O rovnicích kvadratických
On a Stratification Defined by Real Roots of Polynomials
2000 Mathematics Subject Classification: 12D10We prove smoothness of the strata and a transversality property of their tangent spaces.
On Arrangements of Real Roots of a Real Polynomial and Its Derivatives
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 cubic factors of certain trinominals.
On equations and properties concerning some classes of chordal polygons.
On generalized “ham sandwich” theorems
In this short note we utilize the Borsuk-Ulam Anitpodal Theorem to present a simple proof of the following generalization of the “Ham Sandwich Theorem”: Let be subsets with finite Lebesgue measure. Then, for any sequence of -linearly independent polynomials in the polynomial ring there are real numbers , not all zero, such that the real affine variety simultaneously bisects each of subsets , . Then some its applications are studied.
On intervals containing full sets of conjugates of algebraic integers
On multiple zeros of Bernoulli polynomials
On multivariate Descartes' rule – a counterexample.
On Polynomials and Exponential Polynomials in Several Complex Variables.
On Rolle's theorem for polynomials over the complex numbers.
On Root Arrangements of Polynomial-Like Functions and their Derivatives
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).
On Roots of Polynomials with Positive Coefficients
On stability of parametrized families of polynomials and matrices.
On stable polynomials
The article is a survey on problem of the theorem of Hurwitz. The starting point of explanations is Schur's decomposition theorem for polynomials. It is showed how to obtain the well-known criteria on the distribution of roots of polynomials. The theorem on uniqueness of constants in Schur's decomposition seems to be new.
On the arithmetic of two constructions of Salem numbers.
On the Diophantine equation f(y) - x = 0
On the distribution of the number of real zeros of a random polynomial.
On the equation
On the Fundamental Theorem of Algebra