On near-standardness in Hilbert spaces.
Lyantse, W.E., Kudrik, T.S. (2002)
Sibirskij Matematicheskij Zhurnal
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Lyantse, W.E., Kudrik, T.S. (2002)
Sibirskij Matematicheskij Zhurnal
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Keiko Narita, Noboru Endou, Yasunari Shidama (2013)
Formalized Mathematics
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In this article, we describe the differential equations on functions from R into real Banach space. The descriptions are based on the article [20]. As preliminary to the proof of these theorems, we proved some properties of differentiable functions on real normed space. For the proof we referred to descriptions and theorems in the article [21] and the article [32]. And applying the theorems of Riemann integral introduced in the article [22], we proved the ordinary differential equations...
Grzegorz Bancerek (2012)
Formalized Mathematics
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In the paper the semantics of MML Query queries is given. The formalization is done according to [4]
Saharon Shelah (2000)
Fundamenta Mathematicae
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We prove that it is consistent that the covering number of the ideal of measure zero sets has countable cofinality.
J. Barnett (1992)
Fundamenta Mathematicae
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Examples exist of smooth maps on the boundary of a smooth manifold M which allow continuous extensions over M without fixed points but no such smooth extensions. Such maps are studied here in more detail. They have a minimal fixed point set when all transversally fixed maps in their homotopy class are considered. Therefore we introduce a Nielsen fixed point theory for transversally fixed maps on smooth manifolds without or with boundary, and use it to calculate the minimum number of...
Combarro, E.F. (2004)
Sibirskij Matematicheskij Zhurnal
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Grzegorz Bancerek (2008)
Formalized Mathematics
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This paper is a continuation of [5] and concerns if-while algebras over integers. In these algebras the only elementary instructions are assignment instructions. The instruction assigns to a (program) variable a value which is calculated for the current state according to some arithmetic expression. The expression may include variables, constants, and a limited number of arithmetic operations. States are functions from a given set of locations into integers. A variable is a function...
Takao Inoué, Adam Naumowicz, Noboru Endou, Yasunari Shidama (2011)
Formalized Mathematics
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In this article, we define and develop partial differentiation of vector-valued functions on n-dimensional real normed linear spaces (refer to [19] and [20]).
Karol Pąk (2014)
Formalized Mathematics
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In this article we formalize the Bertrand’s Ballot Theorem based on [17]. Suppose that in an election we have two candidates: A that receives n votes and B that receives k votes, and additionally n ≥ k. Then this theorem states that the probability of the situation where A maintains more votes than B throughout the counting of the ballots is equal to (n − k)/(n + k). This theorem is item #30 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/. ...
Richard N. Ball, Aleš Pultr, Jiří Sichler (2005)
Commentationes Mathematicae Universitatis Carolinae
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We show that prohibiting a combinatorial tree in the Priestley duals determines an axiomatizable class of distributive lattices. On the other hand, prohibiting -crowns with does not. Given what is known about the diamond, this is another strong indication that this fact characterizes combinatorial trees. We also discuss varieties of 2-Heyting algebras in this context.