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.     

Fractional generalization of memristor and higher order elements

Fractional calculus generalizes integer order derivatives and integrals. Memristor systems generalize the notion of electrical elements. Both concepts were shown to model important classes of phenomena. This paper goes a step further by embedding both tools in a generalization considering complex-order objects. Two complex operators leading to real-valued results are proposed. The proposed class of models generate a broad universe of elements. Several combinations of values are tested and the corresponding dynamical behavior is analyzed.     

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.     

1‐(7‐Chloro‐1,4‐dihydroquinolin‐4‐ylidene)thiosemicarbazide and its hydrochloride: evidence for the existence of a stable imine tautomer in the solid state of 4‐aminoquinoline free bases,an anomalous case in nitrogen heterocycles

In the solid state, crystals of both 1‐(7‐chloro‐1,4‐dihydroquinolin‐4‐ylidene)thiosemicarbazide–methanol–water (2/1/1), 2C₁₀H₉ClN₄S·CH₃OH·H₂O, (I), and its hydrochloride salt {systematic name: [(7‐chloro‐1,4‐dihydroquinolin‐4‐ylidene)azaniumyl]thiourea chloride}, C₁₀H₁₀ClN₄S⁺·Cl⁻, (II), assume the imine tautomeric form, contrary to other 4‐amino‐7‐chloroquinolines. Of particular interest are the N—C bond lengths, which have appreciable double‐bond character, and the C—N—C aromatic ring bond angle. Both of these parameters have been studied extensively in 4‐amino‐substituted quinolines. The crystal structures of (I) and (II) in this study provide interesting examples of the amino–imino tautomerism which exists in this class of compound and is, to the best of our knowledge, hitherto unreported.     

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.