Fractional derivatives: Probability interpretation and frequency response of rational approximations

The theory of fractional calculus (FC) is a useful mathematical tool in many applied sciences. Nevertheless, only in the last decades researchers were motivated for the adoption of the FC concepts. There are several reasons for this state of affairs, namely the co-existence of different definitions and interpretations, and the necessity of approximation methods for the real time calculation of fractional derivatives (FDs). In a first part, this paper introduces a probabilistic interpretation of the fractional derivative based on the Grünwald-Letnikov definition. In a second part, the calculation of fractional derivatives through Padé fraction approximations is analyzed. It is observed that the probabilistic interpretation and the frequency response of fraction approximations of FDs reveal a clear correlation between both concepts.     

Theoretical analysis of aggregation in block‐copolymer films: The optical signature

We focus this work on the theoretical investigation of the block‐copolymer poly[oxyoctyleneoxy‐(2,6‐dimethoxy‐1,4phenylene‐1,2‐ethinylene‐phenanthrene‐2,4diyl) named as LaPPS19, recently proposed for optoelectronic applications. We used for that a variety of methods, from molecular mechanics to quantum semiempirical techniques (AM1, ZINDO/S‐CIS). Our results show that as expected isolated LaPPS19 chains present relevant electron localization over the phenanthrene group. We found, however, that LaPPS19 could assemble in a π‐stacked form, leading to impressive interchain interaction; the stacking induces electronic delocalization between neighbor chains and introduces new states below the phenanthrene‐related absorption; these results allowed us to associate the red‐shift of the absorption edge, seen in the experimental results, to spontaneous π‐stack aggregation of the chains. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Adsorption/Desorption Behavior of Bovine Serum Albumin and Porcine Insulin on Chemically Patterned Porous Gel Networks

Adsorption/desorption of proteins onto a biomaterial surface plays a major role on the biocompatibility of the implanted material. By modifying the biomaterial surface with specially designed functional groups one may achieve the most specific behavior of the developed material used in a biological system. Based on that, porous gel matrixes with functionalized surfaces offer unlimited possibilities to control the protein-substrate interaction behavior. In the present work, we have functionalized the surface of porous glass with several chemical groups during the synthesis of the silica matrix. The porous glass matrixes were obtained using tetraethoxysilane (TEOS)/ethanol and functionalized with 3-mercaptopropyltrimethoxysilane (MPTMS) and 3-aminopropyltriethoxysilane (APTES). In vitro tests of the kinetics of protein adsorption and desorption from the gel matrix were monitored by UV-visible spectroscopy. The bioactivity of the incorporated protein was verified by in vivo experiments with adult male rats, where they presented an acute hypoglycemic peak.     

The retro-aldol mechanism in the pyrolysis kinetics of primary,secondary, and tertiary β-hydroxy ketones in the gas phase

The pyrolysis kinetics of primary, secondary, and tertiary β-hydroxy ketones have been studied in static seasoned vessels over the pressure range of 21–152 torr and the temperature range of 190°–260°C. These eliminations are homogeneous, unimolecular, and follow a first-order rate law. The rate coefficients are expressed by the following equations: for 1-hydroxy-3-butanone, log k₁(s^?1) = (12.18 ± 0.39) ? (150.0 ± 3.9) kJ mol^?1 (2.303RT)^?1; for 4-hydroxy-2-pentanone, log k₁(s^?1) = (11.64 ± 0.28) ? (142.1 ± 2.7) kJ mol^?1 (2.303RT)^?1; and for 4-hydroxy-4-methyl-2-pentanone, log k₁(s^?1) = (11.36 ± 0.52) ? (133.4 ± 4.9) kJ mol^?1 (2.303RT)^?1. The acid nature of the hydroxyl hydrogen is not determinant in rate enhancement, but important in assistance during elimination. However, methyl substitution at the hydroxyl carbon causes a small but significant increase in rates and, thus, appears to be the limiting factor in a retroaldol type of mechanism in these decompositions. © John Wiley & Sons, Inc.     

Dialkyl phosphates determination by gas chromatography: Evaluation of a microwave‐assisted derivatization†

Dialkyl phosphates are organophosphate insecticide metabolites and their urinary analysis is useful for assessing human exposure to these compounds. This study presents a sample preparation method with microwave‐assisted derivatization for two dialkyl phosphates to make the process faster before gas chromatographic analysis. The optimized conditions for derivatization procedure were: 250 μL of 2,3,4,5,6‐pentafluorobenzyl bromide 3% in acetonitrile for derivative; microwave for 5 min with intensity of 160 W. The electron ionization mass spectrometric analysis was performed using a gas chromatography with mass spectrometry QP‐2010 from the Shimadzu^® equipped with RTx^®‐5MS capillary column. Ions were monitored at selected‐ion monitoring mode at m/z 350 for diethyl thiophosphate and m/z 366 for diethyl dithiophosphate. The developed method was linear for both metabolites. The intra‐assay precision was the values ranged between 1.1 and 9.1%, for diethyl thiophosphate, and between 4.06 and 6.9%, for diethyl dithiophosphate. The interassay precision showed relative standard deviation between 10.3 and 15.1%, for diethyl thiophosphate and between 4.9 and 11.9%, for diethyl dithiophosphate. The results obtained suggests that derivatization assisted by microwave, before gas chromatography with mass spectrometry analysis, can be applied to monitoring of exposure to organophosphates once is fast, sensible, and precise method to determinate dialkyl phosphates.     

Pendimethalin determination in natural water, baby food and river sediment samples using electroanalytical methods

This work describes the electroanalytical determination of pendimethalin herbicide levels in natural waters, river sediment and baby food samples, based on the electro-reduction of herbicide on the hanging mercury drop electrode using square wave voltammetry (SWV). A number of experimental and voltammetric conditions were evaluated and the best responses were achieved in Britton-Robinson buffer solutions at pH 8.0, using a frequency of 500 s^− 1, a scan increment of 10 mV and a square wave amplitude of 50 mV. Under these conditions, the pendimethalin is reduced in an irreversible process, with two reduction peaks at − 0.60 V and − 0.71 V, using a Ag/AgCl reference system. Analytical curves were constructed and the detection limit values were calculated to be 7.79 μg L^− 1 and 4.88 μg L^− 1, for peak 1 and peak 2, respectively. The precision and accuracy were determinate as a function of experimental repeatability and reproducibility, which showed standard relative deviation values that were lower than 2% for both voltammetric peaks. The applicability of the proposed methodology was evaluated in natural water, river sediments and baby food samples. The calculated recovery efficiencies demonstrate that the proposed methodology is suitable for determining any contamination by pendimethalin in these samples. Additionally, adsorption isotherms were used to evaluate information about the behavior of pendimethalin in river sediment samples.     

In vitro anti-HMPV activity of meroditerpenoids from marine alga Stypopodium zonale (Dictyotales)

In this paper, we evaluated the antiviral activity against HMPV replication of crude extract of the marine algae Stypopodium zonale and of two meroditerpenoids obtained from it, atomaric acid and epitaondiol, and a methyl ester derivative of atomaric acid. Their selectivity indexes were 20.78, >56.81, 49.26 and 12.82, respectively. Compared to ribavirin, the substances showed a relatively low cytotoxicity on LLC-MK2 cells, with a significant antiviral activity, inhibiting at least 90% of viral replication in vitro, which demonstrates the potential of these marine natural products to combat infections caused by HMPV in vitro.     

Investigation of sulphur compounds in coal tar using monodimensional and comprehensive two-dimensional gas chromatography

Coal is a non renewable fossil fuel, used mainly as a source of electrical energy and in the production of coke. It is subjected to thermal treatment, pyrolysis, which produces coke as a main product, in addition to a condensed liquid by-product, called tar. Tar is a complex mixture of organic compounds which contains different chemical classes, presenting aromatic and sulphur heterocyclic compounds. In general, identification of these compounds requires steps of isolation and fractionation, mainly due to co-elution of these compounds with polyaromatic hydrocarbons (PAH). The objective of this work is to characterize the sulphur compounds present in the coal tar obtained via pyrolysis, using comprehensive two-dimensional gas chromatography with time-of-flight mass spectrometry detector (GC×GC/TOFMS). Coal samples from the State of Paraná, Brazil were subjected to laboratorial scale pyrolysis. Several experimental conditions were tested, such as sample weight (5, 10 and 15g), heating ramp (10, 25 and 100°C/min) and final temperature (500, 700 and 900°C). Samples were analyzed by one dimensional gas chromatography (1D-GC) coupled to a quadrupole mass spectrometry detector (GC/qMS) and two-dimensional gas chromatography with time-of-flight mass spectrometry detector (GC×GC/TOFMS). The higher amount of sulphur compounds was obtained at a final temperature of 700°C and a heating ramp of 100°C/min. The main classes observed in the color plot were thiophenes, benzothiophenes and alkylated dibenzothiophenes. GC×GC/TOFMS allowed the identification of the greater number of compounds and the separation of several sulphur compounds from one another. Moreover, separation of sulphur compounds from polyaromatic hydrocarbons and phenols was achieved, which was not possible by 1D-GC. Comparing GC×GC/TOFMS and 1D-GC (SIM mode) also showed that 1D-GC, one of the most employed quantification tools for sulphur compounds, can be misleading for detection, identification and quantification, as the number of isomers of sulphur compounds found was greater than theoretically possible.     

Interaction of protonated merocyanine dyes with amines in organic solvents

2,6-Diphenyl-4-(2,4,6-triphenylpyridinium-1-yl)phenolate (1a) and 4-[(1-methyl-4(1H)-pyridinylidene)-ethylidene]-2,5-cyclohexadien-1-one (2a) were protonated in organic solvents (dichloromethane, acetonitrile, and DMSO) to form 1b and 2b, respectively. The appearance of the solvatochromic bands of 1a and 2a was studied UV-vis spectrophotometrically by deprotonation of 1b and 2b in solution in the presence of the following amines: aniline (AN), N-methylaniline (NMAN), N,N-dimethylaniline (NDAN), n-butylamine (BA), diethylamine (DEA), and triethylamine (TEA). Titrations of 1b and 2b with the amines were carried out and the binding constants were determined from the titration curves in each solvent, using a mathematical model adapted from the literature which considers the simultaneous participation of two dye: amine stoichiometries, 1:1 and 1:2. The data obtained showed the following base order for the two compounds in DMSO: BA>DEA>TEA, while aromatic amines did not cause any effect. In dichloromethane, the following base order for 1b was verified: TEA>DEA>BA?NDAN, while for 2b the order was: TEA>DEA>BA, suggesting that 1b is more acidic than 2b. The data in acetonitrile indicated for 1b and 2b the following order for the amines: DEA>TEA>BA. The diversity of the experimental data were explained based on a model that considers the level of interaction of the protonated dyes with the amines to be dependent on three aspects: (a) the basicity of the amine, which varies according to their molecular structure and the solvent in which it is dissolved, (b) the molecular structure of the dye, and (c) the solvent used to study the system.