KaTeX

KaTeX

行内公式

{xAx=b}\{x | Ax = b\}

$\{x | Ax = b\}$

Xc<1,Xq<1\mathcal{X}_{c^*}<1, \mathcal{X}_{q^*}<1

E=mc2E = mc^2

t\frac{\partial}{\partial t}

$E = mc^2$
$\frac{\partial}{\partial t}$

行间公式

E=mc2E = mc^2

$ E = mc^2 $

a=dvdt=d(drdtei+rdθdtej)dt=d2rdt2ei+drdtdeidt+drdtdθdtej+rd2θdt2ej+rdθdtde_jdt\vec a=\frac{d\vec v}{dt}=\frac{d(\frac{dr}{dt}\vec e*{i}+r\frac{d\theta}{dt}\vec e*{j})}{dt}=\frac{d^2r}{dt^2}\vec e*{i}+\frac{dr}{dt}\frac{d\vec e*{i}}{dt}+\frac{dr}{dt}\frac{d\theta}{dt}\vec e*{j}+r\frac{d^2\theta}{dt^2}\vec e*{j}+r\frac{d\theta}{dt}\frac{d\vec e\_{j}}{dt}

$ \vec a=\frac{d\vec v}{dt}=\frac{d(\frac{dr}{dt}\vec e_{i}+r\frac{d\theta}{dt}\vec e_{j})}{dt}=\frac{d^2r}{dt^2}\vec e_{i}+\frac{dr}{dt}\frac{d\vec e_{i}}{dt}+\frac{dr}{dt}\frac{d\theta}{dt}\vec e_{j}+r\frac{d^2\theta}{dt^2}\vec e_{j}+r\frac{d\theta}{dt}\frac{d\vec e_{j}}{dt} $

mt=gtm_t=g_t

Vt=1V_t=1

$ m_t=g_t $
$ V_t=1 $

ηt=lrmtVt=lrgt\eta_t=lr*{\frac {m_t}{\sqrt V_t}}=lr*g_t

w_t+1=wtηt=wtlrmtVt=wtlrgtw\_{t+1}=w_t-\eta_t=w_t-lr*{\frac {m_t}{\sqrt V_t}}=w_t-lr*g_t

qs=kx(T1+T2)x=0=kT1xx=0qskT2xx=00=kT2xx=0q''_s = -k \left.\frac{\partial }{\partial x} (T_1+T_2) \right|_{x=0} = \underbrace{-k \left.\frac{\partial T_1}{\partial x} \right|_{x=0}}_{q''_s} -k \left.\frac{\partial T_2}{\partial x} \right|_{x=0} \rightarrow \boxed{0 = -k \left.\frac{\partial T_2}{\partial x} \right|_{x=0}}

$ \eta_t=lr*{\frac {m_t}{\sqrt V_t}}=lr*g_t $
$ w_{t+1}=w_t-\eta_t=w_t-lr*{\frac {m_t}{\sqrt V_t}}=w_t-lr*g_t $

<div text="red">

$
q''_s = -k \left.\frac{\partial }{\partial x} (T_1+T_2) \right|_{x=0} = \underbrace{-k \left.\frac{\partial T_1}{\partial x} \right|_{x=0}}_{q''_s}  -k \left.\frac{\partial T_2}{\partial x} \right|_{x=0} \rightarrow \boxed{0 = -k \left.\frac{\partial T_2}{\partial x} \right|_{x=0}}
$

</div>

[abcd]\begin{bmatrix} a & b \\ c & d \end{bmatrix}

$
\begin{bmatrix}
  a & b \\
  c & d
\end{bmatrix}
$

{x=acosθy=bsinθ\begin{equation} \left\{ \begin{aligned} x=a\cos\theta\\ y=b\sin\theta\\ \end{aligned} \right. \end{equation}

$
\begin{equation}
  \left\{
    \begin{aligned}
      x=a\cos\theta\\
      y=b\sin\theta\\
    end{aligned}
  \right.
\end{equation}
$