Zobrazeno 1 - 10
of 214
pro vyhledávání: '"Vladimír Petrov"'
Autor:
Kostov, Vladimir Petrov
We consider polynomials $Q:=\sum _{j=0}^da_jx^j$, $a_j\in \mathbb{R}^*$, with all roots real. When the {\em sign pattern} $\sigma (Q):=({\rm sgn}(a_d),{\rm sgn}(a_{d-1})$, $\ldots$, ${\rm sgn}(a_0))$ has $\tilde{c}$ sign changes, the polynomial $Q$ h
Externí odkaz:
http://arxiv.org/abs/2405.18895
Autor:
Kostov, Vladimir Petrov
Publikováno v:
Modern Mathematical Methods 2(2) 2024, p. 103-116
We study real univariate polynomials with non-zero coefficients and with all roots real, out of which exactly two positive. The sequence of coefficients of such a polynomial begins with $m$ positive coefficients followed by $n$ negative followed by $
Externí odkaz:
http://arxiv.org/abs/2404.13943
Publikováno v:
Math. Commun. 29 (2024), 163-176
We consider real univariate degree $d$ real-rooted polynomials with non-vanishing coefficients. Descartes' rule of signs implies that such a polynomial has $\tilde{c}$ positive and $\tilde{p}$ negative roots counted with multiplicity, where $\tilde{c
Externí odkaz:
http://arxiv.org/abs/2310.14698
Autor:
Kostov, Vladimir Petrov
Publikováno v:
Serdica Math. J. 49 (2023) 251-268
We consider univariate real polynomials with all roots real and with two sign changes in the sequence of their coefficients which are all non-vanishing. One of the changes is between the linear and the constant term. By Descartes' rule of signs, such
Externí odkaz:
http://arxiv.org/abs/2304.02307
Autor:
Kostov, Vladimir Petrov
Publikováno v:
Constructive Mathematical Analysis, vol. 6 issue 2 (2023) 128-141
We consider real univariate polynomials with all roots real. Such a polynomial with $c$ sign changes and $p$ sign preservations in the sequence of its coefficients has $c$ positive and $p$ negative roots counted with multiplicity. Suppose that all mo
Externí odkaz:
http://arxiv.org/abs/2302.05127
Publikováno v:
Comptes Rendus, Math\'ematique Volume 362 (2024), p. 863-881
The {\em sign pattern} defined by the real polynomial $Q:=\Sigma _{j=0}^da_jx^j$, $a_j\neq 0$, is the string $\sigma (Q):=({\rm sgn(}a_d{\rm )},\ldots ,{\rm sgn(}a_0{\rm )})$. The quantities $pos$ and $neg$ of positive and negative roots of $Q$ satis
Externí odkaz:
http://arxiv.org/abs/2302.04540
Autor:
Kostov, Vladimir Petrov
Publikováno v:
Mat. Stud. 58 (2022), no. 2, 142-158
We prove that for $q\in (0,1)$, the partial theta function $\theta (q,x):=\sum _{j=0}^{\infty}q^{j(j+1)/2}x^j$ has no zeros in the closed domain $\{ \{ |x|\leq 3\} \cap \{${\rm Re}$x\leq 0\} \cap \{ |${\rm Im}$x|\leq 3/\sqrt{2}\} \} \subset \mathbb{C
Externí odkaz:
http://arxiv.org/abs/2210.16214
Autor:
Kostov, Vladimir Petrov
Publikováno v:
Annual of Sofia University "St. Kliment Ohridski'', Faculty of Mathematics and Informatics 111 (2024) 129-137
We prove that for $q\in (-1,0)\cup (0,1)$, the partial theta function $\theta (q,x):=\sum _{j=0}^{\infty}q^{j(j+1)/2}x^j$ has no zeros in the closed unit disk.
Externí odkaz:
http://arxiv.org/abs/2208.09400
Autor:
Kostov, Vladimir Petrov
Publikováno v:
Constructive Mathematical Analysis, vol. 5 issue 3 (2022) 119-133
We consider the set of monic real univariate polynomials of a given degree $d$ with non-vanishing coefficients, with given signs of the coefficients and with given quantities $pos$ of their positive and $neg$ of their negative roots (all roots are di
Externí odkaz:
http://arxiv.org/abs/2109.07182
Autor:
Kostov, Vladimir Petrov
Publikováno v:
Which Sign Patterns are Canonical?. Results Math 77 (2022) No 6, paper 235
We consider real polynomials in one variable without vanishing coefficients and with all roots real and of distinct moduli. We show that the signs of the coefficients define the order of the moduli of the roots on the real positive half-line exactly
Externí odkaz:
http://arxiv.org/abs/2103.04758