ヘヴィサイドの階段関数の２定義値と複号
ヘヴィサイドの階段関数の２定義値と複号
(1)
\[ H\left(\pm1\right)=\frac{1\pm1}{2} \](2)
\[ H\left(\pm1\right)+H\left(\mp1\right)=1 \](3)
\[ H\left(\pm1\right)-H\left(\mp1\right)=\pm1 \]-
\(H\left(x\right)\)はヘヴィサイドの階段関数(1)
\begin{align*} H\left(\pm1\right) & =\frac{\sgn\left(\pm1\right)+1}{2}\\ & =\frac{1\pm1}{2} \end{align*}(1)-2
\begin{align*} H\left(\pm1\right) & =\begin{cases} 1 & \pm1\rightarrow+1\\ 0 & \pm1\rightarrow-1 \end{cases}\\ & =\frac{1\pm1}{2} \end{align*}(2)
\begin{align*} H\left(\pm1\right)+H\left(\mp1\right) & =\frac{1\pm1}{2}+\frac{1\mp1}{2}\\ & =1 \end{align*}(3)
\begin{align*} H\left(\pm1\right)-H\left(\mp1\right) & =\frac{1\pm1}{2}-\frac{1\mp1}{2}\\ & =\pm1 \end{align*}
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| タイトル | ヘヴィサイドの階段関数の２定義値と複号 |
| URL | https://www.nomuramath.com/ge0l028q/ |
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ヘヴィサイド関数と符号
\[
H_{c}\left(x\right)f\left(\pm x\right)=H_{c}\left(x\right)f\left(\pm\left|x\right|\right)
\]
ヘヴィサイドの階段関数の問題
\[
f\left(H\left(\pm_{1}1\right)\right)g\left(-H\left(\pm_{1}1\right)\right)\pm_{2}f\left(-H\left(\mp_{1}1\right)\right)g\left(H\left(\mp_{1}1\right)\right)=\left\{ f\left(0\right)g\left(0\right)+f\left(\pm1\right)g\left(\mp1\right)\right\} H\left(\pm_{2}1\right)\mp_{1}\left\{ f\left(0\right)g\left(0\right)-f\left(\pm_{1}1\right)g\left(\mp_{1}1\right)\right\} H\left(\mp_{2}1\right)
\]
ヘヴィサイドの階段関数の２定義値を引数に持つ関数の和と差
\[
f\left(H\left(\pm_{1}1\right)\right)\pm_{2}f\left(-H\left(\mp_{1}1\right)\right)=\left(f\left(0\right)+f\left(\pm_{1}1\right)\right)H\left(\pm_{2}1\right)\mp_{1}\left(f\left(0\right)-f\left(\pm_{1}1\right)\right)H\left(\mp_{2}1\right)
\]
ヘヴィサイドの階段関数の２定義値の和と差
\[
H\left(\pm_{1}1\right)\pm_{2}H\left(\pm_{1}1\right)=H\left(\pm_{2}1\right)\pm_{1}H\left(\pm_{2}1\right)
\]