Proceedings of the American Mathematical Society, ISSN 0002-9939, 04/2014, Volume 142, Issue 4, pp. 1337 - 1349

Sendov's conjecture says that if all zeros of a complex polynomial P denotes one of them, then the closed disk of center a contains a critical point of P...

Complex numbers | Integers | Geometry | Line segments | Zero | Mathematical theorems | Real numbers | Critical points | Polynomials | Degrees of polynomials | Polynomial | Sendov conjecture | Geometry of polynomial | Zeroes | Inequalities | MATHEMATICS | MATHEMATICS, APPLIED | zeroes | inequalities | polynomial | geometry of polynomial

Complex numbers | Integers | Geometry | Line segments | Zero | Mathematical theorems | Real numbers | Critical points | Polynomials | Degrees of polynomials | Polynomial | Sendov conjecture | Geometry of polynomial | Zeroes | Inequalities | MATHEMATICS | MATHEMATICS, APPLIED | zeroes | inequalities | polynomial | geometry of polynomial

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2010, Volume 365, Issue 1, pp. 93 - 102

...]). We look at Blaschke products' role in the Sendov conjecture.

Sendov's conjecture | Blaschke product | Numerical range | Poncelet curve | Unitary dilation | MATHEMATICS | MATHEMATICS, APPLIED | NORMAL COMPRESSION | POLYGONS | CURVES

Sendov's conjecture | Blaschke product | Numerical range | Poncelet curve | Unitary dilation | MATHEMATICS | MATHEMATICS, APPLIED | NORMAL COMPRESSION | POLYGONS | CURVES

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2008, Volume 348, Issue 1, pp. 461 - 468

.... In this notation, Sendov's conjecture asserts that d ( P ) is at most 1 for every P in S ( n ) . Define P in S ( n ) to be locally extremal if d...

Polynomial | Derivative | Extremal | Sendov | Critical points | MATHEMATICS | MATHEMATICS, APPLIED | polynomial | derivative | critical points | extremal

Polynomial | Derivative | Extremal | Sendov | Critical points | MATHEMATICS | MATHEMATICS, APPLIED | polynomial | derivative | critical points | extremal

Journal Article

Hiroshima Mathematical Journal, ISSN 0018-2079, 07/2011, Volume 41, Issue 2, pp. 235 - 273

On Sendov's conjecture, V. Vajaitu and A. Zaharescu (and M. J. Miller, independently...

Polynomial | Sendov's conjecture | Zero | Critical point | zero | POLYNOMIALS | MATHEMATICS | critical point | ILYEFF | polynomial | 12D10 | 26C10, 30C15

Polynomial | Sendov's conjecture | Zero | Critical point | zero | POLYNOMIALS | MATHEMATICS | critical point | ILYEFF | polynomial | 12D10 | 26C10, 30C15

Journal Article

Proceedings of the Japan Academy Series A: Mathematical Sciences, ISSN 0386-2194, 12/2010, Volume 86, Issue 10, pp. 165 - 168

On Sendov's conjecture, M. J. Miller states the following in his paper [10,11]; if a zero beta of a polynomial which has all the zeros in the closed unit disk...

Polynomial | Sendov's conjecture | Zero | Critical point | zero | MATHEMATICS | critical point | ILYEFF | polynomial | SENDOV CONJECTURE | CIRCLE | 26C10 | 12D10 | Sendov’s conjecture | 30C15

Polynomial | Sendov's conjecture | Zero | Critical point | zero | MATHEMATICS | critical point | ILYEFF | polynomial | SENDOV CONJECTURE | CIRCLE | 26C10 | 12D10 | Sendov’s conjecture | 30C15

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 01/2010, Volume 432, Issue 1, pp. 107 - 115

...–Aronszajn Formula which will then be used to prove some inequalities similar to Sendov conjecture and Schoenberg conjecture and to study the distribution of equilibrium points of logarithmic...

Zeros | [formula omitted]-companion matrices | Schoenberg conjecture | Polynomials | Weinstein–Aronszajn Formula | Sendov conjecture | D-companion matrices | Weinstein-Aronszajn Formula | MATHEMATICS, APPLIED | GAUSS-LUCAS THEOREM | NORMAL MATRICES | Weinstein-Aronszajn formula

Zeros | [formula omitted]-companion matrices | Schoenberg conjecture | Polynomials | Weinstein–Aronszajn Formula | Sendov conjecture | D-companion matrices | Weinstein-Aronszajn Formula | MATHEMATICS, APPLIED | GAUSS-LUCAS THEOREM | NORMAL MATRICES | Weinstein-Aronszajn formula

Journal Article

Constructive Approximation, ISSN 0176-4276, 1/2008, Volume 27, Issue 1, pp. 75 - 98

...: the Sendov Conjecture. We use this fact to obtain estimates on the location of the zeros of the Blaschke product.

Numerical Analysis | Analysis | Mathematics | Blaschke product | Sendov's conjecture | Lagrange interpolation | Newton interpolation method | MATHEMATICS | LAGRANGE

Numerical Analysis | Analysis | Mathematics | Blaschke product | Sendov's conjecture | Lagrange interpolation | Newton interpolation method | MATHEMATICS | LAGRANGE

Journal Article

Advanced Studies in Contemporary Mathematics (Kyungshang), ISSN 1229-3067, 01/2010, Volume 20, Issue 1, pp. 81 - 88

Journal Article

COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES, ISSN 1310-1331, 2010, Volume 63, Issue 5, pp. 659 - 664

...). In this paper a stronger conjecture is announced and proved for polynomials of degree n = 3. A similar, stronger than the Smale's mean value conjecture, is formulated.

zeros and critical points of polynomials | Smale's mean value conjecture | MULTIDISCIPLINARY SCIENCES | SENDOV CONJECTURE | ILIEFF | ZEROS

zeros and critical points of polynomials | Smale's mean value conjecture | MULTIDISCIPLINARY SCIENCES | SENDOV CONJECTURE | ILIEFF | ZEROS

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 9/1990, Volume 321, Issue 1, pp. 285 - 303

.... We conjecture that any such polynomial has all the roots of its derivative on a circle centered at the fixed point, and as many of its own roots as possible on the unit circle...

Lying | Roots of functions | Rational functions | Polynomials | Counterexamples | Mathematical functions | Matrices | Complex roots | Degrees of polynomials | Geometry of polynomials | Roots of polynomials | Ilietr | Sendov | Maximal polynomials | MATHEMATICS

Lying | Roots of functions | Rational functions | Polynomials | Counterexamples | Mathematical functions | Matrices | Complex roots | Degrees of polynomials | Geometry of polynomials | Roots of polynomials | Ilietr | Sendov | Maximal polynomials | MATHEMATICS

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 5/1992, Volume 115, Issue 1, pp. 79 - 83

A maximal polynomial is a complex polynomial that has all of its roots in the unit disk, one fixed root, and all of its critical points as far as possible from...

Circles | Linear systems | Polynomials | Coefficients | Critical points | Degrees of polynomials | Sendov | Ilieff | Maximal polynomial | Continuous independence | MATHEMATICS | MATHEMATICS, APPLIED | MAXIMAL POLYNOMIAL | SENDOV | ILIEFF | CONTINUOUS INDEPENDENCE

Circles | Linear systems | Polynomials | Coefficients | Critical points | Degrees of polynomials | Sendov | Ilieff | Maximal polynomial | Continuous independence | MATHEMATICS | MATHEMATICS, APPLIED | MAXIMAL POLYNOMIAL | SENDOV | ILIEFF | CONTINUOUS INDEPENDENCE

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 03/2005, Volume 357, Issue 3, pp. 851 - 873

...) \}. In this notation, a conjecture of Bl. Sendov claims that r_n(\beta)\le1. In this paper we investigate Sendov's conjecture near the unit circle, by computing constants C_1...

Circles | Integers | Mathematical theorems | Quadratic approximation | Linear transformations | Mathematical constants | Polynomials | Coefficients | Degrees of polynomials | Sendov | Ilyeff | Ilieff | MATHEMATICS | MAXIMAL POLYNOMIALS | CONJECTURE

Circles | Integers | Mathematical theorems | Quadratic approximation | Linear transformations | Mathematical constants | Polynomials | Coefficients | Degrees of polynomials | Sendov | Ilyeff | Ilieff | MATHEMATICS | MAXIMAL POLYNOMIALS | CONJECTURE

Journal Article

Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 02/1998, Volume 57, Issue 1, pp. 173 - 174

... of p, the disc contains at least one zero of p′; see [3, Problem 4.1]. This conjecture has attracted much attention-see, for example, [1...

MATHEMATICS | SENDOV CONJECTURE

MATHEMATICS | SENDOV CONJECTURE

Journal Article

Mathematica Scandinavica, ISSN 0025-5521, 1/2006, Volume 99, Issue 1, pp. 53 - 75

... conjecture.

Circles | Maximality | Mathematical theorems | Approximation | Local maximum | Variational methods | Critical points | Polynomials | Degrees of polynomials | MATHEMATICS | ILIEFF-SENDOV CONJECTURE | ILYEFF | UNIT-CIRCLE

Circles | Maximality | Mathematical theorems | Approximation | Local maximum | Variational methods | Critical points | Polynomials | Degrees of polynomials | MATHEMATICS | ILIEFF-SENDOV CONJECTURE | ILYEFF | UNIT-CIRCLE

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 11/1998, Volume 350, Issue 11, pp. 4461 - 4472

... attempt to further characterize the location of the zeros of p' , which are also called the critical points of , is the Sendov Conjecture. Conj Sendov If p(z...

Circles | Zero | Mathematical theorems | Critical points | Polynomials | Centroids | Geometric centers | Mathematical inequalities | Coefficients | Location of zeros | MATHEMATICS | ILIEFF-SENDOV CONJECTURE | location of zeros | polynomials

Circles | Zero | Mathematical theorems | Critical points | Polynomials | Centroids | Geometric centers | Mathematical inequalities | Coefficients | Location of zeros | MATHEMATICS | ILIEFF-SENDOV CONJECTURE | location of zeros | polynomials

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/1997, Volume 214, Issue 1, pp. 283 - 291

Journal Article

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743, 2003, Volume 2542, pp. 61 - 69

The purpose of this paper is to demonstrate the potential of a fruitful collaboration between Numerical Analysis and Geometry of Polynomials. This is natural...

Geometry of polynomials | Smale's Conjecture | Zeros of polynomials | Gauss-Lucas Theorem | Critical points | Sendov's Conjecture | zeros of polynomials | mathematics subject classification : 30C10 | Smale's conjecture | Sendov's conjecture | ILIEFF-SENDOV CONJECTURE | COMPUTER SCIENCE, THEORY & METHODS | critical points | geometry of polynomials | Gauss-Lucas theorem | CRITICAL-POINTS | ZEROS

Geometry of polynomials | Smale's Conjecture | Zeros of polynomials | Gauss-Lucas Theorem | Critical points | Sendov's Conjecture | zeros of polynomials | mathematics subject classification : 30C10 | Smale's conjecture | Sendov's conjecture | ILIEFF-SENDOV CONJECTURE | COMPUTER SCIENCE, THEORY & METHODS | critical points | geometry of polynomials | Gauss-Lucas theorem | CRITICAL-POINTS | ZEROS

Journal Article

Complex Variables, Theory and Application: An International Journal, ISSN 0278-1077, 03/2002, Volume 47, Issue 3, pp. 239 - 241

... for the number of zeros of P on jzj¼1 resp. P 0 on jz null null j¼j Pj null . Keywords: Maximal polynomial; Derivative zeros; Sendov conjecture AMS Classification: 30C15 1...

Sendov Conjecture | Maximal Polynomial | Derivative Zeros

Sendov Conjecture | Maximal Polynomial | Derivative Zeros

Journal Article

Complex Variables, Theory and Application: An International Journal, ISSN 0278-1077, 03/1998, Volume 35, Issue 2, pp. 121 - 155

The Sendov-Ilyeff conjecture asserts that if p is a polynomial all of whose zeros lie in the closed unit disc, and if z 1 is such a zero, then the disc contains a zero of the derivative p...

zeros of polynomials | Sendov | Ilyeff | O. Szász | Classification Categories: 30C16

zeros of polynomials | Sendov | Ilyeff | O. Szász | Classification Categories: 30C16

Journal Article

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