Extending lazy 2-cocycles on Hopf algebras and lifting projective representations afforded by them

AbstractWe study some problems related to lazy 2-cocycles, such as: extension of (lazy) 2-cocycles to a Drinfeld double and to a Radford biproduct, Yetter–Drinfeld data obtained from lazy 2-cocycles, lifting of projective representations afforded by lazy 2-cocycles

Forest Hydrology, Soil Conservation and Green Barriers in Canary Islands

In volcanic islands, the rainfall regime and its torrential nature, together with the steep slopes and the soil types present are considered to be some of the main factors affecting forest hydrology and soil conservation. In such environments, rain regime is generally irregular and characterized by short and intense rainfalls, which could cause destructive flows at times, followed by long periods of rain absence. The volcanic nature of these islands have as a direct resultant steep slopes which influences the runoff volume and speed, as well as the amount of topsoil susceptible to be detached and transported downstream. The soil type also affects the susceptibility to erosion processes. Andisols are the most typical soil on volcanic islands. Their particularities derive their mineral constituents, called short-range-order products, which provide these soils with an increased structural stability, which in turn reduces their susceptibility to erosion. However, the land use changes and the environmental factors such as rain regime and steep slopes may be determinant factor in destabilizing these soils and ultimately a cause for soil erosion and runoffs, which become a threat to the population downstream. Green barriers have been traditionally used to prevent or reduce these processes, also to enhance the dew effect and the fog water collection, and as a firebreak which acts as a barrier to slow or stop the progress of a wildfire. Wooded species present and subsequently their performance have a major influence on their effectiveness. The use of this natural erosion and fire control methods on volcanic islands is discussed in this paper

Grape musts differentiation based on selected aroma compounds using SBSE-GC-MS and statistical analysis

Fifty-one aroma compounds in musts from 'Muscat Ottonel', 'Aligoté', 'Muscat of Alexandria' and 'Pedro Ximénez' white grapes have been determined, three of them identified for the first time in grapes. Two fingerprints for each cultivar, based in 6 groups of aroma compounds before and after acidic hydrolysis of the musts were obtained by Multiple Variable Analysis. Only 17 aroma compounds before and 21 after hydrolysis, were selected by their high discriminating power. The Principal Component Analysis carried out with data of these selected compounds provided two components explaining 85.11 % of the overall variance for free aroma compounds and 87.58 % for those obtained after hydrolysis of musts, allowing an objective differentiation of each cultivar

Ceramic Nanofiltration Membrane Fouling: Application of Mathematical Modelling to the Use of Excitation Emission Matrix Spectroscopy

This paper presents a mathematical modeling for a series of experiments in which humic acid (AH) and calcium chloride (CaCl2) were used, in order to visualize the amount of contaminant before and after the nanofiltration (NF) process, using Excitation Emission Matrix Spectroscopy (EEMS). It allows to a better understanding of membrane fouling. The membrane used for these experiments was a NF ceramic membrane made of titanium dioxide (TiO2). For the experimental determinations, a constant amount of 10 mg/L HA and different amounts of CaCl2, respectively 1, 2, 3 and 4 mmol/L were used, considering the working methodology presented in this article. The presence of the amount of contaminant in water was determined using the EEMS method using the FP-8300 Spectrophotometer, after which a spectral analysis was performed. TableCurve 3D software was used to make the mathematical models in order to ensure that the equations obtained had the same shape. The values of the correlation coefficients, corresponding to the generated equations, have values ranging from 0.91 to 0.93. In order to verify the mathematical models thus obtained, graphs of the difference between the surface obtained with the help of the mathematical models and the surface obtained by means of real data were drawn. In conclusion, it turns out that, the largest difference was obtained in the case of samples taken from the feed, with a maximum difference of 31 fluorescence intensity arbitrary units (a.u.), and for the samples taken from the permeate the deference is 14 fluorescence intensity a.u