<affiliation>
<orgname>Astronomy Department, University of California, Berkeley, CA 94720</orgname>
</affiliation>
-<affiliation role="alternate">
+<affiliation role='alternate'>
<orgname>Visiting Astronomer Cerro Tololo Inter-American Observatory.CTIO is operated by AURA Inc. under contract to the National Science Foundation.</orgname>
</affiliation>
-<affiliation role="alternate">
+<affiliation role='alternate'>
<orgname>Society of Fellows, Harvard University.</orgname>
</affiliation>
-<affiliation role="alternate">
+<affiliation role='alternate'>
<orgname>present address: Center for Astrophysics60 Garden Street, Cambridge, MA 02138</orgname>
</affiliation>
</author>
<affiliation>
<orgname>National Optical Astronomy Observatories, Tucson, AZ 85719</orgname>
</affiliation>
-<affiliation role="alternate">
+<affiliation role='alternate'>
<orgname>Visiting Programmer, Space Telescope Science Institute</orgname>
</affiliation>
-<affiliation role="alternate">
+<affiliation role='alternate'>
<orgname>Patron, Alonso's Bar and Grill</orgname>
</affiliation>
<email>aastex-help@aas.org</email>
<affiliation>
<orgname>Space Telescope Science Institute, Baltimore, MD 21218</orgname>
</affiliation>
-<affiliation role="alternate">
+<affiliation role='alternate'>
<orgname>Patron, Alonso's Bar and Grill</orgname>
</affiliation>
</author>
</m:mrow>
</m:mrow>
</m:math>
-</informalequation> where <inlineequation>
+</informalequation>
+ where <inlineequation>
<alt role='tex'>p</alt>
<m:math>
</m:mtr>
</m:mtable>
</m:math>
-</informalequation> giving
+</informalequation>
+ giving
<informalequation>
<alt role='tex'>\hat{a}=\left(\begin{array}{cc}
0 & (\hat{a})_{+}\\
</m:mrow>
</m:mrow>
</m:math>
-</informalequation> The spinors are expressed in terms of two-component Weyl spinors as
+</informalequation>
+ The spinors are expressed in terms of two-component Weyl spinors as
<informalequation>
<alt role='tex'>u=\left(\begin{array}{c}
(u)_{-}\\
(u)_{+}
\end{array}\right),v={\textbf{(}}\vdag_{+}{\textbf{,}}\vdag_{-}{\textbf{)}}.</alt>
<mathphrase>MathML export failed. Please report this as a bug.</mathphrase>
-</informalequation></para>
+</informalequation>
+</para>
<para>The Weyl spinors are given in terms of helicity eigenstates <inlineequation>
<alt role='tex'>\chi_{\lambda}(p)</alt>
<m:math>
</m:mtr>
</m:mtable>
</m:math>
-</informalequation></section>
+</informalequation>
+</section>
</section>
<section>
<title>Floating material and so forth</title>
</m:mrow>
</m:mrow>
</m:math>
-</informalequation> where
+</informalequation>
+ where
<informalequation>
<alt role='tex'>d_{1}=\sqrt{\left(\begin{array}{c}
\frac{x_{1}}{R_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
</m:mrow>
</m:mrow>
</m:math>
-</informalequation></para>
+</informalequation>
+</para>
<para>In these expressions <inlineequation>
<alt role='tex'>x_{0}</alt>
<m:math>