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Über eine elementare Fläche

Josef Matušů, Josef Novák (1979)

Aplikace matematiky

In vorliegender Arbeit wird die Konstruktion eines Flächenpflasters behandelt. Die Hauptgeneratrizen dieses Pflasters sind Kurvensegmente, deren Konstruktion in der Arbeit [J. Matušů, J. Novák: Über ein Interpolationsproblem. Apl. mat. 2(1976)] entwickelt wurde.

Weakly Increasing Zero-Diminishing Sequences

Bakan, Andrew, Craven, Thomas, Csordas, George, Golub, Anatoly (1996)

Serdica Mathematical Journal

The following problem, suggested by Laguerre’s Theorem (1884), remains open: Characterize all real sequences {μk} k=0...∞ which have the zero-diminishing property; that is, if k=0...n, p(x) = ∑(ak x^k) is any P real polynomial, then k=0...n, p(x) = ∑(μk ak x^k) has no more real zeros than p(x). In this paper this problem is solved under the additional assumption of a weak growth condition on the sequence {μk} k=0...∞, namely lim n→∞ | μn |^(1/n) < ∞. More precisely, it is established that...

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