Failure of the local-global principle for isotropy of quadratic forms over rational function fields

We prove the failure of the local-global principle, with respect to all discrete valuations, for isotropy of quadratic forms over a rational function field of transcendence degree at least 2 over the complex numbers. Our construction involves the generalized Kummer varieties considered by Borcea and Cynk--Hulek.Comment: 7 pages, comments welcome

Helicity Conservation via the Noether Theorem

The conservation of helicity in ideal barotropic fluids is discussed from a group theoretical point of view. A new symmetry group is introduced i.e. the alpha group of translations. It is proven via the Noether theorem that this group generates helicity conservation.Comment: 7 pages of te

The transcendental lattice of the sextic Fermat surface

We prove that the integral polarized Hodge structure on the transcendental lattice of a sextic Fermat surface is decomposable. This disproves a conjecture of Kulikov related to a Hodge theoretic approach to proving the irrationality of the very general cubic fourfold.Comment: 15 pages; v2: minor changes, streamlined the argument in Section

Diffusional Relaxation in Random Sequential Deposition

The effect of diffusional relaxation on the random sequential deposition process is studied in the limit of fast deposition. Expression for the coverage as a function of time are analytically derived for both the short-time and long-time regimes. These results are tested and compared with numerical simulations.Comment: 9 pages + 2 figure

Insight into resolution enhancement in generalized two-dimensional correlation spectroscopy

Generalized two-dimensional correlation spectroscopy (2D-COS) can be used to enhance spectral resolution in order to help differentiate highly overlapped spectral bands. Despite the numerous extensive 2D-COS investigations, the origin of the 2D spectral resolution enhancement mechanism(s) is not completely understood. In the work here, we studied the 2D-COS of simulated spectra in order to develop new insights into the dependence of 2D-COS spectral features on the overlapping band separations, their intensities and bandwidths, and their band intensity change rates. We found that the features in the 2D-COS maps that are derived from overlapping bands were determined by the spectral normalized half-intensities and the total intensity changes of the correlated bands. We identified the conditions required to resolve overlapping bands. In particular, 2D-COS peak resolution requires that the normalized half-intensities of a correlating band have amplitudes between the maxima and minima of the normalized half-intensities of the overlapping bands. © 2013 Society for Applied Spectroscopy

The 1-soliton in the SO(3) gauged Skyrme model with mass term

The solitons of the SO(3) gauged Skyrme model with no pion-mass potential were studied in Refs. {nl,jmp}. Here, the effects of the inclusion of this potential are studied. In contrast with the (ungauged) Skyrme model, where the effect of this potential on the solitons is marginal, here it turns out to be decisive, resulting in very different dependence of the energy as a function of the Skyrme coupling constant.Comment: new title, typos corrected, LaTeX, 8 pages, 4 figure