on 04-Dec-2023 (Mon)

Alicia Johansen spent her childhood moving with her drug-addicted mom from one place to the next, trying to brace herself for the moment when the water and the electricity would get cut off. So at twenty-two, when she had a chance to run Dolittle’s pool hall, in the ranching town of Akron, Colorado, she was intent on making some money. She kept the bar open deep into the night, after the older guys who bet on horse races departed, and the truckers and the younger crowd, with the meth, drifted in. Meth, she soon discovered, helped her work longer hours.

Alicia’s period was irregular because of the meth, which also dimmed her self-awareness. She was six months along before she realized that she was pregnant; a month after that, she woke up in pain. She had preeclampsia, which caused dangerously high blood pressure, and needed an immediate C- section. She was airlifted to a hospital in Denver, a hundred miles away. Her and Fred’s son, Carter James Thornton, was born on August 6, 2019—two and a half months premature, two and a half pounds in weight, and, according to his lab work, exposed to meth and to THC.

对于任何给定方阵\(\mathbf{A}\)，特征值\(\lambda\)都一定满足

\(\det(\mathbf{A}-\lambda\mathbf{I})=\mathbf{0}\)

并且特征向量\(x\)满足

\((\mathbf{A}-\lambda\mathbf{I})x=0\)

函数的内积是一种函数之间的二元运算。在复数域\(\mathbb{C}\)中，给定两个复数函数\(f(x), g(x)\)，则函数的内积定义为：

\(\displaystyle\left\langle f(x), g(x)\right\rangle_{w(x),x\in(a,b)}:=\int^{x=b}_{x=a}f^{*}(x)g(x)w(x)dx\)

其中，\(w(x)\)是权重函数(weight function)，\((a,b)\)是函数内积的定义域，\(f^{*}(x)\)是函数\(f(x)\)的复数共轭
- 权重函数一般是1

当函数内积定义在实数域\(\mathbb{R}\)中时，函数内积为：\(\displaystyle\left\langle f(x), g(x)\right\rangle_{w(x),x\in(a,b)}:=\int^{x=b}_{x=a}f(x)g(x)w(x)dx\)