Complex Geometry and Dirac Equation

Complex geometry represents a fundamentalingredient in the formulation of the Dirac equation bythe Clifford algebra. The choice of appropriate complexgeometries is strictly related to the geometricinterpretation of the complex imaginary unit . We discuss two possibilities which appearin the multivector algebra approach: the₁₂₃ and ₂₁ complexgeometries. Our formalism provides a set of rules which allows an immediate translation between thecomplex standard Dirac theory and its version withingeometric algebra. The problem concerning a doublegeometric interpretation for the complex imaginary unit is also discussed.     

Optimization model for a production,inventory, distribution and routing problem in small furniture companies

Production and distribution are two key decisions in supply chain planning. In order to achieve an effective operational performance, it is important for these two decisions to be integrated, especially in supply chains with low inventory levels. In this paper, we propose a mixed integer programming model to integrate production, inventory, distribution and routing decisions in a single framework. The model was inspired by small Brazilian furniture companies and focuses on production and distribution decisions at an operational level. In particular, we consider a scenario in which only one production line and one vehicle, which makes multiple trips over the planning horizon, are available to produce items and deliver final products, respectively. We also take into account some features rarely considered in the literature, but commonly found in real-world applications, such as producing and stocking multiple items, distribution routes extending over one or more periods, multiple time windows and customers’ due dates. Computational tests on a set of randomly generated instances were carried out using a well-known optimization software and six relax-and-fix heuristics, which explore different criteria for partitioning and fixing variables. We also implemented two hybrid heuristics in which an initial solution is first constructed and then fed into the optimization software to improve it. The results showed that one relax-and-fix and the two hybrid heuristics performed better than the solver on the largest instances.     

A genetic algorithm with neural network fitness function evaluation for IMRT beam angle optimization

Intensity Modulated Radiotherapy Treatment (IMRT) is a technique used in the treatment of cancer, where the radiation beams are modulated by a multileaf collimator allowing the irradiation of the patient using non-uniform radiation fields from selected angles. Beam angle optimization consists in trying to find the best set of angles that should be used in IMRT planning. The choice of this set of angles is patient and pathology dependent and, in clinical practice, most of the times it is made using a trial and error procedure or simply using equidistantly distributed angles. In this paper we propose a genetic algorithm that aims at calculating good sets of angles in an automated way, given a predetermined number of angles. We consider the discretization of all possible angles in the interval [0 \(^{\circ }\) , 360 \(^{\circ }\) ], and each individual is represented by a chromosome with 360 binary genes. As the calculation of a given individual’s fitness is very expensive in terms of computational time, the genetic algorithm uses a neural network as a surrogate model to calculate the fitness of most of the individuals in the population. To explicitly consider the estimation error that can result from the use of this surrogate model, the fitness of each individual is represented by an interval of values and not by a single crisp value. The genetic algorithm is capable of finding improved solutions, when compared to the usual equidistant solution applied in clinical practice. The genetic algorithm will be described and computational results will be shown.     

Refratometric study of ternary mixtures formed by water,glucose and acetonitrile at temperatures ranging from 293 K to 333 K

The study of thermodynamic properties of solutions provides important information on existing molecular interactions between the components present in a solution. These studies are critical for testing, validation and development of theories and mathematical models. The refractometric study of a solution is a simple assessment that can contribute to the understanding of these interactions. In this context, the behaviour of the binary water and glucose mixture was studied as well as ternary mixtures of water, glucose and acetonitrile at five different temperatures in the range 293–333 K by the determination of the refractive index of the solution. Due to the weakening of the molecular interactions with the increasing of the temperature, a decreasing dependence of refractive index with temperature was observed. The addition of acetonitrile provides an increase in the refractive index indicating the formation of clusters in the solution.     

Electrochemical properties of Meldola's Blue immobilized on silica-titania phosphate prepared by the sol-gel method

The mixed oxide phosphate (≡SiO)₂Ti(O₃POH)₂ having a specific surface area of S_BET= 595 m² g⁻¹ and an average pore volume of 0.43 mL g⁻¹ was prepared by the sol-gel processing method. The material showed the following characteristics: Ti=11.6 wt% and P=10.5 wt%; ion exchange capacity of 0.60 mmol g⁻¹. Meldola's Blue (MLB) dye was adsorbed, by an ion exchange reaction, from an aqueous solution in a quantity of 0.62 mmol g⁻¹. The dye was strongly retained and was not easily leached from the matrix even in presence of 0.5 M electrolyte solution. Changing the solution pH between 2.5 and 7.0, the midpoint potential of the dye-adsorbed (≡SiO)₂ Ti(O₃POMLB)₂ matrix carbon paste electrode remained practically constant, i.e. about 20 mV vs. SCE. This is not the usual behaviour of MLB since its midpoint potential changes considerably in solution phase as the pH is changed. The modified electrode has proved to be stable and electrocatalytically active for hydrazine oxidation at pH 6. Received: 22 June 1999 / Accepted: 7 September 1999     

Comparison of direct solid sampling and slurry sampling for the determination of cadmium in wheat flour by electrothermal atomic absorption spectrometry

Two analytical methods for the determination of cadmium in wheat flour by electrothermal atomic absorption spectrometry without prior sample digestion have been compared: direct solid sampling analysis (SS) and slurry sampling (SlS). Besides the conventional modifier mixture of palladium and magnesium nitrates (10 μg Pd + 3 μg Mg), 0.05% (v/v) Triton X-100 has been added to improve the penetration of the modifier solution into the solid sample, and 0.1% H₂O₂ in order to promote an in situ digestion for SS. For SlS, 30 μg Pd, 12 μg Mg and 0.05% (v/v) Triton X-100 have been used as the modifier mixture. Under these conditions, and using a pyrolysis temperature of 800 °C, essentially no background absorption was observed with an atomization temperature of 1600 °C. About 2 mg of sample have been typically used for SS, although as much as 3-5 mg could have been introduced. In the case of SlS multiple injections had to be used to achieve the sensitivity required for this determination. Calibration against aqueous standards was feasible for both methods. The characteristic mass obtained with SS was 0.6 pg, and that with SlS was 1.0 pg. The limits of detection were 0.4 and 0.7 ng g⁻¹, the limits of quantification were 1.3 and 2.3 ng g⁻¹ and the relative standard deviation (n = 5) was 6-16% and 9-23% for SS and SlS, respectively. The accuracy was confirmed by the analysis of certified reference materials. The two methods were applied for the determination of cadmium in six wheat flour samples acquired in supermarkets of different Brazilian cities. The cadmium content varied between 8.9 ± 0.5 and 13 ± 2 ng g⁻¹ (n = 5). Direct SS gave results similar to those obtained with SlS using multi-injections; the values of both techniques showed no statistically significant difference at the 95% confidence level. Direct SS was finally adopted as the method of choice, due to its greater simplicity, the faster speed of analysis and the better figures of merit.     

Optical,electrical, and thermochromic properties of polyazothiophene Langmuir–Blodgett films

The conductivity and luminescence of conjugated polymers may be combined with the photoisomerization capability of azobenzene materials to achieve unique properties for a variety of applications, particularly if conjugated polymers with azobenzene side chains are processed as nanostructured films. In this study, we report on Langmuir–Blodgett (LB) films of a polythiophene-bearing azobenzene moieties, which displayed photoluminescence, thermochromism, electroactivity, and photoinduced birefringence. The latter three properties were enhanced in the LB films, as compared to spin-coated films of the polyazothiophene, and this has been attributed to differences in film morphology that could be probed with atomic force microscopy.     

Chemical Approach to the Optimization of Conditions Using HS-SPME/GC–MS for Characterization of Volatile Compounds in Eugenia brasiliensis Fruit

Grumixama (Eugenia brasiliensis Lam.) is a native fruit of the Brazilian Atlantic Forest, belonging to the Myrtaceae family, which designatesthe most significant number of species with food potential. It stands out due to its phytochemical characteristics because of the presence of polyphenols and volatile organic compounds. Volatile compounds are substances released by foods that give off an aroma and influence flavor. Solid-phase microextraction is a technique that allows for low-cost, fast, and solvent-free extraction, has an affinity for numerous analytes, and is easily coupled to gas chromatography. The objectives of this work were to evaluate the efficiency of different fibers of SPME (solid-phase microextraction) in the extraction of volatile organic compounds from grumixama pulp; optimize a method for extraction time, temperature, and sample weight; and to determine the characteristic volatile profile of this fruit. For the extraction of volatile compounds, three fibers of different polarities were used: polar polyacrylate (PA) fibers, divinylbenzene/carboxyne/polydimethylsiloxane (DVB/CAR/PDMS) semipolar fibers, and polydimethylsiloxane/divinylbenzene (PDMS/DVB). Fourteen volatile organic compounds (VOCs) were identified by DVB/CAR/PDMS, six by PA, and seven by PDMS/DVB through solid-phase microextraction in the headspace mode (SPME-HS). Considering the total number of compounds identified, regardless of the fiber used, and the optimization of the method, Eugenia brasiliensis presented sesquiterpene fractions (85.7%, 83.3%, and 85.7% of total VOCs) higher than the monoterpene fractions (14.3%, 16.7%, and 14.3%) for DVB/CAR/PDMS, PA, and PDMS/DVB, respectively in its composition. In addition, it was possible to verify that the fiber DVB/CAR/PDMS presented a better efficiency due to the larger chromatographic area observed when the grumixama pulp was subjected to conditions of 75 °C, 2.0 g, and an adsorption time of 20 min.     

Multivariate optimization of a solid phase microextraction-headspace procedure for the determination of benzene, toluene, ethylbenzene and xylenes in effluent samples from a waste treatment plant

A method based on solid-phase microextraction (SPME) and gas chromatography with flame ionization detection (GC-FID) has been optimized for the determination of benzene, toluene, ethylbenzene and xylenes (BTEX) in water released from a waste treatment plant. The extraction step was optimized using fractional factorial and central composite designs including the following experimental factors: saline concentration; extraction time; desorption time; agitation velocity; headspace volume. A multiple function was used to describe the experimental conditions for simultaneous extraction of the compounds. The procedure, based on direct SPME at 50 degrees C, using a polydimethylsiloxane fiber, showed good linearity (r>0.997 over a concentration range 2-200 microg L(-1)) and repeatability (relative standard deviation (RSD)<4.23%) for all compounds, with limits of detection ranging from 0.05 to 0.28 microg L(-1), and limits of quantification ranging from 0.14 to 0.84 microg L(-1). Concentrations of the target compounds in these samples were between 145.8 and 1891 microg L(-1).     

High-impact polystyrene/polyaniline membranes for acid solution treatment by electrodialysis: preparation, evaluation, and chemical calculation

In this study different membranes were produced, aiming to evaluate their use in electrodialysis. These membranes were produced using conventional polymer (high-impact polystyrene) and polyaniline. The membrane characterization was done by FTIR spectroscopy, scanning electron microscopy (SEM), and thermogravimetry (TGA). The studies of the zinc and proton extraction ionic transport through the membranes were evaluated using a three-compartment cell. The results obtained using the produced membranes were compared to the results obtained with the commercial membrane Nafion 450. It was found that a synthesized membrane can be used to recover zinc in acid media. In addition, a preliminary computational essay about the structures of PAni and CSA is presented.