引理1:gcd(F[n],f[n-1])=1 因为 F[n]=f[n-1]+F[n-2] 所以 gcd(F[n],f[n-1]) = gcd(F[n-1]+F[n-2],F[n-1]) gcd的更损相减的性质可知 gcd(a,b)=gcd(b,a-b) 故  gcd(F[n],f[n-1]) = gcd(F[n-1],F[n-2]) 而 F[1]=F[2]=1故该定理成立 引理2:F[m+n]=F[m-1]F[n]+F[m]F[n+1]  F[m+n] = F[m+n-1] + F[m+n-2]…

在 [Chae, Dongho; Lee, Jihoon. On the geometric regularity conditions for the 3D Navier-Stokes equations. Nonlinear Anal. 151 (2017), 265--273] 中, 作者证明了如果$$u\times \f{\om}{|\om|}\cdot \f{\vLm^\be u}{|\vLm^\be u|}\in L^p(0,T;L^q(\bbR^3)),\quad \f{2}{p}…

Number Sequence Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 187893    Accepted Submission(s): 46820 Problem Description A number sequence is defined as follows: f(1) = 1, f(2) = 1, f(n) = (A…

前言 廓清认知 1.函数\(y=f(x)\)的奇偶性 ①\(y=f(x)\)为奇函数,则满足\(f(-x)+f(x)=0\),即关于点\((0,0)\)对称: ②\(y=f(x)\)为偶函数,则满足\(f(-x)-f(x)=0\),即关于直线\(x=0\)对称: ③奇偶性的推广即为对称性, 比如函数满足\(f(x)+f(2-x)=4\),则函数\(y=f(x)\)关于点\((1,2)\)对称: 函数满足\(f(x)-f(2-x)=0\),则函数\(y=f(x)\)关于直线\(x=1\)对称: 2…

原文链接:https://swlaschin.gitbooks.io/fsharpforfunandprofit/content/posts/fvsc-sum-of-squares.html Comparing F# with C#: A simple sumF# PK C#:简单的求和 To see what some real F# code looks like, let's start with a simple problem: "sum the squares from 1 to N…

原文地址:http://fsharpforfunandprofit.com/why-use-fsharp/ Why use F#?Why you should consider using F# for your next project 为什么要用F#?为什么你应该考虑在下一个项目使用F# Although F# is great for specialist areas such as scientific or data analysis, it is also an excellent…

abstract: V const & a 加速 F. Mirror 题意 链接 问题: 有n个人在y=0的平面上(及xoz平面).z=0平面上有一面镜子(边平行于坐标轴).z=a平面上有q个点(保证a大于所有人的z坐标). 所有人面朝镜子,且在镜子和q个点之间(即每个人的z坐标保证0<z<a). 问对于某个点,让所有人能够通过镜子看到那个点的镜子的最小面积. 题解 三维几何+镜像+凸包 首先考虑镜面,我们可以通过(初中科学的)镜面反射原理,关于z=0做出z=a的对称平面z=-a.问题…

rm -f catalina.2018-10-22.*    与*号间无空格 rm -f catalina.2018-10-22. *    :多了空格:…

file.seek()方法标准格式是:seek(offset,whence=0)offset:开始的偏移量,也就是代表需要移动偏移的字节数whence:给offset参数一个定义,表示要从哪个位置开始偏移:0代表从文件开头开始算起,1代表从当前位置开始算起,2代表从文件末尾算起.默认为0 whence 的默认参数是0. 所以seek(0)和f.seek(0,0)没有区别. whence 还有两种情况 是1,或者21的时候,相对当前坐标的移动,可以是正的也可以是负的.2的时候相对于文件结束的移动,…

4491. Primes in GCD Table Problem code: PGCD Johnny has created a table which encodes the results of some operation -- a function of two arguments. But instead of a boring multiplication table of the sort you learn by heart at prep-school, he has cre…