{"id":27129,"date":"2026-02-12T08:30:44","date_gmt":"2026-02-12T13:30:44","guid":{"rendered":"https:\/\/blog.utc.edu\/campus-weekly\/?p=27129"},"modified":"2026-02-12T08:30:44","modified_gmt":"2026-02-12T13:30:44","slug":"notice-of-final-defense-caleb-beckler-to-present-masters-research","status":"publish","type":"post","link":"https:\/\/blog.utc.edu\/campus-weekly\/2026\/02\/notice-of-final-defense-caleb-beckler-to-present-masters-research\/","title":{"rendered":"Notice of Final Defense &#8211; Caleb Beckler to Present Master&#8217;s Research"},"content":{"rendered":"\n<p>The UTC Graduate School is pleased to announce that&nbsp;Caleb Beckler will present Master&#8217;s research titled,&nbsp;On the Parametrization of Self-adjoint Extensions of Singular Sturm-Liouville Operators on&nbsp;03\/05\/2026 at&nbsp;12:30 in&nbsp;Lupton 302. Everyone is invited to attend.&nbsp;<br><br>Mathematics<br><br>Chair:&nbsp;Roger Nichols<br><br>Co-Chair:&nbsp;<br><br>Abstract:<br><br>The self-adjoint extensions of a lower semi-bounded minimal Sturm-Liouville operator are parametrized using generalized boundary values defined by fixed choices of special nonoscillatory solutions, called principal and nonprincipal solutions. However, principal and nonprincipal solutions are not unique, and different choices yield different generalized boundary values. Therefore, the parametrization of self-adjoint extensions inherently depends upon the choices of principal and nonprincipal solutions. Using known properties of principal and nonprincipal solutions, Wronskian techniques, and the Plucker identity, we find the relation between self-adjoint extensions for two different parametrizations.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The UTC Graduate School is pleased to announce that&nbsp;Caleb Beckler will present Master&#8217;s research titled,&nbsp;On the Parametrization of Self-adjoint Extensions of Singular Sturm-Liouville Operators on&nbsp;03\/05\/2026 at&nbsp;12:30 in&nbsp;Lupton 302. Everyone is invited to attend.&nbsp; Mathematics Chair:&nbsp;Roger Nichols Co-Chair:&nbsp; Abstract: The self-adjoint extensions of a lower semi-bounded minimal Sturm-Liouville operator are parametrized using generalized boundary values defined&hellip; <\/p>\n<p class=\"more-link-wrap\"><span><a class=\"more-link button text\" href=\"https:\/\/blog.utc.edu\/campus-weekly\/2026\/02\/notice-of-final-defense-caleb-beckler-to-present-masters-research\/\"><span>Continue Reading <\/span><\/a><\/span><\/p>\n","protected":false},"author":1493,"featured_media":3939,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[8,15,120183,120186],"tags":[],"class_list":{"0":"post-27129","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-campus","8":"category-faculty-staff","9":"category-news","10":"category-students-news","11":"entry"},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Notice of Final Defense - Caleb Beckler to Present Master&#039;s Research - Campus Updates<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/blog.utc.edu\/campus-weekly\/2026\/02\/notice-of-final-defense-caleb-beckler-to-present-masters-research\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Notice of Final Defense - Caleb Beckler to Present Master&#039;s Research - Campus Updates\" \/>\n<meta property=\"og:description\" content=\"The UTC Graduate School is pleased to announce that&nbsp;Caleb Beckler will present Master&#8217;s research titled,&nbsp;On the Parametrization of Self-adjoint Extensions of Singular Sturm-Liouville Operators on&nbsp;03\/05\/2026 at&nbsp;12:30 in&nbsp;Lupton 302. Everyone is invited to attend.&nbsp; Mathematics Chair:&nbsp;Roger Nichols Co-Chair:&nbsp; Abstract: The self-adjoint extensions of a lower semi-bounded minimal Sturm-Liouville operator are parametrized using generalized boundary values defined&hellip; Continue Reading\" \/>\n<meta property=\"og:url\" content=\"https:\/\/blog.utc.edu\/campus-weekly\/2026\/02\/notice-of-final-defense-caleb-beckler-to-present-masters-research\/\" \/>\n<meta property=\"og:site_name\" content=\"Campus Updates\" \/>\n<meta property=\"article:published_time\" content=\"2026-02-12T13:30:44+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/blog.utc.edu\/app\/uploads\/sites\/138\/2022\/10\/Lupton-21-1195-1024x692.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1024\" \/>\n\t<meta property=\"og:image:height\" content=\"692\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Chuck Wasserstrom\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Chuck Wasserstrom\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/blog.utc.edu\\\/campus-weekly\\\/2026\\\/02\\\/notice-of-final-defense-caleb-beckler-to-present-masters-research\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/blog.utc.edu\\\/campus-weekly\\\/2026\\\/02\\\/notice-of-final-defense-caleb-beckler-to-present-masters-research\\\/\"},\"author\":{\"name\":\"Chuck Wasserstrom\",\"@id\":\"https:\\\/\\\/blog.utc.edu\\\/campus-weekly\\\/#\\\/schema\\\/person\\\/028a71bd6215de86078a717b45430622\"},\"headline\":\"Notice of Final Defense &#8211; 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