http://hdl.handle.net/11320/3540 2026-06-01T16:12:08Z 2026-06-01T16:12:08Z Pąk, Karol http://hdl.handle.net/11320/3565 2017-10-05T22:45:45Z 2010-01-01T00:00:00Z

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.

2010-01-01T00:00:00Z Pąk, Karol http://hdl.handle.net/11320/3564 2017-10-05T22:45:45Z 2010-01-01T00:00:00Z

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.

2010-01-01T00:00:00Z Liang, Xiquan Tang, Ling http://hdl.handle.net/11320/3560 2017-10-05T22:45:34Z 2010-01-01T00:00:00Z

Tytuł: Difference and Difference Quotient. Part III Autorzy: Liang, Xiquan; Tang, Ling Abstrakt: In this article, we give some important theorems of forward difference, backward difference, central difference and difference quotient and forward difference, backward difference, central difference and difference quotient formulas of some special functions.

2010-01-01T00:00:00Z Jastrzębska, Magdalena http://hdl.handle.net/11320/3562 2017-10-05T22:45:34Z 2010-01-01T00:00:00Z

Tytuł: Representation of the Fibonacci and Lucas Numbers in Terms of Floor and Ceiling Autorzy: Jastrzębska, Magdalena Abstrakt: In the paper we show how to express the Fibonacci numbers and Lucas numbers using the floor and ceiling operations.

2010-01-01T00:00:00Z