Zobrazeno 1 - 10
of 86
pro vyhledávání: '"Prodanov, Emil M."'
Autor:
Prodanov, Emil M.
Publikováno v:
Journal of Computational Science (Elsevier) 73 (2023) 102123
The real roots of the cubic and quartic polynomials are studied geometrically with the help of their respective Siebeck--Marden--Northshield equilateral triangle and regular tetrahedron. The Vi\`ete trigonometric formulae for the roots of the cubic a
Externí odkaz:
http://arxiv.org/abs/2206.03855
Autor:
Prodanov, Emil M.
Publikováno v:
Physica B: Condensed Matter 640, 414077 (2022)
The parametric cubic van der Waals polynomial $p V^3 - (R T + b p) V^2 + a V - a b$ is analysed mathematically and some new generic features (theoretically, for any substance) are revealed - if the pressure is not allowed to take negative values [tem
Externí odkaz:
http://arxiv.org/abs/2201.04009
Autor:
Prodanov, Emil M.
Publikováno v:
Journal of Computational Mathematics and Data Science (Elsevier) 6 (2023)100076
Analysing the cubic sectors of a real polynomial of degree n, a modification of the Newton Rule is Signs is proposed with which stricter upper bound on the number of real roots can be found. A new necessary condition for reality of the roots of a pol
Externí odkaz:
http://arxiv.org/abs/2109.12577
Autor:
Prodanov, Emil M.
Publikováno v:
Advanced Theory and Simulations (Wiley) 2022, 2100638
The isolation intervals of the real roots of the real symbolic monic cubic polynomial $p(x) = x^3 + a x^2 + b x + c\,\,$ are found in terms of simple functions of the coefficients of the polynomial (such as: $-a$, $-a/3$, $-c/b$, $\pm \sqrt{-b}$, whe
Externí odkaz:
http://arxiv.org/abs/2108.02009
Autor:
Prodanov, Emil M.
Publikováno v:
Resultate der Mathematik (Birkhauser) 77, 126 (2022)
The isolation intervals of the real roots of the symbolic monic cubic polynomial $x^3 + a x^2 + b x + c$ are determined, in terms of the coefficients of the polynomial, by solving the Siebeck-Marden-Northshield triangle - the equilateral triangle tha
Externí odkaz:
http://arxiv.org/abs/2107.01847
Autor:
Prodanov, Emil M.
Publikováno v:
Advanced Theory and Simulations (Wiley) 2022, 2200011
A method is proposed with which the locations of the roots of the monic symbolic quintic polynomial $x^5 + a_4 x^4 + a_3 x^3 + a_2 x^2 + a_1 x + a_0$ can be determined using the roots of two resolvent quadratic polynomials: $q_1(x) = x^2 + a_4 x + a_
Externí odkaz:
http://arxiv.org/abs/2106.02977
Autor:
Prodanov, Emil M.
Publikováno v:
Comptes Rendus de l'Academie Bulgare des Sciences, 75(2), 178-186 (2022)
The presented analysis determines several new bounds on the roots of the equation $a_n x^n + a_{n-1} x^{n-1} + \cdots + a_0 = 0$ (with $a_n > 0$). All proposed new bounds are lower than the Cauchy bound max$\{1, \sum_{j=0}^{n-1} |a_j/a_n| \}$. Firstl
Externí odkaz:
http://arxiv.org/abs/2008.11039
Autor:
Prodanov, Emil M.
Publikováno v:
Int. J. Appl. Comput. Math 7, 218 (2021)
Presented is a two-tier analysis of the location of the real roots of the general quartic equation $x^4 + ax^3 + bx^2 + cx + d = 0$ with real coefficients and the classification of the roots in terms of $a$, $b$, $c$, and $d$, without using any numer
Externí odkaz:
http://arxiv.org/abs/2008.07529
Autor:
Ivanov, Rossen I., Prodanov, Emil M.
Publikováno v:
Physical Review D 99, 063501 (2019)
A cosmological model with van der Waals gas and dust has been studied in the context of a three-component autonomous non-linear dynamical system involving the time evolution of the particle number density, the Hubble parameter and the temperature. Du
Externí odkaz:
http://arxiv.org/abs/1911.04487