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 → ℝ k , where I is a real interval and k ∈ ℕ , a counterpart of the Lagrange mean-value theorem is presented. Necessary and sufficient conditions for the existence of a mean M : I 2 → I such that 𝐟 ( x ) - 𝐟 ( y ) = ( x - y ) 𝐟 ' ( M ( x , y ) ) , x , y ∈ 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 ⊆ G × 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 .