{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T00:52:44Z","timestamp":1777423964068,"version":"3.51.4"},"reference-count":13,"publisher":"Walter de Gruyter GmbH","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2010,1,1]]},"abstract":"<jats:title>Vector Functions and their Differentiation Formulas in 3-dimensional Euclidean Spaces<\/jats:title>\n        <jats:p>In this article, we first extend several basic theorems of the operation of vector in 3-dimensional Euclidean spaces. Then three unit vectors: <jats:italic>e<\/jats:italic>1, <jats:italic>e<\/jats:italic>2, <jats:italic>e<\/jats:italic>3 and the definition of vector function in the same spaces are introduced. By dint of unit vector the main operation properties as well as the differentiation formulas of vector function are shown [12].<\/jats:p>","DOI":"10.2478\/v10037-010-0001-2","type":"journal-article","created":{"date-parts":[[2011,1,6]],"date-time":"2011-01-06T02:24:51Z","timestamp":1294280691000},"page":"1-10","source":"Crossref","is-referenced-by-count":3,"title":["Vector Functions and their Differentiation Formulas in 3-dimensional Euclidean Spaces"],"prefix":"10.2478","volume":"18","author":[{"given":"Xiquan","family":"Liang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Piqing","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ou","family":"Bai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","reference":[{"issue":"1","key":"1","first-page":"91","article-title":"The ordinal numbers","volume":"1","author":"Grzegorz Bancerek","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"1","key":"2","first-page":"107","article-title":"Segments of natural numbers and finite sequences","volume":"1","author":"Grzegorz Bancerek","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"3","key":"3","first-page":"529","article-title":"Finite sequences and tuples of elements of a non-empty sets","volume":"1","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"1","key":"4","first-page":"153","article-title":"Functions from a set to a set","volume":"1","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"2","key":"5","first-page":"357","article-title":"Partial functions","volume":"1","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"4","key":"6","first-page":"661","article-title":"The sum and product of finite sequences of real numbers","volume":"1","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"4","key":"7","first-page":"599","article-title":"The Euclidean space","volume":"2","author":"Agata Darmochwa\u0142","year":"1991","journal-title":"Formalized Mathematics"},{"issue":"1","key":"8","first-page":"35","article-title":"Basic properties of real numbers","volume":"1","author":"Krzysztof Hryniewiecki","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"4","key":"9","first-page":"703","article-title":"Partial functions from a domain to the set of real numbers","volume":"1","author":"Jaros\u0142aw Kotowicz","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"2","key":"10","first-page":"269","article-title":"Real sequences and basic operations on them","volume":"1","author":"Jaros\u0142aw Kotowicz","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"4","key":"11","first-page":"797","article-title":"Real function differentiability","volume":"1","author":"Konrad Raczkowski","year":"1990","journal-title":"Formalized Mathematics"},{"key":"12","volume-title":"Vector Analysis and an Introduction to Tensor Analysis","author":"Murray Spiegel","year":"1959"},{"issue":"3","key":"13","first-page":"445","article-title":"Some properties of real numbers","volume":"1","author":"Andrzej Trybulec","year":"1990","journal-title":"Formalized Mathematics"}],"container-title":["Formalized Mathematics"],"original-title":[],"link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/forma\/18\/1\/article-p1.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/view\/j\/forma.2010.18.issue-1\/v10037-010-0001-2\/v10037-010-0001-2.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,30]],"date-time":"2020-05-30T15:27:55Z","timestamp":1590852475000},"score":1,"resource":{"primary":{"URL":"https:\/\/content.sciendo.com\/doi\/10.2478\/v10037-010-0001-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1,1]]},"references-count":13,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.2478\/v10037-010-0001-2","relation":{},"ISSN":["1898-9934","1426-2630"],"issn-type":[{"value":"1898-9934","type":"electronic"},{"value":"1426-2630","type":"print"}],"subject":[],"published":{"date-parts":[[2010,1,1]]}}}