On Some Classical Methods to Improve Algebraic Curves and Surfaces

First, a modern presentation of the theory of the Halphen transform is given. This method associates to a plane projective curve C, once a general conic has been chosen, another birationally equivalent plane curve, whose singularities are simpler than those of C. Repeating, a curve is obtained whose only singularities are nodes. Next, it is studied how to apply this process to a family of plane curves. With this technique it is possible to transform a given family (with irreducible general member) into one where, generically, the curves are nodal. Finally, it is studied a similar process, called the Halphen–Picard transformation, for surfaces in three-space. By suitably reiterating this procedure, a surface can be transformed into a birationally equivalent one (in the same projective space), such that the sections with planes in a general pencil are, generically, nodal curves.     

Bestimmung des specifischen Gewichtes

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Optimal Production of a <Emphasis Type="Italic">Rhodococcus erythropolis</Emphasis> ATCC 4277 Biocatalyst for Biodesulfurization and Biodenitrogenation Applications

Rhodococcus sp. has a broad catabolic diversity and unique enzymatic capabilities, and it is able to adapt under extreme conditions. Thereby, the production of this remarkable bacterium has a great biotechnological and industrial importance. In this sense, we sought to improve the R. erythropolis ATCC 4277 growth through a central composite design, by varying the components of nutrient medium (glucose, malt extract, yeast extract, CaCO₃), temperature, and agitation. It was found that the concentrations of glucose and malt extract are not statistically significant, being reduced of 4.0 and 10.0 g L^-1 to 2.0 and 5.0 g L^?1, respectively. The CaCO₃ concentration and temperature were also diminished of 2.0 to 1.16 g L^?1and 28 to 23.7 °C, respectively. Optimal growth conditions provided a 240% increase in final biomass concentration, an increment in specific growth rate, and a growth yield coefficient about five times greater. Application of the optimal conditions in biodesulfurization and biodenitrogenation processes showed that desulfurization capability is not associated with optimal growth conditions; however, it was achieved a 47% of nitrogen removal in the assay containing 10% (w/w) of heavy gas oil.

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Metastable flow in capillary tubes: An experimental evaluation

This work presents the results of an experimental study with pure refrigerants R-134a and R-600a and refrigerant–oil mixtures flowing through capillary tubes in order to analyse the metastable flow. A large number of experiments were carried out to verify the influence of several variables on the underpressure of vaporization, mainly the inlet subcooling, internal diameter and inlet pressure. Capillary tubes with internal diameter of 0.69 mm and 0.82 mm were tested for condensation temperatures between 40 °C and 50 °C and subcooling degrees between 3 °C and 12 °C. Measurements for oil concentrations of 1% and 3% were conducted and compared with those for pure refrigerant R-134a. The oil influence on the metastable flow was tested and the effect on the underpressure of vaporization is addressed for lower oil concentrations.     

Preparation of the Ca–diclofenac complex in solid state

Two ONNO type naphtaldehyde derivative Schiff base compounds were reduced and two symmetric phenol-amine ligands containing naphthalene groups were obtained; bis-N,N′[(2-hydroxy-1-naphtyl) methyl]-1,3-propanediamine (NAFL^H) and bis-N,N′[(2-hydroxy-1-naphtyl) methyl]-2,2′-dimetyhyl-1,3-propanediamine (NAFLDM^H). Homotrinuclear Ni(II) complexes of these ligands were prepared. The solid-state molecular structures of representative nickel complex of NAFLDM^H were determined using single crystal X-ray diffraction analysis. The terminal Ni(II) ions were found to be situated in between the donor atoms of the organic ligand. The central Ni(II) ion was observed to be bonded via two different μ-bridges. The phenolic oxygens and carboxylate ion were seen to form two different μ-bridges. TG analysis proved that the compounds have different thermal characteristics than those cited in literature. The complexes showed extreme exothermic degradation reactions in inert atmosphere. The complexes are ruptured with a two stepped exothermic reaction which appears huge heat over 300 °C. The heat appeared in O₂ atmosphere is observed to be higher than the heat appeared in inert atmosphere. Revealed heat is observed to be higher than the conventional explosive materials.     

Density functional theory and RRKM calculations of decompositions of the metastable E‐2,4‐pentadienal molecular ions

The potential energy profiles for the fragmentations that lead to [C₅H₅O]⁺ and [C₄H₆]^+? ions from the molecular ions [C₅H₆O]^+? of E‐2,4‐pentadienal were obtained from calculations at the UB3LYP/6‐311G + + (3df,3pd)//UB3LYP/6‐31G(d,p) level of theory. Kinetic barriers and harmonic frequencies obtained by the density functional method were then employed in Rice–Ramsperger–Kassel–Marcus calculations of individual rate coefficients for a large number of reaction steps. The pre‐equilibrium and rate‐controlling step approximations were applied to different regions of the complex potential energy surface, allowing the overall rate of decomposition to be calculated and discriminated between three rival pathways: C? H bond cleavage, decarbonylation and cyclization. These processes should have to compete for an equilibrated mixture of four conformers of the E‐2,4‐pentadienal ions. The direct dissociation, however, can only become important in the high‐energy regime. In contrast, loss of CO and cyclization are observable processes in the metastable kinetic window. The former involves a slow 1,2‐hydrogen shift from the carbonyl group that is immediately followed by the formation of an ion‐neutral complex which, in turn, decomposes rapidly to the s‐trans‐1,3‐butadiene ion [C₄H₆]^+?. The predominating metastable channel is the second one, that is, a multi‐step ring closure which starts with a rate‐limiting cis—trans isomerization. This process yields a mixture of interconverting pyran ions that dissociates to the pyrylium ions [C₅H₅O]⁺. These results can be used to rationalize the CID mass spectrum of E‐2,4‐pentadienal in a low‐energy regime. Copyright © 2010 John Wiley & Sons, Ltd.     

Measuring technique for thermal ionisation mass spectrometry of human tracer kinetic study with stable cerium isotopes

Thermal ionisation mass spectrometry (TIMS) method has been developed for the simultaneous detection of different cerium isotopes in biological samples (i.e., blood and urine) at very low concentrations. The work has been done in the frame of a biokinetic study, where different stable cerium isotopes have been administered orally and intravenously as tracers to the human body. In order to develop an appropriate detection method for the tracers in the biological samples, an optimum sample preparation technique has been set and adapted to the specific requirements of the analysis technique used, i.e., TIMS. For sample evaporation and ionisation, the double tantalum filament technique showed the best results. The ions produced were simultaneously collected on a secondary electron multiplier so that the isotopic ratios of the cerium isotopes in the biological samples could be measured. The technique has been optimised for the determination of cerium down to 1?ng loaded on the evaporation filament corresponding to cerium concentrations of down to 1?ng?ml(-1) in the blood or urine samples. It has been shown that the technique is reliable in application and enables studies on cerium metabolism and biokinetics in humans without employing radioactive tracers.     

Stability of benzoporphyrin photosensitizers in water/ethanol mixtures: pKa determination and self‐aggregation processes

Benzoporphyrin monoacid derivatives, here named B3A and B3B, are promising new drugs for photodynamic therapy. Although both isomers show interesting characteristics as photosensitizing compounds, they have some distinct physicochemical properties such as the tendency to self‐aggregate in water‐rich media. Because pH drives the presence of each species, the pK_a of these compounds assumes strategic importance. However, traditional micro‐titration methods and UV–Vis absorption techniques fail to give reliable pK_a values due to the characteristics of this highly complex system, such as the precipitation of hydrophobic species, close pK_a values, and high absorption band superposition. In the present work, chemometric tools are employed to evaluate pK_a, and the kinetic tendency of monomers to undergo self‐aggregation is investigated. In solvent mixtures at low water percentage in ethanol, both B3A and B3B are stabilized in a monomeric state. However, in mixtures with a high water content, self‐aggregation takes place, mainly under a mild pH acid condition (3 < pH < 6), in which the prevalent protolytic species of both isomers is the neutral charged form, compounds with carboxylic and porphyrin free‐base groups. It is demonstrated that both isomers can undergo aggregation following a self‐catalytic mechanism, which is 2000 times slower to B3A than B3B. For B3A, the aggregation is manifested by a decrease in the monomer band with the aggregation band probably superposed to that of the monomer. For B3B, together with the decrease in the monomer band, a new band related to self‐aggregates is observed. Copyright © 2010 John Wiley & Sons, Ltd.     

Computing with multi-row Gomory cuts

Recent advances on the understanding of valid inequalities from the infinite group relaxation has opened the possibility of finding a computationally effective extension to GMI cuts. In this paper, we investigate the computational impact of using a subclass of minimally valid inequalities from this relaxation on a wide set of instances.     

Arithmetic families of smooth surfaces and equisingularity of embedded schemes

This article deals with the foundations of a theory of equisingularity for families of zero-dimensional sheaves of ideals on smooth algebraic surfaces, in the arithmetic context, i.e., where one works with schemes defined over Dedekind rings. Here, different equisingularity conditions are analyzed and compared, based on one of the following requirements: 1) each member of the the family has the same desingularization tree, 2) the family admits a simultaneous desingularization, 3) a naturally associated family of curves is equisingular. Similar conditions had been investigated, in the context of Complex Local Analytic Geometry, by J. J. Risler. Received: 17 November 1997 / Revised version: 19 April 1999