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Ideal version of Ramsey's theorem

Rafał Filipów, Nikodem Mrożek, Ireneusz Recław, Piotr Szuca (2011)

Czechoslovak Mathematical Journal

We consider various forms of Ramsey's theorem, the monotone subsequence theorem and the Bolzano-Weierstrass theorem which are connected with ideals of subsets of natural numbers. We characterize ideals with properties considered. We show that, in a sense, Ramsey's theorem, the monotone subsequence theorem and the Bolzano-Weierstrass theorem characterize the same class of ideals. We use our results to show some versions of density Ramsey's theorem (these are similar to generalizations shown in [P....

Identifiability, stability and reconstruction results of point sources by boundary measurements in heteregeneous trees.

Serge Nicaise, Ouahiba Zaïr (2003)

Revista Matemática Complutense

We consider the inverse problem of determining point wave sources in heteregeneous trees, extensions of one-dimensional stratified sets. We show that the Neumann boundary observation on a part of the lateral boundary determines uniquely the point sources if the time of observation is large enough. We further establish a conditional stability and give a reconstructing scheme.

Identities arising from higher-order Daehee polynomial bases

Dae San Kim, Taekyun Kim (2015)

Open Mathematics

Here we will derive formulas for expressing any polynomial as linear combinations of two kinds of higherorder Daehee polynomial basis. Then we will apply these formulas to certain polynomials in order to get new and interesting identities involving higher-order Daehee polynomials of the first kind and of the second kind.

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