Rene Descartes. Eine Einfuhrung in Seine Werke.

Emotion , Desire , and Numismatic Experience in Rene Descartes , Zhu Xi , and Wang Y Angming

Zhu Xi writes, "To extend understanding, one must first cultivate understanding. To cultivate understanding, there is only reduction of desires." I Wang Yangming writes, "When this heartmind is free of the obscurations of selfish desire, it is none other than the natural patterning. Nothing external need be added.,,2 Rene Descartes writes, "Because these passions cannot lead us to perform any a...

Ein Architekturmodell für eine generische Datenbankanwendung im Intranet und seine prototypische Realisierung

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 ...

Arithmetic 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...

7 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.