Probe into the Internal Roots of Anna Karenina's Tragedy

Anna was a vivid literature figure in the international literature history. Besides the obvious social factors of Anna 's tragedy, some internal roots of her tragedy shouldn't be neglected, such as her particular spiritual world, merit and drawback of her character, her love value and conflicts about her thought. Analyzing into internal factors for Anna 's tragedy would offer further appreciation to readers.     

古巴比伦人求算术平方根的探究

分析了古巴比伦人求算术平方根的算法，证明了其正确性。然后将其算法推广到求n次算术根，并证明了其正确性。     

一个特殊本原不可幂定号有向图的基

为了进一步了解本原不可幂定号有向图基的相关性质,对一个含有3个圈的特殊的本原不可幂定号有向图的基进行了研究。首先通过利用有关本原不可幂定号有向图的引理及定义得到基的上界,再运用反证法并结合图中的＂异圈对＂、Frobenius集及本原指数等相关知识,讨论了在这个图中是否存在所需的SSSD途径对,从而得到了这个图的基。     

柱心为A53的SD型拟本原置换群的次轨道

 分析了SD型拟本原置换群的作用,确定了柱心为A₅³的SD型拟本原置换群G的次轨道的个数及其长度,从而确定了所有G弧传递图的度数.     

关于丢番图方程x8+py2=4z4与x4+16py8=z2

设p为奇数,证明了丢番图方程x^8＋py^2=4z^4（x,y）;1除开p=3时仅有正整数解（z,y,z）=（1,1,1）和p=7时仅有正整数解（x,y,z）=（1,3,2）之外,无其它正整数解。证明了方程x^4＋16py^8=z^2,p≡3（mod 4）,2/z,（x,y）=1,无正整数解。证明了P≡3（mod 4）,方程x^4＋16py^8=z^2,（x,y）=1当2/x时,除开p=3时仅有正整数解（x,y,z）-（1,1,7）外,无其它正整数解;当2｜x时,有解x^2=2｜pr^8-s^8｜,y=rs,z=2（pr^8＋s^8）,2/rs,（r,s）=1。从而推广了文[4]的结果。由此可知（x,y,z）=（2,1,8）是方程x^4＋48y^8=z^2的一个本原解,文[4]漏掉了此解,这说明文[4]引理2不是完全正确的,依据引理2证明的结论也是不可靠的。     

Randomized unit root processes for modelling and forecasting financial time series: Theory and applications

This paper considers the problems of statistically analysing the levels of financial time series rather than their differences, which are often equivalent to returns and which are traditionally analysed in econometric modelling. This focus on differences is a consequence of the inherent nonstationarity of the levels, and hence analysing the latter requires introducing an alternative framework for modelling nonstationary behaviour. We do this by considering randomized unit root processes, arguing that these can have a natural interpretation in the financial context. The paper thus develops methods for testing for randomized unit roots and for modelling such processes. It then applies these techniques to various financial time series, so as to ascertain their potential usefulness, particularly for forecasting.     

一类本原图的Scrambling指数

文章主要研究了一类特殊的含有6个圈3个不同圈长的本原有向图的Scrambling指数,通过分析每一点经过t长途径可到达的点的集合,给出了此类图的Scrambling指数.     

剩余类环Z_M与Z_M上的数论变换

剩余ZM类环是一类特殊的环.数论变换是以正整数M为模的正整数环(域)ZM上定义的线性正交变换.所用的计算方法是数论中的同余运算.介绍了剩余类环ZM上的几个方面的知识点,以及ZM上的数论变换的有关理论,及其数论变换应注意的几个问题.     

浅谈我国古汉字的绘画艺术美

本文从绘画的角度，阐释了古汉字的起源、演变以及汉字本身所蕴含的绘画艺术美和书法艺术。     

勾股向量的矩阵表示

研究Hall矩阵与规范本原勾股向量的关系,得到任意规范本原勾股向量可唯一表示成(3,4,5)右乘若干次Hall矩阵的形式,并由此得到任意勾股向量的矩阵表示.设(a,b,c)是任意一个规范本原勾股向量,并且c≥5,记W={A|A=Xt11Xt22…Xtnn,Xi∈{F1,F2,F3},ti∈Z,ti≥0},则存在唯一的A∈W,使得(a,b,c)=(3,4,5)A.