DSpace Kolekcja:
http://hdl.handle.net/11320/3540
2024-03-28T13:15:54ZAffine Independence in Vector Spaces
http://hdl.handle.net/11320/3564
Tytuł: Affine Independence in Vector Spaces
Autorzy: Pąk, Karol
Abstrakt: In this article we describe the notion of affinely independent subset of a real linear space. First we prove selected theorems concerning operations on linear combinations. Then we introduce affine independence and prove the equivalence of various definitions of this notion. We also introduce the notion of the affine hull, i.e. a subset generated by a set of vectors which is an intersection of all affine sets including the given set. Finally, we introduce and prove selected properties of the barycentric coordinates.2010-01-01T00:00:00ZAbstract Simplicial Complexes
http://hdl.handle.net/11320/3565
Tytuł: Abstract Simplicial Complexes
Autorzy: Pąk, Karol
Abstrakt: In this article we define the notion of abstract simplicial complexes and operations on them. We introduce the following basic notions: simplex, face, vertex, degree, skeleton, subdivision and substructure, and prove some of their properties.2010-01-01T00:00:00ZFixpoint Theorem for Continuous Functions on Chain-Complete Posets
http://hdl.handle.net/11320/3558
Tytuł: Fixpoint Theorem for Continuous Functions on Chain-Complete Posets
Autorzy: Ishida, Kazuhisa; Shidama, Yasunari
Abstrakt: This text includes the definition of chain-complete poset, fix-point theorem on it, and the definition of the function space of continuous functions on chain-complete posets [10].2010-01-01T00:00:00ZA Model of Mizar Concepts - Unification
http://hdl.handle.net/11320/3561
Tytuł: A Model of Mizar Concepts - Unification
Autorzy: Bancerek, Grzegorz
Abstrakt: The aim of this paper is to develop a formal theory of Mizar linguistic concepts following the ideas from [6] and [7]. The theory presented is an abstraction from the existing implementation of the Mizar system and is devoted to the formalization of Mizar expressions. The concepts formalized here are: standarized constructor signature, arity-rich signatures, and the unification of Mizar expressions.2010-01-01T00:00:00Z