Displaying similar documents to “Asymptotic aspects of the Diophantine equation p k x n k - z k = l ”

Property C'', strong measure zero sets and subsets of the plane

Janusz Pawlikowski (1997)

Fundamenta Mathematicae

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Let X be a set of reals. We show that  • X has property C" of Rothberger iff for all closed F ⊆ ℝ × ℝ with vertical sections F x (x ∈ X) null, ∪ x ∈ X F x is null;  • X has strong measure zero iff for all closed F ⊆ ℝ × ℝ with all vertical sections F x (x ∈ ℝ) null, ∪ x ∈ X F x is null.

On inhomogeneous Diophantine approximation and the Nishioka-Shiokawa-Tamura algorithm

Takao Komatsu (1998)

Acta Arithmetica

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We obtain the values concerning ( θ , ϕ ) = l i m i n f | q | → ∞ | q | ‖ q θ - ϕ ‖ using the algorithm by Nishioka, Shiokawa and Tamura. In application, we give the values (θ,1/2), (θ,1/a), (θ,1/√(ab(ab+4))) and so on when θ = (√(ab(ab+4)) - ab)/(2a) = [0;a,b,a,b,...].

Inverse limit of M -cocycles and applications

Jan Kwiatkowski (1998)

Fundamenta Mathematicae

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For any m, 2 ≤ m < ∞, we construct an ergodic dynamical system having spectral multiplicity m and infinite rank. Given r > 1, 0 < b < 1 such that rb > 1 we construct a dynamical system (X, B, μ, T) with simple spectrum such that r(T) = r, F*(T) = b, and C ( T ) / w c l T n : n ∈ ℤ = ∞

A deceptive fact about functions

Wiesław Dziobiak, Andrzej Ehrenfeucht, Jacqueline Grace, Donald Silberger (2000)

Fundamenta Mathematicae

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The paper provides a proof of a combinatorial result which pertains to the characterization of the set of equations which are solvable in the composition monoid of all partial functions on an infinite set.