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1)  recurrence propagation equation
递推传输公式
1.
Based on the expansion of the window function of a hard edge aperture into a finite sum of complex Gaussian functions,the recurrence propagation equation of cosh Gaussian(ChG) beams through a multi apertured paraxial ABCD optical system is derived,which permits us to study the propagation of ChG beams through hard edge optics analytically.
基于将硬边光阑窗口函数展开为有限个复高斯函数之和的方法 ,推导出了双曲余弦 高斯光束 (ChG)通过多个光阑近轴ABCD光学系统的递推传输公式 ,该公式可用来解析地研究光束通过硬边光阑光学系统的传输特性。
2)  Recurrence formula
递推公式
1.
The recurrence formula for beam transform in bending was deduced.
推导了求梁的变形的递推公式并对其应用方法做了说明。
2.
This paper put forward a recurrence formula through calculation and synthesis,based an harmonic series theory.
通过计算、综合、证明等步骤,得出飞机空中加油问题的递推公式,并以调和级数等相应的数学理论为基础来解决。
3.
A new kind of dependent Legendre polynomial,and general expression of orthogonal polynomial of its derivatives and recurrence formula are researched,and are obtained good conclusion.
探求了一类相关Legendre多项式及其导数的正交多项式的一般表示形式及其递推公式 ,得到了较好的结论 。
3)  recursive formula
递推公式
1.
Based on the special matrix operations including Kronecker product, Hadamard product and vectorization, the integration of monomial integrand on simplex domain is expressed in matrix form and a recursive formula for the simplex integration is presented.
基于Kronecker积、Hadamard积和拉直等矩阵特殊运算,将单项式函数在单纯形上的积分表示为矩阵形式,提出了单纯形积分的递推公式。
2.
The recursive formulae suitable to computer programming are given.
对多窗口函数之一的物理实现原理和方法进行了讨论与分析,找出了其对应的可实现有理函数的求取方法,导出了很适合计算机编程计算的递推公式,并在此基础上建立了其实现的数学模型和原理框图。
3.
on the basis of studying the recursive formula of the rigid manipulator inverse dynamics.
本文在对刚性机械臂逆动力学的递推公式研究的基础上,针对递推形式的 Lagrange-Euler 方法提出了一种并行算法,并在计算效率上与不采用并行计算的 Lagrange—Euler 法作了比较,其结果是令人满意的。
4)  recursion formula
递推公式
1.
The mathematic form of computer spline is a set of recursion formula which keep away from solution of inear equations.
计算机样条的数学形式是一组递推公式,避免了线性方程组的求解。
2.
Moreover the Proof of recursion formula in paper [1](namely recursion formula (two) in this paper) is simplifie
这些方法只需计算特征函数A(r)及其各阶导数在某点的值,方法简单,两种递推公式适合计算饥计算,本文还简化了文[1]中递推公式(即本文的递推公式(二))的证明。
3.
The article gives the reversible condition of a kind of jump Vandermonde matrix through linear equations, and recursion formula and the expression of its inverse Matrix.
利用线性方程组给出了一类跳行范德蒙矩阵可逆的条件,并给出了逆矩阵的递推公式和逆矩阵的显式表示式。
5)  recurrent formula
递推公式
1.
By letting A(n,k) be the number of nonnegative integer solutions for the indeterminate equation∑ki=1ixi=n, this paper proves recurrent formula, gives corresponding table, and presents an accurate formula of A(n,4) using the recurrent formula.
 设A(n,k)为不定方程∑ki=1ixi=n的非负整数解的个数,本文作者给出了A(n,k)递推公式的证明及由此公式得到的A(n,k)取值表,用该递推公式求出了A(n,4)的精确公式。
2.
A self-similar analytical solution of the Boussinesq equation of groundwater flow in a semi-infinite porous medium when the hydraulic head at the boundary behaves like a power of time was presented(Barenblatt(1952) obtained a power series solution,but he listed only the first three coefficients and did not give the recurrent formula among the coefficients.
通过幂级数展开的方法推求得出了Barenblatt幂级数解的各项系数之间的递推公式(对半无限长多孔介质中地下水流动的Boussinesq方程的自相似解,在边界水头随时间幂函数变化的条件下,Barenblatt(1952)得到了一个幂级数解,但他仅仅列出了其前3项的系数,既没有给出整个幂级数解所有系数的递推关系式,也没有证明该幂级数解的收敛性。
3.
In addition, two recurrent formulas are derived which provide a mathematical approach to the calculations of the elements of the transformation matrices.
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。
6)  Recursion formulae
递推公式
1.
The Recursion formulae of the node corner displacement are derived in the text and that internal of the beam can be solved.
推出了求解无结点侧移连续梁的结点转角位移的递推公式,进而求得梁板的内力。
2.
The recursion formulae of the node angle displacement are derived in the text and that internal forces of the beam can be solved.
推出了求解结点转角位移的递推公式 ,进而求得梁的内力 。
补充资料:递推公式


递推公式
recurrent formula

  递推公式〔recul侧翻t fomll山或犯currence fonntlla;pe叮ppeltTH朋加pMy几a」 同递推关系(肥cluTence rela石on)
  
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