{"id":2688546,"date":"2013-08-26T20:20:25","date_gmt":"2013-08-27T06:20:25","guid":{"rendered":"https:\/\/math.hawaii.edu\/wordpress\/?p=2688546"},"modified":"2025-10-13T11:35:21","modified_gmt":"2025-10-13T21:35:21","slug":"marriotts-doctoral-defense","status":"publish","type":"post","link":"https:\/\/math.hawaii.edu\/wordpress\/marriotts-doctoral-defense\/","title":{"rendered":"Marriott&#8217;s doctoral defense"},"content":{"rendered":"<p><a href=\"https:\/\/math.hawaii.edu\/wordpress\/marriotts-doctoral-defense\/o1_to_o2\/\" rel=\"attachment wp-att-2710357\"><img loading=\"lazy\" decoding=\"async\" class=\"alignright size-medium wp-image-2710357\" title=\" Among the singular trajectories of the control system for this problem are the exceptional singular trajectories, for which the control is defined as a rational function, u = D'\/D.  The sets of points such that D=0 or D=D'=0 are of key interest in classifying the behavior of the exceptional singular trajectories.  Here we illustrate properties of these sets.\" src=\"https:\/\/math.hawaii.edu\/wordpress\/wp-content\/uploads\/2013\/08\/O1_to_O2-300x175.png\" alt=\"O1_to_O2\" width=\"300\" height=\"175\" srcset=\"https:\/\/math.hawaii.edu\/wordpress\/wp-content\/uploads\/2013\/08\/O1_to_O2-300x175.png 300w, https:\/\/math.hawaii.edu\/wordpress\/wp-content\/uploads\/2013\/08\/O1_to_O2-1024x600.png 1024w, https:\/\/math.hawaii.edu\/wordpress\/wp-content\/uploads\/2013\/08\/O1_to_O2.png 1087w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><img decoding=\"async\" class=\"alignright\" src=\"http:\/\/math.hawaii.edu\/home\/board\/john-marriotts.jpg\" \/><br \/>\nJohn Marriott, a student of Prof. <a href=\"http:\/\/math.hawaii.edu\/people\/chyba\/\">Monique Chyba<\/a>, will defend his doctoral dissertation on September 5.<\/p>\n<h4>Abstract<\/h4>\n<blockquote><p>This work addresses the contrast problem in nuclear magnetic resonance as a Mayer problem in<br \/>\noptimal control. This is a problem motivated by improving the visible contrast in magnetic resonance<br \/>\nimaging, in which the magnetization of the nuclei of the substances imaged are \ffirst prepared by<br \/>\nbeing set to a particular con\ffiguration by an external magnetic \ffield, the control. In particular we<br \/>\nexamine the contrast problem by saturation, wherein the magnetization of the \ffirst substance is<br \/>\nset to zero. This system is modeled by a pair of Bloch equations representing the evolution of the<br \/>\nmagnetization vectors of the nuclei of two di\u000bfferent substances, both influenced by the same control<br \/>\nfield.<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>John Marriott, a student of Prof. Monique Chyba, will defend his doctoral dissertation on September 5. Abstract This work addresses the contrast problem in nuclear magnetic resonance as a Mayer problem in optimal control. This is a problem motivated by improving the visible contrast in magnetic resonance imaging, in which the magnetization of the nuclei &hellip; <a href=\"https:\/\/math.hawaii.edu\/wordpress\/marriotts-doctoral-defense\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Marriott&#8217;s doctoral defense<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[72,22],"tags":[],"class_list":["post-2688546","post","type-post","status-publish","format-standard","hentry","category-graduate-news","category-research-posts"],"_links":{"self":[{"href":"https:\/\/math.hawaii.edu\/wordpress\/wp-json\/wp\/v2\/posts\/2688546","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math.hawaii.edu\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/math.hawaii.edu\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/math.hawaii.edu\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/math.hawaii.edu\/wordpress\/wp-json\/wp\/v2\/comments?post=2688546"}],"version-history":[{"count":10,"href":"https:\/\/math.hawaii.edu\/wordpress\/wp-json\/wp\/v2\/posts\/2688546\/revisions"}],"predecessor-version":[{"id":5713421,"href":"https:\/\/math.hawaii.edu\/wordpress\/wp-json\/wp\/v2\/posts\/2688546\/revisions\/5713421"}],"wp:attachment":[{"href":"https:\/\/math.hawaii.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=2688546"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/math.hawaii.edu\/wordpress\/wp-json\/wp\/v2\/categories?post=2688546"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.hawaii.edu\/wordpress\/wp-json\/wp\/v2\/tags?post=2688546"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}