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On Root Arrangements of Polynomial-Like Functions and their Derivatives

Kostov, Vladimir (2005)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 12D10.We show that for n = 4 they are realizable either by hyperbolic polynomials of degree 4 or by non-hyperbolic polynomials of degree 6 whose fourth derivatives never vanish (these are a particular case of the so-called hyperbolic polynomial-like functions of degree 4).

On stable polynomials

Miloslav Nekvinda (1989)

Aplikace matematiky

The article is a survey on problem of the theorem of Hurwitz. The starting point of explanations is Schur's decomposition theorem for polynomials. It is showed how to obtain the well-known criteria on the distribution of roots of polynomials. The theorem on uniqueness of constants in Schur's decomposition seems to be new.

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