w http://planetmath.org/sites/default/files/texpdf/33795.pdf Stolz–Cesàro theorem - Wikipedia  https://en.wikipedia.org/wiki/Stolz%E2%80%93Ces%C3%A0ro_theorem 张筑生…

Source: wiki: Parseval's theorem As for signal processing, the power within certain frequency band = the sum of (power spectrum at all frequencies within the frequency band)^2.…

平时有关线性递推的题,很多都可以利用矩阵乘法来解决. 时间复杂度一般是O(K3logn)因此对矩阵的规模限制比较大. 下面介绍一种利用利用Cayley-Hamilton theorem加速矩阵乘法的方法. Cayley-Hamilton theorem: 记矩阵A的特征多项式为f(x). 则有f(A)=0. 证明可以看 维基百科 https://en.wikipedia.org/wiki/Cayley–Hamilton_theorem#A_direct_algebraic_proof 另外我在高…

The Representer Theorem, 表示定理. 给定: 非空样本空间: \(\chi\) \(m\)个样本:\(\{(x_1, y_1), \dots, (x_m, y_m)\}, x_i in \chi, y_i \in R\) 非负的损失函数: \(J:(\chi \times R^2)^m \to R^+\). 这个符号表示初看挺别扭的, 从wikipedia上抄来的. 含义是\(J\)有\(m \times 3\)个参数, 3代表: 样本\(x_i\) (一个\(\chi\…

Stat2.2x Probability(概率)课程由加州大学伯克利分校(University of California, Berkeley)于2014年在edX平台讲授. PDF笔记下载(Academia.edu) Summary Standard Error The standard error of a random variable $X$ is defined by $$SE(X)=\sqrt{E((X-E(X))^2)}$$ $SE$ measures the rough size…

树有很多种形态,给定结点个数,求生成不同形态二叉树的个数,显然要用到Catalan数列. 那如果给定一个图(Graph)\(G=(V,E)\),要求其最小生成树G',最好的方法莫过于Prim或Kruskal了. 上图就是一种求最小生成树的方法. 可要求图G中不同生成树的总个数呢? 这里要用到Kirchhoff's theoreom,一个神奇的定理. 这里只做简单的介绍,并不给出严格的证明. 详细内容请参见Wikipedia::Kirchhoff's theorem 以及芜湖一中 周冬さん的生成树…

http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=2119 11178 - Morley's Theorem Time limit: 3.000 seconds Problem DMorley’s TheoremInput: Standard Input Output: Standard Output Morley’s theorem stat…

Dirichlet's Theorem on Arithmetic Progressions Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 16733   Accepted: 8427 Description If a and d are relatively prime positive integers, the arithmetic sequence beginning with a and increasing…

Kaushik Sathupadi Programmer. Creator. Co-Founder. Dad. See all my projects and blogs → A plain english introduction to CAP Theorem You’ll often hear about the CAP theorem which specifies some kind of an upper limit when designing distributed systems…

Problem Description 我知道部分同学最近在看中国剩余定理,就这个定理本身,还是比较简单的: 假设m1,m2,-,mk两两互素,则下面同余方程组: x≡a1(mod m1) x≡a2(mod m2) - x≡ak(mod mk) 在0<=<m1m2-mk内有唯一解. 记Mi=M/mi(1<=i<=k),因为(Mi,mi)=1,故有二个整数pi,qi满足Mipi+miqi=1,如果记ei=Mi/pi,那么会有: ei≡0(mod mj),j!=i ei≡1(mod m…