ar X iv : 0 70 6 . 04 00 v 1 [ m at h . A C ] 4 J un 2 00 7 BOUNDS FOR HILBERT COEFFICIENTS

ar X iv : 0 70 6 . 09 93 v 1 [ m at h . A T ] 7 J un 2 00 7 v 1 - PERIODIC HOMOTOPY GROUPS OF THE DWYER - WILKERSON SPACE

The Dwyer-Wilkerson space DI(4) is the only exotic 2-compact group. We compute its v1-periodic homotopy groups v 1 π∗(DI(4)).

ar X iv : 0 70 9 . 04 00 v 1 [ m at h . O C ] 4 S ep 2 00 7 Noether ’ s Theorem on Time Scales ∗

We show that for any variational symmetry of the problem of the calculus of variations on time scales there exists a conserved quantity along the respective Euler-Lagrange extremals. Mathematics Subject Classification 2000: 49K05, 39A12.

ar X iv : 0 90 6 . 07 63 v 1 [ m at h . C O ] 3 J un 2 00 9 HIGHER DIMENSIONAL

We prove upper bounds on the face numbers of simplicial complexes in terms on their girths, in analogy with the Moore bound from graph theory. Our definition of girth generalizes the usual definition for graphs.

ar X iv : h ep - p h / 04 02 19 0 v 2 2 6 M ay 2 00 4 1 Pentaquarks in the 10 F - and 10 F - plets

ar X iv : m at h - ph / 0 40 70 25 v 6 2 J un 2 00 6 Clifford Valued Differential Forms , and Some Issues in Gravitation , Electromagnetism and ”

This version includes some corrections of misprints and of some formulas appearing in the original text.