含对称非零元的奇数阶本原矩阵的指标集

本文证明了:当n为奇数时,含对称非零元的n阶本原矩阵类B的指标集E_B的上确界为3n-4;并且E_B={1, 2, …, 3n-4},不存在缺数段;又设N(A)是A中含正元的个数,则A是含最少正元的n阶本原矩阵的充要条件是A同构于定理6中的A.     

对不定积分的新处理

以胶用不定积分∫ｆ（ｘ）ｄｘ表示全体的原函数Ｆ（ｘ）＋Ｃ，从而把Ｃ看作任意常数变元，比较新近的说法则用∫ｆ（ｘ）ｄｘ表示原函数族，从而∫ｆ（ｘ）ｄｘ不再是函数（而是函数集），这些说法都有其本身的问题，难以服从，本把∫ｆ（ｘ）ｄｘ写成∫＾ｘｆ（ｘ）ｄｘ（分清现行变元与积分变元），用它表示一个确定的（但尚未具体指定的）原函数，Ｃ为待定常数，并作约定，在此基础上重新建立不定积分论。     

关于猜想γ（A）≤（m－1）~2＋1

设Ａ是一个非负矩阵，若存在正整数ｋ，使得Ａ~ｋ＞０，则称Ａ为本原矩阵，而上述ｋ的最小者称为Ａ的本原指数，记作γ（Ａ）．设ｍ为Ａ的最小多项式的次数，ｇ为Ａ的伴随有向图的围长，当ｇ≤ｍ－１时，猜想γ（Ａ）≤（ｍ－１）~２＋１成立。     

Histological observation of some primitive euconodonts of Late Cambrian from Liaoning

The histology of some euconodonts of Late Cambrian from Benxi and Fuxian County, Liaoning Province is studied by the oil-immersion technique. The histological characteristics of six primitive species of euconodonts - Proconodontus muelleri， Proconodontus tenuiserratus， Granatodontus ani， Rotundoconus tricarinatus， Teridontus nakamurai and Cordylodus proavus are described in detail. Tubular dentine and atubular (parallel- and wavy-lamellar) dentine are found in the basal bodies of the primitive euconodonts Proconodontus tenuiserratus and Proconodontus muelleri, respectively. The tubular dentine and spherulitic dentine are also recognized from the basal bodies of Granatodontus ani and Rotundoconus tricarinatus. Since the histological characteristics of the studied six species of euconodonts belonging to Proconodontus lineage and Teridontus lineage Sensu Miller (Univ Kansas Paleontol Contr, 1980, 99: 1?39) seems to be almost the same, euconodonts are proposed as possibly monophyletic herein.     

论文艺起源研究的原始生存切入——对原始文艺的动力学解读

在中外有关原始文艺的动力学研究中,逐渐相对稳定地形成了第一推动力分析方式和媒介推动力分析方式两种最基本的思考路向。这种思考路向有助于文艺起源体系脉络性的形成。     

数学中特殊高次方程的解法研究

基于五次或五次以上方程没有一般通用的求根公式,本文列举了一些特殊的高次方程的解法。最后阐述了方程的发展历程对代数领域的贡献。     

Improved Non-Sieving Quadratic Sieve

In this paper, we give about prime numbers and Blum two theorems and one guess integers.We prove the two theorems about Blum integers.Combining the guess with the primitive non-sieving quadratic sieve,we proposed a improved non-sieving quadratic sieve（INQS）.In INQS,we not only reduce the times of squares and modulo n, but also imply another important conclusion,that is,we don＇t need to find the greatest common divisor of two integers as we do in PNQS.By some examples,we compare it with the primitive non-sieving quadratic sieve（PNQS）. It＇s faster to factor a integer by using improved non-sieving quadratic sieve than the primitive one.