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摘要: Problem proposed by Armenia/Australia for the 35th international mathematical olympiad (held in Hong Kong, July 12–19, 1994). $ABC$ is an isoscelestri... 阅读全文
posted @ 2012-10-28 21:58 叶卢庆 阅读(122) 评论(0) 推荐(0)
摘要: (L.Euler 1770,Vollst.Anleitung zur Algebra ,St.Petersburg,OperaOmnia,vol.I).Consider an equation of degree four with symmetric coefficients,e.g., \b... 阅读全文
posted @ 2012-10-28 13:48 叶卢庆 阅读(108) 评论(0) 推荐(0)
摘要: (L.Euler 1770,Vollst.Anleitung zur Algebra ,St.Petersburg,OperaOmnia,vol.I).Consider an equation of degree four with symmetric coefficients,e.g., \b... 阅读全文
posted @ 2012-10-28 13:48 叶卢庆 阅读(109) 评论(0) 推荐(0)
摘要: Solve: \begin{equation} \label{eq:27.21.23} x^4+Bx^2+Cx+D=(x^2+ux+\alpha)(x^2-ux+\beta) \end{equation} So \begin{equation} \label{eq:27.21... 阅读全文
posted @ 2012-10-28 02:38 叶卢庆 阅读(140) 评论(0) 推荐(0)
摘要: Solve: \begin{equation} \label{eq:27.21.23} x^4+Bx^2+Cx+D=(x^2+ux+\alpha)(x^2-ux+\beta) \end{equation} So \begin{equation} \label{eq:27.21... 阅读全文
posted @ 2012-10-28 02:38 叶卢庆 阅读(101) 评论(0) 推荐(0)
摘要: The polynomial of degree $n$ taking the values\begin{equation} \label{eq:27.13.22} y_0(x=0),y_1(x=1),\cdots,y_n(x=n)\end{equation}is given by the f... 阅读全文
posted @ 2012-10-27 20:34 叶卢庆 阅读(179) 评论(0) 推荐(0)
摘要: The polynomial of degree $n$ taking the values\begin{equation} \label{eq:27.13.22} y_0(x=0),y_1(x=1),\cdots,y_n(x=n)\end{equation}is given by the f... 阅读全文
posted @ 2012-10-27 20:34 叶卢庆 阅读(145) 评论(0) 推荐(0)
摘要: 一个由所有实数组成的集合$(t\in\mathbf{R})$所标记的,由集合$M$到它自身的映射族$\{g^t\}$称为$M$的单参数变换群,如果对于所有的$s,t\in\mathbf{R}$满足 \begin{equation} \label{eq:26.21.07} g^{t+s... 阅读全文
posted @ 2012-10-26 22:31 叶卢庆 阅读(309) 评论(0) 推荐(0)
摘要: 一个由所有实数组成的集合$(t\in\mathbf{R})$所标记的,由集合$M$到它自身的映射族$\{g^t\}$称为$M$的单参数变换群,如果对于所有的$s,t\in\mathbf{R}$满足 \begin{equation} \label{eq:26.21.07} g^{t+s... 阅读全文
posted @ 2012-10-26 22:31 叶卢庆 阅读(386) 评论(0) 推荐(0)
摘要: 1. Verify that $y^2=e^{2x}+c$ is a solution of the differentialequation $yy'=e^{2x}$.Verify:Let $F(x,y)=y^2-e^{2x}-c$,then according to the implicitfu... 阅读全文
posted @ 2012-10-26 16:50 叶卢庆 阅读(202) 评论(0) 推荐(0)
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