Artur Korniłowicz (2010)
Formalized Mathematics
Similarity:
In the article we prove that a family of open n-hypercubes is a basis of n-dimensional Euclidean space. The equality of the space and the product of n real lines has been proven.
Karol Pąk (2014)
Formalized Mathematics
Similarity:
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/. ...
Takao Inoué, Adam Naumowicz, Noboru Endou, Yasunari Shidama (2011)
Formalized Mathematics
Similarity:
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]).
Grzegorz Bancerek (2012)
Formalized Mathematics
Similarity:
In the paper the semantics of MML Query queries is given. The formalization is done according to [4]
Karol Pąk (2014)
Formalized Mathematics
Similarity:
In this article we prove the Tietze extension theorem for an arbitrary convex compact subset of εn with a non-empty interior. This theorem states that, if T is a normal topological space, X is a closed subset of T, and A is a convex compact subset of εn with a non-empty interior, then a continuous function f : X → A can be extended to a continuous function g : T → εn. Additionally we show that a subset A is replaceable by an arbitrary subset of a topological space that is homeomorphic...
Takao Inoué, Noboru Endou, Yasunari Shidama (2010)
Formalized Mathematics
Similarity:
In this article, we define and develop differentiation of vector-valued functions on n-dimensional real normed linear spaces (refer to [16] and [17]).
Saharon Shelah (2000)
Fundamenta Mathematicae
Similarity:
The Kalikow problem for a pair (λ,κ) of cardinal numbers,λ > κ (in particular κ = 2) is whether we can map the family of ω-sequences from λ to the family of ω-sequences from κ in a very continuous manner. Namely, we demand that for η,ν ∈ ω we have: η, ν are almost equal if and only if their images are. We show consistency of the negative answer, e.g., for but we prove it for smaller cardinals. We indicate a close connection with the free subset property and its variants. ...
Boonpok, Chawalit (2009)
Acta Universitatis Apulensis. Mathematics - Informatics
Similarity:
L. H. Erbe, W. Krawcewicz, Shaozhu Chen (1991)
Annales Polonici Mathematici
Similarity:
Using the topological transversality method of Granas we prove an existence result for a system of differential inclusions with retardations of the form y'' ∈ F(t,y,y',Φ(y)). The result is applied to the study of the existence of solutions to an equation of the trajectory of an r-stage rocket with retardations.
Freyd, Peter (2008)
Theory and Applications of Categories [electronic only]
Similarity: