ABSTRACT We describe how analytic solutions for linear hydromagnetic waves can be used testing cosmological magnetohydrodynamic (MHD) codes. start from the comoving MHD equations and derive amplitude evolution of in a matter-dominated, flat Einstein-de-Sitter (EdS) universe. The considered are comoving, linearly polarized Alfvén magnetosonic (fast) modified by self-gravity. solution compressibl...

Veech groups uniformize Teichmüller geodesics in Riemann moduli space. We gave examples of infinitely generated Veech groups; see Duke Math. J. 123 (2004), 49–69. Here we show that the associated Teichmüller geodesics can even have both infinitely many cusps and infinitely many infinite ends.

In this note we exhibit a condition under which a sequence of elements a19 , an in a commutative noetherian local ring A form an Asequence, and derive a number of corollaries. Recall that if M is an A-module, then a19 , an is an M-sequence if 1) ai+1 is a nonzerodivisor on M/(a19 9a1)M for i = 0, 9n — 1,. and 2) M Φ (al9 . . . , α n ) M . If a19 , an is an A-sequence and / is the ideal generate...