多项式方程

Through the Radon transformation of the normally ordered Wigner operator we introduce two mutually conjugate intermediate coordinate- momentum representations. Based on them we construct the appropriate quantum phase space theory which includes the new Wigner operator adapting to this space and construct the appropriate generalized Fredholm operator equation and then find its solution. We then deriving the Hermite polynomials operator identities by applying the Fredholm equation. We also reveal the connection between the generalized Wigner operator and the 2-dimension normal distribution in statistics, which is useful to study the quantum tomogram. As the application of the entanglement Husimi operator theory we calculate the Wigner function and the Husimi function of the one- and two-mode combination squeezed state , study their characters through drawing the three-dimensional graphics.

由正规序Wigner算符的拉登变换引入了两个互为共轭的中介坐标-动量表象，在此基础上我们建立了相应的量子相空间理论，其中包括引入适合该空间的新的Wigner算符；并在该表象的基础上，建立了广义Fredholm算符方程，求出了它的解，并运用该方程导出有关厄米多项式的算符公式；揭示广义Wigner算符与统计学中的随机变量的二维正态分布形式上的相似，这对于研究量子态的tomogram(是英文Tomography的派生词)有用。

Applying the Hermite polynomial expansion, this integral-differential equation is creatively transformed into deterministic differential equation.

创造性地使用Hermite多项式展开，将确定性的积分——微分方程转换为确定性的微分方程。

For the group representation, this paper improves the known method of determining the irreducibility. Instead of solving equations and checking every combination of the roots, we calculate the value of a polynomial.

对于自由群的表示，本文首先将不可约性的判别方法，由已有文献中解方程，并对方程的根作组合的方法，改进为直接计算某个多项式的值的方法，并进一步给出区分绝对不可约性和非绝对不可约性的判别准则。

Here pis 1 or 2.In chapter 8. we extend the Runge-Kutta methods to variable delay differentialalgebraic system. It is proved that if the Runge-Kutta method which is algebraicallystable and diagonally stable is consistent with order p , the extended Runge-Kuttamethod with Lagrange interpolation procedure is D_A-convergence with order M. HereM=min{p, u + q + 1 }, and u + q is the degree of Lagrange interpolation polynomial.

第八章将求解常微分方程的Runge-Kutta方法改造后用于求解变延迟微分代数系统，并且证明如果代数稳定且对角稳定的Runge-Kutta方法对于常微分方程初值问题在经典意义下是p阶相容的，那么具有Lagrange插值过程的该方法是M阶D_A-收敛的，M=min{p，u+q+1}，u+q为Lagrange插值多项式的次数。

The relation between the limit state function of large and complex structural systems and input random parameters is always unknown. A quadratic polynomial is considered to simulate the physical limit state function.

工程中大型、复杂结构的极限状态方程与输入随机变量的关系往往是未知的，利用响应面法，用一个二次多项式来模拟结构的极限状态方程。

According to real tested data,it builds up CVC cambering curve equation by polynomial regression.

根据实测数据，采用多项式回归方法，建立CVC 辊形曲线方程，并探讨了该方程的重要实际意义。

Weinnovativly introduce Dickson polynomial to solve the equation, which makes theprocess easy and feasible.

在证明过程中创造性地引入Dickson多项式来求解方程，使得方程的求解变得简单可行。

The conductivity field and hydraulic field are represented by Karhunen-Loeve expansion and polynomial expansion, respectively. The original stochastic partial differential equation is transformed into a series of deterministic equation at the collocation points.

其渗透系数场和水头场分别被表示为Karhunen-Loeve展开和多项式展开的形式；初始随机偏微分方程被转化为在相应配点上的确定性方程。

The conductivity field and hydraulic field are represented by Karhunen-Loeve expansion and polynomial expansion , respectively. The original stochastic partial differential equation is transformed into aseries of deterministic equation at the collocation points.

其渗透系数场和水头场分别被表示为 Karhunen-Loeve 展开和多项式展开的形式；初始随机偏微分方程被转化为在相应配点上的确定性方程。

Based on Wu's elimination method and "divide-and-conquer" strategy, the undetermined coefficient method for constructing polynomial conservation laws of nonlinear differential-difference equations was improved. Furthermore, a Maple package CLawDDEs was developed to automatically derive conserved densities and associated fluxes of polynomial differential-difference equations.

基于吴消元法和"分治"策略，改进了基于标度不变性构造非线性微分差分方程多项式形式守恒律的待定系数算法，并在计算机代数系统Maple上实现了改进后的算法，其中的软件包CLawDDEs可自动推导出微分差分方程的守恒密度及连带流。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。