REPOZYTORIUM UNIWERSYTETU
W BIAŁYMSTOKU
UwB

Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/3635
Pełny rekord metadanych
Pole DCWartośćJęzyk
dc.contributor.authorEndou, Noboru-
dc.contributor.authorOkazaki, Hiroyuki-
dc.contributor.authorShidama, Yasunari-
dc.date.accessioned2015-12-06T19:05:35Z-
dc.date.available2015-12-06T19:05:35Z-
dc.date.issued2012-
dc.identifier.citationFormalized Mathematics, Volume 20, Issue 2, 2012, Pages 113-124-
dc.identifier.issn1426-2630-
dc.identifier.issn1898-9934-
dc.identifier.urihttp://hdl.handle.net/11320/3635-
dc.description.abstractIn 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).-
dc.description.sponsorshipThis work was supported by JSPS KAKENHI 22300285 and 23500029-
dc.language.isoen-
dc.publisherDe Gruyter Open-
dc.titleHigher-Order Partial Differentiation-
dc.typeArticle-
dc.identifier.doi10.2478/v10037-012-0015-z-
dc.description.AffiliationEndou Noboru - Nagano National College of Technology, Japan-
dc.description.AffiliationOkazaki Hiroyuki - Shinshu University, Nagano, Japan-
dc.description.AffiliationShidama Yasunari - Shinshu University, Nagano, Japan-
dc.description.referencesGrzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.-
dc.description.referencesGrzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.-
dc.description.referencesCzesław Bylinski. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.-
dc.description.referencesCzesław Bylinski. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.-
dc.description.referencesCzesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.-
dc.description.referencesCzesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.-
dc.description.referencesCzesław Bylinski. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.-
dc.description.referencesAgata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.-
dc.description.referencesNoboru Endou and Yasunari Shidama. Completeness of the real Euclidean space. Formalized Mathematics, 13(4):577-580, 2005.-
dc.description.referencesNoboru Endou, Yasunari Shidama, and Keiichi Miyajima. Partial differentiation on normed linear spaces Rn. Formalized Mathematics, 15(2):65-72, 2007, doi:10.2478/v10037-007-0008-5.-
dc.description.referencesKrzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.-
dc.description.referencesTakao Inou´e, Noboru Endou, and Yasunari Shidama. Differentiation of vector-valued functions on n-dimensional real normed linear spaces. Formalized Mathematics, 18(4):207-212, 2010, doi: 10.2478/v10037-010-0025-7.-
dc.description.referencesTakao Inou´e, Adam Naumowicz, Noboru Endou, and Yasunari Shidama. Partial differentiation of vector-valued functions on n-dimensional real normed linear spaces. Formalized Mathematics, 19(1):1-9, 2011, doi: 10.2478/v10037-011-0001-x.-
dc.description.referencesJarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.-
dc.description.referencesKeiichi Miyajima and Yasunari Shidama. Riemann integral of functions from R into Rn. Formalized Mathematics, 17(2):179-185, 2009, doi: 10.2478/v10037-009-0021-y.-
dc.description.referencesKeiko Narita, Artur Kornilowicz, and Yasunari Shidama. More on the continuity of real functions. Formalized Mathematics, 19(4):233-239, 2011, doi: 10.2478/v10037-011-0032-3.-
dc.description.referencesTakaya Nishiyama, Keiji Ohkubo, and Yasunari Shidama. The continuous functions on normed linear spaces. Formalized Mathematics, 12(3):269-275, 2004.-
dc.description.referencesBeata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.-
dc.description.referencesBeata Perkowska. Functional sequence from a domain to a domain. Formalized Mathematics, 3(1):17-21, 1992.-
dc.description.referencesJan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991.-
dc.description.referencesYasunari Shidama. Banach space of bounded linear operators. Formalized Mathematics, 12(1):39-48, 2004.-
dc.description.referencesZinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.-
dc.description.referencesEdmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.-
Występuje w kolekcji(ach):Formalized Mathematics, 2012, Volume 20, Issue 2

Pliki w tej pozycji:
Plik Opis RozmiarFormat 
v10037-012-0015-z.pdf312,41 kBAdobe PDFOtwórz
Pokaż uproszczony widok rekordu Zobacz statystyki


Pozycja ta dostępna jest na podstawie licencji Licencja Creative Commons CCL Creative Commons