Search results for "Power series"

A rank theorem for analytic maps between power series spaces

1994

The Magnus expansion and some of its applications

2008

Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem, shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory. When formulated in operator or matrix form, the Magnus expansion furnishes an elegant setting to build up approximate exponential representations of the solution of the system. It provides a power series expansion for the corresponding exponent and is sometimes referred to as Time-Dependent Exponential Perturbation Theory. Every Magnus approximant corresponds in Perturbation Theory to a partial re-summation of infinite terms with the important additional property of prese…

The Two Loop Crossed Ladder Vertex Diagram with Two Massive Exchanges

2008

We compute the (three) master integrals for the crossed ladder diagram with two exchanged quanta of equal mass. The differential equations obeyed by the master integrals are used to generate power series expansions centered around all the singular (plus some regular) points, which are then matched numerically with high accuracy. The expansions allow a fast and precise numerical calculation of the three master integrals (better than 15 digits with less than 30 terms in the whole real axis). A conspicuous relation with the equal-mass sunrise in two dimensions is found. Comparison with a previous large momentum expansion is made finding complete agreement.

Semi-Universal unfoldings and orbits of the contact group

1996

Construction of O-minimal Structures from Quasianalytic Classes

2012

I present the method of constructing o-minimal structures based on local reduction of singularities for quasianalytic classes.

Improving the understanding of the melting behaviour of Mo, Ta, and W at extreme pressures

2004

We discus existent conflicts between experimentally measured and theoretically calculated melting curves of Mo, Ta, and W. By assuming that vacancy formation plays a fundamental role in the melting process, an explanation for the measured melting curves is provided. Furthermore, we show that the Lindemann law fits well all the measured melting curves of bcc transition metals if the Grueneisen parameter is written as a power series of the interatomic distance. For completeness, we examine possible reasons for current disagreements between shock-wave and DAC experiments. To solve them, we propose the existence of an extra high P-T phase for Mo, Ta, and W

Broglie and Young, visionaries who shed light in the polar topology that grounds our reality: a hypothesis

2020

Una observación matemática que relaciona los patrones fractales y la operación de convolución en el contexto del procesamiento de imágenes digitales interrumpió una investigación que nos lleva a plantear la hipótesis de que el concepto de onda de materia (o dualidad onda-partícula) se encuentra en la dicotomía entre el par débil y un topología fuerte en el ámbito del marco de atractores singulares continuos en ninguna parte diferenciables y el concepto de fotón-solitón de Vigier. Tal inferencia parece ser más evidente en la interpretación de Broglie-Bohm de la mecánica cuántica en el cruce de características locales x globales. De esto se deduce también que la relación de los fenómenos natu…