ar X iv : 0 70 4 . 27 95 v 1 [ m at h - ph ] 2 0 A pr 2 00 7 Laplace Operator in Networks of Thin Fibers : Spectrum Near the Threshold

ar X iv : 0 70 4 . 39 02 v 1 [ m at h . PR ] 3 0 A pr 2 00 7 On the number of collisions in Λ - coalescents ∗

We examine the total number of collisions Cn in the Λ-coalescent process which starts with n particles. A linear growth and a stable limit law for Cn are shown under the assumption of a power-like behaviour of the measure Λ near 0 with exponent 0 < α < 1.

ar X iv : 0 70 7 . 33 03 v 1 [ m at h . O A ] 2 3 Ju l 2 00 7 OPERATOR - VALUED FRAMES

ar X iv : m at h - ph / 0 20 70 25 v 2 1 4 N ov 2 00 2 Bound states due to a strong δ interaction supported by a curved surface

We study the Schrödinger operator −∆ − αδ(x − Γ) in L 2 (R 3) with a δ interaction supported by an infinite non-planar surface Γ which is smooth, admits a global normal parameterization with a uniformly elliptic metric. We show that if Γ is asymptotically planar in a suitable sense and α > 0 is sufficiently large this operator has a non-empty discrete spectrum and derive an asymptotic expansion...

ar X iv : 0 70 4 . 01 15 v 2 [ m at h . G T ] 9 A pr 2 00 7 Smooth maps with singularities of bounded K - codimensions ∗ † Yoshifumi ANDO

ar X iv : m at h - ph / 0 51 10 25 v 1 7 N ov 2 00 5 L 2 - index of the Dirac operator of generalized Euclidean Taub - NUT metrics

We compute the axial anomaly for the Taub-NUT metric on R. We show that the axial anomaly for the generalized Taub-NUT metrics introduced by Iwai and Katayama is finite, although the Dirac operator is not Fredholm. We show that the essential spectrum of the Dirac operator is the whole real line. Pacs: 04.62.+v