Displaying similar documents to “Local characterization of algebraic manifolds and characterization of components of the set S f ”

On infinite composition of affine mappings

László Máté (1999)

Fundamenta Mathematicae

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 Let F i = 1 , . . . , N be affine mappings of ℝ n . It is well known that if there exists j ≤ 1 such that for every σ 1 , . . . , σ j ∈ 1 , . . . , N the composition (1) F σ 1 ∘ . . . ∘ F σ j is a contraction, then for any infinite sequence σ 1 , σ 2 , . . . ∈ 1 , . . . , N and any z ∈ ℝ n , the sequence (2) F σ 1 ∘ . . . ∘ F σ n ( z ) is convergent and the limit is independent of z. We prove the following converse result: If (2) is convergent for any z ∈ ℝ n and any σ = σ 1 , σ 2 , . . . belonging to some subshift Σ of N symbols (and the limit is independent of z), then there exists j ≥ 1 such that for every σ = σ 1 , σ 2 , . . . ∈ Σ the composition (1) is a contraction....

Finitely generated almost universal varieties of 0 -lattices

Václav Koubek, Jiří Sichler (2005)

Commentationes Mathematicae Universitatis Carolinae

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A concrete category 𝕂 is (algebraically) if any category of algebras has a full embedding into 𝕂 , and 𝕂 is if there is a class 𝒞 of 𝕂 -objects such that all non-constant homomorphisms between them form a universal category. The main result of this paper fully characterizes the finitely generated varieties of 0 -lattices which are almost universal.

Baireness of C k ( X ) for ordered X

Michael Granado, Gary Gruenhage (2006)

Commentationes Mathematicae Universitatis Carolinae

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We show that if X is a subspace of a linearly ordered space, then C k ( X ) is a Baire space if and only if C k ( X ) is Choquet iff X has the Moving Off Property.

On Kelvin type transformation for Weinstein operator

Martina Šimůnková (2001)

Commentationes Mathematicae Universitatis Carolinae

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The note develops results from [5] where an invariance under the Möbius transform mapping the upper halfplane onto itself of the Weinstein operator W k : = Δ + k x n ∂ ∂ x n on ℝ n is proved. In this note there is shown that in the cases k ≠ 0 , k ≠ 2 no other transforms of this kind exist and for case k = 2 , all such transforms are described.

On the vanishing of Iwasawa invariants of absolutely abelian p-extensions

Gen Yamamoto (2000)

Acta Arithmetica

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1. Introduction. Let p be a prime number and ℤ p the ring of p-adic integers. Let k be a finite extension of the rational number field ℚ, k ∞ a ℤ p -extension of k, k n the nth layer of k ∞ / k , and A n the p-Sylow subgroup of the ideal class group of k n . Iwasawa proved the following well-known theorem about the order A n of A n : Theorem A (Iwasawa). Let k ∞ / k be a ℤ p -extension and A n the p-Sylow subgroup of the ideal class group of k n , where k n is the n th layer of k ∞ / k . Then there exist integers λ = λ ( k ∞ / k ) ≥ 0 , μ = μ ( k ∞ / k ) ≥ 0 , ν = ν ( k ∞ / k ) , and n₀ ≥ 0...

A problem of Galambos on Engel expansions

Jun Wu (2000)

Acta Arithmetica

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1. Introduction. Given x in (0,1], let x = [d₁(x),d₂(x),...] denote the Engel expansion of x, that is, (1) x = 1 / d ₁ ( x ) + 1 / ( d ₁ ( x ) d ₂ ( x ) ) + . . . + 1 / ( d ₁ ( x ) d ₂ ( x ) . . . d n ( x ) ) + . . . , where d j ( x ) , j ≥ 1 is a sequence of positive integers satisfying d₁(x) ≥ 2 and d j + 1 ( x ) ≥ d j ( x ) for j ≥ 1. (See [3].) In [3], János Galambos proved that for almost all x ∈ (0,1], (2) l i m n → ∞ d n 1 / n ( x ) = e . He conjectured ([3], P132) that the Hausdorff dimension of the set where (2) fails is one. In this paper, we prove this conjecture: Theorem. d i m H x ∈ ( 0 , 1 ] : ( 2 ) f a i l s = 1 . We use L¹ to denote the one-dimensional Lebesgue measure on (0,1] and d i m H to denote...