Asymptotic Behavior: An Overview

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Steve P. Riley (Editor)

Series: Mathematics Research Developments
BISAC: MAT037000

Asymptotic Behavior: An Overview is designed to provide the reader with an exposition of some aspects of the oscillation theory of first order delay partial dynamic equations on time scales. Oscillation theory of differential equations, originated from the monumental paper of C. Sturm published in 1836, has now been recognized as an important branch of mathematical analysis from both theoretical and practical viewpoints.

Asymptotic behavior in the deep Euclidean region of momenta for four-dimensional models of quantum field theory is studied through the system of Schwinger-Dyson equations. This system is truncated by a sequence of n-particle approximations in which n → ∞ goes into the complete system of Schwinger-Dyson equations.

Lastly, the authors discuss the exact analytical solution of the Schrödinger equation corresponding to the hydrogen atom confined by four spherical potentials: infinite potential, parabolic potential, constant potential, and dielectric continuum.
(Imprint: Nova)

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Table of Contents

Preface

Chapter 1. Oscillation Criteria for First Order Partial Dynamic Equations with Several Delays on Time Scales
(Svetlin G. Georgiev, Sorbonne University, Paris, France)

Chapter 2. Asymptotic Behavior in Quantum-Field Models from Schwinger-Dyson Equations
(V. E. Rochev, Division of Theoretical Physics, A. A. Logunov Institute for High Energy Physics, NRC “Kurchatov Institute“, Protvino, Russia)

Chapter 3. Asymptotic Behavior for the Hydrogen Atom Confined by Different Potentials
(Michael-Adán Martínez-Sánchez, Rubicelia Vargas and Jorge Garza, Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Iztapalapa, México City, México)

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