\begin{thm}
Quisque aliquam $x$ ipsum sed turpis.
Pellentesque $y\in K$ laoreet velit nec justo.
Nam sed augue.
Maecenas rutrum quam eu dolor.
\begin{equation}
\int_5^6 x^2\,dx=A_{xt} \label{eq:first}
\end{equation}
Fusce consectetuer.
Proin tellus est, luctus vitae, molestie a, mattis et, mauris.
\begin{equation}\begin{split}
H_c&=\frac{1}{2n} \sum^n_{l=0}(-1)^{l}(n-{l})^{p-2}
\sum_{l _1+\dots+ l _p=l}\prod^p_{i=1} \binom{n_i}{l _i}\\
&\quad\cdot[(n-l )-(n_i-l _i)]^{n_i-l _i}\cdot
\Bigl[(n-l )^2-\sum^p_{j=1}(n_i-l _i)^2\Bigr].
\end{split}\end{equation}
Donec tempor.
Pellentesque habitant morbi tristique senectus et netus et malesuada
fames ac turpis egestas.
\end{thm}
\begin{proof}
Fusce adipiscing justo nec ante.
Nullam in enim equation~\ref{eq:first}.
\begin{equation*}
\left.\begin{aligned}
B'&=-\partial\times E,\\
E'&=\partial\times B - 4\pi j
\end{aligned}
\right\}
\qquad \text{Maxwell's equations}
\end{equation*}
Pellentesque felis orci, sagittis ac, malesuada et, facilisis in, ligula.
Nunc non magna sit amet mi aliquam dictum.
\begin{equation}
\frac{1}{k}\log_2 c(f)\quad\tfrac{1}{k}\log_2 c(f)\quad
\sqrt{\frac{1}{k}\log_2 c(f)}\quad\sqrt{\dfrac{1}{k}\log_2 c(f)}
\end{equation}
In mi.
\end{proof}
\lipsum[26]
\begin{defn}
Aenean adipiscing auctor est. Morbi quam
arcu, malesuada sed, volutpat et, elementum sit amet, libero. Duis
accumsan. Curabitur urna.
\begin{equation}
\begin{pmatrix} a&b&c&d\\
e&\hdotsfor{3} \end{pmatrix}
\end{equation}
In sed ipsum.
\end{defn}
\begin{lem}
Donec lobortis nibh.
Duis $x\in K_2$ mattis.
Sed cursus lectus quis odio.
Phasellus arcu.
Praesent imperdiet dui in sapien.
\end{lem}
\begin{proof}
Vestibulum tellus pede, auctor a, pellentesque sit amet, vulputate sed, purus.
\begin{align}
A_1&=N_0(\lambda;\Omega')-\phi(\lambda;\Omega'),\\
A_2&=\phi(\lambda;\Omega')-\phi(\lambda;\Omega),\\
\intertext{and}
A_3&=\mathcal{N}(\lambda;\omega).
\end{align}
Nunc pulvinar, dui at eleifend adipiscing, tellus nulla placerat massa,
sed condimentum nulla tellus sed ligula.
Nulla vitae odio sit amet leo imperdiet blandit.
In vel massa.
\begin{equation*}
\sum_{\begin{subarray}{l}
i\in\Lambda\\ 0<j<n
\end{subarray}}
P(i,j)
\end{equation*}
Maecenas varius dui at turpis.
Sed odio.
\end{proof}
\begin{thm}
Sed justo.
Maecenas lacinia, turpis sed commodo congue, odio urna elementum nunc,
vitae molestie velit nunc eu sem.
Maecenas enim.
\begin{equation}
\displaystyle
\sum_{\substack{0\le i\le m\\ 0<j<n}} P(i,j)
\end{equation}
Proin quis neque nec tortor sollicitudin volutpat.
\end{thm}
\begin{proof}
Sed at ante.
Sed vitae mauris non ante egestas hendrerit.
Cum sociis natoque penatibus et magnis dis parturient montes, nascetur
ridiculus mus.
\begin{equation}\label{xx}
\begin{split}
a& =b+c-d\\
& \quad +e-f\\
& =g+h\\
& =i
\end{split}
\end{equation}
\end{proof}
\begin{cor}
In venenatis $2\leq y,z\leq 5$ facilisis magna.
Cras quis mauris.
Aliquam eget
\begin{math}
\bigl( \begin{smallmatrix}
a&b\\ c&d
\end{smallmatrix} \bigr)
\end{math}
magna.
Donec rutrum sagittis mi.
Morbi elementum, est sit amet sollicitudin feugiat, orci magna semper risus,
eu congue nulla metus vel elit.
\end{cor}
