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Tool path generation problem is one of the most complexes in computer aided manufacturing (CAM). Although some efficient algorithms have been developed to solve it, their technological dependency makes them efficient in only a limited number of cases. In the article we propose a model that will set apart the geometrical issues involved in the manufacturing process from the purely technology-dependent physical issues by means of a topological system. Presented in the paper there is a method for offsetting any kind of curve regardless of the machining technology (i.e., independent of any tool geometry: spherical, conical, toroidal and so on). Specifically, we use parametric cubic curves, which is one of the most general and popular models in CAD/CAM applications. [ABSTRACT FROM AUTHOR]

We prove that the Schrödinger operator H=− d/ dx+ V( x)+ F· x has purely absolutely continuous spectrum for arbitrary constant external field F, for a large class of potentials; this result applies to many periodic, almost periodic and random potentials and in particular to random wells of independent depth for which we prove that when F=0, the spectrum is almost surely pure point with exponentially decaying eigenfunctions. [ABSTRACT FROM AUTHOR]

By using Agmon's geodesic ideas to single out particular regions in path space, we obtain optimal lower bounds on the leading behavior for the fall off of the ground state of multiparticle system. [ABSTRACT FROM AUTHOR]