Bogdan Batko

Coreduction Homology Algorithm

This paper presents a new reduction algorithm for the efficient computation of the homology of cubical sets and polotypes. The algorithm—particularly strong for low-dimensional sets embedded in high dimensions—runs in linear time. The paper presents the theoretical background of the algorithm, the algorithm itself, experimental results based on an implementation for cubical sets as well as some theoretical complexity estimates.

Stability of the generalized alternative cauchy equation

AbstractLet G be a commutative semigroup and letL be a complete Archimedean Riesz Space. Suppose thatF: G → L satisfies for somee ∈ L+ the inequality

Note on Superstability of Mikusiński’s Functional Equation

\left| {|F(x + y)| - |F(x) + F(y)|} \right| \leqslant e for x, y \in G.

Superstability of the Cauchy equation with squares in finite-dimensional normed algebras

Then there exists a unique additive mappingA : G → L such that

Weak Index Pairs and the Conley Index for Discrete Multivalued Dynamical Systems. Part II: Properties of the Index

\left| {F(x) - A(x)} \right| \leqslant e for x \in G.

A Remark on Some Simultaneous Functional Inequalities in Riesz Spaces

As the method of the proof we use the Johnson-Kist Representation Theorem.