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Statistical cluster points of sequences in finite dimensional spaces

Serpil Pehlivan, A. Güncan, M. A. Mamedov (2004)

Czechoslovak Mathematical Journal

In this paper we study the set of statistical cluster points of sequences in m -dimensional spaces. We show that some properties of the set of statistical cluster points of the real number sequences remain in force for the sequences in m -dimensional spaces too. We also define a notion of Γ -statistical convergence. A sequence x is Γ -statistically convergent to a set C if C is a minimal closed set such that for every ϵ > 0 the set { k ρ ( C , x k ) ϵ } has density zero. It is shown that every statistically bounded sequence...

Statistical convergence of subsequences of a given sequence

Martin Máčaj, Tibor Šalát (2001)

Mathematica Bohemica

This paper is closely related to the paper of Harry I. Miller: Measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc. 347 (1995), 1811–1819 and contains a general investigation of statistical convergence of subsequences of an arbitrary sequence from the point of view of Lebesgue measure, Hausdorff dimensions and Baire’s categories.

Steinitz classes of some abelian and nonabelian extensions of even degree

Alessandro Cobbe (2010)

Journal de Théorie des Nombres de Bordeaux

The Steinitz class of a number field extension K / k is an ideal class in the ring of integers 𝒪 k of k , which, together with the degree [ K : k ] of the extension determines the 𝒪 k -module structure of 𝒪 K . We denote by R t ( k , G ) the set of classes which are Steinitz classes of a tamely ramified G -extension of k . We will say that those classes are realizable for the group G ; it is conjectured that the set of realizable classes is always a group.In this paper we will develop some of the ideas contained in [7] to obtain some...

Stern Polynomials as Numerators of Continued Fractions

A. Schinzel (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

It is proved that the nth Stern polynomial Bₙ(t) in the sense of Klavžar, Milutinović and Petr [Adv. Appl. Math. 39 (2007)] is the numerator of a continued fraction of n terms. This generalizes a result of Graham, Knuth and Patashnik concerning the Stern sequence Bₙ(1). As an application, the degree of Bₙ(t) is expressed in terms of the binary expansion of n.

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