CINXE.COM
Analysis & PDE Vol. 1, No. 2, 2008
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <title>Analysis & PDE Vol. 1, No. 2, 2008</title> <link href="/apde/etc/journal.css" type="text/css" rel="stylesheet" /> <link href="/apde/etc/abstract.css" type="text/css" rel="stylesheet" /> <link rel="shortcut icon" href="/apde/etc/favicon.ico" /> <script type="text/javascript" src="/apde/etc/cover.js"> </script> <script type="text/javascript" src="/apde/etc/journal.js"> </script> <script type="text/javascript" src="/apde/etc/archive.js"> </script> </head> <body onload="javascript:void(0);"> <table cellspacing="0" cellpadding="0" class="masthead" id= "masthead-area"> <tr> <td class="volume-h" onclick= "javascript:window.location='index.xhtml';"> <h4>Vol. 1, No. 2, 2008</h4> </td> </tr> </table> <table cellspacing="0" cellpadding="0" class="main" id="main-area"> <tr> <td class="activity-column" id="activity-area"> <table cellspacing="0" cellpadding="0" class="action"> <tr> <td align="left"> <table cellspacing="0" cellpadding="0" width="100%"> <tr> <td colspan="2" class="action-title-area"> <div class="action-title"> Download this issue </div> </td> </tr> <tr> <td rowspan="2" class="download-icon-area"><a href= "/apde/2008/1-2/apde-v1-n2-s.pdf"><img class= "download-icon" src="/apde/etc/icon-pdf-lg.gif" alt= "Download this issue " /></a></td> <td class="download-caption-area"><a class= "download-caption" href= "/apde/2008/1-2/apde-v1-n2-s.pdf">For screen</a></td> </tr> <tr> <td class="download-caption-area"><a class= "download-caption" href= "/apde/2008/1-2/apde-v1-n2-p.pdf">For printing</a></td> </tr> </table> </td> </tr> </table> <table cellspacing="0" cellpadding="0" class="pause"> <tr> <td class="action-end"><img src="/apde/etc/z.gif" alt="" /></td> <!-- underline (close) the action area above --> </tr> <tr> <td class="pause"><img src="/apde/etc/z.gif" alt="" /></td> <!-- create white space between sections --> </tr> </table> <table cellspacing="0" cellpadding="0" class="action"> <tr> <td> <table cellspacing="0" cellpadding="0" width="100%"> <tr> <td class="action-title-area"><div class="action-title">Recent Issues</div></td> </tr> <tr><td class="issues-area"> <p class="p-about-dropdown" id="volume-short-18" style="display:none;"> <a class="about" onclick="showIssues('18');">Volume 18, 2 issues</a> </p> <p class="p-about-dropdown" id="volume-all-18"> <a class="about" onclick="collapseIssues('18');">Volume 18</a> <br/><a class="about" href="/apde/2025/18-2/index.xhtml">Issue 2, 279–548</a> <br/><a class="about" href="/apde/2025/18-1/index.xhtml">Issue 1, 1–278</a> </p> <p class="p-about-dropdown" id="volume-short-17"> <a class="about" onclick="showIssues('17');">Volume 17, 10 issues</a> </p> <p class="p-about-dropdown" id="volume-all-17" style="display:none;"> <a class="about" onclick="collapseIssues('17');">Volume 17</a> <br/><a class="about" href="/apde/2024/17-10/index.xhtml">Issue 10, 3371–3670</a> <br/><a class="about" href="/apde/2024/17-9/index.xhtml">Issue 9, 2997–3369</a> <br/><a class="about" href="/apde/2024/17-8/index.xhtml">Issue 8, 2619–2996</a> <br/><a class="about" href="/apde/2024/17-7/index.xhtml">Issue 7, 2247–2618</a> <br/><a class="about" href="/apde/2024/17-6/index.xhtml">Issue 6, 1871–2245</a> <br/><a class="about" href="/apde/2024/17-5/index.xhtml">Issue 5, 1501–1870</a> <br/><a class="about" href="/apde/2024/17-4/index.xhtml">Issue 4, 1127–1500</a> <br/><a class="about" href="/apde/2024/17-3/index.xhtml">Issue 3, 757–1126</a> <br/><a class="about" href="/apde/2024/17-2/index.xhtml">Issue 2, 379–756</a> <br/><a class="about" href="/apde/2024/17-1/index.xhtml">Issue 1, 1–377</a> </p> <p class="p-about-dropdown" id="volume-short-16"> <a class="about" onclick="showIssues('16');">Volume 16, 10 issues</a> </p> <p class="p-about-dropdown" id="volume-all-16" style="display:none;"> <a class="about" onclick="collapseIssues('16');">Volume 16</a> <br/><a class="about" href="/apde/2023/16-10/index.xhtml">Issue 10, 2241–2494</a> <br/><a class="about" href="/apde/2023/16-9/index.xhtml">Issue 9, 1989–2240</a> <br/><a class="about" href="/apde/2023/16-8/index.xhtml">Issue 8, 1745–1988</a> <br/><a class="about" href="/apde/2023/16-7/index.xhtml">Issue 7, 1485–1744</a> <br/><a class="about" href="/apde/2023/16-6/index.xhtml">Issue 6, 1289–1483</a> <br/><a class="about" href="/apde/2023/16-5/index.xhtml">Issue 5, 1089–1288</a> <br/><a class="about" href="/apde/2023/16-4/index.xhtml">Issue 4, 891–1088</a> <br/><a class="about" href="/apde/2023/16-3/index.xhtml">Issue 3, 613–890</a> <br/><a class="about" href="/apde/2023/16-2/index.xhtml">Issue 2, 309–612</a> <br/><a class="about" href="/apde/2023/16-1/index.xhtml">Issue 1, 1–308</a> </p> <p class="p-about-dropdown" id="volume-short-15"> <a class="about" onclick="showIssues('15');">Volume 15, 8 issues</a> </p> <p class="p-about-dropdown" id="volume-all-15" style="display:none;"> <a class="about" onclick="collapseIssues('15');">Volume 15</a> <br/><a class="about" href="/apde/2022/15-8/index.xhtml">Issue 8, 1861–2108</a> <br/><a class="about" href="/apde/2022/15-7/index.xhtml">Issue 7, 1617–1859</a> <br/><a class="about" href="/apde/2022/15-6/index.xhtml">Issue 6, 1375–1616</a> <br/><a class="about" href="/apde/2022/15-5/index.xhtml">Issue 5, 1131–1373</a> <br/><a class="about" href="/apde/2022/15-4/index.xhtml">Issue 4, 891–1130</a> <br/><a class="about" href="/apde/2022/15-3/index.xhtml">Issue 3, 567–890</a> <br/><a class="about" href="/apde/2022/15-2/index.xhtml">Issue 2, 273–566</a> <br/><a class="about" href="/apde/2022/15-1/index.xhtml">Issue 1, 1–272</a> </p> <p class="p-about-dropdown" id="volume-short-14"> <a class="about" onclick="showIssues('14');">Volume 14, 8 issues</a> </p> <p class="p-about-dropdown" id="volume-all-14" style="display:none;"> <a class="about" onclick="collapseIssues('14');">Volume 14</a> <br/><a class="about" href="/apde/2021/14-8/index.xhtml">Issue 8, 2327–2651</a> <br/><a class="about" href="/apde/2021/14-7/index.xhtml">Issue 7, 1977–2326</a> <br/><a class="about" href="/apde/2021/14-6/index.xhtml">Issue 6, 1671–1976</a> <br/><a class="about" href="/apde/2021/14-5/index.xhtml">Issue 5, 1333–1669</a> <br/><a class="about" href="/apde/2021/14-4/index.xhtml">Issue 4, 985–1332</a> <br/><a class="about" href="/apde/2021/14-3/index.xhtml">Issue 3, 667–984</a> <br/><a class="about" href="/apde/2021/14-2/index.xhtml">Issue 2, 323–666</a> <br/><a class="about" href="/apde/2021/14-1/index.xhtml">Issue 1, 1–322</a> </p> <p class="p-about-dropdown" id="volume-short-13"> <a class="about" onclick="showIssues('13');">Volume 13, 8 issues</a> </p> <p class="p-about-dropdown" id="volume-all-13" style="display:none;"> <a class="about" onclick="collapseIssues('13');">Volume 13</a> <br/><a class="about" href="/apde/2020/13-8/index.xhtml">Issue 8, 2259–2480</a> <br/><a class="about" href="/apde/2020/13-7/index.xhtml">Issue 7, 1955–2257</a> <br/><a class="about" href="/apde/2020/13-6/index.xhtml">Issue 6, 1605–1954</a> <br/><a class="about" href="/apde/2020/13-5/index.xhtml">Issue 5, 1269–1603</a> <br/><a class="about" href="/apde/2020/13-4/index.xhtml">Issue 4, 945–1268</a> <br/><a class="about" href="/apde/2020/13-3/index.xhtml">Issue 3, 627–944</a> <br/><a class="about" href="/apde/2020/13-2/index.xhtml">Issue 2, 317–625</a> <br/><a class="about" href="/apde/2020/13-1/index.xhtml">Issue 1, 1–316</a> </p> <p class="p-about-dropdown" id="volume-short-12"> <a class="about" onclick="showIssues('12');">Volume 12, 8 issues</a> </p> <p class="p-about-dropdown" id="volume-all-12" style="display:none;"> <a class="about" onclick="collapseIssues('12');">Volume 12</a> <br/><a class="about" href="/apde/2019/12-8/index.xhtml">Issue 8, 1891–2146</a> <br/><a class="about" href="/apde/2019/12-7/index.xhtml">Issue 7, 1643–1890</a> <br/><a class="about" href="/apde/2019/12-7/index.xhtml">Issue 7, 1397–1644</a> <br/><a class="about" href="/apde/2019/12-6/index.xhtml">Issue 6, 1397–1642</a> <br/><a class="about" href="/apde/2019/12-5/index.xhtml">Issue 5, 1149–1396</a> <br/><a class="about" href="/apde/2019/12-4/index.xhtml">Issue 4, 867–1148</a> <br/><a class="about" href="/apde/2019/12-3/index.xhtml">Issue 3, 605–866</a> <br/><a class="about" href="/apde/2019/12-2/index.xhtml">Issue 2, 259–604</a> <br/><a class="about" href="/apde/2019/12-1/index.xhtml">Issue 1, 1–258</a> </p> <p class="p-about-dropdown" id="volume-short-11"> <a class="about" onclick="showIssues('11');">Volume 11, 8 issues</a> </p> <p class="p-about-dropdown" id="volume-all-11" style="display:none;"> <a class="about" onclick="collapseIssues('11');">Volume 11</a> <br/><a class="about" href="/apde/2018/11-8/index.xhtml">Issue 8, 1841–2148</a> <br/><a class="about" href="/apde/2018/11-7/index.xhtml">Issue 7, 1587–1839</a> <br/><a class="about" href="/apde/2018/11-6/index.xhtml">Issue 6, 1343–1586</a> <br/><a class="about" href="/apde/2018/11-5/index.xhtml">Issue 5, 1083–1342</a> <br/><a class="about" href="/apde/2018/11-4/index.xhtml">Issue 4, 813–1081</a> <br/><a class="about" href="/apde/2018/11-3/index.xhtml">Issue 3, 555–812</a> <br/><a class="about" href="/apde/2018/11-2/index.xhtml">Issue 2, 263–553</a> <br/><a class="about" href="/apde/2018/11-1/index.xhtml">Issue 1, 1–261</a> </p> <p class="p-about-dropdown" id="volume-short-10"> <a class="about" onclick="showIssues('10');">Volume 10, 8 issues</a> </p> <p class="p-about-dropdown" id="volume-all-10" style="display:none;"> <a class="about" onclick="collapseIssues('10');">Volume 10</a> <br/><a class="about" href="/apde/2017/10-8/index.xhtml">Issue 8, 1793–2041</a> <br/><a class="about" href="/apde/2017/10-7/index.xhtml">Issue 7, 1539–1791</a> <br/><a class="about" href="/apde/2017/10-6/index.xhtml">Issue 6, 1285–1538</a> <br/><a class="about" href="/apde/2017/10-5/index.xhtml">Issue 5, 1017–1284</a> <br/><a class="about" href="/apde/2017/10-4/index.xhtml">Issue 4, 757–1015</a> <br/><a class="about" href="/apde/2017/10-3/index.xhtml">Issue 3, 513–756</a> <br/><a class="about" href="/apde/2017/10-2/index.xhtml">Issue 2, 253–512</a> <br/><a class="about" href="/apde/2017/10-1/index.xhtml">Issue 1, 1–252</a> </p> <p class="p-about-dropdown" id="volume-short-9"> <a class="about" onclick="showIssues('9');">Volume 9, 8 issues</a> </p> <p class="p-about-dropdown" id="volume-all-9" style="display:none;"> <a class="about" onclick="collapseIssues('9');">Volume 9</a> <br/><a class="about" href="/apde/2016/9-8/index.xhtml">Issue 8, 1772–2050</a> <br/><a class="about" href="/apde/2016/9-7/index.xhtml">Issue 7, 1523–1772</a> <br/><a class="about" href="/apde/2016/9-6/index.xhtml">Issue 6, 1285–1522</a> <br/><a class="about" href="/apde/2016/9-5/index.xhtml">Issue 5, 1019–1283</a> <br/><a class="about" href="/apde/2016/9-4/index.xhtml">Issue 4, 773–1018</a> <br/><a class="about" href="/apde/2016/9-3/index.xhtml">Issue 3, 515–772</a> <br/><a class="about" href="/apde/2016/9-2/index.xhtml">Issue 2, 259–514</a> <br/><a class="about" href="/apde/2016/9-1/index.xhtml">Issue 1, 1–257</a> </p> <p class="p-about-dropdown" id="volume-short-8"> <a class="about" onclick="showIssues('8');">Volume 8, 8 issues</a> </p> <p class="p-about-dropdown" id="volume-all-8" style="display:none;"> <a class="about" onclick="collapseIssues('8');">Volume 8</a> <br/><a class="about" href="/apde/2015/8-8/index.xhtml">Issue 8, 1807–2055</a> <br/><a class="about" href="/apde/2015/8-7/index.xhtml">Issue 7, 1541–1805</a> <br/><a class="about" href="/apde/2015/8-6/index.xhtml">Issue 6, 1289–1539</a> <br/><a class="about" href="/apde/2015/8-5/index.xhtml">Issue 5, 1025–1288</a> <br/><a class="about" href="/apde/2015/8-4/index.xhtml">Issue 4, 765–1023</a> <br/><a class="about" href="/apde/2015/8-3/index.xhtml">Issue 3, 513–764</a> <br/><a class="about" href="/apde/2015/8-2/index.xhtml">Issue 2, 257–511</a> <br/><a class="about" href="/apde/2015/8-1/index.xhtml">Issue 1, 1–255</a> </p> <p class="p-about-dropdown" id="volume-short-7"> <a class="about" onclick="showIssues('7');">Volume 7, 8 issues</a> </p> <p class="p-about-dropdown" id="volume-all-7" style="display:none;"> <a class="about" onclick="collapseIssues('7');">Volume 7</a> <br/><a class="about" href="/apde/2014/7-8/index.xhtml">Issue 8, 1713–2027</a> <br/><a class="about" href="/apde/2014/7-7/index.xhtml">Issue 7, 1464–1712</a> <br/><a class="about" href="/apde/2014/7-6/index.xhtml">Issue 6, 1237–1464</a> <br/><a class="about" href="/apde/2014/7-5/index.xhtml">Issue 5, 1027–1236</a> <br/><a class="about" href="/apde/2014/7-4/index.xhtml">Issue 4, 771–1026</a> <br/><a class="about" href="/apde/2014/7-3/index.xhtml">Issue 3, 529–770</a> <br/><a class="about" href="/apde/2014/7-2/index.xhtml">Issue 2, 267–527</a> <br/><a class="about" href="/apde/2014/7-1/index.xhtml">Issue 1, 1–266</a> </p> <p class="p-about-dropdown" id="volume-short-6"> <a class="about" onclick="showIssues('6');">Volume 6, 8 issues</a> </p> <p class="p-about-dropdown" id="volume-all-6" style="display:none;"> <a class="about" onclick="collapseIssues('6');">Volume 6</a> <br/><a class="about" href="/apde/2013/6-8/index.xhtml">Issue 8, 1793–2048</a> <br/><a class="about" href="/apde/2013/6-7/index.xhtml">Issue 7, 1535–1791</a> <br/><a class="about" href="/apde/2013/6-6/index.xhtml">Issue 6, 1243–1533</a> <br/><a class="about" href="/apde/2013/6-5/index.xhtml">Issue 5, 1001–1242</a> <br/><a class="about" href="/apde/2013/6-4/index.xhtml">Issue 4, 751–1000</a> <br/><a class="about" href="/apde/2013/6-3/index.xhtml">Issue 3, 515–750</a> <br/><a class="about" href="/apde/2013/6-2/index.xhtml">Issue 2, 257–514</a> <br/><a class="about" href="/apde/2013/6-1/index.xhtml">Issue 1, 1–256</a> </p> <p class="p-about-dropdown" id="volume-short-5"> <a class="about" onclick="showIssues('5');">Volume 5, 5 issues</a> </p> <p class="p-about-dropdown" id="volume-all-5" style="display:none;"> <a class="about" onclick="collapseIssues('5');">Volume 5</a> <br/><a class="about" href="/apde/2012/5-5/index.xhtml">Issue 5, 887–1173</a> <br/><a class="about" href="/apde/2012/5-4/index.xhtml">Issue 4, 705–885</a> <br/><a class="about" href="/apde/2012/5-3/index.xhtml">Issue 3, 423–703</a> <br/><a class="about" href="/apde/2012/5-2/index.xhtml">Issue 2, 219–422</a> <br/><a class="about" href="/apde/2012/5-1/index.xhtml">Issue 1, 1–218</a> </p> <p class="p-about-dropdown" id="volume-short-4"> <a class="about" onclick="showIssues('4');">Volume 4, 5 issues</a> </p> <p class="p-about-dropdown" id="volume-all-4" style="display:none;"> <a class="about" onclick="collapseIssues('4');">Volume 4</a> <br/><a class="about" href="/apde/2011/4-5/index.xhtml">Issue 5, 639–795</a> <br/><a class="about" href="/apde/2011/4-4/index.xhtml">Issue 4, 499–638</a> <br/><a class="about" href="/apde/2011/4-3/index.xhtml">Issue 3, 369–497</a> <br/><a class="about" href="/apde/2011/4-2/index.xhtml">Issue 2, 191–367</a> <br/><a class="about" href="/apde/2011/4-1/index.xhtml">Issue 1, 1–190</a> </p> <p class="p-about-dropdown" id="volume-short-3"> <a class="about" onclick="showIssues('3');">Volume 3, 4 issues</a> </p> <p class="p-about-dropdown" id="volume-all-3" style="display:none;"> <a class="about" onclick="collapseIssues('3');">Volume 3</a> <br/><a class="about" href="/apde/2010/3-4/index.xhtml">Issue 4, 359–489</a> <br/><a class="about" href="/apde/2010/3-3/index.xhtml">Issue 3, 227–358</a> <br/><a class="about" href="/apde/2010/3-2/index.xhtml">Issue 2, 109–225</a> <br/><a class="about" href="/apde/2010/3-1/index.xhtml">Issue 1, 1–108</a> </p> <p class="p-about-dropdown" id="volume-short-2"> <a class="about" onclick="showIssues('2');">Volume 2, 3 issues</a> </p> <p class="p-about-dropdown" id="volume-all-2" style="display:none;"> <a class="about" onclick="collapseIssues('2');">Volume 2</a> <br/><a class="about" href="/apde/2009/2-3/index.xhtml">Issue 3, 261–366</a> <br/><a class="about" href="/apde/2009/2-2/index.xhtml">Issue 2, 119–259</a> <br/><a class="about" href="/apde/2009/2-1/index.xhtml">Issue 1, 1–81</a> </p> <p class="p-about-dropdown" id="volume-short-1"> <a class="about" onclick="showIssues('1');">Volume 1, 3 issues</a> </p> <p class="p-about-dropdown" id="volume-all-1" style="display:none;"> <a class="about" onclick="collapseIssues('1');">Volume 1</a> <br/><a class="about" href="/apde/2008/1-3/index.xhtml">Issue 3, 267–379</a> <br/><a class="about" href="/apde/2008/1-2/index.xhtml">Issue 2, 127–266</a> <br/><a class="about" href="/apde/2008/1-1/index.xhtml">Issue 1, 1–126</a> </p> </td></tr> </table> </td> </tr> </table> <table cellspacing="0" cellpadding="0" class="pause"> <tr> <td class="action-end"><img src="/apde/etc/z.gif" alt="" /></td> <!-- underline (close) the action area above --> </tr> <tr> <td class="pause"><img src="/apde/etc/z.gif" alt="" /></td> <!-- create white space between sections --> </tr> </table> <table cellspacing="0" cellpadding="0" class="action"> <tr> <td> <table cellspacing="0" cellpadding="0" width="100%"> <tr> <td class="action-title-area"><div class="action-title">The Journal</div></td> </tr> <tr><td class="about-area"> <a class="about" href="/apde/about/journal/about.html">About the journal</a></td></tr> <tr><td class="about-area"> <a class="about" href="/apde/about/journal/policies.html">Ethics and policies</a></td></tr> <tr><td class="about-area"> <a class="about" href="/apde/about/journal/peer.html">Peer-review process</a></td></tr> <tr><td> </td></tr> <tr><td class="about-area"> <a class="about" href="/apde/about/journal/submissions.html">Submission guidelines</a></td></tr> <!--journal specific link --> <tr><td class="about-area"> <a class="about" href="https://ef.msp.org/submit/apde" target="_blank">Submission form</a></td></tr> <!-- journal specific link --> <tr><td class="about-area"> <a class="about" href="/apde/about/journal/editorial.html">Editorial board</a></td></tr> <tr><td class="about-area"> <a class="about" href="/apde/about/journal/areas.html">Editors' interests</a></td></tr> <tr><td> </td></tr> <!-- journal specific link --> <tr><td class="about-area"> <a class="about" href="https://msp.org/publications/journals/#apde">Subscriptions</a></td></tr> <tr><td> </td></tr> <tr><td class="about-area issn"> ISSN 1948-206X (online) </td></tr> <tr><td class="about-area issn"> ISSN 2157-5045 (print) </td></tr> <tr><td> </td></tr> <!-- journal specific link --> <tr><td class="about-area"> <a class="about" href="/index/ai.php?jpath=apde">Author index</a></td></tr> <!-- journal specific link --> <tr><td class="about-area"> <a class="about" href="/soon/coming.php?jpath=apde">To appear</a></td></tr> <tr><td> </td></tr> <tr><td class="about-area"> <a class="about" href="https://msp.org/p">Other MSP journals</a></td></tr> </table> </td> </tr> </table> <script async="true" defer="true" src="https://eye.msp.org/app.js"></script> <noscript><img src="https://eye.msp.org/image.gif" alt="" /></noscript> </td> <td class="content-column" id="content-area"> <table cellspacing="0" cellpadding="0" class="navigation" id= "navigation-area"> <tr> <td> <div class="issue-doi"> DOI: <a href= "http://dx.doi.org/10.2140/apde.2008.1-2">10.2140/apde.2008.1-2</a> </div> </td> </tr> <tr> <td> <div class="section-title"> Contents </div> </td> </tr> </table> <table cellspacing="0" cellpadding="0" class="toc" id="toc-area"> <tr> <td class="title-area"> <a class="title" href="p01.xhtml">Microlocal propagation near radial points and scattering for symbolic potentials of order zero</a> <div class="page-numbers"> 127–196 </div> <h3>Andrew Hassell, Richard Melrose and András Vasy</h3> </td> </tr> <tr> <td class="title-area"> <a class="title" href="p02.xhtml">CR-invariants and the scattering operator for complex manifolds with boundary</a> <div class="page-numbers"> 197–227 </div> <h3>Peter D. Hislop, Peter A. Perry and Siu-Hung Tang</h3> </td> </tr> <tr> <td class="title-area"> <a class="title" href="p03.xhtml">The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher</a> <div class="page-numbers"> 229–266 </div> <h3>Rowan Killip, Monica Visan and Xiaoyi Zhang</h3> </td> </tr> </table> </td> </tr> <tr> <td> <table cellspacing="0" cellpadding="0" class="pause"> <tr> <td class="action-end"><img src="/apde/etc/z.gif" alt= "" /></td> </tr> </table> </td> <td id="content-area-end"></td> </tr> </table> <table cellspacing="0" cellpadding="0" id="footer-area"> <tr> <td class="box-footer" onclick= "javascript:window.location='http://msp.org/';"> <img src="/mod/images/msp-logo.png" alt= "Mathematical Sciences Publishers" /> <p class="copyright">© Copyright 2008 Mathematical Sciences Publishers. All rights reserved.</p> </td> </tr> </table> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ jax: [ "input/TeX", "input/MathML", "output/CommonHTML" ], tex2jax: { inlineMath: [['$', '$'], ['\\(', '\\)']], processEscapes: true }, extensions: [ "tex2jax.js", "mml2jax.js" ], TeX: { extensions: [ "autoload-all.js" ] } }); </script> <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js"> </script> </body> </html>