--- trunk/tengDissertation/Introduction.tex	2006/05/25 21:32:14	2776
+++ trunk/tengDissertation/Introduction.tex	2006/05/26 17:56:36	2778
@@ -846,12 +846,12 @@ can obtain
 \]
 Applying Baker-Campbell-Hausdorff formula to Sprang splitting, we
 can obtain
-\begin{equation}
-\exp (h X/2)\exp (h Y)\exp (h X/2) & = & \exp (h X + h Y + h^2
-[X,Y]/4 + h^2 [Y,X]/4 \\ & & \mbox{} + h^2 [X,X]/8 + h^2 [Y,Y]/8 \\
-& & \mbox{} + h^3 [Y,[Y,X]]/12 - h^3 [X,[X,Y]]/24 & & \mbox{} +
-\ldots )
-\end{equation}
+\begin{eqnarray}
+\exp (h X/2)\exp (h Y)\exp (h X/2) & = & \exp (h X + h Y + h^2 [X,Y]/4 + h^2 [Y,X]/4 \\
+                                   &   & \mbox{} + h^2 [X,X]/8 + h^2 [Y,Y]/8 \\
+                                   &   & \mbox{} + h^3 [Y,[Y,X]]/12 - h^3[X,[X,Y]]/24\\
+                                   &   & \mbox{} + \ldots )
+\end{eqnarrary}
 Since \[ [X,Y] + [Y,X] = 0\] and \[ [X,X] = 0\], the dominant local
 error of Spring splitting is proportional to $h^3$. The same
 procedure can be applied to general splitting,  of the form