منابع مشابه
The Descartes Rule of Sweeps and the Descartes Signature
The Descartes Rule of Signs, which establishes a bound on the number of positive roots of a polynomial with real coefficients, is extended to polynomials with complex coefficients. The extension is modified to bound the number of complex roots in a given direction on the complex plane, giving rise to the Descartes Signature of a polynomial. The search for the roots of a polynomial is sometimes ...
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Let L be any number field or p-adic field and consider F := (f1, . . . , fk) where fi∈L[x ±1 1 , . . . , x ±1 n ]\{0} for all i and there are exactlym distinct exponent vectors appearing in f1, . . . , fk. We prove that F has no more than 1+ ( σm(m− 1)2n2 logm )n geometrically isolated roots in Ln, where σ is an explicit and effectively computable constant depending only on L. This gives a sign...
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Numerous hypotheses have been devised to explain the occurrence of the Salem witchcraft trials in 1692, yet a sense of bewilderment and doubt pervades most of the historical perspectives on the subject. The physical afflictions of the accusing girls and the imagery of the testimony, therefore, is dismissed as imaginary in foundation. One avenue of understanding that has yet to be sufficiently e...
متن کامل7 Descartes ’ Perfect Lens
We give a new, elementary, purely analytical development of Descartes’ theorem that a smooth connected surface is a perfect focusing lens if and only if it is a connected subset of the ovoid obtained by revolving a cartesian oval around its axis of symmetry.
متن کاملDescartes' carton--On plausibility.
n t odern healthcare operates under the banner of “evidencebased” medicine. The pursuit of such evidence, however, is ot exclusively driven by need, but by the vailability of funds, which in turn deends partly on the likelihood of profit. ore portentously, the pursuit of data is ounded by the prevailing conceptions of iological plausibility. This essay makes he case that such borders are not re...
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ژورنال
عنوان ژورنال: Les Cahiers du Centre de recherches historiques
سال: 2006
ISSN: 0990-9141,1760-7906
DOI: 10.4000/ccrh.3158