A method to search for correlations of ultra-high energy cosmic ray masses with the large scale structures in the local galaxy density field

One of the main goals of investigations using present and future giant extensive air shower (EAS) arrays is the mass composition of ultra-high energy cosmic rays (UHECRs). A new approach to the problem is presented, combining analysis of arrival directions with the statistical test of the paired EAS samples. An idea of the method is to search for possible correlations of UHECR masses with their separate sources, for instance, if there are two sources in different areas of the celestial sphere injecting different nuclei, but fluxes are comparable so that arrival directions are isotropic, the aim is to reveal a difference in the mass composition of CR fluxes. The method is based on a non-parametric statistical test -- the Wilcoxon signed-rank routine -- which does not depend on the populations fitting any parameterized distributions. Two particular algorithms are proposed: first, using measurements of the depth of EAS maximum position in the atmosphere; and second, relying on the age variance of air showers initiated by different primary particles. The formulated method is applied to the Yakutsk array data, in order to demonstrate the possibility of searching for a difference in average mass composition of the two UHECR sets, arriving particularly from the supergalactic plane and a complementary region.Comment: Presented at International Symposium on Future Directions in UHECR Physics, 13-16 February 2012 CERN. Accepted for publication in AP

Allowed charge transfers between coherent conductors driven by a time-dependent scatterer

We derive constraints on the statistics of the charge transfer between two conductors in the model of arbitrary time-dependent instant scattering of non-interacting fermions at zero temperature. The constraints are formulated in terms of analytic properties of the generating function: its zeroes must lie on the negative real axis. This result generalizes existing studies for scattering by a time-independent scatterer under time-dependent bias voltage.Comment: 5 pages, no figures, corrected misprints and minor changes in version

Some Remarks on Noncommutative Instantons

We make some comments on noncommutative $U(N)$-instantons on $\mathbb{R}^4_{\theta}$. We elaborate on the equations for the ASD-connection for free modules. Further we make some remarks on the computation of the topological index of ADHM instantons.Comment: 13 page

Discrete Symmetries Underlying Some Continuous Ones: Two Examples From Gravity And Particle Physics

Two examples, not connected at present, from author's papers (Nuovo Cim., 1992, v.105A, p.77 [hep-th/0207210] and GRG, 1999, v.31, p.1431 [gr-qc/0207017]) are considered here in which a physical model has discrete symmetries and additional non-observable coordinates or parameters. Then it is possible to introduce some apparent continuous symmetries of the model for an observer which cannot know values of these additional quantities.Comment: Contribution to the 5th Conference 'Symmetry In Nonlinear Mathematical Physics' which will be held in June 23-29, 2003, Kyiv, Ukrain