On three problems from the Scottish Book connected with orthogonal systems
A. Plichko, A. Razenkov (1996)
Colloquium Mathematicae
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A. Plichko, A. Razenkov (1996)
Colloquium Mathematicae
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Keiichi Miyajima, Takahiro Kato (2010)
Formalized Mathematics
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This article extends the [10]. We define the sum and the product of the sequence of complex numbers, and formalize these theorems. Our method refers to the [11].
Artur Korniłowicz (2010)
Formalized Mathematics
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We prove that basic arithmetic operations preserve continuity of functions.
Jovanka Nikić, Irena Čomić (2005)
Kragujevac Journal of Mathematics
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Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama (2011)
Formalized Mathematics
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In this article, we formalize integral linear spaces, that is a linear space with integer coefficients. Integral linear spaces are necessary for lattice problems, LLL (Lenstra-Lenstra-Lovász) base reduction algorithm that outputs short lattice base and cryptographic systems with lattice [8].
Katsumi Wasaki (2008)
Formalized Mathematics
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We continue to formalize the concept of the Generalized Full Addition and Subtraction circuits (GFAs), define the structures of calculation units for the Redundant Signed Digit (RSD) operations, then prove its stability of the calculations. Generally, one-bit binary full adder assumes positive weights to all of its three binary inputs and two outputs. We define the circuit structure of two-types n-bit GFAs using the recursive construction to use the RSD arithmetic logical units that...
Artur Korniłowicz (2010)
Formalized Mathematics
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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.
Kulczycki, Marcin (2002)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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Jean-Paul Allouche, Pierre Liardet (1991)
Acta Arithmetica
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Gunawan, Hendra, Neswan, Oki, Setya-Budhi, Wono (2005)
Beiträge zur Algebra und Geometrie
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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/. ...