M ay 2 00 4 Almost All Palindromes Are Composite ∗

Almost All Palindromes Are Composite

We study the distribution of palindromic numbers (with respect to a fixed base g ≥ 2) over certain congruence classes, and we derive a nontrivial upper bound for the number of prime palindromes n ≤ x as x → ∞. Our results show that almost all palindromes in a given base are composite. ∗MSC Numbers: 11A63, 11L07, 11N69 †Corresponding author 1

2 M ay 2 00 9 Typical case behaviour of spin systems in random graph and composite ensembles

ar X iv : h ep - t h / 01 01 05 9 v 2 1 4 M ay 2 00 1

We consider the complex scalar field coupled to background NC U(1) YM and calculate the correlator of two gauge invariant composite operators. We show how the noncommutative gauge invariance is restored for higher correlators (though the Green's function itself is not invariant). It is interesting that the recently discovered noncommutative solitons appear in the calculation.

ar X iv : a st ro - p h / 02 05 19 6 v 1 1 4 M ay 2 00 2 The Radio Properties of Composite LINER / H ii Galaxies

Arcsec-resolution VLA observations – newly obtained as well as published – of 40 nearby galaxies are discussed, completing a study of the radio properties of a magnitude-limited sample of nearby galaxies of the composite LINER/H ii type. Our results reveal an overall detection rate of at least 25% AGN candidates among these composite sources. The general properties of these AGN candidates, as c...

ep - l at / 0 10 50 07 v 1 8 M ay 2 00 1 Fermion propagator at finite temperatures on extremely anisotropic lattice . Vladimir

Fermion propagator is computed in a simple model on an extremely anisotropic lattice ξ ≫ 1. Fermion determinant is evaluated up to ξ−4 order. Chiral condensate is estimated in mean field approximation.