Symmetries of the free Schrödinger equation in the non-commutative plane

We study all the symmetries of the free Schr odinger equation in the non-commu- tative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schröodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.

Symmetries of the free Schrödinger equation in the non-commutative plane

We study all the symmetries of the free Schrödinger equation in the non-commu- tative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schröodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.

The Mont Collon mafic complex (Austroalpine Dent Blanche nappe) : permian evolution of the Western European mantle

Résumé: Le complexe du Mont Collon (nappe de la Dent Blanche, Austroalpin) est l'un des exemples les mieux préservés du magmatisme mafique permien des Alpes occidentales. Il est composé d'affleurements discontinus et d'une stratification magmatique en son centre (Dents de Bertol) et est composé à 95% de roches mafiques cumulatives (gabbros à olivine et/ou cpx, anorthositiques, troctolites, wehrlites et wehrlites à plagioclase) et localement de quelques gabbros pegmatitiques. Ces faciès sont recoupés par de nombreux filons acides (aphtes, pegmatites quartziques, microgranodiorites et filons anorthositiques) et mafiques tardifs (dikes mélanocrates riches en Fe et Ti). Les calculs thermométriques (équilibre olivine-augite) montrent des températures de 1070-1120 ± 6°C, tandis que le thermomètre amphibole-plagioclase indique une température de 740 ± 40°C à 0.5 GPa pour les amphiboles magmatiques tardives. La geobarométrie sur pyroxène donne des pressions moyennes de 0.3-0.6 GPa, indiquant un emplacement dans la croûte moyenne. De plus, les températures obtenues sur des amphiboles coronitiques indiquent des températures de l'ordre de 700 ± 40°C confirmant que les réactions coronitiques apparaissent dans des conditions subsolidus. Les âges concordants U/Pb sur zircons de 284.2 ± 0.6 et 282.9 ± 0.6 Ma obtenus sur un gabbro pegmatitique et une pegmatitique quartzique, sont interprétés comme des âges de cristallisation. Les datations 40Ar/39Ar sur amphiboles des filons mélanocrates donnent un âge plateau de 260.2 ± 0.7 Ma, qui est probablement très proche de l'âge de cristallisation. Ainsi, cet age 40Ar/39Ar indique un second évènement magmatique au sein du complexe. Les compositions des roches totales en éléments majeurs et traces montrent peu de variations, ainsi que le Mg# (75-80). Les éléments traces enregistrent le caractère cumulatif des roches (anomalie positive en Eu) et révèlent des anomalies négatives systématiques en Nb, Ta, Zr, Hf et Ti dans les faciès basiques. Le manque de corrélation entre éléments majeurs et traces est caractéristique d'un processus de cristallisation in situ impliquant une quantité variable de liquide interstitiel (L) entre les phases cumulus. Les distributions des éléments traces dans les minéraux sont homogènes, indiquant une rééquilibration .subsolidus entre cristaux et liquide interstitiel. Un modèle quantitatif basé sur les équations de cristallisation in situ de Langmuir reproduisent correctement les concentrations en terres rares légères des minéraux cumulatifs montrant la présence de 0 à 35% de liquide interstitiel L pour des degrés de différenciation F de 0 à 45%, par rapport au faciès les moins évolués du complexe. En outre, les valeurs de L sont bien corrélées avec les proportions modales d'amphibole interstitielle et les concentrations en éléments incompatibles des roches (Zr, Nb). Le liquide parental calculé des cumulats du Mont Collon est caractérisé par un enrichissement relatif en terres rares légères et Th, un appauvrissement en terres rares lourdes typique d'une affinité transitionnelle (T-MORB) et une forte anomalie négative en Nb-Ta. Les roches cumulatives montrent des compositions isotopiques en Nd-Sr proches de la terre globale silicatée (BSE), soit 0.6<εNdi<+3.2, 0.7045<87Sr/86Sri<0.7056. Les rapports initiaux en Pb indiquent une source dans le manteau enrichi subcontinental lithosphérique, préalablement contaminé par des sédiments océaniques. Les dikes mélanocrates Fe-Ti sont représentatifs de liquides et ont des spectres de terres rares enrichis, une anomalie positive en Nb-Ta et des εNdi de +7, des 87Sr/86Sri de 0.703 et des rapports initiaux en Pb, similaires à ceux des basaltes d'île océanique, indiquant une source asthénosphérique modérément appauvrie. Ainsi, la fusion partielle du manteau lithosphérique subcontinental est induite par l'amincissement post-orogénique et la remontée de l'asthénosphère. Les filons mélanocrates proviennent, après délamination du manteau lithosphérique, de la fusion de l'asthénosphère. Abstract The early Permian Mont Collon mafic complex (Dent Blanche nappe, Austroalpine nappe system) is one of the best preserved examples of the Permian mafic magmatism in the Western Alps. It is composed of discontinuous exposures and a well-preserved magmatic layering (the Dents de Bertol cliff) crops out in the center part of the complex. It mainly consists of cumulative mafic rocks, which represent 95 vol-% of the mafic complex (ol- and cpx-bearing gabbros and rare anorthositic layers, troctolites, wehrlites and plagioclase-wehrlites) and locally pegmatitic gabbros. All these facies are crosscut by widespread acidic (aplites, quartz-rich pegmatites, microgranodiorites) and late mafic Fe-Ti melanocratic dikes. Olivine-augite thermometric calculations yield a range of 1070-1120 ± 6°C, while amphibole-plagioclase thermometer yields a temperature of 740 ± 40°C at 0.5 GPa. Pyroxene geobarometry points to a pressure of 0.3-0.6 GPa, indicating a middle crustal level of emplacement. Moreover, temperature calculations on the Mont Conon coronitic amphiboles indicate temperatures of 700 ± 40°C, close to those calculated for magmatic amphiboles. These temperatures confirm that coronitic reactions occurred at subsolidus conditions. ID-TIMS U/Pb zircon ages of 284.2 ± 0.6 and 282.9 ± 0.6 Ma obtained on a pegmatitic gabbro and a quartz-pegmatitic dike, respectively, were interpreted as the crystallization ages of these rocks. 40Ar/39Ar dating on amphiboles from Fe-Ti melanocratic dikes yields a plateau age of 260.2 ± 0.7 Ma, which is probably very close to the crystallization age. Consequently, this 40Ar/P39Ar age indicates a second magmatic event. Whole-rock major- and trace-element compositions show little variation across the whole intrusion and Mg-number stays within a narrow range (75-80). Trace-element concentrations record the cumulative nature of the rocks (e.g. positive Eu anomaly) and reveal systematic Nb, Ta, Zr, Hf and Ti negative anomalies for all basic facies. The lack of correlation between major and trace elements is characteristic of an in situ crystallization process involving variable amounts of interstitial liquid (L) trapped between the cumulus mineral phases. LA-ICPMS measurements show that trace-element distributions in minerals are homogeneous, pointing to subsolidus re-equilibration between crystals and interstitial melts. A quantitative modeling based on Langmuir's in situ crystallization equation successfully reproduced the Rare Earth Element (REE) concentrations in cumulitic minerals. The calculated amounts of interstitial liquid L vary between 0 and 35% for degrees of differentiation F of 0 to 45%, relative to the least evolved facies of the intrusion. Furthermore, L values are well correlated with the modal proportions of interstitial amphibole and whole-rock incompatible trace-element concentrations (e.g. Zr, Nb) of the tested samples. The calculated parental melt of the Mont Collon cumulates is characterized by a relative enrichment in Light REE and Th, a depletion in Heavy REE, typical of a transitional affinity (T-MORB), and strong negative Nb-Ta anomaly. Cumulative rocks display Nd-Sr isotopic compositions close to the BSE (-0.6 < εNdi < +3.2, 0.7045 < 87Sr/86Sri < 0.7056). Initial Pb ratios point to an origin from the melting of an enriched subcontinental lithospheric mantle source, previously contaminated at the source by oceanic sediments. The contrasted alkaline Fe-Ti melanocratic dikes are representative of liquids. They display enriched fractionated REE patterns, a positive Nb-Ta anomaly and εNdi of +7, 87Sr/86Sri of 0.703 and initial Pb ratios, all reminiscent of Ocean Island Basalt-type rocks, pointing to a moderately

Increased risk of cardiovascular disease (CVD) with age in HIV-positive men : a comparison of the D:A:D CVD risk equation and general population CVD risk equations

OBJECTIVES: The aim of the study was to statistically model the relative increased risk of cardiovascular disease (CVD) per year older in Data collection on Adverse events of anti-HIV Drugs (D:A:D) and to compare this with the relative increased risk of CVD per year older in general population risk equations. METHODS: We analysed three endpoints: myocardial infarction (MI), coronary heart disease (CHD: MI or invasive coronary procedure) and CVD (CHD or stroke). We fitted a number of parametric age effects, adjusting for known risk factors and antiretroviral therapy (ART) use. The best-fitting age effect was determined using the Akaike information criterion. We compared the ageing effect from D:A:D with that from the general population risk equations: the Framingham Heart Study, CUORE and ASSIGN risk scores. RESULTS: A total of 24 323 men were included in analyses. Crude MI, CHD and CVD event rates per 1000 person-years increased from 2.29, 3.11 and 3.65 in those aged 40-45 years to 6.53, 11.91 and 15.89 in those aged 60-65 years, respectively. The best-fitting models included inverse age for MI and age + age(2) for CHD and CVD. In D:A:D there was a slowly accelerating increased risk of CHD and CVD per year older, which appeared to be only modest yet was consistently raised compared with the risk in the general population. The relative risk of MI with age was not different between D:A:D and the general population. CONCLUSIONS: We found only limited evidence of accelerating increased risk of CVD with age in D:A:D compared with the general population. The absolute risk of CVD associated with HIV infection remains uncertain.

Local thermodynamics and the generalized Gibbs-Duhem equation in systems with long-range interactions

The local thermodynamics of a system with long-range interactions in d dimensions is studied using the mean-field approximation. Long-range interactions are introduced through pair interaction potentials that decay as a power law in the interparticle distance. We compute the local entropy, Helmholtz free energy, and grand potential per particle in the microcanonical, canonical, and grand canonical ensembles, respectively. From the local entropy per particle we obtain the local equation of state of the system by using the condition of local thermodynamic equilibrium. This local equation of state has the form of the ideal gas equation of state, but with the density depending on the potential characterizing long-range interactions. By volume integration of the relation between the different thermodynamic potentials at the local level, we find the corresponding equation satisfied by the potentials at the global level. It is shown that the potential energy enters as a thermodynamic variable that modifies the global thermodynamic potentials. As a result, we find a generalized Gibbs-Duhem equation that relates the potential energy to the temperature, pressure, and chemical potential. For the marginal case where the power of the decaying interaction potential is equal to the dimension of the space, the usual Gibbs-Duhem equation is recovered. As examples of the application of this equation, we consider spatially uniform interaction potentials and the self-gravitating gas. We also point out a close relationship with the thermodynamics of small systems.

Effective Electrodiffusion equation for non uniform nanochannels

We derive a one dimensional formulation of the Planck-Nernst-Poisson equation to describe the dynamics of of a symmetric binary electrolyte in channels whose section is of nanometric section and varies along the axial direction. The approach is in the spirit of the Fick-Jacobs di fusion equation and leads to a system of coupled equations for the partial densities which depends on the charge sitting at the walls in a non trivial fashion. We consider two kinds of non uniformities, those due to the spatial variation of charge distribution and those due to the shape variation of the pore and report one and three-dimensional solutions of the electrokinetic equations.

Gas-phase photocatalytic oxidation of volatile organic compounds

Substances emitted into the atmosphere by human activities in urban and industrial areas cause environmental problems such as air quality degradation, respiratory diseases, climate change, global warming, and stratospheric ozone depletion. Volatile organic compounds (VOCs) are major air pollutants, emitted largely by industry, transportation and households. Many VOCs are toxic, and some are considered to be carcinogenic, mutagenic, or teratogenic. A wide spectrum of VOCs is readily oxidized photocatalytically. Photocatalytic oxidation (PCO) over titanium dioxide may present a potential alternative to air treatment strategies currently in use, such as adsorption and thermal treatment, due to its advantageous activity under ambient conditions, although higher but still mild temperatures may also be applied. The objective of the present research was to disclose routes of chemical reactions, estimate the kinetics and the sensitivity of gas-phase PCO to reaction conditions in respect of air pollutants containing heteroatoms in their molecules. Deactivation of the photocatalyst and restoration of its activity was also taken under consideration to assess the practical possibility of the application of PCO to the treatment of air polluted with VOCs. UV-irradiated titanium dioxide was selected as a photocatalyst for its chemical inertness, non-toxic character and low cost. In the present work Degussa P25 TiO2 photocatalyst was mostly used. In transient studies platinized TiO2 was also studied. The experimental research into PCO of following VOCs was undertaken: - methyl tert-butyl ether (MTBE) as the basic oxygenated motor fuel additive and, thus, a major non-biodegradable pollutant of groundwater; - tert-butyl alcohol (TBA) as the primary product of MTBE hydrolysis and PCO; - ethyl mercaptan (ethanethiol) as one of the reduced sulphur pungent air pollutants in the pulp-and-paper industry; - methylamine (MA) and dimethylamine (DMA) as the amino compounds often emitted by various industries. The PCO of VOCs was studied using a continuous-flow mode. The PCO of MTBE and TBA was also studied by transient mode, in which carbon dioxide, water, and acetone were identified as the main gas-phase products. The volatile products of thermal catalytic oxidation (TCO) of MTBE included 2-methyl-1-propene (2-MP), carbon monoxide, carbon dioxide and water; TBA decomposed to 2-MP and water. Continuous PCO of 4 TBA proceeded faster in humid air than dry air. MTBE oxidation, however, was less sensitive to humidity. The TiO2 catalyst was stable during continuous PCO of MTBE and TBA above 373 K, but gradually lost activity below 373 K; the catalyst could be regenerated by UV irradiation in the absence of gas-phase VOCs. Sulphur dioxide, carbon monoxide, carbon dioxide and water were identified as ultimate products of PCO of ethanethiol. Acetic acid was identified as a photocatalytic oxidation by-product. The limits of ethanethiol concentration and temperature, at which the reactor performance was stable for indefinite time, were established. The apparent reaction kinetics appeared to be independent of the reaction temperature within the studied limits, 373 to 453 K. The catalyst was completely and irreversibly deactivated with ethanethiol TCO. Volatile PCO products of MA included ammonia, nitrogen dioxide, nitrous oxide, carbon dioxide and water. Formamide was observed among DMA PCO products together with others similar to the ones of MA. TCO for both substances resulted in the formation of ammonia, hydrogen cyanide, carbon monoxide, carbon dioxide and water. No deactivation of the photocatalyst during the multiple long-run experiments was observed at the concentrations and temperatures used in the study. PCO of MA was also studied in the aqueous phase. Maximum efficiency was achieved in an alkaline media, where MA exhibited high fugitivity. Two mechanisms of aqueous PCO – decomposition to formate and ammonia, and oxidation of organic nitrogen directly to nitrite - lead ultimately to carbon dioxide, water, ammonia and nitrate: formate and nitrite were observed as intermediates. A part of the ammonia formed in the reaction was oxidized to nitrite and nitrate. This finding helped in better understanding of the gasphase PCO pathways. The PCO kinetic data for VOCs fitted well to the monomolecular Langmuir- Hinshelwood (L-H) model, whereas TCO kinetic behaviour matched the first order process for volatile amines and the L-H model for others. It should be noted that both LH and the first order equations were only the data fit, not the real description of the reaction kinetics. The dependence of the kinetic constants on temperature was established in the form of an Arrhenius equation.

When Langmuir is too simple: H2 dissociation on Pd(111) at high coverage

Recent experiments of H2 adsorption on Pd(111) [T. Mitsui et al., Nature (London) 422, 705 (2003)] have questioned the classical Langmuir picture of second order adsorption kinetics at high surface coverage requiring pairs of empty sites for the dissociative chemisorption. Experiments find that at least three empty sites are needed. Through density functional theory, we find that H2 dissociation is favored on ensembles of sites that involve a Pd atom with no direct interaction with adsorbed hydrogen. Such active sites are formed by aggregation of at least 3 H-free sites revealing the complex structure of the "active sites."

Adsorção de íons Cu2+ em latossolo vermelho-amarelo húmico

In environmental studies it is necessary to know the adsorption behavior of metals by soils, since the unfavorable effects of heavy metals and even the micronutrients at high concentrations in the environment are related to these adsorbents' ability to immobilize them. A sample of a humic yellow red oxisol from Araponga region in the State of Minas Gerais, Brazil, was used to verify the adsorption behavior of Cu2+ ions in this substrate. The mathematical model described by Langmuir's adsorption equation in its linearized form was applied and the values of the maximum capacity b and those of the constant related to the bonding energy a were obtained. Aliquots of copper nitrate solutions containing several concentrations of this metal were added to soil samples, the pH being predetermined for developing the adsorption experiments. The chemical and physical characterization of soil sample were performed by determining the organic carbon, nitrogen and phosphorus concentrations, cation exchange capacity (CEC), pH, concentration of metals (Al, Fe, K, Mg, Ca, Zn, Cu, Ni, Cr, Co, Pb, and Cd), granulometric analysis and X-ray diffraction. Langmuir isotherms presented two distinct adsorption regions at both pH 4 and pH 5, showing that the adsorptive phenomenon occurs in two distinct stages. The adsorption sites for the lower part presented greater bonding energy and low adsorption capacity compared with the adsorption sites of the part of the curve corresponding to higher Cu concentrations in the equilibrating solution.

Irving langmuir: o milagre da ciência

Irving Langmuir received the Nobel Prize in Chemistry in 1932 "...for his outstanding discoveries and investigations within the field of surface chemistry", according to the Swedish Academy. However, few people know that his work comprises other very important contributions, and not only for chemistry, such as the discovery of plasma, the atomic hydrogen, the pure thermoionic phenomenon, the development of the cloud seeding technique for weather modification, among many others. This paper summarizes Langmuir's most important discoveries and theories, with an especial mention for his practical inventions and his work on the atomic theory.

Técnicas de caracterização para investigar interações no nível molecular em filmes de Langmuir e Langmuir-Blodgett (LB)

This paper discusses fundamental concepts for the characterization of Langmuir monolayers and Langmuir-Blodgett (LB) films, with emphasis on investigations of material properties at the molecular level. By way of illustration, results for phospholipid monolayers interacting with the drug dipyridamole are highlighted. These results were obtained with several techniques, including in situ grazing incidence X-ray diffraction, Fourier transform infrared (FTIR) spectroscopy, fluorescence microscopy, in addition to surface pressure and surface potential isotherms. Also mentioned are the difficulties in producing Langmuir and LB films from macromolecules, and how molecular-level interactions in mixed polymer LB films can be exploited in sensors.

Predicting overall service quality: a structural equation modelling approach

In this article, the results of a modified SERVQUAL questionnaire (Parasuraman et al., 1991) are reported. The modifications consisted in substituting questionnaire items particularly suited to a specific service (banking) and context (county of Girona, Spain) for the original rather general and abstract items. These modifications led to more interpretable factors which accounted for a higher percentage of item variance. The data were submitted to various structural equation models which made it possible to conclude that the questionnaire contains items with a high measurement quality with respect to five identified dimensions of service quality which differ from those specified by Parasuraman et al. And are specific to the banking service. The two dimensions relating to the behaviour of employees have the greatest predictive power on overall quality and satisfaction ratings, which enables managers to use a low-cost reduced version of the questionnaire to monitor quality on a regular basis. It was also found that satisfaction and overall quality were perfectly correlated thus showing that customers do not perceive these concepts as being distinct

Adsorção de arsênio(V) pela quitosana ferro - III reticulada

The removal of As(V) by a crosslinked iron(III)-chitosan adsorbent was evaluated under various conditions. The adsorption capacity of CH-FeCL was around 54 mg/g of As(V). The kinetics of adsorption obeys a pseudo-first-order model with rate constants equal to 0.022, 0.028, and 0.033 min-1 at 15, 25 and 35 ºC respectively. Adsorption data were well described by the Langmuir model, although they could be modeled also by the Langmuir-Freundlich equation. The maximum adsorption capacity, calculated with the Langmuir model, was 127 mg g-1 of As(V). The inhibition by competing anions is dependant on their kind and valence.

Remoção de azul de metileno de solução aquosa usando zeólitas sintetizadas com amostras de cinzas de carvão diferentes

Batch sorption experiments were carried out to remove methylene blue from its aqueous solutions using zeolites synthesized from fly ashes as an adsorbent. The adsorbents were characterized by XFR, XRD and SEM. Nearly 90 min of contact time are found to be sufficient for the adsorption of dye to reach equilibrium. Equilibrium data have been analyzed using Langmuir and Freundlich isotherms and the results were found to be well represented by the Freundlich isotherm equation. Adsorption data were fitted to both Lagergren first-order and pseudo-second-order kinetic models and the data were found to follow pseudo-second-order kinetics.