298 Matching Annotations
  1. Jan 2022
  2. Nov 2021
  3. Oct 2021
    1. emplate cos ⁡ ( 2 π f x ) . {\displaystyle \cos(2\pi fx).} Its peak value is a relative measure of the presence of frequency f {\displaystyle f} in function s . {\displaystyle s.} The analysis process determines, for certain key frequencies, the maximum correlation and the corresponding phase offset, ( τ f ) . {\displaystyle (\tau f).} The synthesis process (the actual Fourier series), in terms of parameters to be determined by analysis, is:

      confused about these paragraphs

    1. The benefit of making it costly to validate transactions is that validation can no longer be influenced by the number of network identities someone controls, but only by the total computational power they can bring to bear on validation

      ?

    1. corresponds to a = 1, b = 2):
      1. 此处 \({1 \over 2 a + 1} + \cdots + {1 \over 4 a - 1} - {1 \over 2b + 2} - \cdots\)

      只是为了 表示一个无穷项罢了 实际排列是 还是

      1. if a=1,b=2 we can have the permutation

    2. odd terms satisfies

      证明 $$proof\ {1} + {1 \over 3} + {1 \over 5} + \cdots + {1 \over 2 p - 1} = {1 \over 2} \, \gamma + {1 \over 2} \ln p + \ln 2 + o(1).\quad (1)\ 1 + {1 \over 2} + {1 \over 3} + \cdots + {1 \over 2p-1} = \gamma + \ln (2p-1) + o(1),\quad (2)\

      {1 \over 2} + {1 \over 4} + {1 \over 6} + \cdots + {1 \over 2(p-1)} = {1 \over 2} \, \gamma + {1 \over 2} \ln (p-1)+ o(1),\quad (3)\ \

      \ now \quad proof \quad (2)-(3) \to (1)\\ first \quad proof \ \lim{p \to \infty } {\ln (2p-1) - \ln \sqrt{p-1} }=\lim{p \to \infty }\ln {2 \sqrt{p} }\ \lim{p \to \infty } {\ln (2p-1) -{\ln 2\sqrt{(p-1)p}} }= \lim{p \to \infty }\ln {2p-1 \over 2\sqrt{(p-1)p}}\ = \ln{2 \over 2} =0$$

    1. show that
      1. 这里 其实就是 四元数 相乘

      因为 实数 虚数都包含在 四元数 里

      1. po应该是 从左往右乘 , 就类似与 数字相乘

      2. 运算时 可以先把 \(sin(\frac{\alpha }{2})\);\(cos(\frac{\alpha }{2})\) 提出来 计算

  4. Sep 2021
    1. The eigenvectors are unit vectors representing the direction of the largest variance of the data, while the eigenvalues represent the magnitude of this variance in the corresponding directions.

      就是3b1b视频

    1. e shown that:

      二项式定理 可以证明 前面的 $$p \choose m$$ 是从 p个 因式里 选择m个 当作x 后面的同理

      $$(-{\bar {x}})^{{(p-m)}}$$

      则是 从 p个 因式里 选择p-m个 当作 $$-{\bar {x}}$$

    1. s the process of adapting software for the purpose of achieving some form of execution in a computing environment that is different from the one that a given program (meant for such execution) was originally designed for (e.g., different CPU, operating system, or third party library).

      可以 看做端口转发 即 修改代码功能 其实就是 可移植

    1. All of these frames are in motion relative to one another.

      举个简单例子 人在地球上是 相对于地球这个坐标系(rest frame)不动 但是 地球肯定是绕着 太阳转的 所以人 在太阳坐标系里 是动的 (上述 坐标系表述 只是为了方便理解 并不严谨)

    1. (like __builtin_saveregs) is provided by the compiler, but does not correspond to a function in the standard library.

      即 你 查找源码 应该是找不到的

    1. commonly only concerned with the handling of events,

      说白了 这里的反转 不是颠倒 而是 把许多工作 交给一个 framework 自己只做一个初步处理

    1. An intuitive understanding of this property is that under a projective transformation, all multiples of PhP_h are mapped to the same point.

      可以理解为 降维 直观的就是 一个直线 降到一维 必然是同一个点 其余同理

    1. 或者lynx都没太大压力吧。不过要来干嘛呢?大部分用vim的人相信厨房客厅卧室各有各的功能,不会象emacs那样喜欢吃喝拉撒睡全在一个地方吧。

      打算

    2. 扩展动态库来模拟实现异步任务。而7.4.1700后官方新增了timer和jobs,channel的支持后相信不久就会出现一个可用性较高的内嵌shell了,有了内

      dsa