Displaying similar documents to “Length of continued fractions in principal quadratic fields”

Shift spaces and attractors in noninvertible horseshoes

H. Bothe (1997)

Fundamenta Mathematicae

Similarity:

As is well known, a horseshoe map, i.e. a special injective reimbedding of the unit square I 2 in 2 (or more generally, of the cube I m in m ) as considered first by S. Smale [5], defines a shift dynamics on the maximal invariant subset of I 2 (or I m ). It is shown that this remains true almost surely for noninjective maps provided the contraction rate of the mapping in the stable direction is sufficiently strong, and bounds for this rate are given.

A combinatorial approach to partitions with parts in the gaps

Dennis Eichhorn (1998)

Acta Arithmetica

Similarity:

Many links exist between ordinary partitions and partitions with parts in the “gaps”. In this paper, we explore combinatorial explanations for some of these links, along with some natural generalizations. In particular, if we let p k , m ( j , n ) be the number of partitions of n into j parts where each part is ≡ k (mod m), 1 ≤ k ≤ m, and we let p * k , m ( j , n ) be the number of partitions of n into j parts where each part is ≡ k (mod m) with parts of size k in the gaps, then p * k , m ( j , n ) = p k , m ( j , n ) .

Index for subgroups of the group of units in number fields

Tsutomu Shimada (1998)

Acta Arithmetica

Similarity:

We define a sequence of rational integers u i ( E ) for each finite index subgroup E of the group of units in some finite Galois number fields K in which prime p ramifies. For two subgroups E’ ⊂ E of finite index in the group of units of K we prove the formula v p ( [ E : E ' ] ) = i = 1 r u i ( E ' ) - u i ( E ) . This is a generalization of results of P. Dénes [3], [4] and F. Kurihara [5].

Universal spaces in the theory of transfinite dimension, II

Wojciech Olszewski (1994)

Fundamenta Mathematicae

Similarity:

We construct a family of spaces with “nice” structure which is universal in the class of all compact metrizable spaces of large transfinite dimension ω 0 , or, equivalently, of small transfinite dimension ω 0 ; that is, the family consists of compact metrizable spaces whose transfinite dimension is ω 0 , and every compact metrizable space with transfinite dimension ω 0 is embeddable in a space of the family. We show that the least possible cardinality of such a universal family is equal to the...

The space of ANR’s in n

Tadeusz Dobrowolski, Leonard Rubin (1994)

Fundamenta Mathematicae

Similarity:

The hyperspaces A N R ( n ) and A R ( n ) in 2 n ( n 3 ) consisting respectively of all compact absolute neighborhood retracts and all compact absolute retracts are studied. It is shown that both have the Borel type of absolute G δ σ δ -spaces and that, indeed, they are not F σ δ σ -spaces. The main result is that A N R ( n ) is an absorber for the class of all absolute G δ σ δ -spaces and is therefore homeomorphic to the standard model space Ω 3 of this class.

The Zahorski theorem is valid in Gevrey classes

Jean Schmets, Manuel Valdivia (1996)

Fundamenta Mathematicae

Similarity:

Let Ω,F,G be a partition of n such that Ω is open, F is F σ and of the first category, and G is G δ . We prove that, for every γ ∈ ]1,∞[, there is an element of the Gevrey class Γγ which is analytic on Ω, has F as its set of defect points and has G as its set of divergence points.

The relative coincidence Nielsen number

Jerzy Jezierski (1996)

Fundamenta Mathematicae

Similarity:

We define a relative coincidence Nielsen number N r e l ( f , g ) for pairs of maps between manifolds, prove a Wecken type theorem for this invariant and give some formulae expressing N r e l ( f , g ) by the ordinary Nielsen numbers.

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

Janusz Pawlikowski (1997)

Fundamenta Mathematicae

Similarity:

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.

Dugundji extenders and retracts on generalized ordered spaces

Gary Gruenhage, Yasunao Hattori, Haruto Ohta (1998)

Fundamenta Mathematicae

Similarity:

For a subspace A of a space X, a linear extender φ:C(A) → C(X) is called an L c h -extender (resp. L c c h -extender) if φ(f)[X] is included in the convex hull (resp. closed convex hull) of f[A] for each f ∈ C(A). Consider the following conditions (i)-(vii) for a closed subset A of a GO-space X: (i) A is a retract of X; (ii) A is a retract of the union of A and all clopen convex components of X; (iii) there is a continuous L c h -extender φ:C(A × Y) → C(X × Y), with respect to both the compact-open topology...

On the category of modules of second kind for Galois coverings

Piotr Dowbor (1996)

Fundamenta Mathematicae

Similarity:

Let F: R → R/G be a Galois covering and m o d 1 ( R / G ) (resp. m o d 2 ( R / G ) ) be a full subcategory of the module category mod (R/G), consisting of all R/G-modules of first (resp. second) kind with respect to F. The structure of the categories ( m o d ( R / G ) ) / [ m o d 1 ( R / G ) ] and m o d 2 ( R / G ) is given in terms of representation categories of stabilizers of weakly-G-periodic modules for some class of coverings.

The Iwasawa λ-invariants of ℤₚ-extensions of real quadratic fields

Takashi Fukuda, Hisao Taya (1995)

Acta Arithmetica

Similarity:

1. Introduction. Let k be a totally real number field. Let p be a fixed prime number and ℤₚ the ring of all p-adic integers. We denote by λ=λₚ(k), μ=μₚ(k) and ν=νₚ(k) the Iwasawa invariants of the cyclotomic ℤₚ-extension k of k for p (cf. [10]). Then Greenberg’s conjecture states that both λₚ(k) and μₚ(k) always vanish (cf. [8]). In other words, the order of the p-primary part of the ideal class group of kₙ remains bounded as n tends to infinity, where kₙ is the nth layer of k / k . We know...

Homotopy orbits of free loop spaces

Marcel Bökstedt, Iver Ottosen (1999)

Fundamenta Mathematicae

Similarity:

Let X be a space with free loop space ΛX and mod two cohomology R = H*X. We construct functors Ω λ ( R ) and ℓ(R) together with algebra homomorphisms e : Ω λ ( R ) H * ( Λ X ) and ψ : ( R ) H * ( E S 1 × S 1 Λ X ) . When X is 1-connected and R is a symmetric algebra we show that these are isomorphisms.

A theory of non-absolutely convergent integrals in Rn with singularities on a regular boundary

W. Jurkat, D. Nonnenmacher (1994)

Fundamenta Mathematicae

Similarity:

Specializing a recently developed axiomatic theory of non-absolutely convergent integrals in n , we are led to an integration process over quite general sets A q n with a regular boundary. The integral enjoys all the usual properties and yields the divergence theorem for vector-valued functions with singularities in a most general form.

Operators on C(ω^α) which do not preserve C(ω^α)

Dale Alspach (1997)

Fundamenta Mathematicae

Similarity:

It is shown that if α,ζ are ordinals such that 1 ≤ ζ < α < ζω, then there is an operator from C ( ω ω α ) onto itself such that if Y is a subspace of C ( ω ω α ) which is isomorphic to C ( ω ω α ) , then the operator is not an isomorphism on Y. This contrasts with a result of J. Bourgain that implies that there are uncountably many ordinals α for which for any operator from C ( ω ω α ) onto itself there is a subspace of C ( ω ω α ) which is isomorphic to C ( ω ω α ) on which the operator is an isomorphism.