ar X iv : m at h - ph / 0 51 10 53 v 1 1 6 N ov 2 00 5 Normal bundles to Laufer rational curves in local

ar X iv : h ep - l at / 0 11 00 06 v 3 6 N ov 2 00 1 1 Matrix elements of ∆ S = 2 operators with Wilson fermions

ar X iv : m at h / 04 10 61 1 v 2 [ m at h . A G ] 1 1 N ov 2 00 4 ON RATIONAL CUSPIDAL PROJECTIVE PLANE CURVES

ar X iv : 0 71 1 . 27 58 v 1 [ m at h . A G ] 1 7 N ov 2 00 7 Rational curves of degree 11 on a general quintic threefold ∗

We prove the “strong form” of the Clemens conjecture in degree 11. Namely, on a general quintic threefold F in P, there are only finitely many smooth rational curves of degree 11, and each curve C is embedded in F with normal bundle O(−1) ⊕ O(−1). Moreover, in degree 11, there are no singular, reduced, and irreducible rational curves, nor any reduced, reducible, and connected curves with ration...

ar X iv : m at h - ph / 0 51 10 74 v 1 2 5 N ov 2 00 5 1 / f Noise in Fractal Quaternionic Structures

We consider the logistic map over quaternions H ∼ R 4 and different 2D projections of Mandelbrot set in 4D quaternionic space. The approximations (for finite number of iterations) of these 2D projections are fractal circles. We show that a point process defined by radiuses Rj of those fractal circles exhibits pure 1/f noise.

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