Nikola Obrechkoff. Selected Papers I

The outstanding Bulgarian mathematician NIKOLA OBRECHKOFF (1896 –1963) was born in Varna (Bulgaria) on March 6. He graduated from the Mathematical Department of Sofia University in 1920 and worked there all his life as assistant professor (1920 - 1922), associated professor (1922 - 1928), full professor and Chief of Chair of Higher Algebra (1928 - 1963). He got his first Doctoral Degree from the University of Palermo, Italy, on October 13, 1932, and the Degree docteur es sciences from the Sorbone, Paris, on July 20, 1933. N. OBRECHKOF has lectured at the Universities of Hamburg, Berlin, Geneva, Rome, Palermo, Leipzig, Dresden and others. He has patricipated in a great number of Scientific Conferences as well as in the World Congresses of Mathematicians in Oslo (1936) and Edinburgh (1958), and in the First Congres of Hungarian Mathematicians (1950). The fact, that he was invited from abroad to be a reviewer of scientific monographs and of works presented for receiving academic ranks or degrees, speaks for his indisputed international authority. The scientific heritage of N. OBRECHKOFF is enormous. He is an author of about 250 papers and of several textbooks and monographs. The variety and deepness of his work are impressive. It is and, we hope, it will be a matchless pattern not only for local use. Classical algebra, analysis, Diophantin approximations, probability and statistics, mechanical quadratures and numerical analysis, equations of mathematical physics, mechanics, integral geometry - these are the main regions in which OBRECHKOFF has got numerious complete results. Some of them are unsurpassed even till now. The location of the zeros of algebraic polynomials was a particularly beloved subject for OBRECHKOFF”S scientific studies. After his first remarkable achievement, an extension of the classical Descartes Rule of Signs, he gave a great number of contributions to this region. They are included in his monograph Zeros of polynomials at first published in Bulgarian in 1963, and in English in 2003 by Marin Drinov Academic Publishing House as No 7 of the series Bulgarian Academic Monographs.