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2012 | 20 | 1 | 65-71
Tytuł artykułu

The Differentiable Functions from R intoRn

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In control engineering, differentiable partial functions from R into Rn play a very important role. In this article, we formalized basic properties of such functions.
Słowa kluczowe
Wydawca
Rocznik
Tom
20
Numer
1
Strony
65-71
Opis fizyczny
Daty
wydano
2012-01-01
online
2012-09-12
Twórcy
autor
  • Hirosaki-city, Aomori, Japan
  • Institute of Informatics, University of Białystok, Sosnowa 64, 15-887 Białystok, Poland
  • Shinshu University, Nagano, Japan
Bibliografia
  • Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
  • Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
  • Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
  • Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.
  • Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.
  • Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
  • Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  • Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.
  • Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.
  • Noboru Endou and Yasunari Shidama. Completeness of the real Euclidean space. Formalized Mathematics, 13(4):577-580, 2005.
  • 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.[Crossref]
  • Hiroshi Imura, Morishige Kimura, and Yasunari Shidama. The differentiable functions on normed linear spaces. Formalized Mathematics, 12(3):321-327, 2004.
  • Takao Inoué, 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.[Crossref]
  • 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.[Crossref]
  • 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.[Crossref]
  • Takaya Nishiyama, Keiji Ohkubo, and Yasunari Shidama. The continuous functions on normed linear spaces. Formalized Mathematics, 12(3):269-275, 2004.
  • Hiroyuki Okazaki, Noboru Endou, Keiko Narita, and Yasunari Shidama. Differentiable functions into real normed spaces. Formalized Mathematics, 19(2):69-72, e2011, doi: 10.2478/v10037-011-0012-7.[Crossref]
  • Hiroyuki Okazaki, Noboru Endou, and Yasunari Shidama. More on continuous functions on normed linear spaces. Formalized Mathematics, 19(1):45-49, 2011, doi: 10.2478/v10037-011-0008-3.[Crossref]
  • Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.
  • Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991.
  • Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.
  • Yasunari Shidama. Banach space of bounded linear operators. Formalized Mathematics, 12(1):39-48, 2004.
  • Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.
  • Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
  • Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
  • Hiroshi Yamazaki and Yasunari Shidama. Algebra of vector functions. Formalized Mathematics, 3(2):171-175, 1992.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_v10037-012-0009-x
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