M. HENRI POINCARE

Charles-Jules-Henri Nicolle

sia. Nicolle's many accomplishments include the discovery that epidemic typhus is transmitted by body lice (Pediculus humanis corporis), discovery of the phenomenon of inap-parent infection, and possibly the first isolation of human influenza virus after experimental transmission. Nicolle made many other fundamental contributions to knowledge of infectious diseases. This year is the centenary o...

Henri De Mondeville *

Poincare Inequalities

Poincare inequalities are a simple way to obtain lower bounds on the distortion of mappings X into Y. These are shown below to be sharp when we consider the Lp spaces. A Poincare inequality is one of the following type: suppose Ψ : [0, ∞) → [0, ∞) is a nondecreasing function and that au,v, bu,v are finite arrays of real numbers (for u, v ∈ X, and not all of the numbers 0). We say that functions...

Henri ’ s Crystal Ball

O n April 10, 1908, at the general session of the Fourth International Congress of Mathematicians held in Rome, Gaston Darboux presented a talk by Henri Poincaré (1854–1912) entitled The Future of Mathematics (Poincaré was unfortunately unable to deliver the talk himself). The original can be found on the web at: http://gallica. bnf.fr/ark:/12148/bpt6k17083c/f934n10. capture. It is now a full c...

Inverse Poincare Halfmaps

A family of critical curves t h a t lie in the r ange of a class of Po inca re h a l f m a p s induced by a saddle focus in three-space is inves t iga ted analyt ical ly . It compr i s e s all " f a r f inal po in t s " of the images of invar iant curves tha t a re subjec t to a s e p a r a t i n g m e c h a n i s m . T h e n u m b e r of b ranches occurr ing on a speci f ic critical cu rve is ...