An algebra $A$ over a field $\K$ is said to be \textit{invertible} if it has a basis $\B$ consisting only of of units; if $\B^{-1}$ is again a basis, $A$ is \textit{invertible-2}, or \textit{I2}. The question of when an invertible algebra is necessarily I2 arises naturally. The study of these algebras was recently initiated by Lòpez-Permouth, Moore, Szabo, Pilewski \cite{lopezIJM}, \cite{lopez1}. In this work, we prove several positive results on this problem, answering also some questions and generalizing a few results from these papers. We show that every field is an I2 algebra over any subfield, and that any subalgebra of the rational functions field $K(x)$ that strictly contains $K[x]$, with $K$ an algebraically closed field, has a symmetric basis $\B=\B^{-1}$. Using this, we expand the class of examples of algebras known to be invertible or I2 with several classes, such as semiprimary rings over fields $K\neq \F_2$ satisfying some additional mild conditions. We also show that every commutative, finitely generated, invertible algebra without zero divisors is almost I2 in the sense that it becomes I2 after localization at a single element.

This paper develops a model in which it is possible to evaluate alternatives of higher education financing. The alternative systems under discussion are: total fecing, graduates' taxes and uniform taxes (this can be associated to the scheme presently used in the Argentina to finance the universities). Assessment of the alternatives is performed over welfare, based on the indicators of poverty, equality, and the average levels of utility and wealth. Likewise, the functions of welfare presented by Bentham, Rawls, Atkinson, Sen and Kakwani are also considered. The most remarkable results are obtained through the simulation of an economy under two scenarios. In that way, the system of graduates' taxation is found to be better for welfare; whereas the system of uniform taxation only can be justified as it maximizes the number of students.

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Species must interact with air—aqueous interfaces in order to transport between either phase, however organic coated water surfaces are ubiquitous in the environment, and the physical and chemical processes that occur at organic coated aqueous surfaces are often different than those at pure air—water interfaces. Three studies were performed investigating the transport of species across air—aqueous interfaces with organic coatings in an effort to gain further insight into these processes. Gas and solution phase absorption spectroscopy were used to study the effect of octanol coatings on the formation of molecular iodine (I2) by the heterogeneous ozonation of iodide and its partitioning between phases. Compared to uncoated solutions, the presence of octanol monolayers had a minor effect on the total amount of I2 produced, however, it did significantly enhance the gas to solution partitioning of I2. Incoherent broadband cavity-enhanced absorption spectroscopy (IBBC-EAS) was used to measure the gas-phase nitrogen dioxide (NO2) evolved via photolysis of aqueous nitrate solutions either uncoated or containing octanol, octanoic acid and stearic acid monolayers. Both octanol and stearic acid reduced the rate of gaseous NO2 evolution, and octanol also decreased the steady-state amount of gaseous NO2. Alternatively, octanoic acid enhanced the rate of gaseous NO2 evolution. Finally, the loss of aqueous carbon dioxide (CO2) from aqueous solutions saturated with CO2 was measured using a CO2 electrode in the absence and presence of stearic acid monolayers and octanol coatings, and a greenhouse gas analyzer was used to measure the evolution of gaseous CO2 from solutios with octanol monolayers. Enhanced losses of aqueous and evolved gaseous CO2 were observed with organic coated solutions compared to those uncoated. The results of these studies suggest that organic coatings influence the transport of I2, NO2 and CO2 via one, or a combination of: barrier effects, surface tension effects, chemistry effects and aqueous – surface – gas partitioning effects. These results, particularly the enhanced partitioning of these species to octanol coated aqueous surfaces, have important implications for species transport at air—aqueous interfaces, and may provide useful insight for future studies and parameters for atmospheric models of these species.

Species must interact with air—aqueous interfaces in order to transport between either phase, however organic coated water surfaces are ubiquitous in the environment, and the physical and chemical processes that occur at organic coated aqueous surfaces are often different than those at pure air—water interfaces. Three studies were performed investigating the transport of species across air—aqueous interfaces with organic coatings in an effort to gain further insight into these processes. Gas and solution phase absorption spectroscopy were used to study the effect of octanol coatings on the formation of molecular iodine (I2) by the heterogeneous ozonation of iodide and its partitioning between phases. Compared to uncoated solutions, the presence of octanol monolayers had a minor effect on the total amount of I2 produced, however, it did significantly enhance the gas to solution partitioning of I2. Incoherent broadband cavity-enhanced absorption spectroscopy (IBBC-EAS) was used to measure the gas-phase nitrogen dioxide (NO2) evolved via photolysis of aqueous nitrate solutions either uncoated or containing octanol, octanoic acid and stearic acid monolayers. Both octanol and stearic acid reduced the rate of gaseous NO2 evolution, and octanol also decreased the steady-state amount of gaseous NO2. Alternatively, octanoic acid enhanced the rate of gaseous NO2 evolution. Finally, the loss of aqueous carbon dioxide (CO2) from aqueous solutions saturated with CO2 was measured using a CO2 electrode in the absence and presence of stearic acid monolayers and octanol coatings, and a greenhouse gas analyzer was used to measure the evolution of gaseous CO2 from solutios with octanol monolayers. Enhanced losses of aqueous and evolved gaseous CO2 were observed with organic coated solutions compared to those uncoated. The results of these studies suggest that organic coatings influence the transport of I2, NO2 and CO2 via one, or a combination of: barrier effects, surface tension effects, chemistry effects and aqueous – surface – gas partitioning effects. These results, particularly the enhanced partitioning of these species to octanol coated aqueous surfaces, have important implications for species transport at air—aqueous interfaces, and may provide useful insight for future studies and parameters for atmospheric models of these species.

Esta dissertação de mestrado consiste de uma resenha crítica da teoria econômica da educação no que se refere à análise de sistemas educativos, e de um estudo empírico do desempenho do sistema educativo brasileiro, com ênfase em indicadores de iniqüidade. Procura-se apresentar a evolução e o estado atual do debate relacionados aos seguintes assuntos: demanda por educação, oferta de educação (insumos monetários e não-monetários), arranjo institucional do sistema educativo, arranjo institucional sócio-econômico (em que se insere o sistema educativo), e os produtos do sistema educativo. Por fim, por meio da análise estatística de uma base de dados internacional (PISA 2000), apresenta-se um estudo empírico que visa a avaliar o desempenho do sistema educativo brasileiro, especialmente seu grau de iniqüidade. / This MA dissertation thesis consists of a critical survey of the economics of education literature concerning educational system analysis, and of a study of the performance of the Brazilian educational system, with an emphasis in equity measurement. I discuss the evolution and the current state of the debate on the following subjects: demand for education, supply of education (monetary and non-monetary inputs), educational system institutional framework, socio-economic institutional framework (in which the educational system is imbedded), and the output of the educational system. Finally, by means of a statistical analysis of an international database (PISA 2000), I present an empirical study aiming at assessing the Brazilian educational system performance, especially its degree of inequity.

Esta dissertação de mestrado consiste de uma resenha crítica da teoria econômica da educação no que se refere à análise de sistemas educativos, e de um estudo empírico do desempenho do sistema educativo brasileiro, com ênfase em indicadores de iniqüidade. Procura-se apresentar a evolução e o estado atual do debate relacionados aos seguintes assuntos: demanda por educação, oferta de educação (insumos monetários e não-monetários), arranjo institucional do sistema educativo, arranjo institucional sócio-econômico (em que se insere o sistema educativo), e os produtos do sistema educativo. Por fim, por meio da análise estatística de uma base de dados internacional (PISA 2000), apresenta-se um estudo empírico que visa a avaliar o desempenho do sistema educativo brasileiro, especialmente seu grau de iniqüidade. / This MA dissertation thesis consists of a critical survey of the economics of education literature concerning educational system analysis, and of a study of the performance of the Brazilian educational system, with an emphasis in equity measurement. I discuss the evolution and the current state of the debate on the following subjects: demand for education, supply of education (monetary and non-monetary inputs), educational system institutional framework, socio-economic institutional framework (in which the educational system is imbedded), and the output of the educational system. Finally, by means of a statistical analysis of an international database (PISA 2000), I present an empirical study aiming at assessing the Brazilian educational system performance, especially its degree of inequity.