An Eulerian Method for Representing $\pi^2$ by Series

An Eulerian Numerical Method for Geometric Optics

R esum e. La description classique du probl eme de l'optique g eom etrique est La-grangienne. Le passage a la repr esentation Eul erienne est possible mais, en pr esence de caustiques, ne permet pas de calculer la solution Lagrangienne compl ete. On pr esente le contexte math ematique du probl eme ainsi que quelques outils num eriques d evelop-p es pour lever cette limitation. Abstract. The cla...

An Extremal Series of Eulerian Synchronizing Automata

We present an infinite series of n-state Eulerian automata whose reset words have length at least (n − 3)/2. This improves the current lower bound on the length of shortest reset words in Eulerian automata. We conjecture that (n − 3)/2 also forms an upper bound for this class and we experimentally verify it for small automata by an exhaustive computation.

development of an explicit eulerian method for treating particle laden turbulent flow in dust collectors

Ramanujan's Eisenstein series and new hypergeometric-like series for 1/pi2

Using hypergeometric identities and certain representations for Eisenstein series, we uniformly derive several new series representations for 1/ 2. © 2008 Elsevier Inc. All rights reserved. MSC: 33C05; 33E05; 11F11; 11R29

Eulerian Series as Modular Forms

Since this series is essentially the reciprocal of Dedekind’s weight 1/2 modular form, this provides another example of an Eulerian series which is a modular form. The literature on such identities is extensive, and the pursuit of further identities and their interpretations remains an active area of research largely due to applications in combinatorics, Lie theory, number theory and physics (f...