The number of ramified coverings of the sphere by the double torus, and a general form for higher genera

An explicit expression is obtained for the generating series for the number of ramified coverings of the sphere by the double torus, with elementary branch points and prescribed ramification type over infinity. Thus we are able to prove a conjecture of Graber and Pandharipande, giving a linear recurrence equation for the number of these coverings with no ramification over infinity. The general form of the series is conjectured for the number of these coverings by a surface of arbitrary genus that is at least two.Comment: 14pp.; revised version has two additional results in Section

A proof of a conjecture for the number of ramified coverings of the sphere by the torus

An explicit expression is obtained for the generating series for the number of ramified coverings of the sphere by the torus, with elementary branch points and prescribed ramification type over infinity. This proves a conjecture of Goulden, Jackson and Vainshtein for the explicit number of such coverings.Comment: 10 page

Transitive factorizations of permutations and geometry

We give an account of our work on transitive factorizations of permutations. The work has had impact upon other areas of mathematics such as the enumeration of graph embeddings, random matrices, branched covers, and the moduli spaces of curves. Aspects of these seemingly unrelated areas are seen to be related in a unifying view from the perspective of algebraic combinatorics. At several points this work has intertwined with Richard Stanley's in significant ways.Comment: 12 pages, dedicated to Richard Stanley on the occasion of his 70th birthda

Comment on "Finite Size Corrections to the Radiation Reaction Force in Classical Electrodynamics" [arXiv:1005.2617]

In [1, arXiv:1005.2617] effective field theory methods have been employed to compute the equations of motion of a spherically symmetric charged shell of radius R, taking into account the radiation reaction force exerted by the shell's own electromagnetic field up to O(R^2). The authors of Ref. [1] have stated that the known result for the self force of the shell as can be found from Eq. (16.28) of the textbook of Jackson [2] (see also Chap. 4 in the review of Pearle [3]) is incorrect, in that the term linear in R should be absent. We claim that this conclusion of Ref. [1] is incorrect, and that the textbook result, Eq. (1) does hold.Comment: 1 pag

Universal factorized formula for the cross-section of two-particle scattering

We analyze the process of two-particle scattering with unstable particle in an intermediate state. It was shown that the cross-section can be represented in the universal factorized form for an arbitrary set of particles. Phenomenological analysis of factorization effect is fulfilled.Comment: 8 pages, corrected typos. change conten

Simulation of colloidal chain movements under a magnetic field

Short colloidal chains are simulated by the slithering-snake-algorithm on a simple cubic lattice. The dipole character of the colloidal particles leads to a long range dipole-dipole interaction. The solvent is simulated by the nearest neighbor Ising model. The aligning of the dipoles under a magnetic field gives rise to the chains to align on their part with the field direction.Comment: 3 pages for Int. J. Mod. Phys. C 16, issue

Tidal influence on self-potential measurements

DJM was supported by NERC CASE studentship NE/I018417/1. The authors would also like to thank Southern Water for access to the borehole at Saltdean. Atkins Global and Southern Water are thanked for funding installation of the equipment and for additional funding under the NERC studentship. The laboratory components of this work were carried out in the TOTAL Reservoir Physics Laboratory at Imperial College London and their support is gratefully acknowledged. Jackson acknowledges partial support from TOTAL under the TOTAL Chairs programme. The data supporting the conclusions of this work are available through the corresponding author.Peer reviewedPublisher PD