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Displaying similar documents to “On a Stratification Defined by Real Roots of Polynomials”

On Arrangements of Real Roots of a Real Polynomial and Its Derivatives

Kostov, Vladimir (2003)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 12D10. We prove that all arrangements (consistent with the Rolle theorem and some other natural restrictions) of the real roots of a real polynomial and of its s-th derivative are realized by real polynomials.

On the Hyperbolicity Domain of the Polynomial x^n + a1x^(n-1) + 1/4+ an

Kostov, Vladimir (1999)

Serdica Mathematical Journal

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∗ Partially supported by INTAS grant 97-1644 We consider the polynomial Pn = x^n + a1 x^(n−1) + · · · + an , ai ∈ R. We represent by figures the projections on Oa1 . . . ak , k ≤ 6, of its hyperbolicity domain Π = {a ∈ Rn | all roots of Pn are real}. The set Π and its projections Πk in the spaces Oa1 . . . ak , k ≤ n, have the structure of stratified manifolds, the strata being defined by the multiplicity vectors. It is known that for k > 2 every non-empty fibre of the...