A general formula for the Magnus expansion in terms of iterated integrals of right-nested commutators

We present a general expression for any term of the Magnus series as an iterated integral of a linear combination of independent right-nested commutators with given coefficients. The relation with the Malvenuto--Reutenauer Hopf algebra of permutations is also discussed.Comment: 16 page

La evolución del arte fantástico en México : Daniel Lezama

Es importante para la historia del arte mexicano considerar la posibilidad de una continuidad del arte fantástico, desde José Guadalupe Posada hasta la pintura figurativa de fin del siglo XX y comienzos de XXI. Mi propuesta se basa en el libro de la historiadora Ida Rodríguez Prampolini, El surrealismo y el arte fantástico de México, escrito en 1969. Para una definición más amplia e incluyente recurro a la tesis literaria del escritor mexicano Omar Nieto Arroyo, publicada en 2015. Desde esta lejanía podremos ver claramente el hilo conductor de la producción fantástica mexicana, y por ende lo más importante: la estupenda maleabilidad del género para mostrar todo tipo de conceptos. Como un ejemplo del arte fantástico de México en la actualidad presento la obra del pintor Daniel Lezama.It is important for the history of Mexican art to consider the possibility of a continuity in fantastic art, from José Guadalupe Posada to the figurative painting of the end of the twentieth and beginning of the twenty-first century. My proposal is based on the historian Ida Rodríguez Prampolini's book El surrealismo y el arte fantástico de México [Surrealism and fantastic art in Mexico], written in 1969. For a broader and more inclusive definition I make use of Omar Nieto Arroyo's literary thesis published in 2015. From this distance we will be able to see clearly the thread unifying Mexican production of the fantastic, and thus what is most important: the wonderful malleability of the genre to show all manner of conceits. I use Daniel Lezama as an example of contemporary Mexican art

A Lie-Deprit perturbation algorithm for linear differential equations with periodic coefficients

A perturbative procedure based on the Lie-Deprit algorithm of classical mechanics is proposed to compute analytic approximations to the fundamental matrix of linear di erential equations with periodic coe cients. These approximations reproduce the structure assured by the Floquet theorem. Alternatively, the algorithm provides explicit approximations to the Lyapunov transformation reducing the original periodic problem to an autonomous sys- tem and also to its characteristic exponents. The procedure is computationally well adapted and converges for su ciently small values of the perturbation pa- rameter. Moreover, when the system evolves in a Lie group, the approximations also belong to the same Lie group, thus preserving qualitative properties of the exact solution

Exponential Perturbative Expansions and Coordinate Transformations

We propose a unified approach for different exponential perturbation techniques used in the treatment of time-dependent quantum mechanical problems, namely the Magnus expansion, the Floquet–Magnus expansion for periodic systems, the quantum averaging technique, and the Lie–Deprit perturbative algorithms. Even the standard perturbation theory fits in this framework. The approach is based on carrying out an appropriate change of coordinates (or picture) in each case, and it can be formulated for any time-dependent linear system of ordinary differential equations. All of the procedures (except the standard perturbation theory) lead to approximate solutions preserving by construction unitarity when applied to the time-dependent Schrödinger equation

A note on the Baker–Campbell–Hausdorff series in terms of right-nested commutators

We get compact expressions for the Baker–Campbell–Hausdorff series Z = log(eX eY ) in terms of right-nested commutators. The reduction in the number of terms originates from two facts: (i) we use as a starting point an explicit expression directly involving independent commutators and (ii) we derive a complete set of identities arising among right-nested commutators. The procedure allows us to obtain the series with fewer terms than when expressed in the classical Hall basis at least up to terms of grade 10

Magnus integrators for linear and quasilinear delay differential equations

A procedure to numerically integrate non-autonomous linear delay differential equations is presented. It is based on the use of an spectral discretization of the delayed part to transform the original problem into a matrix linear ordinary differential equation which is subsequently solved with numerical integrators obtained from the Magnus expansion. The algorithm can be used in the periodic case to get both accurate approximations of the characteristic multipliers and the solution itself. In addition, it can be extended to deal with certain quasilinear delay equations

Food Indicators and Their Relationship with 10 to 12 Year-olds' Subjective Well-Being

This study aimed to test subjective indicators designed to analyze the role food plays in children’s lives, explore children’s personal well-being, and evaluate the relationship between these two phenomena. It was conducted on 371 children aged 10 to 12 by means of a selfadministered questionnaire. Results showed a marked interest in food on the part of children, who consider taste and health the most important indicators when it comes to eating. They demonstrated a high level of personal well-being, measured using Cummins & Lau’s adapted version of the Personal Well- Being Index–School Children (PWI-SC) (2005), overall life satisfaction (OLS) and satisfaction with various life domains (friends, family, sports, food and body). Regression models were conducted to explain satisfaction with food, taking as independent variables the interest children have in food, the importance they give to different reasons for eating, scores from the PWI-SC, OLS and satisfaction with various life domains. In the final model, it was found that OLS, health indicators, satisfaction with health from the PWI-SC and satisfaction with your body contribute to explaining satisfaction with food. The results obtained suggest that satisfaction with food is a relevant indicator in the exploration of children’s subjective well-being, calling into question the widespread belief that these aspects are of exclusive interest to adults. They also seem to reinforce the importance of including food indicators in any study aimed at exploring the well-being of the 10 to 12 year-old population

SARS-CoV-2 Vaccines and the Skin

Coronavirus SARS-CoV-2; COVID-19; 2019-nCoV; Skin reactions; VacinesCoronavirus SARS-CoV-2; COVID-19; 2019-nCoV; Reacciones cutáneas; VacunasCoronavirus SARS-CoV-2; COVID-19; 2019-nCoV; Reaccions cutànies; VacunesVaccines against the severe acute respiratory coronavirus 2, which are the first to be used in humans against any coronavirus, were developed and produced in record time. Dermatologic adverse effects appeared during clinical trials and have also been described in the population since approval. Just as descriptions and categorization of skin manifestations of the coronavirus disease 2019 proved important for understanding the disease itself, characterizing the effects of vaccines may also further that goal. This paper reviews the properties of the different types of vaccines currently available and under development and describes how they interact with the immune system and the clinical signs they may cause. We focus on dermatologic adverse effects reported to date and recommendations for managing them