parabolic systems with a nonlinear term involving the state and the gradient ,the null controllability property of a 1-d parabolic equation involving a fractional power of the Laplace operator ,null controllability of some systems of two parabolic equations with one control force ,and exact controllability of the parabolic system with bilinear control.

我们研究了含有状态和梯度的非线性的项抛物系统的能控性，含有拉普拉斯算子的分数阶的1-d抛物方程的零能控性，带有一个强控制的两个抛物方程的一些系统的零能控性和具有双线性控制抛物系统的精确能控性。

The cusp catastrophe theory was described. The cusp catastrophe model of seismic signal was established, and it was converted into the standard form of cusp catastrophe.

阐述了尖点突变理论，建立了地震信号尖点突变模型，并将其转化为尖点突变的标准形式。

In the present paper,we first investigate the following initial-boundary valueproblem of parabolic Monge-Ampere equation〓 in 〓(1)〓 on 〓(2)where Ω is a bounded convex domain in 〓 denotes the parabolic boundaryof Q,and second give a preliminary probe into the initial value problem of aspecial kind of parabolic Monge-Ampere equation which comes from the theoryof optimal investment in mathematical finance.

本文首先讨论如下抛物型Mongc-Ampère方程的第一初边值问题〓（1）〓（2）其中〓为〓中的有界凸区域，〓为Q的抛物边界，然后针对一种在数学金融学的最优投资理论中导出的特殊形式的抛物型Monge-Ampère方程的初值问题进行了初步的探讨。

In order to achieve the setting up angle should be monitored and debugged, a new approach is brought up. With the CCD receiving the focusing spot of parabolic mirror, while rotating the parabolic mirror, collecting the focusing spot location information, the eccentric angle between the optical axis and the structural central axis could be found. System principle and design have been studied.The experimental results meet the need to test and monitor to the setting up angle of the discal parabolic mirror.

为了实现对抛物面反射镜的装配角度进行监控和调试，提出了一种通过CCD接收回转抛物面镜的聚焦光斑，同时旋转抛物面镜，采集光斑重心位置信息，从而计算出光轴与结构中心轴之间的偏心角的实现方案，并从方案原理和设计上对其进行研究和实验，实验结果证明该系统能应用于对盘状抛物面反射镜装配角度的测试和监控。

The paper consists of four chapters:In chaper 1, we introduce the background and signficance, research and actuality on oscillation of functional partial differential equations; we present research subject in this paper;In chaper 2, we discuss oscillatory property of systems of parabolic differential equations with delays and obtain necessary and sufficient conditions for the oscillation of their solutions; we show the difference between oscillatory property of systems of parabolic differential equations with delays and that of systems of partial differential equtions without delays; we explain the main results with examples;In chapter 3, we discuss oscillatory property of systems of functional parabolic differential equations of neutral type; we obtain some sufficient conditions for the oscillation or full oscillation of their solutions under some conditions; we explain the main results with examples;In chapter 4, we discuss oscillatory property of systems of functional hyperbolic differential equations of neutral type; we obtain sufficient conditions for the oscillation or full oscillation of their solutions under some conditions; we explain the main results with examples.

全文共分四章：第一章简要介绍了泛函偏微分方程的振动的背景和意义、对其研究的简单历史和现状，给出了本文的主要研究对象；第二章讨论了一类时滞抛物方程组解的振动性质，获得了判断其所有解振动的一个易于验证的充要条件；指出了这类具有时滞偏差变元的抛物方程组解的振动性质和不具有时滞偏差变元的抛物方程组解的振动性质的差异；并举例对主要结果进行阐明；第三章讨论了一类中立型抛物方程组解的振动性质，获得了在给定的条件下其所有解振动或全振动的若干充分条件；并举例对主要结果进行阐明；第四章讨论了一类中立型双曲方程组解的振动性质，获得了在给定的条件下其所有解振动或全振动的若干充分条件；并举例对主要结果进行阐明。

When and we show that system (1) has the cusp bifurcation of codimension 2(ie,Bogdanov-Takens bifurcation); when ,we show that this system has the cusp bifurcation with codimension at least S.

而且我们选择了系统的原参数中的二个作为分支参数，可以使系统(1)进行Bogdanov-Takens余维2普适开折，从而证明系统(1)同宿轨的存在性。

The first step was the preparation of bismuth octanoate.

第一步是准备铋辛酸。

A younger woman reaffirms for me that I've still got it going on.

与年轻女人在一起让我觉得我还行