矢量方程

Parikh and Wilczek further refined and extended the thought of Keski-Vakkuri and Kraus, the radiation was explained as a tunneling process crossing the barrier of horizon, and in literatures the method is called Parikh-Wilczek tunneling method. In our paper, we further studied the effect of Hawking radiation of the apparent horizon of the dynamical spacetime, the FRW universe, and the thermodynamics of the apparent horizon of the dynamical black hole modes, the Vaidya black hole and the McVittie black hole.

更为重要的是，近年来联系于视界热力学一些新的性质被发现：Einstein方程在视界上可以作为热力学第一定律的形式出现；在Friedmann-Robertson-Walker宇宙表观视界上，时空动力学方程(Friedmann方程)也可以写成一个所谓的统一热力学第一定律的形式；局域定义的FRW宇宙表观视界，也存在着在Kodama矢量观测者看来的Hawking辐射效应。

The key point of this paper made a study of the application of FDTD method to dispersive, nonlinear materials. Two methods are introduced to deal with the relationship between the electric flux density vector and the electric field vector: auxiliary differential equation method and Z transform method.

本文的重点在于研究时域有限差分法在非线性色散媒质中的应用，主要采用了两种方法来处理电通量密度矢量D和电场强度矢量E之间的关系：辅助差分方程法和Z变换法。

The cross-high-order-cumulant such as the cross-fourth-order cumulant is firstly proposed to measure the signal and for the first time prove that the CHOC can control the non-relevant noises and Gaussian noises. And based on the cross-high-order spectral Yule-Walker equations, the sinusoidal signal matrix is decomposed by the way of singular value decomposition method.

摘 要：本文以互四阶累积量为依据，首次证明了互高阶累积量可以有效地抑制非相关噪声和高斯噪声；并在建立互高阶累积量的Yule-Walker方程的基础上，通过该矩阵的奇异值分解，建立了信号矢量空间与噪声矢量空间；首次提出了混合噪声背景下正弦参数估计的互高阶谱Pisarenko方法。

The motion of a discrete curve in Minkowski space is first introduced. Then by identifying the spin vector of HF models with the unit vectors of discrete curve, respectively, we obtain the corresponding DNLS.

我们将主要考虑闵可夫斯基空间中离散曲线的运动情况，并利用离散曲线的单位矢量分别替代离散的MHF方程中的自旋矢量，给出相应的离散非线性薛定谔方程，从而建立了两者之间的几何等价性。

A.Einstein's personal experience had founded his belief in mathematics and relevant methodology,success in the general theory of relativity had his belief enhanced,and this had led Einstein astray in introducing the semivector for research Dirac's equation.

爱因斯坦；数学信仰；半矢量；爱因斯坦的科学经历铸就了他的数学信仰以及相应的方法论，广义相对论的成功使这种数学信仰得到强化，并使他在引入半矢量研究狄拉克方程过程中误入歧途。

Firstly, four geometric loop equations are set up by using vector method in complex number fields. Secondly, three constraint equations are used to construct the Dixon resultants, which is a 6×6 matrix and contain two variables to be eliminated. Extract the greatest common divisor of two rows and two columns of Dixon matrix and compute its determinant to obtain a new equation. This equation together with the forth constraint equation can be used to construct a Sylvester resultant.

首先使用矢量法和复数法建立4个几何约束方程式；再使用Dixon结式法对3个方程式构造一个含有2个变元的6×6 Dixon矩阵，提取其中2行列元素的公因式，将新矩阵的行列式展开后得到二元高次多项式方程，该方程与剩下一个方程使用Sylvester结式消去一变元，得到一元高次方程。

To do that,the integral definition of vector magnetic potential and the Lorentz gauge is used to expand the integral equation of the PEEC model.

为此它以矢量磁位的积分表达式和洛仑兹规范代替了矢量磁位和标量电位的积分表达式，对积分方程进行展开。

From K-G Equation and Dirac equation,using 2-D invariant line element, the radius equation and event horizon formula of particles are obtained.A simpler method to the research of quantum effect of the scalar and vector particles in black hole with spherical symmetry is singgested.

分别从K-G方程和Dirac方程入手，利用简化后的二维不变线元，直接给出了粒子的径向方程和视界面方程公式，为研究球对称黑洞中标量粒子和矢量粒子的量子效应提供了一个更简单的方法。

Based on the wave equations of electromagnetic field, a new time-domain numerical method-direct difference solution of vector wave equation is researched. Calculating formulas of electric field and magnetic field are also given.

对电磁场波动方程进行了分析，研究了一种基于电场波动方程的时域数值方法―矢量波动方程的直接差分解法，给出了电场和磁场的计算公式。

Second, based on the spherical vector wave function in uniaxial anisotropic medium, and the first, second, third and fourth spherical Bessel functions satisfy the same differential equation and recursive formula. The scattering fields in terms of spherical vector wave function from a uniaxial anisotropic spherical shell and an anisotropic uniaxial-coated conducting sphere by a plane wave are derived. The electromagnetic fields in uniaxial anisotropic medium and free space can be expressed in terms of spherical vector wave functions in uniaxial anisotropic media and isotropic medium.

二、在建立均匀各向异性单轴介质球矢量波函数理论的基础上，利用二阶线性偏微分方程的性质和第一、第二、第三和第四类球Bessel函数满足相同的微分方程和递推关系，我们分别研究了单轴介质球壳和单轴介质涂覆导体球对平面波的电磁散射特性，首先给出了各个区域的电磁场用球矢量波函数来表示的解析表达式，进而利用电磁场在边界上满足电磁场切向连续的边界条件和球谐函数的正交性，得出了各向异性单轴介质球结构中电磁场用球矢量波函数表示的系数所满足的矩阵方程。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。