Polynomial and regular images of R-n

We obtain new necessary conditions for an n-dimensional semialgebraic subset of R-n to be a polynomial image of R-n. Moreover, we prove that a large family of planar bidimensional semialgebraic sets with piecewise linear boundary are images of polynomial or regular maps, and we estimate in both cases the dimension of their generic fibers

Conserved Quantities from the Equations of Motion (with applications to natural and gauge natural theories of gravitation)

We present an alternative field theoretical approach to the definition of conserved quantities, based directly on the field equations content of a Lagrangian theory (in the standard framework of the Calculus of Variations in jet bundles). The contraction of the Euler-Lagrange equations with Lie derivatives of the dynamical fields allows one to derive a variational Lagrangian for any given set of Lagrangian equations. A two steps algorithmical procedure can be thence applied to the variational Lagrangian in order to produce a general expression for the variation of all quantities which are (covariantly) conserved along the given dynamics. As a concrete example we test this new formalism on Einstein's equations: well known and widely accepted formulae for the variation of the Hamiltonian and the variation of Energy for General Relativity are recovered. We also consider the Einstein-Cartan (Sciama-Kibble) theory in tetrad formalism and as a by-product we gain some new insight on the Kosmann lift in gauge natural theories, which arises when trying to restore naturality in a gauge natural variational Lagrangian.Comment: Latex file, 31 page

The ITER toroidal field model coil project

The ITER toroidal field model coil (TFMC) was designed, constructed and tested by the European Home Team in the framework of the ITER research and development program of the Engineering Design Activities (EDA). The project was performed under the leadership of European Fusion Development Activity/Close Support Unit (EFDA/CSU), Ciarching. in collaboration with the European superconductor laboratories and the European industry. The TFMC wits developed and constructed in collaboration with the European industry consortium (AGAN) and Europa Metalli LMI supplied the conductor, The TFMC was tested in the test phase I as single coil and in phase 11 in the background field of the EURATOM LCT coil in the TOSKA facility of the Forschungszentrum Karlsruhe. In phase 1, the TFMC achieved an ITER TF coil relevant current of about 80kA and further representative test results before the end of the EDA. In the more complex test phase [I. the coil was exposed to ITER TF coil relevant mechanical stresses in the winding pack and case. The tests confirmed that engineering design principles and manufacturing procedures are sound and suitable for the ITER TF full size coils. The electromagnetic. thermo hydraulic and mechanical operation parameters agree well with predictions. The achieved Lorentz force on the conductor was about 800 kN/m. That has been equivalent to the Lorentz forces in ITER TF coils