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of 177
pro vyhledávání: '"KOSTOV, VLADIMIR 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:
GATI, YOUSRA1 yousra.gati@gmail.com, KOSTOV, VLADIMIR PETROV2 vladimir.kostov@unice.fr, TARCHI, MOHAMED CHAOUKI1 mohamedchaouki.tarchi@gmail.com
Publikováno v:
Mathematical Communications. 2024, Vol. 29 Issue 2, p163-176. 14p.
