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A GENERALISATION OF DESCARTES’ RULE OF SIGNS

Part of: Polynomials, rational functions

Published online by Cambridge University Press:  24 January 2012

DANIEL V. TOKAREV
DANIEL V. TOKAREV*
Affiliation:
School of Mathematical Sciences, Monash University, Clayton 3800, Australia (email: daniel.tokarev@monash.edu)
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Abstract

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A generalisation of Descartes’ rule of signs to other functions is derived and a bound for the number of positive zeros of a class of integral transforms is deduced from that. A more precise rule of signs is also discussed in the light of these results.

Keywords

Descartes’ rule of signszeros of polynomialszeros of integral transforms

MSC classification

Secondary: 26C10: Polynomials
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 91 , Issue 3 , December 2011 , pp. 415 - 420
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

References

[1]Anderson, B., Jackson, J. and Sitharam, M., ‘Descartes Rule of Signs revisited’, Amer. Math. Monthly 105 (1998), 447–451.CrossRefGoogle Scholar
[2]Carnicer, J. and Peña, J. M., ‘Characterizations of the optimal Descartes rules of signs’, Math. Nachr. 189 (1998), 33–48.CrossRefGoogle Scholar
[3]Cauchy, A. L., ‘Exercises de mathématiques. IV Année’. Chez de Bure Frères, Paris, 1829.Google Scholar
[4]Curtis, D. R., ‘Recent extensions of Descartes’ rule of signs’, Ann. Math. 19 (1918), 251–278.CrossRefGoogle Scholar
[5]Grabine, D. J., ‘Descartes’ Rule of Signs: another construction’, Amer. Math. Monthly 106 (1999), 854–855.CrossRefGoogle Scholar
[6]Itenberg, U. and Roy, M.-F., ‘Multivariate Descartes’ Rule’, Beiträge Algebra Geom. 37 (1996), 337–346.Google Scholar
[7]Komornik, V., ‘Another short proof of Descartes’s Rule of Signs’, Amer. Math. Monthly 113 (2006), 829–830.CrossRefGoogle Scholar
[8]Schmitt, M., ‘New designs for the Descartes Rule of Signs’, Amer. Math. Monthly 111 (2004), 159–164.CrossRefGoogle Scholar
[9]Tokarev, D. and Borovkov, K., ‘On the expectations of maxima of sets of independent random variables’, Statist. Probab. Lett. 79 (2009), 2381–2388.CrossRefGoogle Scholar
[10]Wang, X., ‘A simple proof of Descartes’s Rule of Signs’, Amer. Math. Monthly 111 (2004), 525–526.CrossRefGoogle Scholar