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 ...
متن کاملArithmetic Multivariate Descartes' Rule Arithmetic Multivariate Descartes' Rule
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...
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...
متن کاملAnswering Descartes: Beyond Turing
The first half of the 20th Century was filled with a stunning group of scientists, Einstein, Bohr, von Neumann and others. Alan Turing ranks near the top of this group. I am honored to write in this Centennial Volume commemorating his work. How much do we owe one mind? His was a pivotal role in cracking the Nazi war code that profoundly aided the defeat of Nazism. His invention of the Turing ma...
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ژورنال
عنوان ژورنال: Nature
سال: 1953
ISSN: 0028-0836,1476-4687
DOI: 10.1038/1711083a0