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We shall show that although Palatini -theories are equivalent to Brans-Dicke theories, still the first pass the Mercury precession of perihelia test, while the second do not. We argue that the two models are not physically equivalent due to different assumptions about free fall. We shall also go through perihelia test without fixing a conformal gauge (clocks or rulers) in order to highlight what can be measured in a conformal invariant way and what cannot. We shall argue that the conformal gauge is broken by choosing a definition of clock, rulers or, equivalently, of masses. [ABSTRACT FROM AUTHOR]

We consider systems of local variational problems defining nonvanishing cohomology classes. Symmetry properties of the Euler-Lagrange expressions play a fundamental role since they introduce a cohomology class which adds up to Noether currents; they are related with invariance properties of the first variation, thus with the vanishing of a second variational derivative. In particular, we prove that the conserved current associated with a generalized symmetry, assumed to be also a symmetry of the variation of the corresponding local inverse problem, is variationally equivalent to the variation of the strong Noether current for the corresponding local system of Lagrangians. This current is conserved and a sufficient condition will be identified in order that such a current be global. [ABSTRACT FROM AUTHOR]

In the framework of Digital Art applied to Scientific Visualization we have realized a short video together with an interactive multimedia aimed at visualizing and diffusing the main concepts of Special Relativity. This note makes a short presentation of it. [ABSTRACT FROM AUTHOR]

A preface for the March 2007 issue of the "International Journal of Geometric Methods in Modern Physics" is presented.