{"id":13580,"date":"2021-10-21T09:27:23","date_gmt":"2021-10-21T06:27:23","guid":{"rendered":"https:\/\/umram.bilkent.edu.tr\/index.php\/2021\/10\/21\/dogrusal-kanonik-donusumlerin-operator-kuramina-dayali-hesaplanmasi\/"},"modified":"2026-11-04T10:59:03","modified_gmt":"2026-11-04T07:59:03","slug":"dogrusal-kanonik-donusumlerin-operator-kuramina-dayali-hesaplanmasi","status":"publish","type":"post","link":"https:\/\/umram.bilkent.edu.tr\/index.php\/tr\/2021\/10\/21\/dogrusal-kanonik-donusumlerin-operator-kuramina-dayali-hesaplanmasi\/","title":{"rendered":"Do\u011frusal kanonik d\u00f6n\u00fc\u015f\u00fcmlerin operat\u00f6r kuram\u0131na dayal\u0131 hesaplanmas\u0131"},"content":{"rendered":"<p><a href=\"https:\/\/umram.bilkent.edu.tr\/index.php\/teams\/aykut-koc\/\">Dr. Ko\u00e7<\/a> ve \u00e7al\u0131\u015fma arkada\u015flar\u0131n\u0131n <em>Signal Processing<\/em> dergisinde yay\u0131mlanan \u201cOperator Theory-based Computation of Linear Canonical Transforms\u201d ba\u015fl\u0131kl\u0131 makalesinde operat\u00f6r kuram\u0131 do\u011frusal kanonik d\u00f6n\u00fc\u015f\u00fcmlerin hesaplanmas\u0131na uygulanm\u0131\u015ft\u0131r.<\/p>\n<p>Hiperdiferansiyel operat\u00f6rlerden yararlanan ve olas\u0131 parametreler ile tasar\u0131m se\u00e7eneklerini sistematik olarak inceleyen \u00f6nerilen algoritma, hem kuramsal olarak tutarl\u0131 hem de y\u00fcksek do\u011fruluklu bir ayr\u0131k do\u011frusal kanonik d\u00f6n\u00fc\u015f\u00fcm (DLCT) tan\u0131m\u0131 elde etmektedir.<\/p>\n<p>Bu yakla\u015f\u0131m\u0131n \u00fcst\u00fcnl\u00fc\u011f\u00fc, karma\u015f\u0131k ayr\u0131k d\u00f6n\u00fc\u015f\u00fcmleri tan\u0131mlama problemini ayr\u0131k koordinat \u00e7arp\u0131m\u0131 ve t\u00fcrev alma i\u015flemlerini tan\u0131mlamak gibi \u00e7ok daha basit bir probleme indirgemesidir. Yakla\u015f\u0131m, ayr\u0131k d\u00f6n\u00fc\u015f\u00fcmler kuram\u0131nda yeni ara\u015ft\u0131rma y\u00f6nlerine kap\u0131 a\u00e7abilir.<\/p>\n<p>Makaleye [<a href=\"https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0165168421003285?via%3Dihub\" target=\"_blank\" rel=\"noopener\">buradan<\/a>] eri\u015filebilir.<\/p>\n\n<p><strong>\u00d6zet: <\/strong><\/p>\n<p>Do\u011frusal kanonik d\u00f6n\u00fc\u015f\u00fcmler (LCT) bilim ve m\u00fchendisli\u011fin pek \u00e7ok alan\u0131nda yayg\u0131n olarak kullan\u0131lmakta ve tatmin edici bir ayr\u0131k ger\u00e7ekle\u015ftirme gerektirmektedir. Son zamanlarda hiperdiferansiyel operat\u00f6rler ayr\u0131k LCT&#8217;yi (DLCT) tan\u0131mlaman\u0131n yeni bir yolu olarak \u00f6nerilmi\u015ftir. Bu \u00e7al\u0131\u015fmada \u00f6nce alternatif ayr\u0131k koordinat \u00e7arp\u0131m\u0131 ve t\u00fcrev alma i\u015flemleri ele al\u0131narak bu yakla\u015f\u0131m\u0131n do\u011frulu\u011funun art\u0131r\u0131lmas\u0131na odaklan\u0131lmaktad\u0131r. LCT&#8217;lerin kanonik ayr\u0131\u015f\u0131mlar\u0131 da ele al\u0131nmakta ve ilk \u00f6nerilen Iwasawa ayr\u0131\u015f\u0131m\u0131yla kar\u015f\u0131la\u015ft\u0131r\u0131lmaktad\u0131r. S\u00fcrekli LCT&#8217;nin DLCT ile yakla\u015f\u0131klanmas\u0131n\u0131n do\u011frulu\u011funun b\u00fcy\u00fck \u00f6l\u00e7\u00fcde art\u0131r\u0131labildi\u011fi g\u00f6sterilmektedir. Yakla\u015f\u0131m\u0131n \u00fcst\u00fcnl\u00fc\u011f\u00fc, d\u00f6n\u00fc\u015f\u00fcmleri bu i\u015flemlere indirgeyerek karma\u015f\u0131k ayr\u0131k d\u00f6n\u00fc\u015f\u00fcmleri tan\u0131mlama problemini yaln\u0131zca ayr\u0131k koordinat \u00e7arp\u0131m\u0131 ve t\u00fcrev alma i\u015flemlerini tan\u0131mlamaya indirgemesidir. Olas\u0131 parametrelerin ve tasar\u0131m se\u00e7eneklerinin sistematik incelenmesi sonucunda hem kuramsal olarak tutarl\u0131 hem de y\u00fcksek do\u011fruluklu bir DLCT elde edilmektedir.<\/p>\n\n","protected":false},"excerpt":{"rendered":"<p>Dr. Ko\u00e7 ve \u00e7al\u0131\u015fma arkada\u015flar\u0131n\u0131n Signal Processing dergisinde yay\u0131mlanan \u201cOperator Theory-based Computation of Linear Canonical Transforms\u201d ba\u015fl\u0131kl\u0131 makalesinde operat\u00f6r kuram\u0131 do\u011frusal kanonik d\u00f6n\u00fc\u015f\u00fcmlerin hesaplanmas\u0131na uygulanm\u0131\u015ft\u0131r. Hiperdiferansiyel operat\u00f6rlerden yararlanan ve olas\u0131 parametreler ile tasar\u0131m se\u00e7eneklerini sistematik olarak inceleyen \u00f6nerilen algoritma, hem kuramsal olarak tutarl\u0131 hem de y\u00fcksek do\u011fruluklu bir ayr\u0131k do\u011frusal kanonik d\u00f6n\u00fc\u015f\u00fcm (DLCT) tan\u0131m\u0131 elde\u2026<\/p>\n","protected":false},"author":9,"featured_media":11865,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[445],"tags":[],"class_list":["post-13580","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-duyurular"],"_links":{"self":[{"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/posts\/13580","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/comments?post=13580"}],"version-history":[{"count":1,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/posts\/13580\/revisions"}],"predecessor-version":[{"id":13581,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/posts\/13580\/revisions\/13581"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/media\/11865"}],"wp:attachment":[{"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/media?parent=13580"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/categories?post=13580"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/tags?post=13580"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}