Put period after equation.
@@ -101,7 +101,7 @@ $$
$$
so that when $t = t_0$, $\widetilde{u}$ will always be $u_0$. Accordingly, the objective function becomes
$$
-\min_{\vec{p}}\left(\mathcal{L}\widetilde{u} - f\right)^2
+\min_{\vec{p}}\left(\mathcal{L}\widetilde{u} - f\right)^2.
$$
Both of these two methods have their advantages. The first way is simpler to implement and can be more easily extended to
