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For a sequence x ∈ l 10, one can consider the achievement set E(x) of all subsums of series Σn=1∞ x(n). It is known that E(x) has one of the following structures: a finite union of closed intervals, a set homeomorphic to the Cantor set, a set homeomorphic to the set T of subsums of Σn=1∞ x(n) where c(2n − 1) = 3/4n and c(2n) = 2/4n (Cantorval). Based on ideas of Jones and Velleman [Jones R., Achievement sets of sequences, Amer. Math. Monthly, 2011, 118(6), 508–521] and Guthrie and Nymann [Guthrie...

Nearness relations in linear spaces

Martin Kalina (2004)

Kybernetika

In this paper, we consider nearness-based convergence in a linear space, where the coordinatewise given nearness relations are aggregated using weighted pseudo-arithmetic and geometric means and using continuous t-norms.

New results in discrete asymptotic analysis.

Vernescu, Andrei, Mortici, Cristinel (2008)

General Mathematics

Newer applications of generalized monotone sequences.

Leindler, Laszlo (2006)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Nonabsolutely convergent series

Dana Fraňková (1991)

Mathematica Bohemica

Assume that for any $t$ from an interval $[a, b]$ a real number $u (t)$ is given. Summarizing all these numbers $u (t)$ is no problem in case of an absolutely convergent series $\sum_{t \in [a, b]} u (t)$ . The paper gives a rule how to summarize a series of this type which is not absolutely convergent, using a theory of generalized Perron (or Kurzweil) integral.

Non-embeddability of general unipotent diffeomorphisms up to formal conjugacy

Javier Ribón (2009)

Annales de l’institut Fourier

The formal class of a germ of diffeomorphism $ϕ$ is embeddable in a flow if $ϕ$ is formally conjugated to the exponential of a germ of vector field. We prove that there are complex analytic unipotent germs of diffeomorphisms at $ℂ^{n}$ ( $n > 1$ ) whose formal class is non-embeddable. The examples are inside a family in which the non-embeddability is of geometrical type. The proof relies on the properties of some linear functional operators that we obtain through the study of polynomial families of diffeomorphisms...

Note on product summability of an infinite series.

Sulaiman, W.T. (2008)

International Journal of Mathematics and Mathematical Sciences

Note on the converses of inequalities of Hardy and Littlewood.

Németh, J. (2001)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]