Extensions of D. Jackson's Theorem on Best Complex Polynomial Mean Approximation

1969 ◽  
Vol 138 ◽  
pp. 61 ◽  
Author(s):  
J. L. Walsh ◽  
E. B. Saff
Keyword(s):  
Complex Polynomial

scholarly journals Annular Bounds for the Zeros of a Polynomial

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Le Gao ◽  
N. K. Govil
Keyword(s):  
Complex Polynomial

The problem of obtaining the smallest possible region containing all the zeros of a polynomial has been attracting more and more attention recently, and in this paper, we obtain several results providing the annular regions that contain all the zeros of a complex polynomial. Using MATLAB, we construct specific examples of polynomials and show that for these polynomials our results give sharper regions than those obtainable from some of the known results.

Seismic calibration using the simplex algorithm

1989 ◽  
Vol 79 (5) ◽  
pp. 1618-1628
Author(s):  
Lee Steck ◽  
William A. Prothero
Keyword(s):  
Response Function ◽  
Degrees Of Freedom ◽  
Simplex Algorithm ◽  
Complex Polynomial ◽  
High Signal ◽  
Polynomial Representation ◽  
Important Improvement ◽  
The Time Domain ◽  
Calibration Program ◽  
Starting Model

Abstract We have modified the software of Sauter and Dorman (1986) to produce a robust and flexible calibration program that works in the frequency domain for longer and noisy calibration signals, as well as in the time domain when shorter, high signal-to-noise calibration signals may be used. The most important improvement was to replace the least squares fitting of the complex polynomial representation of the response function with the simplex fitting of the pole-zero representation of the response function. The simplex algorithm always converges to a minimum, regardless of starting model, and by fitting the poles and zeroes directly, we minimize the degrees of freedom of the solution. Typical VAX 11/750 CPU requirements are on the order of 2 to 3 minutes for both codes, with average errors less than 1 per cent in amplitude and 1° in phase.

scholarly journals Finite automorphism groups of laminated near-rings

1983 ◽  
Vol 26 (3) ◽  
pp. 297-306 ◽  
Author(s):  
K. D. Magill ◽  
P. R. Misra ◽  
U. B. Tewari
Keyword(s):  
Finite Group ◽  
Linear Group ◽  
Complex Plane ◽  
Finite Groups ◽  
Automorphism Groups ◽  
The Other ◽  
Complex Polynomial ◽  
Infinite Groups ◽  
Nonsingular Matrices ◽  
A Finite Group

In [3] we initiated our study of the automorphism groups of a certain class of near-rings. Specifically, let P be any complex polynomial and let P denote the near-ring of all continuous selfmaps of the complex plane where addition of functions is pointwise and the product fg of two functions f and g in P is defined by fg=f∘P∘g. The near-ring P is referred to as a laminated near-ring with laminating element P. In [3], we characterised those polynomials P(z)=anzn + an−1zn−1 +…+a0 for which Aut P is a finite group. We are able to show that Aut P is finite if and only if Deg P≧3 and ai ≠ 0 for some i ≠ 0, n. In addition, we were able to completely determine those infinite groups which occur as automorphism groups of the near-rings P. There are exactly three of them. One is GL(2) the full linear group of all real 2×2 nonsingular matrices and the other two are subgroups of GL(2). In this paper, we begin our study of the finite automorphism groups of the near-rings P. We get a result which, in contrast to the situation for the infinite automorphism groups, shows that infinitely many finite groups occur as automorphism groups of the near-rings under consideration. In addition to this and other results, we completely determine Aut P when the coefficients of P are real and Deg P = 3 or 4.

Bounds for the multiplicities of the roots of a complex polynomial

2011 ◽  
Vol 54 (3) ◽  
pp. 587-598
Author(s):  
A. I. Bonciocat ◽  
N. C. Bonciocat ◽  
A. Zaharescu
Keyword(s):  
Complex Polynomial ◽  
Complex Polynomials ◽  
Integer Coefficients ◽  
Separability Criteria ◽  
Maximal Multiplicity

AbstractWe refine a result of Dubickas on the maximal multiplicity of the roots of a complex polynomial, and obtain several separability criteria for complex polynomials with large leading coefficient. We also give p-adic analogous results for polynomials with integer coefficients.

scholarly journals Finitely curved orbits of complex polynomial vector fields

2007 ◽  
Vol 79 (1) ◽  
pp. 13-16
Author(s):  
Albetã C. Mafra
Keyword(s):  
Vector Field ◽  
Gaussian Curvature ◽  
Algebraic Curve ◽  
Vector Fields ◽  
Complex Polynomial ◽  
Holomorphic Foliations ◽  
Holomorphic Curve ◽  
Polynomial Vector ◽  
Polynomial Vector Fields

This note is about the geometry of holomorphic foliations. Let X be a polynomial vector field with isolated singularities on C². We announce some results regarding two problems: 1. Given a finitely curved orbit L of X, under which conditions is L algebraic? 2. If X has some non-algebraic finitely curved orbit L what is the classification of X? Problem 1 is related to the following question: Let C <FONT FACE=Symbol>Ì</FONT> C² be a holomorphic curve which has finite total Gaussian curvature. IsC contained in an algebraic curve?

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