Hodge polynomials of some moduli spaces of Coherent Systems

When $k<n$, we study the coherent systems that come from a BGN extension in which the quotient bundle is strictly semistable. In this case we describe a stratification of the moduli space of coherent systems. We also describe the strata as complements of determinantal varieties and we prove that these are irreducible and smooth. These descriptions allow us to compute the Hodge polynomials of this moduli space in some cases. In particular, we give explicit computations for the cases in which $(n,d,k)=(3,d,1)$ and $d$ is even, obtaining from them the usual Poincar\'e polynomials.Comment: Formerly entitled: "A stratification of some moduli spaces of coherent systems on algebraic curves and their Hodge--Poincar\'e polynomials". The paper has been substantially shorten. Theorem 8.20 has been revised and corrected. Final version accepted for publication in International Journal of Mathematics. arXiv admin note: text overlap with arXiv:math/0407523 by other author

Sobre el problema inverso de difusión

Infiltration is physically described in order to model it as a diffusion stochasticprocess. Theorem M-B 1 is enunciated; whose main objective is the inverse diffusionproblem. The theorem is demonstrated in the specific context of solution injectability,and it is applied to solve the inverse diffusion problem in the presence of Boltzmann’sgroup. The inverse problem of the similarity exponent is solved following group analysismethods. The dispersion of a water drop in a three-dimensional porous medium isapplied; a result which in turn is applicable to drop irrigation.Keywords: inverse problems, group analysis of differential equations, similarity, fractals,diffusion, porous medium.Se describe f´?sicamente la infiltracci´on para modelarla como un proceso estoc´asticode difusi´on. Se enuncia el teorema M-B 1, cuyo objeto principal es el problema inversode difusi´on. Se demuestra dicho teorema, en el contexto particular de la inyectividadde la soluci´on y se aplica para resolver el problema inverso de difusi´on en presencia delgrupo de Boltzmann. Se resuelve el problema inverso del exponente de similaridad porlos m´etodos del an´alisis de grupo. Se aplica a la dispersi´on de una gota en un medioporoso tridimensional, resultado a su vez aplicable en el caso del riego por goteo.Palabras clave: Problemas inversos, an´alisis de grupo de ecuaciones diferenciales, similaridad,fractales, difusi´on, medios porosos

Aproximación fractal para semivariogramas freáticos

Hausdorff’s measure is integrated upon, and H¨older’s exponent is obtained as thecodimension DT ? D of the fractal in the Euclidian space in which it is immersed.This has resulted from the application of Daniell’s integral conception, which makesit possible to integrate Lipschitz’s and H¨older’s functions into Baire’s measures andto define fractal space with Hutchinson’s metric.The power for the potentiated model of the semivariograms of stationary processesis obtained. It is applied to the levels of the phreatic strata of Valle del Carrizo,Sinaloa, Mexico, and the experimental semivariograms, and those of the adjustmentwith a potential model are created, with the finding that its power is = 1,5. It isalso found that the fractal dimension of these strata is 2,25.Keywords: fractals, H¨older, codimension, similarity, semivariogram, groundwater.Se integra sobre la medida de Hausdorff y se obtiene el exponente H¨older como lacodimensi´on DT ?D del fractal, en el espacio Euclidiano en que se encuentra inmerso.´Esto ha resultado de la aplicaci´on de la concepci´on de integral de Daniell, que posibilitaintegrar funciones de Lipschitz y de H¨older sobre las medidas de Baire y tambi´en, dedefinir el espacio de fractales con la m´etrica de Hutchinson.Se obtiene la potencia para el modelo [potenciado]* de los semivariogramas de procesosestacionarios. Se aplica a los niveles de los mantos fre´aticos del Valle del Carrizo,Sinaloa, M´exico, y se crean los semivariogramas experimentales y el de ajuste con unmodelo potencial, encontr´andose que su potencia es = 1,5. Se obtiene tambi´en, quela dimensi´on fractal de estos mantos es de 2,25.Palabras clave: Fractales, H¨older, codimensi´on, similaridad, semivariograma, fre´atico

All downhill from the PhD? The typical impact trajectory of US academic careers

© 2020 The Authors. Published by MIT Press. This is an open access article available under a Creative Commons licence. The published version can be accessed at the following link on the publisher’s website: https://doi.org/10.1162/qss_a_00072.Within academia, mature researchers tend to be more senior, but do they also tend to write higher impact articles? This article assesses long-term publishing (16+ years) United States (US) researchers, contrasting them with shorter-term publishing researchers (1, 6 or 10 years). A long-term US researcher is operationalised as having a first Scopus-indexed journal article in exactly 2001 and one in 2016-2019, with US main affiliations in their first and last articles. Researchers publishing in large teams (11+ authors) were excluded. The average field and year normalised citation impact of long- and shorter-term US researchers’ journal articles decreases over time relative to the national average, with especially large falls to the last articles published that may be at least partly due to a decline in self-citations. In many cases researchers start by publishing above US average citation impact research and end by publishing below US average citation impact research. Thus, research managers should not assume that senior researchers will usually write the highest impact papers

Pre- and Post-Crisis Dynamics of Financial Globalisation for Financial Development in Africa

This study unites two streams of research by simultaneously focusing on the impact of financial globalisation on financial development and pre- and post-crisis dynamics of the investigated relationship. The empirical evidence is based on 53 African countries for the period 2004-2011 and Generalised Method of Moments. The following findings are established. First, whereas marginal effects from financial globalisation are positive on financial dynamics of activity and size, corresponding net effects (positive thresholds) are negative (within range). Second, while decreasing financial globalisation returns are apparent to financial dynamics of depth and efficiency, corresponding net effects (negative thresholds) are positive (not within range). Third, financial development dynamics are more weakly stationary and strongly convergent in the pre-crisis period. Fourth, the net effect from the: pre-crisis period is lower on money supply and banking system efficiency; post-crisis period is positive on financial system efficiency and pre-crisis period is positive on financial size. Policy implications are discussed