Residue Calculus and Applications

Residue Calculus and Applications

We present a new algorithm in order to compute the multidimensional residue of a polynomial map based on a perturbation argument and the Generalized Transformation Law. Then we use it for studying some fundamental problems in Computer Aided Geometric Design.

Residue Calculus and Effective Nullstellensatz

where h is the maximal size in the sense of Mahler of the pj . There does not seem to exist so far an Arithmetic Division Theory that could provide good estimates for the Faltings heights of the cycles corresponding to qj or for the maximal Mahler size of the qj . Nevertheless, using analytic methods based on the existence of integral representation formulas in Complex Analysis and multidimensi...

Calculus, Applications and Theory

Stochastic Calculus and Applications

These notes and other information about the course are available on www.statslab.cam.ac.uk/∼beresty/teach/StoCal/stocal.html Christina Goldschmidt, Stefan Grosskinsky, Gregory Miermont, and James Norris have all contributed to these notes. However, errors are my responsibility only. Comments and corrections are most welcome and should be sent to N.Berestycki AT statslab.cam.ac.uk Date last modi...

Fractional calculus and its applications.

Fractional calculus was formulated in 1695, shortly after the development of classical calculus. The earliest systematic studies were attributed to Liouville, Riemann, Leibniz, etc. [1,2]. For a long time, fractional calculus has been regarded as a pure mathematical realm without real applications. But, in recent decades, such a state of affairs has been changed. It has been found that fraction...