ar X iv : 0 80 2 . 15 86 v 1 [ cs . S E ] 1 2 Fe b 20 08 Program Promises

ar X iv : 0 80 1 . 48 21 v 2 [ he p - ph ] 2 8 Fe b 20 08 X ( 1835 ) and η ( 1760 ) observed by BES Collaboration

ar X iv : 0 80 2 . 30 10 v 1 [ m at h . Q A ] 2 1 Fe b 20 08 THE OPERAD LIE IS FREE

We show that the operad Lie is free as a non-symmetric operad. Then we study the generating series counting the operadic generators, finding a recursive formula for its coefficients, and showing that the asymptotic density of the operadic generators is 1/e.

ar X iv : 0 80 2 . 25 80 v 1 [ m at h . G T ] 1 9 Fe b 20 08 3 - Dimensional Schlaefli Formula and Its Generalization

Several identities similar to the Schlaefli formula are established for tetrahedra in a space of constant curvature.

ar X iv : 0 80 2 . 42 23 v 1 [ m at h . Q A ] 2 8 Fe b 20 08 Local analytic classification of q - difference equations

3 Analytic classification of admissible q-difference modules 10 3.1 Generalities on q-difference modules . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 Simple objects in the category of admissible q-difference modules . . . . . . . 11 3.3 Main results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.4 Analytic vs formal classification . . . . . . . . . . . . ...

ar X iv : 0 80 2 . 38 39 v 1 [ m at h . G R ] 2 6 Fe b 20 08 Quadratic equations over free groups are NP - complete

We prove that the problems of deciding whether a quadratic equation over a free group has a solution is NP-complete