finite sum meaning in English
有限和
Examples
- In this paper , we will more deeply research on the base of the works , the first part , we give the summarize for the condition and the significance . the second part , we give the preparation knowledge to the whole paper ; the third part , we research the lower and upper bound of the generalized hamming weights for the linear codes ; include d ( r , n , k ) bound , the finite sum representation of the lower and upper bound function of generalized hamming weights for linear codes , generalized griesmer bounds ; the 4 - th part , research the definition , the property of the r - th generalized weights for the non - linear codes and non - linear constant codes , and give the expression of the generalized weight of binary ( n , m , d ) non - linear codes ; the 5 - th part , research the weight hierarchy of linear codes and non - linear codes , for example , necessary condition and sufficient condition , the 6 - th part , we research the expression of the r - th generalized hamming weights of reseaval classes codes
本文在已有的基础之上作了进一步的探讨，第一章综述了广义hamming重量的现状和意义；第二章给出了全文的预备知识；第三章研究了线性码的广义hamming重量的一些上下界；包括d ( r , n , k )界，上下限函数有限和表达式，广义griesmer界；第四章讨论了非线性码及非线性等重码的广义hamming重量的定义、性质，给出了2元( n , m , d )非线性码的第r广义hamming重量的表达式；第五章研究了线性码、非线性码的重量谱系；第六章给出了几类码的广义hamming重量的表达式，这些码包括直和码( directsumcodes ) 、笛卡尔积码( cartesianproductcodes ) 、张量积码( tensorproductcodes ) 、延长hamming码。 - ( 3 ) by means of expanding the aperture function into a finite sum of complex gaussian functions , the propagation of fgbs through a paraxial optical abcd system with hard - edged aperture is studied , and the approximate closed - form equations of apertured fgbs are obtained for the first time . the results obtained by using the approximate closed - form equation and collins formula are compared , and the condition under which the approximate closed - form equation is applicable is analyzed
( 3 )利用光阑函数的复高斯函数展开法对截断平顶高斯光束的传输作了研究，首次得到了截断平顶高斯光束在近轴abcd光学系统中传输时的近似解析传输公式，通过比较用近似传物公式和colhns公式直接数值积分所得的结果，得出了近似公式的适用范围。