It is well known that the geometrical optics approximation, generally valid for high-frequency fields, fails in the vicinity of a caustic. A systematic procedure of V. P. Maslov that remedies this situation will be reviewed in this paper. Maslov's method makes use of a representation of the geometrical optics field in the phase space M = X x K, where a point m = (x, •c) is a pair of a position ...

Abstract We make some considerations and remarks on D = 11 supergravity its integral form. start from the geometrical formulation of by means form technique we provide a superspace action that reproduces (at quadratic level) recent in pure spinor framework. also Chevalley-Eilenberg cocycles their Hodge duals.

This paper presents a new extended output depending nonlinear observer normal form. A sufficient geometrical conditions that guarantee a change of coordinates allowing the transformation of a given nonlinear dynamical system into the proposed observer form are given. Throughout this work, it will be showed that, unlike to the existing observer normal forms, this new form enables to design an ob...

Static deflection as well as free and forced large-amplitude vibrations of thin rectangular rubber plates under uniformly distributed pressure are investigated. Both physical, through a neo-Hookean constitutive law to describe the non-linear elastic deformation of the material, and geometrical non-linearities are accounted for. The deflections of a thin initially flat plate are described by the...

The focus of this paper is a software genre usually referred to as ‘dynamic geometry’ because of the ability of the user to dynamically manipulate geometrical figures created with the software tool. Using data from a longitudinal study of 12-13 students’ use of dynamic geometry software, the focus of the analysis is on the interpretations the students make of geometrical objects and relationshi...