Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji:
http://hdl.handle.net/11320/3635
Pełny rekord metadanych
Pole DC | Wartość | Język |
---|---|---|
dc.contributor.author | Endou, Noboru | - |
dc.contributor.author | Okazaki, Hiroyuki | - |
dc.contributor.author | Shidama, Yasunari | - |
dc.date.accessioned | 2015-12-06T19:05:35Z | - |
dc.date.available | 2015-12-06T19:05:35Z | - |
dc.date.issued | 2012 | - |
dc.identifier.citation | Formalized Mathematics, Volume 20, Issue 2, 2012, Pages 113-124 | - |
dc.identifier.issn | 1426-2630 | - |
dc.identifier.issn | 1898-9934 | - |
dc.identifier.uri | http://hdl.handle.net/11320/3635 | - |
dc.description.abstract | 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). | - |
dc.description.sponsorship | This work was supported by JSPS KAKENHI 22300285 and 23500029 | - |
dc.language.iso | en | - |
dc.publisher | De Gruyter Open | - |
dc.title | Higher-Order Partial Differentiation | - |
dc.type | Article | - |
dc.identifier.doi | 10.2478/v10037-012-0015-z | - |
dc.description.Affiliation | Endou Noboru - Nagano National College of Technology, Japan | - |
dc.description.Affiliation | Okazaki Hiroyuki - Shinshu University, Nagano, Japan | - |
dc.description.Affiliation | Shidama Yasunari - Shinshu University, Nagano, Japan | - |
dc.description.references | Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. | - |
dc.description.references | Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990. | - |
dc.description.references | Czesław Bylinski. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990. | - |
dc.description.references | Czesław Bylinski. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990. | - |
dc.description.references | Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990. | - |
dc.description.references | Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990. | - |
dc.description.references | Czesław Bylinski. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990. | - |
dc.description.references | Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991. | - |
dc.description.references | Noboru Endou and Yasunari Shidama. Completeness of the real Euclidean space. Formalized Mathematics, 13(4):577-580, 2005. | - |
dc.description.references | Noboru 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.references | Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990. | - |
dc.description.references | Takao 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.references | Takao 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.references | Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990. | - |
dc.description.references | Keiichi 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.references | Keiko 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.references | Takaya Nishiyama, Keiji Ohkubo, and Yasunari Shidama. The continuous functions on normed linear spaces. Formalized Mathematics, 12(3):269-275, 2004. | - |
dc.description.references | Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990. | - |
dc.description.references | Beata Perkowska. Functional sequence from a domain to a domain. Formalized Mathematics, 3(1):17-21, 1992. | - |
dc.description.references | Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991. | - |
dc.description.references | Yasunari Shidama. Banach space of bounded linear operators. Formalized Mathematics, 12(1):39-48, 2004. | - |
dc.description.references | Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. | - |
dc.description.references | Edmund 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 | Rozmiar | Format | |
---|---|---|---|---|
v10037-012-0015-z.pdf | 312,41 kB | Adobe PDF | Otwórz |
Pozycja ta dostępna jest na podstawie licencji Licencja Creative Commons CCL