Some sufficient conditions for zero asymptotic density and the expression of natural numbers as sum of values of special functions

Pavel Jahoda; Monika Pěluchová

Displaying similar documents to “Some sufficient conditions for zero asymptotic density and the expression of natural numbers as sum of values of special functions”

Mean-value theorem for vector-valued functions

Janusz Matkowski (2012)

Mathematica Bohemica

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For a differentiable function $𝐟 : I \to ℝ^{k},$ where $I$ is a real interval and $k \in ℕ$ , a counterpart of the Lagrange mean-value theorem is presented. Necessary and sufficient conditions for the existence of a mean $M : I^{2} \to I$ such that $𝐟 (x) - 𝐟 (y) = (x - y) 𝐟^{'} (M (x, y)), x, y \in I,$ are given. Similar considerations for a theorem accompanying the Lagrange mean-value theorem are presented.

Another proof of a result of Jech and Shelah

Péter Komjáth (2013)

Czechoslovak Mathematical Journal

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Shelah’s pcf theory describes a certain structure which must exist if $ℵ_{ω}$ is strong limit and $2^{ℵ_{ω}} > ℵ_{ω_{1}}$ holds. Jech and Shelah proved the surprising result that this structure exists in ZFC. They first give a forcing extension in which the structure exists then argue that by some absoluteness results it must exist anyway. We reformulate the statement to the existence of a certain partially ordered set, and then we show by a straightforward, elementary (i.e., non-metamathematical) argument that...

Incidence structures of type $(p, n)$

František Machala (2003)

Czechoslovak Mathematical Journal

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Every incidence structure $𝒥$ (understood as a triple of sets $(G, M, I)$ , $I \subseteq G \times M$ ) admits for every positive integer $p$ an incidence structure $𝒥^{p} = (G^{p}, M^{p}, I^{p})$ where $G^{p}$ ( $M^{p}$ ) consists of all independent $p$ -element subsets in $G$ ( $M$ ) and $I^{p}$ is determined by some bijections. In the paper such incidence structures $𝒥$ are investigated the $𝒥^{p}$ ’s of which have their incidence graphs of the simple join form. Some concrete illustrations are included with small sets $G$ and $M$ .

Displaying similar documents to “Some sufficient conditions for zero asymptotic density and the expression of natural numbers as sum of values of special functions”

Mean-value theorem for vector-valued functions

Another proof of a result of Jech and Shelah

Incidence structures of type ( p , n )

Incidence structures of type $(p, n)$