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On realizability of sign patterns by real polynomials

Vladimir Kostov (2018)

Czechoslovak Mathematical Journal

The classical Descartes’ rule of signs limits the number of positive roots of a real polynomial in one variable by the number of sign changes in the sequence of its coefficients. One can ask the question which pairs of nonnegative integers ( p , n ) , chosen in accordance with this rule and with some other natural conditions, can be the pairs of numbers of positive and negative roots of a real polynomial with prescribed signs of the coefficients. The paper solves this problem for degree 8 polynomials.

On Sakaguchi functions.

Yang, Ding-Gong, Liu, Jin-Lin (2003)

International Journal of Mathematics and Mathematical Sciences

On semi-typically real functions

Leopold Koczan, Katarzyna Trąbka-Więcław (2009)

Annales UMCS, Mathematica

Suppose that A is the family of all functions that are analytic in the unit disk Δ and normalized by the condition [...] For a given A ⊂ A let us consider the following classes (subclasses of A): [...] and [...] where [...] and S consists of all univalent members of A.In this paper we investigate the case A = τ, where τ denotes the class of all semi-typically real functions, i.e. [...] We study relations between these classes. Furthermore, we find for them sets of variability of initial coeffcients,...

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