Isometric immersions into a homogeneous Lorentzian Heisenberg group and rigidity

In this paper we prove an existence result for local and global isometric immersions of semi-Riemannian surfaces into the three dimensional Heisenberg group endowed with a homogeneous left-invariant Lorentzian metric. As a corollary, we prove a rigidity result for such immersions.

Electronic, vibrational and related properties of group IV metal oxides by ab initio calculations

We present our theoretical results for the structural, electronic, vibrational and optical properties of MO(2) (M = Sn, Zr, Hf and Ti) obtained by first-principles calculations. Relativistic effects are demonstrated to be important for a realistic description of the detailed structure of the electronic frequency-dependent dielectric function, as well as of the carrier effective masses. Based on our results, we found that the main contribution of the high values calculated for the oxides dielectric constants arises from the vibrational properties of these oxides, and the vibrational static dielectric constant values diminish with increasing pressure. (c) 2008 Elsevier B.V. All rights reserved.

ALTERNATING UNITS AS FREE FACTORS IN THE GROUP OF UNITS OF INTEGRAL GROUP RINGS

Let G be a group of odd order that contains a non-central element x whose order is either a prime p >= 5 or 3(l), with l >= 2. Then, in U(ZG), the group of units of ZG, we can find an alternating unit u based on x, and another unit v, which can be either a bicyclic or an alternating unit, such that for all sufficiently large integers m we have that < u(m), v(m)> = < u(m)> * < v(m)> congruent to Z * Z.