Abstract I consider black body radiation. The wall of the exchanges photons with radiation field in equilibrium, therefore a common temperature Planck’s law. underlying process consists creation and annihilation photons. want to present an alternate model motions, where small steps positive negative direction, not zero mean. detection storing restoring packages energy. get analogue law, emerges...

A rigorous geometric proof of the Lie’s Theorem on nonlinear superposition rules for solutions of non-autonomous ordinary differential equations is given filling in all the gaps present in the existing literature. The proof is based on an alternative but equivalent definition of a superposition rule: it is considered as a foliation with some suitable properties. The problem of uniqueness of the...

The various types of synthetic discriminant function (sdf) filter result in a weighted linear superposition of the training set images. Neural network training procedures result in a non-linear superposition of the training set images or, effectively, a feature extraction process, which leads to better interpolation properties than achievable with the sdf filter. However, generally, shift invar...

In this paper we solve a long-standing open problem by showing that strict superposition|that is, superposition without equality factoring|is refutationally complete. The diiculty of the problem arises from the fact that the strict calculus, in contrast to the standard calculus with equality factoring, is not compatible with arbitrary removal of tautologies, so that the usual techniques for pro...

In this paper, we present a method of decomposing a highly oscillatory wave field into a sparse superposition of Gaussian beams. The goal is to extract the necessary parameters for a Gaussian beam superposition from this wave field, so that further evolution of the high frequency waves can be computed by the method of Gaussian beams. The methodology is described for R with numerical examples fo...