Related papers: Resurgence and Mould Calculus
In a previous article we gave the general foundations of the theory of movement considered from a philosophical and mathematical point of view. Philosophical it meant to understand the opposition of the one and the multiple, mathematically…
Thermal state reconstruction -- reversing convection to recover the thermal structure of the mantle at an earlier geologic time -- is an important tool to understand the evolution of mantle convection and its relation to seismic tomographic…
Lagrangian algorithms to simulate the evolution of cold dark matter (CDM) are invaluable tools to generate large suites of mock halo catalogues. In this paper, we first show that the main limitation of current semi-analytical schemes to…
We provide an overview of the tools and techniques of resurgence theory used in the Borel-Ecalle resummation method, which we then apply to the massless Wess-Zumino model. Starting from already known results on the anomalous dimension of…
We introduce an original approach to geometric calculus in which we define derivatives and integrals on functions which depend on extended bodies in space--that is, paths, surfaces, and volumes etc. Though this theory remains to be fully…
The coefficient of restitution $\epsilon$ characterizes the energy retained when a ball bounces, and can easily be measured in an ``at home'' experiment. For thin-walled gas-filled balls such as basketballs, we construct a simple two…
We present a higher genus generalization of $bc$-Motzkin numbers, which are themselves a generalization of Catalan numbers, and we derive a recursive formula which can be used to calculate them. Further, we show that this leads to a…
There is increasing interest within the research community in the design and use of recursive probability models. Although there still remains concern about computational complexity costs and the fact that computing exact solutions can be…
The mass returned to the ambient medium by aging stellar populations over cosmological times sums up to a significant fraction (20% - 30% or more) of their initial mass. This continuous mass injection plays a fundamental role in phenomena…
The aim of this work is twofold. First, we survey the techniques developed in (Perthame, Zubelli, 2007) and (Doumic, Perthame, Zubelli, 2008) to reconstruct the division (birth) rate from the cell volume distribution data in certain…
A recursive calculational scheme is developed for matrix elements in the generalized seniority scheme for the nuclear shell model. Recurrence relations are derived which permit straightforward and efficient computation of matrix elements of…
The early Universe inflation is well known as a promising theory to explain the origin of large scale structure of the Universe, a causal theory for the origin of primordial density fluctuations which may explain the observed density…
In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…
In 1946, Magnus presented an addition theorem for the confluent hypergeometric function of the second kind $U$ with argument $x+y$ expressed as an integral of a product of two $U$'s, one with argument $x$ and another with argument $y$. We…
By the early 1960's advances in statistical physics had established the existence of universality classes for systems with second-order phase transitions and characterized these by critical exponents which are different to the classical…
Polydisperse linear polymer melts can be microscopically described by the tube model and fractal reptation dynamics, while on the macroscopic side the generalized Maxwell model is capable of correctly displaying most of the rheological…
In this paper we continue the investigation of partition functions of critical systems on a rectangle initiated in [R. Bondesan et al, Nucl.Phys.B862:553-575,2012]. Here we develop a general formalism of rectangle boundary states using…
We study the cosmological inflation and reheating in a teleparallel model of gravity. Reheating is assumed to be due to the decay of a scalar field to radiation during its rapid oscillation. By using cosmological perturbations during…
Marmi Moussa and Yoccoz conjectured that some error function Upsilon, related to the approximation of the size of Siegel disk by some arithmetic function of the rotation number theta, is a Holder continuous function of theta with exponent…
We revisited an analysis made by Euler in a memoir of 1753 'Sur une nouvelle maniere d'elever de l'eau propose par M. de Mour' (On a new method to raise water proposed by Mr. de Mour), addressing a type of water sprinkler, consisting of an…