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Gonzalo E. Reyes

Publications and source records attributed to Gonzalo E. Reyes.

4 recordsLinked to original sources
arXiv2004

Categorical distribution theory; heat equation

The aim of this paper is to develop the theory of distributions, not necessarily of compact support, in a topos model of Synthetic Differential Geometry, the so-called "Cahiers Topos". As an application, we study the evolution through time of a heat distribution. In the first part of the paper we study distributions in the sense of Schwartz in the context of convenient vector spaces. In particular, we study smoothness (with respect to time) of the fundamental distribution solution of the heat equation. In the second part, we show how the results of the first part may be used to internalize these notions to prove the existence of the fundamental distribution solution of the heat equation in the Cahiers topos.}

math.CT↗
arXiv2003

On the law of motion in Special Relativity

Newton's law of motion relative to an inertial frame ("the laboratory") for a particle subject to a force acting at a certain time may be interpreted in either of two ways: (1) The force acting on the particle during an infinitesimal time imparts to the laboratory a boost (impulse divided by the mass) while the particle maintains the original velocity relative to the new frame and (2) The force acting on the particle during an infinitesimal time imparts to the particle the same boost relative to the proper frame of the particle which moves with the original velocity with respect to the laboratory. We show that the relativistic law of motion admits both interpretations, the first of which is in fact equivalent to the law of motion. As a consequence, we show that the relativistic law of motion may also be reformulated as "force equals mass times acceleration" in analogy with Newton's law, but with a relativistic mass and a relativistic acceleration defined in terms of the relativistic addition law of velocities, rather than ordinary mass and ordinary vectorial addition of velocities that lead to the classical acceleration and to Newton's law.

physics.class-ph↗
arXiv2001

Some differential equations in synthetic differential geometry

Some differential equations are considered in the context of Synthetic Differential Geometry. Here, this means that not only nilpotent infinitesimals, but also the formation of function spaces, is exploited. In particular, we utilize distribution spaces in our study of wave and heat equations.

math.CT↗