代数多项式

A polynomial system PS over the rational number field is constructed from the formula...,in a given many-valued logic system such that follows from ...,iff the algebraic variety defined by PS is empty, iff the idealenerated by PS is trivial.

由给定的多值逻辑系统中的一组公式，。。。，，出发，构造出了一组有理数域上的多项式PS，使得是，。。。，的逻辑结论，当且仅当PS定义的代数簇为空集，当且仅当PS生成的理想是平凡理想。

A polynomial is a sum of two or more algebraic terms.

多项式是两个或者更多代数项的和。

What s more, we wonder whether there are some qualities about algebroid function corresponding to meromorphic func-tion,specially, concerning deficiency, characteristic function,differential polynomial and so on.

而且一些亚纯函数中存在的性质在代数体函数中是否相应存在仍有待研究，特别是涉及亏量、特征函数及微分多项式等方面。

The main theory results includes:(1) Using the properties of Hilbert transform, perfectly reconstruction and new type of lifting scheme, a new type of dual-tree binary coefficients complex wavelet with linear phase is achieved.(2) For linear systems that can be diagonalized by GFT and DST-II matrices, an efficient MGM method is proposed, convergence is proved.(3) We discuss the algebraic structure when Toeplitz matrix is transformed by multi-band wavelet,show that Toeplitz matrix is composed of generating function is transformed to a band and sparse matrix when wavelet applied to this matrix, based on the above results, an efficient solution of Toeplitz equations is obtained, and the computational complex is O,where N is the order of matrix.

理论成果主要包括：(1)对于对偶树二进制系数复数小波，利用Hilbert变换对性质、完全重构条件并结合新的提升格式构造研究了含参系数多进制小波构造方法，作为特例得到具有线性相位的对偶树二进制系数复数小波构造方法；(2)对于广义离散傅立叶变换与正弦变换对角化系统，提出了高效、快速的多重网格算法，理论上证明了算法的收敛性；(3)研究了Toeplitz矩阵在多进制小波变换下的代数结构，验证了多项式生成函数构成的Toeplitz系统在小波变换下的稀疏带宽性质，从而建立基于小波变换求解Toeplitz系统的快速求解方法，运算量级控制在O，其中N为系统的阶。

For the beam buckling problem, this paper presents the Barycentric Lagrange interpolation collocation method to get the differentiation Matrix of unknown function.

采用重心Lagrange插值多项式建立未知函数的微分矩阵，采用配点法将梁的控制方程表示为代数方程组。

To solve the characteristic polynomial and the eigenvalues of square matrices with higher order normally is not an easy way.

1引言在高等代数中，求一个n阶方阵A的特征值时，常用的方法是求解A的特征多项式|λE-A|的根。

In the given algorithm, a matrix is first transformed into its Hessenberg form by using row- and column-transformation and the characteristic polynomial can be then determined by means of the formulas and a recursive algorithm given in this paper.

例如，在确定系统矩阵的规范形，在用代数方法判别系统的稳定性，在控制器和观测器的设计等时，就通常需要计算矩阵的特征多项式。

In graph theory,we have the algebraic graph theory[8]which involving spectrum,chromatic polynomial and so on.

在图论中，我们有代数图论[8]，通过研究图的谱，色多项式等来研究图的性质。

We designed the algorithm which can perform the closed domain inclusion test in real time, realized quick search in the algebraic inclusion test algorithm by transforming polynomials with dichotomy.

设计了可实时计算的高斯图闭域包含测试算法，通过引入二分法改造多项式包含测试代数算法，实现快速查找。

The cohomology of q-polynomial coalgebras with coefficients in trivialcomodule K are also determined(see Theorem 6.3.11).Having obtained Theorem 5.2.3 andTheorem 5.2.4,we determine(see Theorem 7.2.6)all the nonzero 〓.

对于这一类q-多项式余代数，我们决定了（见定理6.3.11）系数在它的平凡余模K中的上同调，有了定理5.2.3与定理5.2.4以后，我们决定了（见定理7.2.6）所有非零的〓。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。