查询词典 algebraic form

We get the following conclusions: the Weil Descent's algebraic attack method is not a threat to hyperelliptic curves with the form of y〓+xy=f defined over GF (2〓) when r is large.

得出结论：Weil Descent代数攻击对这类超椭圆曲线所建立的密码体制并未造成太大的威胁。

We give another form of the infinitesimal time translation operator in algebraic dynamical algorithm so that it is more easy to use new operator to solve evolution equations.

我们给出了求解偏微分演化方程的代数动力学解法中关于时间平移的无穷小算子的构造的另一个形式，使得在应用代数动力学方法求解偏微分方程时更简洁更方便。

Content of the course consists of:(1)Basic Theories of Polynomials ;(2)Linear Algebra: topics on basic matrix theory, determinant, system of linear equations, vector space, linear transformation, eigenvalue problems, inner product and Euclidean space , and quadratic form etc.;(3) Analytic Geometry: topics on algebraic operations of vectors, coordinates, lines and planes, curves and curved surfaces, etc.

学习本课程后，学生应学会用线性空间与线性变换的观点处理包括线性代数方程组在内的有关理论与实际问题；学会熟练地运用矩阵工具；本课程还学习基本的多项式知识和空间解析几何的基本知识。课程内容包括几个主要部分：（1）多项式代数；（2）线性代数：矩阵，行列式，线性代数方程组，向量空间与线性变换理论，特征值问题，欧氏空间理论，二次型等；（3）解析几何：几何空间向量代数，通过建立坐标系以及借助向量方法研究空间平面与直线及点﹑线﹑面的相互关系，借助曲面方程研究空间曲面，尤其是柱面，锥面，旋转面和二次曲面以及曲面的交线等。

By using the techniques of an explicit criterion to determine the number of real roots of a univariate polynomial in ( [13] , [73] ); B-net form of bivariate splines function; discriminant sequence of polynomial (cf. [13] , [73] ) and the number of sign changes in the sequence of coefficients of the highest degree terms of sturm sequence, this paper determines the number of real intersection points two piecewise algebraic curves whose common points are finite.

3：利用杨路，张景中，侯晓荣在文献（[13]，[73]）中关于一元多项式实根的显式判准，以及二元样条函数的B-网形式，多项式的判别序列和Sturm序列的最高次数项系数序列的变号数，本文给出了两个分片代数曲线的实交点数的计算公式。

In this dissertation, we construct the Bariev model with nine kinds of boundary fields by the matrices K_± defining the boundaries. And then the Lax operator is given in the form ofmatrix, as well as the basic quantities, e.g., the R -matrix, the monodromy matrices and the transfer matrices are defined. By using the expression of the local Lax operator of the model,the action of the monodromy matrices T, T~(-1), U_ on the pseudo-vacuum state is given outin detail. Furthermore, the main fundamental commutation relations are obtained through the reflection equations, the recursive n-particle state as well as the one-particle exact solution is given and the Bethe ansatz equations are found accordingly. Finally, we list the nesting boundary K matrices, which play a crucial role for obtaining the n-particle solution and finding the Bethe ansatz equations, the eigenvalues of the transfer matrices and the energy spectrum of the system by means of the nested algebraic Bethe ansatz method.

在这篇文章中，我们利用边界K_±矩阵构造出了具有九种边界场的Bariev模型，同时给出了该模型L算子的具体矩阵表示形式，并定义了R矩阵，monodromy矩阵以及转移矩阵；接着利用L算子的矩阵形式，给出了其对应monodromy矩阵T、逆矩阵T~(-1)作用到真空态上的值，并利用Yang-Baxter关系及反射方程得到了双行monodromy矩阵U作用到真空态上的值；然后利用反射方程通过复杂的计算得到了一系列重要的基本对易关系式，并给出了模型的递推的多粒子波函数、单粒子解及Bethe ansat方程；最后给出了模型的嵌套的边界K矩阵的具体形式，从而为运用嵌套Bethe ansatz方法求解该模型的多粒子解、Bethe ansatz方程以及系统的能谱打下了很好的基础。

Therefore,the study of the the algebraic properties of automata with truth-values in lattice-ordered monoid and the study of the minimization algorithm form two crucial subjects in fuzzy automata theory.

因此，对取值于格半群的自动机代数性质的研究和极小化问题的研究是格值自动机理论的两个重要课题。

Utilizequadratic form and Perron value of bottleneck matrices, we study how the algebraic connectivityof a weighted tree changes under shifting its branches and changing its edge s weights and obtainmore entire information about algebrai.

利用代数连通度的二次型形式和瓶颈矩阵的Perron值，我们研究了当迁移或改变分支和变动一些边的权重时树的代数连通度的变化，得到了比过去更多的关于赋权树的代数连通度的结论。

The basic idea of the method is as follows: an algebraic theorem is used to avoid computing the composition and multiplication of B-spline basis function by Blossom and Polar form, and to reduce the computation by solving linear equations.

基本思想是：运用代数基本定理避免通常B样条基函数复合所采用的极形式以及非常烦琐复杂的开花运算，把B样条基函数的复合、乘积运算转化为求解线性方程组。

The polynomial function bases are used to form the approximately matching function. Moreover, the discrete values of grey image is transformed to polinomial function that are exact fit at the considered pixel locations. As a result, The mathematical operations performed such as derivation, integration, and gradient evaluation also give out the polynomial functions, therefore, the system of undetermined coefficient equations is derived to be a system of linear algebraic equations.

我们把立体匹配过程看作泛函的极小化过程，因此选用变分问题近似解法的Ritz法构造数值算法，以多项式函数为基构作匹配函数的近似解，进而又利用多项式过样值点的拟合将离散的灰度图象变换为多项式函数，因此计算中所需的求导，积分，及梯度运算的结果仍然是多项式函数，最终将待定系数方程组化为线性代数方程组。

Liber Abaci emphasizes summed-up algorithm, but does not pay attention to the form of propositions derived, and it mainly reflects the tendency of practical algorithms, such as principal method from India and the algebraic knowledge from the Arab. In Liber Abaci it is found some problems similar to ancient Chinese mathematics like pursuit problems, drainage problems, business problems, hundred fowls problems, remainder problems, indeterminate problems, as well as some Algorithm—fraction addition and subtraction,the compound rule of three, the method Elchataym and the method of Excess and Deficit, and so on.

在系统梳理《计算之书》数学内容过程中，笔者发现《计算之书》中存有与中国古代数学中相似的实用算题，如：追及问题、排水问题、经商问题、百鸡问题、剩余问题、不定问题等，以及和中算一致的算法：分数算法、多率法和重今有术、第二类&Elchataym算法&和盈不足术等。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。