The main results are : ( 1 ) we give an upper bound for kth generalized primitive exponents of primitive digraphs with order n and girth 2 , and determine the exponent set of this class digraphs in section 2 主要内容有三部分： ( 1 )第2节给出了围长为2的n阶本原有向图的第k个顶点指数( exp _ d ( k ) )的上界及相应的指数集。
( 2 ) we give an upper bound for kth generalized primitive exponents of non - primitive digraphs with order n and girth 2 , determine the exponent set of this class digraphs in section 3 , and discuss the extreme cases ( 2 )第3节给出了围长为2的n阶非本原有向图的第k个顶点指数( exp _ d ( k ) )的上界及相应的指数集，讨论了极端情形。
By introducing proper stretchy variable and constructing boundary layer function , it concludes n - order approximate solution , and using theory of differential inequality , uniformly validity of asymptotic expansion is proved 通过引进适当的伸长变量，构造边界层函数，得到了解的n阶近似值，并利用微分不等式理论证明了解的渐近展开式的一致有效性。
Let a graph g is a simple graph of order n . a graph of order n is called pancyclic if it contains cycles of every length l , 3 < l < n , and is called weakly pancyclic if it contains cycles of all lengths between its girth and circumference 设g是n阶简单图，如果对于任意的整数l ： 3 l n ， g中含有长度为l的圈，则称g为泛圈图；如果g中含有长度在围长和周长之间的所有圈，则称g是弱泛圈图。
This article brings forward a new prognostic model , which is based on n _ rank transfer probability coming from the theory of random process and restricted by minimum confidence and adjustment matrix . using this model , ultimately prognostic result can be found 本文将介绍一种新的预测模型，它以随机过程理论中n阶转移概率的概念为基础，并结合最小置信度及调整矩阵对模型进行约束，最终得到预测结果。
The independent index of a graph g , denoted by i ( g ) , is the number of independent sets in g . the trees of order n with the largest and the smallest independent index and the forest of order n with the largest and the smallest independent index are known 图g中独立点集的个数i ( g )称为图g的独立指数。 n阶树(或林)的独立指数的上、下界和独立指数取到上、下界的树(或林) ，以及独立指数第二小的n阶树已经得到。
In this paper , we brought forward the concept of ergodic matrix over finite field fq , simply discussed theory of finite field including property theory of finite field , calculation in finite field and construction from low - degree finite field to high - degree finite field 本文引入了有限域上n阶遍历矩阵的概念,对遍历矩阵进行了初步的探讨,给出了遍历矩阵的一些定理及构造遍历矩阵的递推关系式,讨论了其难破解性。
In section two , the circular graphs with order n that the first row of their adjacent matrix is [ 01100 . . . 0011 ] and [ 010100 . . . 00101 ] are considered and we obtain the fractional chromatic number of them , include the chromatic number of the graphs whose first row of the adjacent matrix is [ 01100 . . . 0011 ] just while n is not the multiple of 3 在第二部分中，考虑了邻接矩阵第一行分别为[ 01100 … 0011 ]和[ 010100 … 00101 ]的n阶循环图，得到了它们的分数色数，以及邻接矩阵第一行为[ 01100 … 0011 ]的n阶循环图当n不是3的倍数时的顶点色数。
After introducing the conventional edge detection operator and multiscale wavelet edge detection operator , we discussed the well quality of b - spline function > n - class derivative of gauss function n harmonic function and hermite function in wavelet theory and their concrete application in the image edge detection 在对单尺度下的传统边缘检测算子和多尺度小波边缘检测算子介绍的基础上，讨论了b样条、 gauss函数的n阶导数、谐波函数以及hermite函数在小波理论中所具有的良好性质，以及它们在图像边缘检测中的具体应用。
The tree of order n with the second smallest independent index is also known . ( [ 1 ] , [ 6 ] ) in this paper , we mainly study the unicyclic graph of order n with independent index , the unicyclic graph of order n with the largest and the smallest independent index are know ( theorem 2 , theorem 3 ) . we also determine the unicyclic graph of order n with the second largest independent index ( theorem 4 , theorem 5 ) , and the unicyclic graph of order n with the second smallest independent index ( theorem 6 , theorem 7 ) ( [ 1 ] 、 [ 6 ] )本文讨论n阶单圈图的独立指数，得到n阶单圈图的独立指数的上、下界(定理2 )和独立指数取得上、下界的n阶单圈图(定理3 ) ，以及独立指数第二大的2阶单圈图(定理4 ，定理5 ) ，独立指数第二小的n阶单圈图(定理6 ，定理7 ) 。
