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The number of zeros of a sum of fractional powers.

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The number of zeros of a sum of fractional powers. / Jameson, Graham J. O.
In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 462, No. 2070, 08.06.2006, p. 1821-1830.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Jameson, GJO 2006, 'The number of zeros of a sum of fractional powers.', Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 462, no. 2070, pp. 1821-1830. https://doi.org/10.1098/rspa.2005.1647

APA

Jameson, G. J. O. (2006). The number of zeros of a sum of fractional powers. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 462(2070), 1821-1830. https://doi.org/10.1098/rspa.2005.1647

Vancouver

Jameson GJO. The number of zeros of a sum of fractional powers. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2006 Jun 8;462(2070):1821-1830. doi: 10.1098/rspa.2005.1647

Author

Jameson, Graham J. O. / The number of zeros of a sum of fractional powers. In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2006 ; Vol. 462, No. 2070. pp. 1821-1830.

Bibtex

@article{899a77eb2add427a90a64aacf1a9144a,
title = "The number of zeros of a sum of fractional powers.",
abstract = "We consider functions of the form f(x=∑j=1ncjx+ajp, where where a1>c⃛>an≥0. A version of Descartes's rule of signs applies. Further, if Cj=∑i=1jci and Cn=0, then the number of zeros of f is bounded by the number of sign changes of Cj. The estimate is reduced by 1 for each relation of the form ∑j=1ncjajr=0.",
keywords = "zeros, Descartes, Laguerre, sign changes, exponential sums",
author = "Jameson, {Graham J. O.}",
note = "RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics",
year = "2006",
month = jun,
day = "8",
doi = "10.1098/rspa.2005.1647",
language = "English",
volume = "462",
pages = "1821--1830",
journal = "Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences",
issn = "1364-5021",
publisher = "Royal Society of Chemistry Publishing",
number = "2070",

}

RIS

TY - JOUR

T1 - The number of zeros of a sum of fractional powers.

AU - Jameson, Graham J. O.

N1 - RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics

PY - 2006/6/8

Y1 - 2006/6/8

N2 - We consider functions of the form f(x=∑j=1ncjx+ajp, where where a1>c⃛>an≥0. A version of Descartes's rule of signs applies. Further, if Cj=∑i=1jci and Cn=0, then the number of zeros of f is bounded by the number of sign changes of Cj. The estimate is reduced by 1 for each relation of the form ∑j=1ncjajr=0.

AB - We consider functions of the form f(x=∑j=1ncjx+ajp, where where a1>c⃛>an≥0. A version of Descartes's rule of signs applies. Further, if Cj=∑i=1jci and Cn=0, then the number of zeros of f is bounded by the number of sign changes of Cj. The estimate is reduced by 1 for each relation of the form ∑j=1ncjajr=0.

KW - zeros

KW - Descartes

KW - Laguerre

KW - sign changes

KW - exponential sums

U2 - 10.1098/rspa.2005.1647

DO - 10.1098/rspa.2005.1647

M3 - Journal article

VL - 462

SP - 1821

EP - 1830

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 1364-5021

IS - 2070

ER -