Lanczos algorithm on the grassmann manifold

5th. European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008) 8th. World Congress on Computational Mechanics (WCCM8)

Local fractional variational iteration and decomposition methods for wave equation on cantor sets within local fractional operators

We perform a comparison between the fractional iteration and decomposition methods applied to the wave equation on Cantor set. The operators are taken in the local sense. The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative.

Systems of Navier-Stokes equations on cantor sets

We present systems of Navier-Stokes equations on Cantor sets, which are described by the local fractional vector calculus. It is shown that the results for Navier-Stokes equations in a fractal bounded domain are efficient and accurate for describing fluid flow in fractal media.

Cantor exchange systems and renormalization

We prove a one-to-one correspondence between (i) C1+ conjugacy classes of C1+H Cantor exchange systems that are C1+H fixed points of renormalization and (ii) C1+ conjugacy classes of C1+H diffeomorphisms f with a codimension 1 hyperbolic attractor Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. However, we prove that there is no C1+alpha Cantor exchange system, with bounded geometry, that is a C1+alpha fixed point of renormalization with regularity alpha greater than the Hausdorff dimension of its invariant Cantor set.

Moodle and multiple-choice tests

Multiple-Choice items are used in many different kinds of tests in several areas of knowledge. They can be considered an interesting tool to the self-assessing or as an alternative or complementary instrument to the traditional methods for assessing knowledge. The objectivity and accuracy of the multiple-choice tests is an important reason to think about. They are especially useful when the number of students to evaluate is too large. Moodle (Modular Object-Oriented Dynamic Learning Environment) is an Open Source course management system centered around learners' needs and designed to support collaborative approaches to teaching and learning. Moodle offers to the users a rich interface, context-specific help buttons, and a wide variety of tools such as discussion forums, wikis, chat, surveys, quizzes, glossaries, journals, grade books and more, that allow them to learn and collaborate in a truly interactive space. Come together the interactivity of the Moodle platform and the objectivity of this kind of tests one can easily build manifold random tests. The proposal of this paper is to relate our journey in the construction of these tests and share our experience in the use of the Moodle platform to create, take advantage and improve the multiple-choices tests in the Mathematic area.

Development of an FIA system with amperometric detection for determination of bentazone in estuarine waters

On the basis of its electrochemical behaviour a new flow-injection analysis (FIA) method with amperometric detection has been developed for quantification of the herbicide bentazone (BTZ) in estuarine waters. Standard solutions and samples (200 µL) were injected into a water carrier stream and both pH and ionic strength were automatically adjusted inside the manifold. Optimization of critical FIA conditions indicated that the best analytical results were obtained at an oxidation potential of 1.10 V, pH 4.5, and an overall flow-rate of 2.4 mL min–1. Analysis of real samples was performed by means of calibration curves over the concentration range 2.5x10–6 to 5.0x10–5 mol L–1, and results were compared with those obtained by use of an independent method (HPLC). The accuracy of the amperometric determinations was ascertained; errors relative to the comparison method were below 4% and sampling rates were approximately 100 samples h–1. The repeatability of the proposed method was calculated by assessing the relative standard deviation (%) of ten consecutive determinations of one sample; the value obtained was 2.1%.

Flow injection electrochemical determination of apomorphine

Few analytical methods are currently available for determination of apomorphine, the active substance of a new oral formulation used in the treatment of erectile dysfunction. In this way a flow injection electrochemical method (FIA-EC) was developed for its quantification and applied to pharmaceutical dosage forms. Based in previous findings regarding the stability of apomorphine in borate buffer and after optimization of several analytical parameters a single channel flow injection manifold was set up that enables the determination of this drug over the concentration range of 3 to 16 µmol L-1 with a detection limit of 0.5 µmol L-1 at a sampling rateof 90 h-1. The simplicity and rapidity of the FIA-EC method used, its reproducibility and sensitivity make it suitable for quality control of pharmaceutical preparations of apomorphine intended for clinical use and research.

Citrate selective electrodes for the flow injection analysis of soft drinks, beers and pharmaceutical products

Aiming the establishment of simple and accurate readings of citric acid (CA) in complex samples, citrate (CIT) selective electrodes with tubular configuration and polymeric membranes plus a quaternary ammonium ion exchanger were constructed. Several selective membranes were prepared for this purpose, having distinct mediator solvents (with quite different polarities) and, in some cases, p-tert-octylphenol (TOP) as additive. The latter was used regarding a possible increase in selectivity. The general working characteristics of all prepared electrodes were evaluated in a low dispersion flow injection analysis (FIA) manifold by injecting 500µl of citrate standard solutions into an ionic strength (IS) adjuster carrier (10−2 mol l−1) flowing at 3ml min−1. Good potentiometric response, with an average slope and a repeatability of 61.9mV per decade and ±0.8%, respectively, resulted from selective membranes comprising additive and bis(2-ethylhexyl)sebacate (bEHS) as mediator solvent. The same membranes conducted as well to the best selectivity characteristics, assessed by the separated solutions method and for several chemical species, such as chloride, nitrate, ascorbate, glucose, fructose and sucrose. Pharmaceutical preparations, soft drinks and beers were analyzed under conditions that enabled simultaneous pH and ionic strength adjustment (pH = 3.2; ionic strength = 10−2 mol l−1), and the attained results agreed well with the used reference method (relative error < 4%). The above experimental conditions promoted a significant increase in sensitivity of the potentiometric response, with a supra-Nernstian slope of 80.2mV per decade, and allowed the analysis of about 90 samples per hour, with a relative standard deviation <1.0%.

Electrochemical determination of dihydrocodeine in pharmaceuticals

Two analytical methods for the quality control of dihydrocodeine in commercial pharmaceutical formulations have been developed and compared with reference methods: a square wave voltammetric (SWV) method and a flow injection analysis system with electrochemical detection (FIA-EC). The electrochemical methods proposed were successfully applied to the determination of dihydrocodeine in pharmaceutical tablets and in oral solutions. These methods do not require any pretreatment of the samples, the formulation only being dissolved in a suitable electrolyte. Validation of the methods showed it to be precise, accurate and linear over the concentration range of analysis. The automatic procedure based on a flow injection analysis manifold allows a sampling rate of 115 determinations per hour.

Amperometric and spectrophotometric determination of carbaryl in natural waters and commercial formulations

The work presented describes the development and evaluation of two flow-injection analysis (FIA) systems for the automated determination of carbaryl in spiked natural waters and commercial formulations. Samples are injected directly into the system where they are subjected to alkaline hydrolysis thus forming 1-naphthol. This product is readily oxidised at a glassy carbon electrode. The electrochemical behaviour of 1-naphthol allows the development of an FIA system with an amperometric detector in which 1-naphthol determination, and thus measurement of carbaryl concentration, can be performed. Linear response over the range 1.0×10–7 to 1.0×10–5 mol L–1, with a sampling rate of 80 samples h–1, was recorded. The detection limit was 1.0×10–8 mol L–1. Another FIA manifold was constructed but this used a colorimetric detector. The methodology was based on the coupling of 1-naphthol with phenylhydrazine hydrochloride to produce a red complex which has maximum absorbance at 495 nm. The response was linear from 1.0×10–5 to 1.5×10–3 mol L–1 with a detection limit of 1.0×10–6 mol L–1. Sample-throughput was about 60 samples h–1. Validation of the results provided by the two FIA methodologies was performed by comparing them with results from a standard HPLC–UV technique. The relative deviation was <5%. Recovery trials were also carried out and the values obtained ranged from 97.0 to 102.0% for both methods. The repeatability (RSD, %) of 12 consecutive injections of one sample was 0.8% and 1.6% for the amperometric and colorimetric systems, respectively.

Chlormequat selective electrodes: construction, evaluation and application at FIA systems

A flow injection analysis (FIA) system having a chlormequat selective electrode is proposed. Several electrodes with poly(vinyl chloride) based membranes were constructed for this purpose. Comparative characterization suggestedthe use of membrane with chlormequat tetraphenylborate and dibutylphthalate. On a single-line FIA set-up, operating with 1x10-2 mol L-1 ionic strength and 6.3 pH, calibration curves presented slopes of 53.6±0.4mV decade-1 within 5.0x10-6 and1.0x10-3 mol L-1, andsquaredcorrelation coefficients >0.9953. The detection limit was 2.2x10-6 mol L-1 and the repeatability equal to ±0.68mV (0.7%). A dual-channel FIA manifold was therefore constructed, enabling automatic attainment of previous ionic strength andpH conditions and thus eliminating sample preparation steps. Slopes of 45.5±0.2mV decade -1 along a concentration range of 8.0x10-6 to 1.0x10-3 mol L-1 with a repeatability ±0.4mV (0.69%) were obtained. Analyses of real samples were performed, and recovery gave results ranging from 96.6 to 101.1%.

Biomimetic sensors of molecularly-imprinted polymers for chlorpromazine determination

A new man-tailored biomimetic sensor for Chlorpromazine host-guest interactions and potentiometric transduction is presented. The artificial host was imprinted within methacrylic acid, 2-vinyl pyridine and 2-acrylamido-2-methyl-1-propanesulfonic acid based polymers. Molecularly imprinted particles were dispersed in 2-nitrophenyloctyl ether and entrapped in a poly(vinyl chloride) matrix. Slopes and detection limits ranged 51–67 mV/decade and 0.46–3.9 μg/mL, respectively, in steady state conditions. Sensors were independent fromthe pHof test solutionswithin 2.0–5.5.Good selectivitywas observed towards oxytetracycline, doxytetracycline, ciprofloxacin, enrofloxacin, nalidixic acid, sulfadiazine, trimethoprim, glycine, hydroxylamine, cysteine and creatinine. Analytical features in flowing media were evaluated on a double-channel manifold, with a carrier solution of 5.0×10−2 mol/L phosphate buffer. Near-Nernstian response was observed over the concentration range 1.0×10−4 to 1.0×10−2 mol/L. Average slopes were about 48 mV/decade. The sensors were successfully applied to field monitoring of CPZ in fish samples, offering the advantages of simplicity, accuracy, automation feasibility and applicability to complex samples.

Medo de Palco: contributo para uma análise e aplicação de estratégias visando o seu controle

“Nós reverenciamos Cláudio Arrau, cuja arte tinha a profundidade e o fôlego de um velho sábio e o virtuosismo estonteante de um jovem vencedor de um concurso”1. Este comentário de Pedro de Alcântara, graduado em música pela Yale School of Music e professor de Técnica Alexander, será seguramente secundado por qualquer melómano. Arrau confessa numa entrevista a Elyse Mach:”… quando tinha dezoito ou dezanove anos, entreguei-me aos cuidados de um psiquiatra2 porque havia em mim uma espécie de bloqueio que me impedia de expressar o meu eu musical […] muitas vezes voltei a visitar este homem maravilhoso […]. Eu aconselharia qualquer intérprete a falar com um psiquiatra e, se necessário fazer análise. A paz de espírito que daí resulta vale a pena.”3 Qualquer intérprete, cantor, instrumentista ou maestro, tem consciência da existência do tipo de bloqueios de que fala Arrau. Conforme se pode constatar pelo comentário extraído do célebre tratado de flauta de Quantz em 1752, nem sequer é um problema recente: “Se o flautista que quer ser ouvido publicamente é timorato e não está ainda acostumado a tocar na presença de muitas pessoas, deve tentar, enquanto está a tocar, dirigir a sua atenção apenas para as notas à sua frente, nunca encarando os presentes, uma vez que isso distrai os pensamentos, e destrói a sua tranquilidade. […] O medo causa uma ebulição do sangue que disturba o regular funcionamento dos pulmões, assim como dos braços, da língua e dos dedos. Daí surge uma tremura dos membros muito obstrutiva ao tocar e, como resultado, o flautista será incapaz de produzir uma passagem mais longa num fôlego, ou quaisquer outros actos especialmente difíceis, tal como faria num estado de espírito tranquilo.”4 Ao longo dos séculos, todos os grandes intérpretes tiveram que lidar com os problemas associados à performance musical pública, e, mais ou menos inconscientemente desenvolveram rotinas, atitudes ou superstições que, com maior ou menor sucesso os ajudam a ultrapassá-los. É obviamente um assunto que muitos intérpretes preferem evitar. A sua racionalização implica enfrentar os próprios fantasmas, e sobretudo, traz implícita a constatação de que esses receios existem, algo que nunca é fácil de admitir por parte de alguém que durante muitos anos poderá ter sobrevivido à custa de um exercício de negação. Existem estratégias muito eficazes para ajudar a superar o stress relacionado com a performance musical. Urge analisá-las, compreendê-las, sistematizá-las e passá-las às gerações vindouras. Só assim se perpetuará o alto nível de execução que o acumular de experiências ao longo dos últimos séculos proporcionou, numa sociedade que cada vez mais pressiona os seus elementos para o êxito profissional como factor indissociável da felicidade e do sentimento de realização enquanto seres humanos.

Biomimetic sensors of molecularly-imprinted polymers for chlorpromazine determination

A new man-tailored biomimetic sensor for Chlorpromazine host-guest interactions and potentiometric transduction is presented. The artificial host was imprinted within methacrylic acid, 2-vinyl pyridine and 2-acrylamido-2-methyl-1-propanesulfonic acid based polymers. Molecularly imprinted particles were dispersed in 2-nitrophenyloctyl ether and entrapped in a poly(vinyl chloride) matrix. Slopes and detection limits ranged 51–67 mV/decade and 0.46–3.9 μg/mL, respectively, in steady state conditions. Sensors were independent from the pH of test solutions within 2.0–5.5. Good selectivity was observed towards oxytetracycline, doxytetracycline, ciprofloxacin, enrofloxacin, nalidixic acid, sulfadiazine, trimethoprim, glycine, hydroxylamine, cysteine and creatinine. Analytical features in flowing media were evaluated on a double-channel manifold, with a carrier solution of 5.0 × 10−2 mol/L phosphate buffer. Near-Nernstian response was observed over the concentration range 1.0 × 10−4 to 1.0 × 10−2 mol/L. Average slopes were about 48 mV/decade. The sensors were successfully applied to field monitoring of CPZ in fish samples, offering the advantages of simplicity, accuracy, automation feasibility and applicability to complex samples.

Hausdorff dimension versus smoothness

There is a one-to-one correspondence between C1+H Cantor exchange systems that are C1+H fixed points of renormalization and C1+H diffeomorphisms f on surfaces with a codimension 1 hyperbolic attractor Λ that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Λ. However, there is no such C1+α Cantor exchange system with bounded geometry that is a C1+α fixed point of renormalization with regularity α greater than the Hausdorff dimension of its invariant Cantor set. The proof of the last result uses that the stable holonomies of a codimension 1 hyperbolic attractor Λ are not C1+θ for θ greater than the Hausdorff dimension of the stable leaves of f intersected with Λ.