224 citations
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math.CA2004★ 24 cited
On rational approximation of algebraic functions
Julius Borcea, Rikard Bögvad, Boris Shapiro
We construct a new scheme of approximation of any multivalued algebraic function by a sequence of rational functions. The latter sequence is…
math.CA2003
Hyperbolic polynomials and spectral order
Julius Borcea, Boris Shapiro
The spectral order on $\bR$ induces a partial ordering on the manifold $\calH_{n}$ of monic hyperbolic polynomials of degree . We show that the semigroup $\tilde{\calS}$ generat…
math.CA2003
A few riddles behind Rolle's theorem
B. Shapiro, M. Shapiro
We call a smooth function of one variable a degree n pseudopolynomial if its n-th derivative has no (real) zeros. An n pseudopolynomial is called hyperbolic if it has exactly n sim…