佩尔方程x^2-py^2=1的求解技巧

在连分数理论中已经给出佩尔方程x2-py2=1的整数解的求解方法,但运算繁琐,求解不便.本文通过利用一个定理得到了求佩尔方程的整数解的简单方法,给教学和学生学习的过程中给出了一定的帮助.

关于不定方程4x^2-py^2=1的一个注记

利用连分数理论证明了不定方程4x2-py2=1(p=19,31,435,96,7,71)分别有最小正整数解(x,y)=(85,39);(xy,)=(760,273);(x,y)=(1 741,531);(x,y)=(530,69);(x,y)=(24 421,5967);(x,y)=(1 7404,13)从而获得不定方程4x2-py2=1(p=19,314,35,9,67,71)的全部正整数解.

闰年的历史沿革及其数学解释

人类历史中,为指导农业生产,制定过许多历法,其中使用最广的是格里历,即公历.公历有闰年之说,闰年一年为366天,平年为365天.判断某年是否为闰年有一口诀:四年一闰,百年不闰,四百年又闰.实数理论中的连分数理论,则从理论上说明了现行历法的科学性.

实二次代数函数域理想类群的子群

给出了实二次代数函数域K的理想类群H（K）含有n阶循环子群的充分必要条件.并构作了8个系列的实二次函数域,使其理想类群均含有n阶循环子群.特别,可知这些函数域的理想类数均含因子n.

Products of Distributions,Conservation Laws and the Propagation of δ'-Shock Waves

This paper contains a study of propagation of singular travelling waves u（x, t） for conservation laws ut ＋ [Ф（u）]x = ψ（u）, where Ф, ψ are entire functions taking real values on the real axis. Conditions for the propagation of wave profiles β ＋ mδ and β ＋ mδt are presented （β is a real continuous function, m ≠ 0 is a real number and δ＇ is the derivative of the Dirac measure 5）. These results are obtained with a consistent concept of solution based on our theory of distributional products. Burgers equation ut ＋ （u2/2）x = 0, the iffusionless Burgers-Fischer equation ut ＋ a（u2/2）x = ru（1 - u/k） with a, r, k being positive numbers, Leveque and Yee equation ut ＋ ux = μx（1 - u）（u - u/k） with μ ≠ 0, and some other examples are studied within such a setting. A ＂tool box＂ survey of the distributional products is also included for the sake of completeness.