σ-polynomials

σ-Automata and Chebyshev-Polynomials

A σ-automaton is an additive, binary cellular automaton on a graph. For product graphs such as a grids and cylinders, reversibility and periodicity properties of the corresponding σautomaton can be expressed in terms of a binary version of Chebyshev polynomials. We will give a detailed analysis of the divisibility properties of these polynomials and apply our results to the study of σ-automata.

Construction of σ-orthogonal Polynomials and Gaussian Quadrature Formulas

Let dα be a measure on R and let σ = (m1,m2, ..., mn), where mk ≥ 1, k = 1, 2, ..., n, are arbitrary real numbers. A polynomial ωn(x) := (x − x1)(x − x2)...(x − xn) with x1 ≤ x2 ≤ ... ≤ xn is said to be the n-th σ-orthogonal polynomial with respect to dα if the vector of zeros (x1, x2, ..., xn) is a solution of the extremal problem ∫

σ-Normality of Topological Spaces

*-σ-biderivations on *-rings

Bresar in 1993 proved that each biderivation on a noncommutative prime ring is a multiple of a commutatot. A result of it is a characterization of commuting additive mappings, because each commuting additive map give rise to a biderivation. Then in 1995, he investigated biderivations, generalized biderivations and sigma-biderivations on a prime ring and generalized the results of derivations fo...

σ-Derivations in Banach algebras