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In the setting of the Stochastic Frontier Production Models, the productive efficiency of the 28 countries belonging to the European Union is analysed. To this end, panel data encompassing a broad period of time is selected, which facilitates the study into whether there is greater efficiency in the years of crisis as a consequence of the adjustment measures. A translog specification of a Cobb-Douglas model is considered, in which the output is measured through the GDP of the countries and two productive factors (capital and labour). The model also includes a trend component that addresses the possible presence of technological change, and dummy variables for each country in order to separate unobserved heterogeneity from productive inefficiency. In relation to the perturbation that models the inefficiency, a model of the type Battese and Coelli (1995) is considered with a trend component and a variable related to economic growth. Finally, the growth of productivity is decomposed into the sum of the changes in technology, in economies of scale, and in inefficiency.

A regression model with deterministic frontier is considered. This type of model has hardly been studied, partly owing to the difficulty in the application of maximum likelihood estimation since this is a non-regular model. As an alternative, the Bayesian methodology is proposed and analysed. Through the Gibbs algorithm, the inference of the parameters of the model and of the individual efficiencies are relatively straightforward. The results of the simulations indicate that the utilized method performs reasonably well.

En este trabajo nos situamos en una perspectiva sociocultural para abordar los cambios que se manifiestan en el discurso matemático de los estudiantes cuando tratan de definir un objeto matemático. En particular, nos planteamos si es posible caracterizar el procedimiento de cambio apoyándonos en herramientas provenientes de dicha perspectiva. Los participantes fueron 51 estudiantes de edades comprendidas entre 16 y 21 años. El análisis realizado nos permitió identificar diferentes cambios en el discurso matemático de los estudiantes, a partir de la caracterización de las relaciones identificadas entre narrativas asumidas y rutinas que se han puesto de manifiesto en el discurso. Estos cambios nos han permitido aproximarnos al proceso de aprendizaje de los estudiantes. On this work, we focus on a sociocultural perspective in order to set forth the changes that are manifested in the students’ mathematical discourse when they try to define a mathematical object. We mainly establish whether it is possible to characterize the process of changing by using the tools as a result of the perspective described above. There were fiftyone participants, students between the ages of 16 and 21. This analysis allowed us to identify different changes on the students’ mathematical discourse by the characterization of the identified relationships between their narrative and their routines manifested in the discourse. These changes have allowed us to get an approximate of the students’ learning process.

Influences of the factors, reaction time, temperature, nitric acid concentration and nitric acid/coal ratio were studied by factorial analysis in relation to the response in the total, hydrolysable and available nitrogen contents of the nitrohumic acids obtained when two Spanish lignites were treated with nitric acid. Correlations between the hydrolysable and the available nitrogen, and the optical properties of the nitrohumic acids have been studied to obtain a more simple and rapid index to determine the available nitrogen of the nitro-lignites.

The humic acids, HA, extracted from a Spanish lignite and the nitrohumic acids, NHA, and nitrofulvic acids, NFA, extracted from the same lignite after its nitration, are hydrolysed with 6N HCI under reflux. The α-amino acids present in the hydrolysates are determined and thirteen α-amino acids are identified. The amounts of nitrogen in the amino-acids released by the hydrolysis increase according to the sequence: NFA > NHA > HA .

A statistically designed experiment was carried out to determine the influence of ionic strength (μ), calcium concentration [Ca], humic acid concentration [HA], phosphorus concentration [P]and pH in fixation of phosphorus by humic acids from a Spanish lignite. The results obtained indicate that fixation increases with increases of pH and [P]and decreases with increases in μ, [Ca]and [HA].

Potentiometric titrations in dimethylformamide and dimethylsulphoxide have been performed in order to differentiate between the acidic groups of fulvic acids. With dimethylformamide as medium the best results have been obtained with potassium hydroxide as titrant, whereas both potassium hydroxide and tetrabutylammonium hydroxide yield good titrations in dimethylsulphoxide. The number of acidic groups differentiated depended on the solvent and titrant used; in the best case four sharp end-points were obtained. Titrations with potassium hydroxide are preferred.