Integrable Top Equations associated with Projective Geometry over Z_2

We give a series of integrable top equations associated with the projective geometry over Z_2 as a (2^n-1)-dimensional generalisation of the 3D Euler top equations. The general solution of the (2^n-1)D top is shown to be given by an integration over a Riemann surface with genus (2^{n-1}-1)^2.Comment: 8 pages, Late

Ordered phase and scaling in ZnZ_n models and the three-state antiferromagnetic Potts model in three dimensions

Based on a Renormalization-Group picture of $Z_n$ symmetric models in three dimensions, we derive a scaling law for the $Z_n$ order parameter in the ordered phase. An existing Monte Carlo calculation on the three-state antiferromagnetic Potts model, which has the effective $Z_6$ symmetry, is shown to be consistent with the proposed scaling law. It strongly supports the Renormalization-Group picture that there is a single massive ordered phase, although an apparently rotationally symmetric region in the intermediate temperature was observed numerically.Comment: 5 pages in REVTEX, 2 PostScript figure

Proper Polynomial Maps - The Real Case

Depto. de Álgebra, Geometría y TopologíaFac. de Ciencias MatemáticasTRUEpu

Critical Casimir effect and wetting by helium mixtures

We have measured the contact angle of the interface of phase-separated $^{3}$He-$^{4}$He mixtures against a sapphire window. We have found that this angle is finite and does not tend to zero when the temperature approaches $T_t$, the temperature of the tri-critical point. On the contrary, it increases with temperature. This behavior is a remarkable exception to what is generally observed near critical points, i.e. "critical point wetting''. We propose that it is a consequence of the "critical Casimir effect'' which leads to an effective attraction of the $^{3}$He-$^{4}$He interface by the sapphire near $T_{t}$.Comment: submitted july 13 (2002), published march 20 (2003

Cohomologically hyperbolic endomorphisms of complex manifolds

We show that if a compact Kahler manifold X admits a cohomologically hyperbolic surjective endomorphism then its Kodaira dimension is non-positive. This gives an affirmative answer to a conjecture of Guedj in the holomorphic case. The main part of the paper is to determine the geometric structure and the fundamental groups (up to finite index) for those X of dimension 3.Comment: International Journal of Mathematics (to appear

Ground-state electric quadrupole moment of 31Al

Ground-state electric quadrupole moment of 31Al (I =5/2+, T_1/2 = 644(25) ms) has been measured by means of the beta-NMR spectroscopy using a spin-polarized 31Al beam produced in the projectile fragmentation reaction. The obtained Q moment, |Q_exp(31Al)| = 112(32)emb, are in agreement with conventional shell model calculations within the sd valence space. Previous result on the magnetic moment also supports the validity of the sd model in this isotope, and thus it is concluded that 31Al is located outside of the island of inversion.Comment: 5 page