On H. Weyl and H. Minkowski polynomials.
On polynomials of Sheffer type arising from a Cauchy problem.
On realizability of sign patterns by real polynomials
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 , 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 polynomials.
On some properties of Hamel bases connected with the continuity of polynomial functions.
On stability and the Łojasiewicz exponent at infinity of coercive polynomials
In this article we analyze the relationship between the growth and stability properties of coercive polynomials. For coercive polynomials we introduce the degree of stable coercivity which measures how stable the coercivity is with respect to small perturbations by other polynomials. We link the degree of stable coercivity to the Łojasiewicz exponent at infinity and we show an explicit relation between them.
On stability of Alexander polynomials of knots and links (survey)
We study distribution of the zeros of the Alexander polynomials of knots and links in S³. After a brief introduction of various stabilities of multivariate polynomials, we present recent results on stable Alexander polynomials.
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 convergence of Halley-like method.
On the derivative and maximum modulus of a polynomial.
On the distribution of the number of real zeros of a random polynomial.
On the distribution on the roots of polynomials
Using classical results on conjugate functions, we give very short proofs of theorems of Erdös–Turán and Blatt concerning the angular distribution of the roots of polynomials. Then we study some examples.
On the fourth order root finding methods of Euler's type.
On the guaranteed convergence of the Japanese zero-finding method.
On the Irreducibility of Polynomials Taking Small Values.
On the Mahler measure of Jones polynomials under twisting.
On the power-series expansion of a rational function
Introduction. The problem of determining the formula for , the number of partitions of an integer into elements of a finite set S, that is, the number of solutions in non-negative integers, , of the equation hs₁ s₁ + ... + hsk sk = n, was solved in the nineteenth century (see Sylvester [4] and Glaisher [3] for detailed accounts). The solution is the coefficient of[(1-xs₁)... (1-xsk)]-1, expressions for which they derived. Wright [5] indicated a simpler method by which to find part of the solution...
On the Sharpness of Theorems Concerning Zero-Free Regions for Certain Sequences of Polynomials.
On the shifted QR iteration applied to companion matrices.
On the Various Bisection Methods Derived from Vincent’s Theorem
In 2000 A. Alesina and M. Galuzzi presented Vincent’s theorem “from a modern point of view” along with two new bisection methods derived from it, B and C. Their profound understanding of Vincent’s theorem is responsible for simplicity — the characteristic property of these two methods. In this paper we compare the performance of these two new bisection methods — i.e. the time they take, as well as the number of intervals they examine in order to isolate the real roots of polynomials — against that...
On tolerance analysis