Level crossings of a random polynomial with hyperbolic elements.

Farahmand, K.

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Displaying similar documents to “Level crossings of a random polynomial with hyperbolic elements.”

On real zeros of random polynomials with hyperbolic elements.

Farahmand, K., Jahangiri, M. (1998)

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Even and Old Overdetermined Strata for Degree 6 Hyperbolic Polynomials

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2000 Mathematics Subject Classification: 12D10. In the present paper we consider degree 6 hyperbolic polynomials (HPs) in one variable (i.e. real and with all roots real). We are interested in such HPs whose number of equalities between roots of the polynomial and/or its derivatives is higher than expected. We give the complete study of the four families of such degree 6 even HPs and also of HPs which are primitives of degree 5 HPs. Research partially supported...

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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).