A novel approach based on spatiotemporal differentialoperators is developed here for broadband, velocity-dependent scattering. Unlike the spectral-domain representations, the new method facilitates a compact formulation for scattering by arbitrary excitation signals, in the presence of moving objects. In free space (vacuum), relativistically exact formulas are developed. After developing the ge...

The problem of collision detection is fundamental to inter active applications such as computer animation and virtual environments In these elds prompt recognition of possible impacts is important for computing real time response We present a simple exact collision detection algorithm for convex polytopes The algorithm nds quickly a separating plane between two polytopes if they are non collidi...

The quantum mechanical harmonic oscillator Hamiltonian H = (t − ∂ t )/2 generates a one–parameter unitary group W (θ) = e in L(R) which rotates the time–frequency plane. In particular, W (π/2) is the Fourier transform. When W (θ) is applied to any frame of Gabor wavelets, the result is another such frame with identical frame bounds. Thus each Gabor frame gives rise to a one–parameter family of ...

Abstract In certain physical cases, the angular momentum of a vector particle may naturally align with direction not exactly contained in production plane, leading to an attenuation polarization magnitude observable any experimentally defined frame. this chapter we consider two possible causes phenomenon: higher-order, non-planar processes contributing Drell--Yan, W and Z production, intrinsic ...

Grand tours are a class of methods for visualizing multivariate data, or any finite set of points in n-space. The idea is to create an animation of data projections by moving a 2-dimensional projection plane through n-space. The path of planes used in the animation is chosen so that it becomes dense, that is, it comes arbitrarily close to any plane. One inspiration for the grand tour was the ex...

this paper is a continuation of [uniformities and covering properties for partial frames (i)], in which we make use of the notion of a partial frame, which is a meet-semilattice in which certain designated subsets are required to have joins, and finite meets distribute over these. after presenting there our axiomatization of partial frames, which we call $sels$-frames, we added structure, in th...

partial frames provide a rich context in which to do pointfree structured and unstructured topology. a small collection of axioms of an elementary nature allows one to do much traditional pointfree topology, both on the level of frames or locales, and that of uniform or metric frames. these axioms are sufficiently general to include as examples bounded distributive lattices, $sigma$-frames, $ka...

Here we extend the Madelung transformation of Schr\"{o}dinger equation into a fluid-like form to include influence an external electromagnetic field on charged particle. The vorticity fluid is then in opposite direction imposed magnetic and equal magnitude cyclotron angular frequency. When particle motion confined plane, perpendicular field, equivalent flow dynamics that zero absolute obtained ...