Embedding Branes in Flat Two-time Spaces

We show how non-near horizon, non-dilatonic $p$-brane theories can be obtained from two embedding constraints in a flat higher dimensional space with 2 time directions. In particular this includes the construction of D3 branes from a flat 12-dimensional action, and M2 and M5 branes from 13 dimensions. The worldvolume actions are found in terms of fields defined in the embedding space, with the constraints enforced by Lagrange multipliers.Comment: LaTex, 8 pages. Contribution to the TMR Conference on Quantum aspects of gauge theories, supersymmetry and unification. Paris, 1-7 September 199

Superspace calculation of the four-loop spectrum in N=6 supersymmetric Chern-Simons theories

Using N=2 superspace techniques we compute the four-loop spectrum of single trace operators in the SU(2) x SU(2) sector of ABJM and ABJ supersymmetric Chern-Simons theories. Our computation yields a four-loop contribution to the function h^2(\lambda) (and its ABJ generalization) in the magnon dispersion relation which has fixed maximum transcendentality and coincides with the findings in components given in the revised versions of arXiv:0908.2463 and arXiv:0912.3460. We also discuss possible scenarios for an all-loop function h^2(\lambda) that interpolates between weak and strong couplings.Comment: LaTeX, feynmp, 34 pages; v2: typos corrected, formulations improved, references adde

BIOMECHANIC EVALUATION OF RUNNING PERFORMANCES

Running is the final result of a very complex coordination involving a lot of different anatomo-physiological supports that are jointly provided by the neuro-muscular, the cardio-vascular, the respiratory and the metabolic systems. Given the obvious difficulties of a detailed evaluation of this specific motor-action, a method for synthetic description and analysis of the running performance has been developed. Such a method, presently tested by taking into account the sagittal plane only), is essentially based on the computation of three suitable indexes (namely P2-D, Kv, q) which integrates the information coming from both kinematic and dynamic data. The index P2-D provides a synthesis of the mean power developed by muscles at the main lower limb joints during the ground contact phase. The index Kv depends on the ratio between the previous index P2-D and the mean kinetic energy developed by the whole body during running. The third index q, pointing out an information which is similar to the well known mechanical efficiency, is depending on the ratio between the running cadence and the previously cited index K, The proposed method has been tested by taking into account various subjects who were running at different mean speed. The kinematic and dynamic data which are necessary to implement the computation of the above three indexes have been captured by using opto-electronic motion analyser (Elite system) and a piezoelectric sensed force plate. The aim of this work is to present in detail the adopted mathematical approach and to discuss, on the basis of some preliminary results, the sensitivity of the proposed method

Conformal boundary and geodesics for AdS5×S5AdS_5\times S^5 and the plane wave: Their approach in the Penrose limit

Projecting on a suitable subset of coordinates, a picture is constructed in which the conformal boundary of $AdS_5\times S^5$ and that of the plane wave resulting in the Penrose limit are located at the same line. In a second line of arguments all $AdS_5\times S^5$ and plane wave geodesics are constructed in their integrated form. Performing the Penrose limit, the approach of null geodesics reaching the conformal boundary of $AdS_5\times S^5$ to that of the plane wave is studied in detail. At each point these null geodesics of $AdS_5\times S^5$ form a cone which degenerates in the limit.Comment: some statements refined, chapter 5 rewritten to make it more precise, some typos correcte

Monge's transport problem in the Heisenberg group

We prove the existence of solutions to Monge transport problem between two compactly supported Borel probability measures in the Heisenberg group equipped with its Carnot-Caratheodory distance assuming that the initial measure is absolutely continuous with respect to the Haar measure of the group