Displaying similar documents to “On the rotation sets for non-continuous circle maps.”

The semi-index product formula

Jerzy Jezierski (1992)

Fundamenta Mathematicae

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We consider fibre bundle maps (...) where all spaces involved are smooth closed manifolds (with no orientability assumption). We find a necessary and sufficient condition for the formula    |ind|(f,g:A) = |ind| (f̅,g̅: p(A)) |ind| ( f b , g b : p - 1 ( b ) ∩ A ) to hold, where A stands for a Nielsen class of (f,g), b ∈ p(A) and |ind| denotes the coincidence semi-index from [DJ]. This formula enables us to derive a relation between the Nielsen numbers N(f,g), N(f̅,g̅) and N ( f b , g b ) .

On the Quotient Function Employed in the Blind Source Separation Problem

Fujita, K. (2010)

Fractional Calculus and Applied Analysis

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MSC 2010: 42C40, 94A12 On the blind source separation problem, there is a method to use the quotient function of complex valued time-frequency informations of two ob-served signals. By studying the quotient function, we can estimate the number of sources under some assumptions. In our previous papers, we gave a mathematical formulation which is available for the sources with-out time delay. However, in general, we can not ignore the time delay. In this paper, we will reformulate...

Commuting functions and simultaneous Abel equations

W. Jarczyk, K. Łoskot, M. C. Zdun (1994)

Annales Polonici Mathematici

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The system of Abel equations α(ft(x)) = α(x) + λ(t), t ∈ T, is studied under the general assumption that f t are pairwise commuting homeomorphisms of a real interval and have no fixed points (T is an arbitrary non-empty set). A result concerning embeddability of rational iteration groups in continuous groups is proved as a simple consequence of the obtained theorems.

On the uniqueness of continuous solutions of functional equations

Bolesław Gaweł (1995)

Annales Polonici Mathematici

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We consider the problem of the vanishing of non-negative continuous solutions ψ of the functional inequalities (1)   ψ(f(x)) ≤ β(x,ψ(x)) and (2)   α(x,ψ(x)) ≤ ψ(f(x)) ≤ β(x,ψ(x)), where x varies in a fixed real interval I. As a consequence we obtain some results on the uniqueness of continuous solutions φ :I → Y of the equation (3)  φ(f(x)) = g(x,φ(x)), where Y denotes an arbitrary metric space. ...