Generalization of a Conjecture in the Geometry of Polynomials

In this paper we survey work on and around the following conjecture, which was first stated about 45 years ago: If all the zeros of an algebraic polynomial p (of degree n ≥ 2) lie in a disk with radius r, then, for each zero z1 of p, the disk with center z1 and radius r contains at least one zero of the derivative p′ . Until now, this conjecture has been proved for n ≤ 8 only. We also put the conjecture in a more general framework involving higher order derivatives and sets defined by the zeros of the polynomials

Adaptive Multiresolution Analysis on the Dyadic Topological Group

AbstractA type of multiresolution analysis on the space of continuous functions defined on the dyadic topological group is proposed, depending on free parameters. The appropriate choice of parameters is used to adapt this analysis to a given function

О некоторых свойствах регулярно-монотонных функций

[Sendov Bl.; Sendov Blagovest; Sendow Bl.; Сендов Благовест]Bulgarian. Russian, German summar

Об одном классе регулярно монотонных функций

[Sendov Bl.; Sendov Blagovest; Sendow Bl.; Сендов Благовест]Bulgarian. Russian, French summar

Ljubomir Iliev – Leader of The Bulgarian Mathematical Community (in the Occasion of His Centenary)

[Sendov Bl.; Sendov Blagovest; Sendow Bl.; Сендов Благовест