Complex Analogues of the Rolle's Theorem

2000 Mathematics Subject Classification: 30C10.Classical Rolle’s theorem and its analogues for complex algebraic polynomials are discussed. A complex Rolle’s theorem is conjectured

Extention of Apolarity and Grace Theorem

MSC 2010: 30C10The classical notion of apolarity is defined for two algebraic polynomials of equal degree. The main property of two apolar polynomials p and q is the classical Grace theorem: Every circular domain containing all zeros of p contains at least one zero of q and vice versa. In this paper, the definition of apolarity is extended to polynomials of different degree and an extension of the Grace theorem is proved. This leads to simplification of the conditions of several well-known results about apolarity

Rolle's Theorem for Complex Polynomials with Real Coefficients

Let p(z) be an algebraic polynomial of degree n ¸ 2 with real coefficients and p(i) = p(¡i). According to Grace-Heawood Theorem, at least one zero of the derivative p0(z) is on the disk with center in the origin and radius cot(¼=n). In this paper is found the smallest domain containing at leas one zero of the derivative p0(z)

Farewell Speech: Stefan Dodunekov (1945-2012)

Dear mournful family and all present, We are here to bow and to send to his eternal rest the President of the Bulgarian Academy of Sciences—Academician Stefan Manev Dodunekov. We have come to share together the enormous loss every one of us has suffered. The family lost their loving and caring father and husband, the mathematical community lost one of  its brightest and most active members, the Bulgarian  Academy of Sciences lost one of  its hopes for a better and more successful development, Bulgaria lost one quiet, but uncompromising patriot ..