Research on calculus: what do we know and where do we need to go?

In this introductory paper we take partial stock of the current state of field on calculus research, exemplifying both the promise of research advances as well as the limitations. We identify four trends in the calculus research literature, starting with identifying misconceptions to investigations of the processes by which students learn particular concepts, evolving into classroom studies, and, more recently research on teacher knowledge, beliefs, and practices. These trends are related to a model for the cycle of research and development aimed at improving learning and teaching. We then make use of these four trends and the model for the cycle of research and development to highlight the contributions of the papers in this issue. We conclude with some reflections on the gaps in literature and what new areas of calculus research are needed.     

Maximum likelihood estimation for stochastic volatility in mean models with heavy‐tailed distributions

In this article, we introduce a likelihood‐based estimation method for the stochastic volatility in mean (SVM) model with scale mixtures of normal (SMN) distributions. Our estimation method is based on the fact that the powerful hidden Markov model (HMM) machinery can be applied in order to evaluate an arbitrarily accurate approximation of the likelihood of an SVM model with SMN distributions. Likelihood‐based estimation of the parameters of stochastic volatility models, in general, and SVM models with SMN distributions, in particular, is usually regarded as challenging as the likelihood is a high‐dimensional multiple integral. However, the HMM approximation, which is very easy to implement, makes numerical maximum of the likelihood feasible and leads to simple formulae for forecast distributions, for computing appropriately defined residuals, and for decoding, that is, estimating the volatility of the process. Copyright © 2017 John Wiley & Sons, Ltd.     

Partial least squares model and design of experiments toward the analysis of the metabolome of Jatropha gossypifolia leaves: Extraction and chromatographic fingerprint optimization

A major challenge in metabolomic studies is how to extract and analyze an entire metabolome. So far, no single method was able to clearly complete this task in an efficient and reproducible way. In this work we proposed a sequential strategy for the extraction and chromatographic separation of metabolites from leaves Jatropha gossypifolia using a design of experiments and partial least square model. The effect of 14 different solvents on extraction process was evaluated and an optimized separation condition on liquid chromatography was estimated considering mobile phase composition and analysis time. The initial conditions of extraction using methanol and separation in 30 min between 5 and 100% water/methanol (1:1 v/v) with 0.1% of acetic acid, 20 μL sample volume, 3.0 mL min^?1 flow rate and 25°C column temperature led to 107 chromatographic peaks. After the optimization strategy using i‐propanol/chloroform (1:1 v/v) for extraction, linear gradient elution of 60 min between 5 and 100% water/(acetonitrile/methanol 68:32 v/v with 0.1% of acetic acid), 30 μL sample volume, 2.0 mL min^?1 flow rate, and 30°C column temperature, we detected 140 chromatographic peaks, 30.84% more peaks compared to initial method. This is a reliable strategy using a limited number of experiments for metabolomics protocols.     

Use of hydrogen peroxide to achieve interference-free stripping voltammetric determination of copper at the bismuth-film electrode

In this work, a new approach is presented to allow interference-free determination of Cu (II) by stripping voltammetry using the bismuth-film electrode. The addition of hydrogen peroxide to the electroanalytical cell has promoted complete resolution between re-dissolution peaks of Bi (III) and Cu (II). The absence of interference could be evaluated by the correlation coefficient (r > 0.99) between Cu (II) concentration and its shifted current peak (at +212 mV) while achieving a slightly fluctuation of the bismuth current peak at −180 mV. Studies were performed aiming towards the optimum conditions for trace determination of Cu (II) using hydrogen peroxide. The methodology was applied to a real sample (sugarcane spirits) and the results were compared to those from graphite furnace atomic absorption spectrometry. The analytical parameters of merit and the results of the analysis indicated that the analytical methodology could be readily used for trace determination of Cu (II).     

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.     

Unusual photochemical C-N bond cleavage in the novel methyl 2-chloro-3-methyl-2H-azirine-2-carboxylate

The structure, preferred conformers, vibrational spectrum, and photochemical behavior of the novel azirine, methyl 2-chloro-3-methyl-2H-azirine-2-carboxylate (MCMAC) were investigated in low-temperature matrixes and in the neat solid amorphous state by infrared spectroscopy and quantum-chemical calculations. Two conformers of the compound were observed in argon, krypton, and xenon matrixes, in agreement with the DFT(B3LYP)/6-311++G(d,p) and MP2/6-311++G(d,p) theoretical calculations. Both conformers were found to exhibit the carboxylic ester group in the cis conformation, differing in the arrangement defined by the O=C-C-Cl dihedral angle (cis and trans, for Ct and Cc forms, respectively). The Ct conformer was found to be the most stable conformer in the gaseous phase as well as in both argon and krypton matrixes, whereas the more polar Cc conformer became the most stable form in the xenon matrix and in the neat solid amorphous phase. In situ broadband UV (lambda > 235 nm) excitation of matrix-isolated MCMAC led to azirine ring C-C and C-N bond cleavages, the latter process corresponding to the most efficient reaction channel. The photochemical cleavage of the C-N bond had never been previously observed in the case of aliphatic 2H-azirines. Two electron withdrawing substituents (methoxycarbonyl group and chlorine atom) are connected to the azirine ring in the novel MCMAC azirine. The simultaneous presence of these two groups accelerates intersystem crossing toward the triplet state where cleavage of the C-N bond takes place. The primary photoproducts resulting from the C-N and C-C ring-opening reactions were also found to undergo further photochemical decarbonylation or decarboxylation reactions.     

Determination of biogenic amines in alcoholic beverages by ion chromatography with suppressed conductivity detection and integrated pulsed amperometric detection

The determination of biogenic amines in alcoholic beverages is important to assess the potential risks associated with the consumption of high concentrations of these compounds. In addition, product storage conditions and the length of storage can cause the formation of biogenic amines that reduce product quality. We report a new method using cation-exchange chromatography with either suppressed conductivity, integrated pulsed amperometry, UV, or a combination of these detection techniques to determine biogenic amines in alcoholic beverages. The main objective was to provide a direct comparison between IPAD and suppressed conductivity detection for determining biogenic amines in alcoholic beverages. Suppressed conductivity is the simplest detection approach for determining putrescine, cadaverine, histamine, agmatine, phenylethylamine, spermidine, and spermine with good sensitivity (0.004-0.08 mg/l) and was used to evaluate the influence of storage time and conditions on the evolution of biogenic amines in alcoholic beverages. Integrated pulsed amperometric detection (IPAD) detects more biogenic amines than suppressed conductivity detection, enabling the detection of dopamine, tyramine, and serotonin. Tyramine was simultaneously determined by UV detection and IPAD to provide confirmation and ensure the accuracy of the analytical results. The linearity of biogenic amine responses was within 0.1-20 mg/l and peak area precisions were 0.24-4.97% for IPAD, suppressed conductivity-IPAD, and UV detection. The sensitivity for the 10 biogenic amines using the 3 detection techniques varied considerably from 0.004-1.1 mg/l and recoveries were within 85-122%.     

Covalent Attachment of Cyclic TAT Peptides to GFP Results in Protein Delivery into Live Cells with Immediate Bioavailability

The delivery of free molecules into the cytoplasm and nucleus by using arginine‐rich cell‐penetrating peptides (CPPs) has been limited to small cargoes, while large cargoes such as proteins are taken up and trapped in endocytic vesicles. Based on recent work, in which we showed that the transduction efficiency of arginine‐rich CPPs can be greatly enhanced by cyclization, the aim was to use cyclic CPPs to transport full‐length proteins, in this study green fluorescent protein (GFP), into the cytosol of living cells. Cyclic and linear CPP–GFP conjugates were obtained by using azido‐functionalized CPPs and an alkyne‐functionalized GFP. Our findings reveal that the cyclic‐CPP–GFP conjugates are internalized into live cells with immediate bioavailability in the cytosol and the nucleus, whereas linear CPP analogues do not confer GFP transduction. This technology expands the application of cyclic CPPs to the efficient transport of functional full‐length proteins into live cells.     

Biosurfactant Production by <Emphasis Type="Italic">Pseudomonas aeruginosa</Emphasis> Grown in Residual Soybean Oil

Pseudomonas aeruginosa PACL strain, isolated from oil-contaminated soil taken from a lagoon, was used to investigate the efficiency and magnitude of biosurfactant production, using different waste frying soybean oils, by submerged fermentation in stirred tank reactors of 6 and 10 l capacities. A complete factorial experimental design was used, with the goal of optimizing the aeration rate (0.5, 1.0, and 1.5 vvm) and agitation speed (300, 550, and 800 rpm). Aeration was identified as the primary variable affecting the process, with a maximum rhamnose concentration occurring at an aeration rate of 0.5 vvm. At optimum levels, a maximum rhamnose concentration of 3.3 g/l, an emulsification index of 100%, and a minimum surface tension of 26.0 dynes/cm were achieved. Under these conditions, the biosurfactant production derived from using a mixture of waste frying soybean oil (WFSO) as a carbon source was compared to production when non-used soybean oil (NUSO), or waste soybean oils used to fry specific foods, were used. NUSO produced the highest level of rhamnolipids, although the waste soybean oils also resulted in biosurfactant production of 75–90% of the maximum value. Under ideal conditions, the kinetic behavior and the modeling of the rhamnose production, nutrient consumption, and cellular growth were established. The resulting model predicted data points that corresponded well to the empirical information.