Newton Relations Research Articles

Resolution of the finite Markov moment problem

We expose in full detail a constructive procedure to invert the so-called ‘finite Markov moment problem’. The proofs rely on the general theory of Toeplitz matrices together with the classical Newton's relations. To cite this article: L. Gosse, O. Runborg, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

Discrete Momentum Mechanics and Faster-than-Light Transition.

In this work a new mechanics will be studied which is based on the hypothesis that the change of linear momentum of a particle happens as a discrete pulses. By using this hypothesis and by considering Newton's relation between energy and momentum, and the law of mass and energy conservation as a priori, the Einstein dispersion relation can be derived as a zero approximation without using Lorentz transformations. Other terms will be derived as a corrections to this relation. It will be shown that the effect of the corrections will be smaller and smaller with the increase of momentum. The work will offer an explanation of why the velocity of light seems to be constant regardless of the velocity of the source, and under which condition this will be changed. Also a prediction is made that faster than light transition could happen theoretically under certain conditions, and a nonzero mass photon can exist in nature. The work is purely classical in the sense that it doesn't involve any uncertainty relations.

Some Generalizations in Geometrical Optics Derived by a Convergence Method

A simple but general treatment of reflection and refraction at spherical surfaces is based on properties of nodal points and the specification of wave fronts by their convergences. Rules for the location and description of images are justified and extended to the images formed by thin lenses, the positions of whose nodal points make apparent an analogy with single refracting surfaces. The formula for the change in convergence of a wave front proceeding in a homogeneous and isotropic medium is applied to describe the images of axial objects, to derive Newton's relation in generalized form, and to consider refraction by separated refracting surfaces of unspecified powers. Solutions to five numerical problems, obtained by methods advocated in the paper, are appended.