一些难以使用识别的疑难公式识别

\theta_{k,\varepsilon}=
\begin{cases}
a &\text{if b}\\
b &\text{if a}\\
\end{cases}

\[\theta_{k,\varepsilon}=\begin{cases}a &\text{if b}\\b &\text{if a}\\\end{cases}\]

\overset{\mathbb{H}_1}{\operatorname*{\underset{\mathbb{H}_2}{\operatorname*{\operatorname*{\leqslant}}}}}

\[\overset{\mathbb{H}_1}{\operatorname*{\underset{\mathbb{H}_2}{\operatorname*{\operatorname*{\leqslant}}}}}\]

\mathbf{\Phi}\\\
lceil{\frac{\vert\mathcal N_k\vert}{2}}\rceil\\
\breve{a}\tilde{a}

\[\mathbf{\Phi}\\\lceil{\frac{\vert\mathcal N_k\vert}{2}}\rceil\\\breve{a}\tilde{a}\]