Surveying the quantum group symmetries of integrable open spin chains

Using anisotropic R-matrices associated with affine Lie algebras $\hat g$ (specifically, $A_{2n}^{(2)}, A_{2n-1}^{(2)}, B_n^{(1)}, C_n^{(1)}, D_n^{(1)}$) and suitable corresponding K-matrices, we construct families of integrable open quantum spin chains of finite length, whose transfer matrices are invariant under the quantum group corresponding to removing one node from the Dynkin diagram of $\hat g$. We show that these transfer matrices also have a duality symmetry (for the cases $C_n^{(1)}$ and $D_n^{(1)}$) and additional $Z_2$ symmetries that map complex representations to their conjugates (for the cases $A_{2n-1}^{(2)}, B_n^{(1)}, D_n^{(1)}$). A key simplification is achieved by working in a certain "unitary" gauge, in which only the unbroken symmetry generators appear. The proofs of these symmetries rely on some new properties of the R-matrices. We use these symmetries to explain the degeneracies of the transfer matrices.Comment: 48 page

Educational System, Altruism and Inequality in the Distribution of Income

This paper studies the impact of public provision of education on the distribution of income in a framework where parents are altruistic toward children. Any child receives two transfers, one as a non-human transfer and the other as a human capital transfer. Under different education regimes, non-human transfers offset the low realization of innate ability, which despite the human capital transfer implies a low level of earnings. Then the questions that will arise are, first, to what extent skill-compensating investments are important as ex-ante income inequality reduction mechanisms in the private provision system, and secondly, how public education can affect this reduction mechanism. I show that tax policy may have unexpected effects on the compensatory effect, that is, on the income gap. The result is that the distribution of income induced by the public provision system is not more equally distributed. Moreover, the fraction of population that does not improve is just at the bottom of the income distribution. I also explore some possibilities to avoid this negative effect and preserve public education as an essential public service.Altruism, human capital and non-human capital transfers, systems of education, inequality

Changes in quantity and quality of time for children: United States, 1981-1997

This paper tries to analyze changes in the allocation of time decided by mothers and how different characteristics of them, such us marital status, employment status, etc., influences that allocation across the period 1981-1997 in the United States. Data reveals that there exists an increase on the quantity and quality of time devoted to children by some types of mothers and children. It is shown that the behavioral component of this change is larger than the structural component. Then, the determinants of direct and indirect time, quality versus quantity, are analyzed in a simultaneous equation framework. Estimations suggest that if a mother works, children's time is reduced. However working time is a substitutes of quantity of time with children, but not quality. Being single reduces not only time but its quality. Mother's earnings and level of education have changed their influence on the allocation of time across time.Time-use, quantity and quality of time with children, family ecomics, simultaneous equation system, three-stage least squares

The spectrum of quantum-group-invariant transfer matrices

Integrable open quantum spin-chain transfer matrices constructed from trigonometric R-matrices associated to affine Lie algebras $\hat g$, and from certain K-matrices (reflection matrices) depending on a discrete parameter p, were recently considered in arXiv:1802.04864 and arXiv:1805.10144. It was shown there that these transfer matrices have quantum group symmetry corresponding to removing the p-th node from the $\hat g$ Dynkin diagram. Here we determine the spectrum of these transfer matrices by using analytical Bethe ansatz, and we determine the dependence of the corresponding Bethe equations on p. We propose formulas for the Dynkin labels of the Bethe states in terms of the numbers of Bethe roots of each type.We also briefly study how duality transformations are implemented on the Bethe ansatz solutions.Comment: 37 page

FTIR Characterization of isolated fruit cuticles from tomato species

La comunicación arriba reseñada ha sido presentado como póster.The plant cuticle is a lipid extracellular membrane which covers the outer surface of leaves, stems and fruits of higher plants acting as a real interphase between the plant and the environment. The cuticle plays a pivotal role in epidermal development, control of water loss, fruit integrity, firmness and resistance to various disorders [1]. From a morphological point of view, the cuticle (Figure 1) can be described as acutinizedepidermal cell wall [2]. Based on its structural and chemical composition, the cuticle is mainly constituted by a polyester matrix of long chainpolyhydroxy fatty acids named cutin. Additionally, a significant amount of polysaccharides (mainly cellulose, hemicellulose and pectin) is also present. Cuticular waxes, a mixture of different very long chain aliphatic compounds, can be either embedded into the cutin matrix (intracuticular waxes) or deposited on the outer surface of the cuticle (epicuticular waxes) [3]. Finally, phenolic compounds (cinnamic acid derivatives and flavonoids) are also present. In tomato, cuticular flavonoids participate in fruit coloration and their presence is influenced by environmental conditions and the stage of development.As it can be observed in Figure 1, the cuticle has an asymmetrical distribution of its components. In its outer surface waxes and aliphatic compounds are very abundant, while the inner surface is rich in polysaccharides from epidermal cell wall. Two parameters have been studied, the esterification index (the ratio between the intensities of the stretching vibration band related to ester functional groups (1730 cm-1) and the stretching vibration associated with methylene groups (2918 cm-1)), which isa relative measure of the cross-linking degree of the cutin matrix, and the amount of flavonoids, calculated as the sum of 1606 cm-1and 1624 cm-1 band areas.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

The Asymmetric Effect of Endowments on Vertical Intra-Industrial Trade

This paper investigates the determinants of Spanish vertical intra-industrytrade with a large sample of countries. We empirically test the comparative advantageexplanation. For this aim, we build physical, human and technologicalcapital stocks. On average, when using OLS techniques, differences in endowmentsare a limitation for vertical intra-industry trade. Using quantile regressionstechniques, we observe that this negative effect decreases in absolute terms asvertical intra-industry trade flows increase and, in some cases, become positivefor the upper tails, thus supporting the view of a reduced version of the comparativeadvantage explanation. Este artículo trata de analizar los determinantes del comercio intra-industrialvertical en Espña con una muestra de países extensa. Se contrasta empíricamentela hipóteis de la ventaja comparativa. Con esta finalidad, hemos construido seriesde capital físico, humano y tecnológico. En media, cuando se utiliza la estimaciónMCO, las diferencias en dotaciones suponen una limitación al comercio intraindustrialvertical. Usando la técnica de regresion por cuantiles, se observa queeste efecto negativo disminuye, en términos absolutos, a medida que los flujos decomercio intra-industrial vertical se incrementan y, en algunos casos, llegan a serpositivos en los cuantiles altos de la distribución. Este resultado ofrece evidenciaa favor de una versión reducida de la hipótesis de la ventaja comparativa.Comercio Intra-industrial, Ventaja Comparativa, Diferenciación Vertical, Stocks de Capital, Regresión Quantilica. Comparative Advantage, Vertical Differentiation, Capital Stocks, Quantile Regressions.

A data base of synthetic photometry in the GALEX ultraviolet bands for the stellar sources observed with the International Ultraviolet Explorer

The Galaxy Evolution Explorer (GALEX) has produced the largest photometric catalogue of ultraviolet (UV) sources. As such, it has defined the new standard bands for UV photometry: the near UV band (NUV) and the far UV band (FUV). However, due to brightness limits, the GALEX mission has avoided the Galactic plane which is crucial for astrophysical research and future space missions. The International Ultraviolet Explorer (IUE) satellite obtained 63,755 spectra in the low dispersion mode during its 18 years lifetime. We have derived the photometry in the GALEX bands for the stellar sources in the IUE Archive to extend the GALEX data base with observations including the Galactic plane.Good quality spectra have been selected for all IUE classes of stellar sources. The GALEX FUV and NUV magnitudes have been computed using the GALEX transmission curves, as well as the conversion equations between flux and magnitudes provided by the mission (galexgi.gsfc.nasa.gov). Consistency between GALEX and IUE synthetic photometries has been tested using White Dwarfs (WD) contained in both samples. The non-linear response performance of GALEX inferred from this data agrees with the results from GALEX calibration. The photometric data base is made available to the community through the services of the Centre de Donn\'ees Stellaires at Strasbourg (CDS). The catalogue contains FUV magnitudes for 1,631 sources, ranging from FUV=1.81 to FUV=18.65 mag. In the NUV band, the catalogue includes observations for 1,005 stars ranging from NUV = 3.08 to NUV= 17.74 mag . UV photometry for 1,493 not included in the GALEX AIS GR5 catalogue is provided; most of them are hot (O-A spectral type) stars. The sources in the catalogue are distributed over the full sky, including the Galactic plane.Comment: Submitted to Astronomy & Astrophysic

Price transmission analysis: A flexible methodological approach applied to European hog markets

The study of spatial price relationships contributes to explain markets performance, their degree of integration or isolation, and the speed at which information is transmitted. A great deal of methods have been used to analyze this issue, being the most important: causality tests, impulse- response functions and cointegration. Normally, these techniques have been individually applied. However, a more rich knowledge of the functioning of markets can be extracted when they are jointly applied. In this paper, we try to conjugate these three techniques in a common econometric model. First, Johansen(1988) multivariate cointegration tests are used to determine the number of long-run equilibrium relationships. Cointegration is considered not only as informative about long-run price transmission but also as an essential step in the correct specification of a vector error correction model (VECM) used in the subsequent analysis. Second, Dolado and Lutkepohl(1996) causality tests are used to investigate the lead-lag behaviour among markets. Finally, impulse-response functions are calculated from the VECM estimated in the first stage for evaluating dynamic price linkages. The method exposed is applied to study spatial pork prices relationships among seven countries in the EU from 1988 to 1995. Weekly prices at farm level published by EUROSTAT: "Agricultural Markets" are used.