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math.CA2019
Grassmann convexity and multiplicative Sturm theory, revisited
Nicolau Saldanha, Boris Shapiro, Michael Shapiro
In this paper we settle a special case of the Grassmann convexity conjecture formulated earlier by B.and M.Shapiro. We present a conjectural formula for the maximal total number of…
math.CA2019★ 1 cited
New aspects of Descartes' rule of signs
Vladimir Petrov Kostov, Boris Zalmanovich Shapiro
Below we summarize some new developments in the area of distribution of roots and signs of real univariate polynomials pioneered by R.~Descartes in the middle of the 17-th century.