{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T01:30:07Z","timestamp":1777426207464,"version":"3.51.4"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012,12,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n\t\t\t\t<jats:p>In this article, we shall extend the formalization of [10] to discuss higher-order partial differentiation of real valued functions. The linearity of this operator is also proved (refer to [10], [12] and [13] for partial differentiation).<\/jats:p>","DOI":"10.2478\/v10037-012-0015-z","type":"journal-article","created":{"date-parts":[[2013,2,4]],"date-time":"2013-02-04T17:14:25Z","timestamp":1359998065000},"page":"113-124","source":"Crossref","is-referenced-by-count":1,"title":["Higher-Order Partial Differentiation"],"prefix":"10.2478","volume":"20","author":[{"given":"Noboru","family":"Endou","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hiroyuki","family":"Okazaki","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yasunari","family":"Shidama","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","container-title":["Formalized Mathematics"],"original-title":[],"link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/forma\/20\/2\/article-p113.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/view\/j\/forma.2012.20.issue-2\/v10037-012-0015-z\/v10037-012-0015-z.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,30]],"date-time":"2020-05-30T15:28:35Z","timestamp":1590852515000},"score":1,"resource":{"primary":{"URL":"https:\/\/content.sciendo.com\/doi\/10.2478\/v10037-012-0015-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12,1]]},"references-count":0,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.2478\/v10037-012-0015-z","relation":{},"ISSN":["1898-9934","1426-2630"],"issn-type":[{"value":"1898-9934","type":"electronic"},{"value":"1426-2630","type":"print"}],"subject":[],"published":{"date-parts":[[2012,12,1]]}}}