Single- and multi-photon events with missing energy are selected in 619 pb−1 of data collected by the L3 detector at LEP at centre-of-mass energies between 189 GeV and 209 GeV. The cross sections of the process e+e− → vv-bar gamma (gamma) are found to be in agreement with the Standard Model expectations, and the number of light neutrino species is determined, including lower energy data, to be N = 2.98 +/- 0.05 +/- 0.04.\ud Selection results are given in the form of tables which can be used to test future models involving single- and multi-photon signatures at LEP. These final states are also predicted by models with large extra dimensions and by several supersymmetric\ud models. No evidence for such models is found. Among others, lower limits between 1.5 TeV and 0.65 TeV are set, at 95% confidence level, on the new scale of gravity for the number of extra dimensions between 2 and 8

0370-2693r98r$ -see front matter q 1998 Elsevier Science B.V. All rights reserved.Ž . PII: S 0 3 7 0 -2 6 9 3 9 8 0 0 7 3 6 -9 ( ) M. Acciarri et al.r Physics Letters B 434 1998 169- AbstractWe analyse e q e y ™ ttg events using 100 pb y1 of data collected by the L3 experiment during the 1991-1995 LEP runs at the Z pole. From the energy of the photons and their isolation from the tau decay products, we determine the anomalous magnetic and electric dipole moments of the tau to be, respectively: a s 0.004 " 0.027 " 0.023; t d s 0.0 " 1.5 " 1.3 = 10 y16 e P cm. Ž .t This is a direct measurement of these t form factors at q 2 s 0. q 1998 Elsevier Science B.V. All rights reserved.

The measurements of hadron and lepton-pair production cross sections and leptonic forward-backward asymmetries performed with the L3 detector at centre-of-mass energies between 130 GeV and 189 GeV are used to search for new physics phenomena such as: contact interactions, exchange of virtual leptoquarks, scalar quarks and scalar neutrinos, effects of TeV strings in models of quantum gravity with large extra dimensions and non-zero sizes of the fermions. No evidence for these phenomena is found and new limits on their parameters are set.

In order to deri¨e closed-form expressions of Green's functions for the¨ector and scalar potentials of a horizontal magnetic dipole in a parallel-plate wa¨eguide filled with a homogeneous dielectric, an impro¨ed complex image method based on the two-le¨el approximation is considered in conjunction with the use of Prony's method. The results for the e¨aluation of the closed-form Green's functions obtained ( ) by the present method two-le¨el approximation are compared with ( ) those obtained by the pre¨ious method one-le¨el approximation . The present method is obser¨ed to gi¨e more accurate results than the pre¨ious method o¨er the wide frequency range as well as the whole spatial range.