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A GENERALISATION OF DESCARTES’ RULE OF SIGNS

  • DANIEL V. TOKAREV (a1)
Abstract

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.

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Copyright
COPYRIGHT: © Australian Mathematical Publishing Association Inc. 2012
References
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[1]Anderson, B., Jackson, J. and Sitharam, M., ‘Descartes Rule of Signs revisited’, Amer. Math. Monthly 105 (1998), 447–451.
[2]Carnicer, J. and Peña, J. M., ‘Characterizations of the optimal Descartes rules of signs’, Math. Nachr. 189 (1998), 33–48.
[3]Cauchy, A. L., ‘Exercises de mathématiques. IV Année’. Chez de Bure Frères, Paris, 1829.
[4]Curtis, D. R., ‘Recent extensions of Descartes’ rule of signs’, Ann. Math. 19 (1918), 251–278.
[5]Grabine, D. J., ‘Descartes’ Rule of Signs: another construction’, Amer. Math. Monthly 106 (1999), 854–855.
[6]Itenberg, U. and Roy, M.-F., ‘Multivariate Descartes’ Rule’, Beiträge Algebra Geom. 37 (1996), 337–346.
[7]Komornik, V., ‘Another short proof of Descartes’s Rule of Signs’, Amer. Math. Monthly 113 (2006), 829–830.
[8]Schmitt, M., ‘New designs for the Descartes Rule of Signs’, Amer. Math. Monthly 111 (2004), 159–164.
[9]Tokarev, D. and Borovkov, K., ‘On the expectations of maxima of sets of independent random variables’, Statist. Probab. Lett. 79 (2009), 2381–2388.
[10]Wang, X., ‘A simple proof of Descartes’s Rule of Signs’, Amer. Math. Monthly 111 (2004), 525–526.
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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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