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Displaying 2201 – 2220 of 4562

Normal numbers and subsets of N with given densities

Haseo Ki, Tom Linton (1994)

Fundamenta Mathematicae

For X ⊆ [0,1], let $D_{X}$ denote the collection of subsets of ℕ whose densities lie in X. Given the exact location of X in the Borel or difference hierarchy, we exhibit the exact location of $D_{X}$ . For α ≥ 3, X is properly $D_{ξ} (Π_{α}^{0})$ iff $D_{X}$ is properly $D_{ξ} (Π_{1 + α}^{0})$ . We also show that for every nonempty set X ⊆[0,1], $D_{X}$ is $Π_{3}^{0}$ -hard. For each nonempty $Π_{2}^{0}$ set X ⊆ [0,1], in particular for X = x, $D_{X}$ is $Π_{3}^{0}$ -complete. For each n ≥ 2, the collection of real numbers that are normal or simply normal to base n is $Π_{3}^{0}$ -complete. Moreover, $D_{ℚ}$ , the...

Normal spaces and the Lusin-Menchoff property

Pavel Pyrih (1997)

Mathematica Bohemica

We study the relation between the Lusin-Menchoff property and the $F_{σ}$ -“semiseparation” property of a fine topology in normal spaces. Three examples of normal topological spaces having the $F_{σ}$ -“semiseparation” property without the Lusin-Menchoff property are given. A positive result is obtained in the countable compact space.

Normalization of almost conformal parabolic germs.

Balogh, Z., Volberg, A. (1995)

Annales Academiae Scientiarum Fennicae. Series A I. Mathematica

Note on a discretization of a linear fractional differential equation

Jan Čermák, Tomáš Kisela (2010)

Mathematica Bohemica

The paper discusses basics of calculus of backward fractional differences and sums. We state their definitions, basic properties and consider a special two-term linear fractional difference equation. We construct a family of functions to obtain its solution.

Note on a theorem by Reshetnyak-Gurov

Ingemar Wik (1987)

Studia Mathematica

Note on a Theorem of Kuratowski-Sierpiński

Jana Farková (1973)

Matematický časopis

Note on an inequality involving ${(n!)}^{1 / n}$ .

Alzer, H. (1995)

Acta Mathematica Universitatis Comenianae. New Series

Note on an inequality of F. Qi and L. Debnath.

Jiang, Wei-Dong (2009)

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