Simple quadratures in the complex plane

On Simple Quadratures

Simple universal bounds for Chebyshev-type quadratures

A Chebyshev-type quadrature for a probability measure σ is a distribution which is uniform on n points and has the same first k moments as σ. We give bounds for the smallest possible n required to achieve a certain degree k. In contrast to previous results of this type, our bounds use only simple properties of σ and are thus applicable in wide generality. In particular, it is shown that wheneve...

The Risk Factors in Children with Simple and Complex Febrile Seizures: An Epidemiological Study

Background Febrile seizure is the most common seizure disorders. Febrile seizure is divided into two groups of simple and complex seizures.  The aim of this epidemiological study was to assess the risk factors involved in the incidence of febrile seizures between the children referred to Besat hospital in the city of Sanandaj (Iran). Materials and Methods The present paper is a cross-sectional...

Archimedes and the Complex Plane

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Point - curve incidences in the complex plane ∗

We prove an incidence theorem for points and curves in the complex plane. Given a set of m points in R and a set of n curves with k degrees of freedom, Pach and Sharir proved that the number of point-curve incidences is O ( m k 2k−1n 2k−2 2k−1 +m+n ) . We establish the slightly weaker bound Oε ( m k 2k−1 n 2k−2 2k−1 +m+n ) on the number of incidences between m points and n (complex) algebraic c...