递推公式

In this paper another deductive proof of the algorithms for the recursive solution of the system of linear equations with a Toeplitz coefficient matrix is considered, and formulas for the specific recursive solution of the various forms of the system of linear equations in accordance with a Toeplitz coefficient matrix are given.

本文给出了具有托布里兹系数矩阵线性方程组递推解法算式的另一推导证明方法，并给出了基于托布里兹系数矩阵的各种线性方程组的具体递推解法公式。

In this paper,a new algorithm is given by means of the complexification of the knots,i.e. the node in the plane is considered as a complex point,the vector as a complex vector,and then based on the construction of vector valued Thiele type rational interpolants and the backward three term recurrence relation for vector valued continued fractions,the recursive algorithm is obtained by appropriate transformation.

文章利用插值型值点复数化的方法讨论并给出了二元向量值有理插值的一种新算法，即把平面上的插值结点视为一个复数，所对应的向量视为一个复向量，使用一元Thiele型向量值有理插值公式的构造方法和向量连分式的向后三项递推关系式以及适当的变换，最后导出了这种递推算法。

The reluctivity matrix is obtained by using the trigonometric function transformation and the form of coefficient matrix is simplified.

该方法利用递推公式进行三角函数的积化和差运算求取谐波平衡有限元算法中的磁阻矩阵，简化了方程组系数矩阵的形成。

Based on parallel recursive synchronous scramble method, an novel extension bit method for parallel frame synchronous scrambler is proposed.

在递推公式并行扰码处理方法的基础上，提出了一种使用扩充比特进行帧同步扰码器设计的新方法。

And by using the initial conditions as well as the end conditions, the dynamic problem is then transferred to a second kind Volterra integral equation about the function of the axial strain with respect to time which can also be solved successfully by the interpolation method. For piezoelectric and pyroelectric hollow cylinders, by following the solving procedure for elastic hollow cylinder and by using the electric boundary conditions, the dynamic problems are transferred to two Volterra integral equations about two functions of time, one is axial strain and the other is related to electric displacement, which can also be solved efficiently and quickly by employing interpolation method. The elastodynamic solutions of hollow spheres, which are made of elastic, piezoelectric and pyroelectric materials, respectively, for spherically symmetric problems are also obtained.

对于弹性空心圆柱，通过引入一特定函数将非齐次边界条件化为齐次边界条件，然后利用正交展开技术，导出关于时间函数的方程，再结合初始条件和端部边界条件，将原问题转化为关于一个时间函数的第二类Volterra积分方程，运用插值法可给出此积分方程的解；对于压电和热释电空心圆柱，利用求解弹性空心圆柱相似的方法，再结合电学边界条件，原问题转化为关于两个时间函数（轴向应变和与电位移有关的函数）的第二类Volterra积分方程组，同样可用插值法来构造相应的递推公式高效地求解此积分方程组。

In order to describe the fatigue damage characteristic under multiaxial proportional and nonproportional loading, a new nonlinear multiaxial fatigue damage cumulative model was presented on the basis of combining multiaxial fatigue damage characteristic. The recurrence formula of multiaxial fatigue damage model was derived under multilevel loading.

为了描述多轴比例与非比例加载下的疲劳损伤特性，结合多轴疲劳损伤的特点，建立了一种新的非线性多轴疲劳损伤累积模型，并推导给出了该疲劳损伤累积模型在多级加载条件下的递推公式。

In this paper, the transformable conditions and the transformation matrices of two arbitrary B-spline bases are studied, and the theoretical results about the representation and properties of the elements of the transformation matrices are given.

本文研究任意两个B样条基可转换的条件及转换矩阵，给出了关于转换矩阵元素的表示及性质等理论结果，并推导出了两个递推公式，为实际计算转换矩阵的元素提供了易于实现的数学方法。

These formulas are used to the computation of the foundation plate for the first time, and the deflection and the moment of the foundation plate in two load cases are given.

将计算结果与Rayleigh-Ritz法结果进行比较，两者较好的一致性表明了所得导函数及其递推公式的正确性，同时也说明了基于正交基函数的无单元方法应用于C1问题的可行性和合理性。

The method of computer simulation on extravehicular activity was reviewed. Based on Kane method, the formula and process of human motion utilizing computational multi-body dynamics were presented.

简要回顾了宇航员舱外活动计算机仿真现状，基于Kane方法给出了应用多刚体系统动力学求解人体运动的递推公式及步骤。

Considering the disadvantage of high complexity and large computation of twodimensional method,a fast recursive formula was presented also.

为了克服二维空间上运算复杂性高、运算量大的缺点，给出了二维交叉熵阈值法的快速递推公式。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。