An algebraic approach to Harder-Narasimhan filtrations

In this article we study chains of torsion classes in an abelian category $\mathcal{A}$. We prove that chains of torsion classes induce a Harder-Narasimhan filtrations for every non-zero object $M$ in $\mathcal{A}$ and we characterise the slicings of $\mathcal{A}$ in terms of chain of torsion classes. Later, we show that all chain of torsion classes form a topological space and we study some of its properties. We finish the paper by showing that wall-crossing formulas can be deduced from chain of torsion classes.Comment: 31 pages. Added Section 8 and minor typos correcte

International Differences in Wage Inequality: A New Glance with European Matched Employer-Employee Data

Using unique international harmonized matched employer-employee microdata from the European Structure of Earnings Survey for nine representative European countries, this comparative study examines the origin of international differences in wage inequality. Our novel evidence uncovers that global wage inequality is highly correlated with the magnitude of inter-firm wage differentials and that workplace- and job-related factors generally have a more significant impact on within-country wage inequality than individual characteristics. On the whole, European countries exhibit considerably different wage structures: they differ significantly not only in the extent of wage inequality but also in the relative influence of factors shaping wage inequality. Comparative analyses reveal that although cross-country differences in labour force composition play a part in the explanation, differences in distribution and, very specially, in labour market prices of workplace and job characteristics are primary reasons contributing to international differences in wage inequality.Wage inequality; matched employer-employee data

Optical third harmonic generation in black phosphorus

We present a calculation of Third Harmonic Generation (THG) for two-band systems using the length gauge that avoids unphysical divergences otherwise present in the evaluation of the third order current density response. The calculation is applied to bulk and monolayer black Phosphorus (bP) using a non-orthogonal tight-binding model. Results show that the low energy response is dominated by mixed inter-intraband processes and estimates of the magnitude of THG susceptibility are comparable to recent experimental reports for bulk bP samples.Comment: 9 pages, 5 figure

Second harmonic spectroscopy to optically detect valley polarization in 2D materials

Valley polarization (VP), an induced imbalance in the populations of a multi-valley electronic system, allows emission of second harmonic (SH) light even in centrosymmetric crystals such as graphene. Whereas in systems such as MoS$\mathrm{_2}$ or BN this adds to their intrinsic quadratic response, SH generation in a multi-valley inversion-symmetric crystal can provide a direct measure of valley polarization. By computing the nonlinear response and characterizing theoretically the respective SH as a function of polarization, temperature, electron density, and degree of VP, we demonstrate the possibility of disentangling and individually quantifying the intrinsic and valley contributions to the SH. A specific experimental setup is proposed to obtain direct quantitative information about the degree of VP and allow its remote mapping. This approach could prove useful for direct, contactless, real-space monitoring of valley injection and other applications of valley transport and valleytronics.Comment: Updating with published version, including typesetting corrections to eqs 3 and 4; 7 pages, 5 figure

Los estudios sobre la juventud en México

Durante gran parte del siglo xx la juventud y las problemáticas que le son inherentes no fueron consideradas objeto de análisis por parte de las ciencias sociales en México, debido a la poca relevancia del tema. Sin embargo, a partir de 1985, con la celebración del Año Internacional de la Juventud, ésta adquirió cierta relevancia dentro de la agenda gubernamental y por ende, en la academia, de ahí que se hayan generado los primeros esbozos teóricos en el estudio de la juventud en México. Por ello el presente trabajo tiene como finalidad identificar las principales aportaciones teóricas y los distintos relatos de investigación en la construcción del conocimiento científico sobre lo juvenil en México. En este sentido, destacan las contribuciones en cuanto a las organizaciones, culturas e identidades juveniles, enfatizando en este último aspecto algunos de los principales hallazgos en cuanto a la heterogeneidad juvenil. Asimismo, se detallan los resultados más importantes respecto a las problemáticas que afectan de manera general a los jóvenes en el país