查询词典 distinguished polynomial

Within the WBEPM theory,the transition probabilities and oscillator strengths of some heavier and light atoms and ions are investigated.We also used the conceptions of spectrum-level-like series and iso-spectrum-level series to study the energy levels of some atoms.Based on the previous work,we used double generalized Laguerre polynomial to calculate the value for the ground-state energy of He atom.

本论文在郑能武教授提出的最弱受约束电子势模型理论基础之上，对若干较重和轻原子离子的跃迁几率和振子强度作了研究；引入类光谱态能级序列的概念和等光谱态能级序列的概念研究了一些原子离子的能级性质；并在前人工作的基础上用双广义拉盖尔函数对氦原子的基态能量做了计算。

After building big data storage structure and constructing decimal code array, an algorithm for high-accuracy value of two-dimensional normal distribution is built through using Laguerre Polynomial expansion, and accelerating operation with Compound Simpson formula, Compound Cotes formula and Romberg formula.

以数组作为大数存储结构，解决受到计算机字节长度制约无法实现高精度运算的问题；并引入复化辛普森公式、复化柯特斯公式和龙贝格公式加速收敛，最终得到所需要的结果。

The state space forms of all these predictive PID control system are given, and their characteristic polynomial are derived by augmentation approach and Laplace expansion. At the same time, the performances of robust stability, close-loop response, and anti-disturbance of these control systems are compared with other control systems.

同时，给出了一阶加纯滞后对象、二阶加纯滞后对象、非最小相位加纯滞后对象和高阶滞后对象的预测PID控制算法，推导出了它们的状态空间形式，并通过状态增扩方法和Laplace展开方法，求出了系统的特征多项式。

The Mahler measure of a polynomial P is the absolute value of the product of all roots of P that have modulus at least 1 multiplied by the leading coefficient.

中文摘要：多项式的Mahler测度指的是它的所有模大于1的根与其首项系数的乘积的绝对值。

Firstly, we prove a proposition : the leading coefficient regarded as a polynomial in q~n, q~(1/2 of the recurrence is not equal to zero for all n ≥ [m/2] + 1, where m is the degree in q~(1/2) of the leading coefficient.

首先，我们证明了一个命题：迭代关系的首项系数关于q~n，q~(1/2的多项式对所有的n≥1[m/2]+1均不为零，其中m为首项系数中q~(1/2)的次数。

It takes the function made up of Legendre orthogonal polynomial as displacement function, and use Galerkin method to solve this function. The methods calculating formulas is very simple, so the method can avoid the great calculating difficulty of traditional simplified methods.

正交多项式伽辽金法选取由勒让德正交多项式组成的函数作为位移函数，利用伽辽金法进行求解，计算公式简单，避免了一般简化计算方法由于计算公式的复杂所带来的计算困难。

According to the orthonormality of Legendre polynomials in the function approximation theory, the exact boundary of the ball Bézier surface was optimally squarely approximated in polynomial form.

依据函数逼近论中Legendre多项式的正交性，得到了采用多项式形式表示的球域Bézier曲面的精确边界的最佳平方逼近。

And the displacement of the shell is expanded as a series of the Legendre polynomial in space.

分析说明了存在的机电耦合项，及由此产生广义刚度的非对称性。

Table 6 presents the value of the parameters of the Legendre polynomial and the pertinent consistency statistics.

表6表示勒让德多项式的参数值以及一致性检验的统计分析。

Some important inequalities about Legendre polynomial are proposed and proved.

3提出并证明了一些关于Legendre多项式的重要的不等式并在此基础上研究了使网络全局指数稳定的充分条件。

Nowadays, most of research are to build a transmutative Petri Nets through adding controlling place sets, controlling arc sets and controlling policy to the basic Petri Nets, while the Controlled Petri Nets could be used to argue many controlling theory problems conveniently and to induce many logically and physically supervisory and solve the Event Feedback Controlling Problems and State Feedback Controlling Problem in DEDS supervisory theory.

目前大多数的研究表现为在变形后的受控Petri网基础上，利用各种方法求得各种逻辑型、结构型控制器，解决DEDS监控理论中的事件反馈控制问题与状态反馈控制问题。

On one hand, there are discussions with the works council and union about extension of short time working up to the end of September.

一方面，有讨论，工程理事会和联盟关于延长工作时间短至9月底。