可解方程

Moreover, Problem I can be transformed equivalently into a problem that finding the minimum norm least-squares solution of a new inconsistent matrix equation.

而问题Ⅰ可等价转化为求一个新的不相容矩阵方程的最小范数最小二乘解的问题。

We expect it will benefit the industry field to break through the optical measuring limits at present by offering some new ideas. Optical measuring research based on moire interferometry has developed for several decades. The main idea of this research is to utilize the moire effect caused by two superimposed gratings of identical or similar spatial frequency. One is the reference grating and it is a virtual grating created by a computer program in this research; The other grating is the image of grating projected on the measured surface by the DLP projector, and this grating will distort because of the different sloped profile of the surface. To superimpose the program-created grating and the captured distorted grating will derive the so-called moire effect. This research combined the basic theory of optical interferometry and moire effect to project the different phases of the projected grating fringes by the phase-shifting method and compute the principal value of arguments between -π,π. In the end, the phase unwrapping program based on discrete Fourier transform of solving PDEs is used to unwrap the phase of the measured surface, and finally the surface profile is derived by the optical measuring system.

以叠纹干涉术为基础的光学检测研究之发展早已行之有年，而在本研究中所采用的投影叠纹法(Projection moiré)之主要精神在於藉由两道空间频率相近或相同的光栅相互叠加而成的效应，其中一道为参考光栅，而本研究中的参考光栅是以程式产生可调整不同空间频率的虚拟光栅；另一道则为投影至待测物表面的光栅影像，而在起伏高度不一的待测表面上的光栅影像会受到待测物表面起伏状况不同而在观测方向产生光栅投影条纹影像的歪曲变形，将电脑产生的参考光栅与由影像撷取装置所获取投影於待测物表面的光栅影像作叠合，便会产生所谓的叠纹效应；利用基本的光学干涉理论与叠纹效应结合，本研究中以相移法来改变投影於待测表面的光栅相位，再以相移法的理论反运算出在带有待测面各点高度资讯之介於-π，π相位主幅角，再以离散傅立叶转换解偏微分方程的相位重建程式还原待测面的相位值，以得知待测面之表面轮廓。

The second part is devided into two chapters, it\'s main aim is to study the global solutions to 1-d compressible Navier-Stokes equations, and it is organized as follows:In Chapter 2, we introduce the second boundary value problem for the compressible Navier-Stokes equations in the half space.

第二部分分为二章，主要讨论一维可压Navier-Stokes方程整体解的存在性，其中：第二章讨论了不可渗透问题(流体的速度在边界上为0情形)，其中对温度给出了第二边值条件。

After using the obtained elementary soluation,the singular integral equation for the collinear crack problem was obtained.

利用此基本解可得共线裂纹问题的奇异积分方程。

In Chapter 4,we prove the existence of global weak solutions to the compressible NSP equations with density-dependent viscosity coefficients when the initial data are large and spherically symmetric by constructing suitable aproximate solutions.

在第四章里，对于粘性系数依赖于密度的等熵可压缩NSP方程，在R~3中包含球心的球状区域内，我们得到了大始值的，球对称弱解的整体存在性。

The solutions of Landau free energy equation indicated that the morphography of martensitic twins was affected by antiferromagnetic transition.

Landau自由能方程的解可证明反铁磁转变对马氏体孪晶形貌的影响。

Since the initial start of buried pipelines results in three-dimen-sional unstable heat transmission , and at initial start the temperature change of the soil around a pipeline is affected by the temperature inside the pipeline and the ground surface temperature annual fluctuation, the differential equation for heat transmission and the boundary value may be line...

埋地输油管道启输过程是三维非稳定传热问题，启输过程中管周土壤温度场的变化受管内热水温度和启输前地表面温度年波幅的影响，可将传热微分方程和边值条件线性组合成两个定解问题，用电子计算机进行数值求解，得出计算公式，以确定预热阶段管路任一点任一时刻的热水介质温度。

In Chapter 4, the Thwaites＇s method for 2-D laminar boundary layer and the Truckenbrodt＇s method for 2-D turbulent boundary layer are developed to solve the"quasi-3-D"equations for the 3-D boundary layers on rotating helical blades, and a integral method, which can be solved by iteration, is resulted.

在第4章中，计算二维层流边界层的Thwaites方法和计算二维湍流边界层的Truckenbrodt方法被推广用以解关于旋转螺旋面上三维边界层的&准三维&方程，得到一种可迭代求解的积分方法。

In chapter 2, we introduce the solitary wave, its definition and generation mechanism and classify these solitons that are known up to now.

本文在TTE的框架下，运用算子理论和方法，证明了组合KdV方程的解算子是可计算的，从而可以。。。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。