The negative sign and exponential expressions: Unveiling students’ persistent errors and misconceptions

The purpose of this study was to determine whether or not certain errors made when simplifying exponential expressions persist as students progress through their mathematical studies. College students enrolled in college algebra, pre-calculus, and first- and second-semester calculus mathematics courses were asked to simplify exponential expressions on an assessment. Persistent errors are identified and characterized. Using quantitative and qualitative methods, we found that the concept of negativity played a prominent role in most of the students’ errors. We theorize that an underdeveloped conception of additive and multiplicative inverses is the root of these errors.     

Novel tricyclic diamines 2. Synthesis of 1,7-diazaisoadamantane, 1,5-diazaisoadamantane and 1,6-diazahomobrendane

Three novel tricyclic diamines (1,7-diazaisoadamantane, 1,5-diazaisoadamantane and 1,6-diazahomobrendane) were prepared. A flexible synthetic strategy was employed which used flat, aromatic azaindoles as the starting materials. The requisite azaindoles were prepared by a tandem Sonogashira coupling/intramolecular cyclization reaction. Ring saturation, appropriate functionalization and intramolecular alkylation provided the three novel tricyclic diamines cores.     

A miniaturized glucocorticoid receptor translocation assay using enzymatic fragment complementation evaluated with qHTS

Nuclear translocation is an important step in glucocorticoid receptor (GR) signaling and assays that measure this process allow the identification of nuclear receptor ligands independent of subsequent functional effects. To facilitate the identification of GR-translocation agonists, an enzyme fragment complementation (EFC) cell-based assay was scaled to a 1536-well plate format to evaluate 9,920 compounds using a quantitative high throughput screening (qHTS) strategy where compounds are assayed at multiple concentrations. In contrast to conventional assays of nuclear translocation the qHTS assay described here was enabled on a standard luminescence microplate reader precluding the requirement for imaging methods. The assay uses beta-galactosidase alpha complementation to indirectly detect GR-translocation in CHO-K1 cells. 1536-well assay miniaturization included the elimination of a media aspiration step, and the optimized assay displayed a Z' of 0.55. qHTS yielded EC(50) values for all 9,920 compounds and allowed us to retrospectively examine the dataset as a single concentration-based screen to estimate the number of false positives and negatives at typical activity thresholds. For example, at a 9 microM screening concentration, the assay showed an accuracy that is comparable to typical cell-based assays as judged by the occurrence of false positives that we determined to be 1.3% or 0.3%, for a 3sigma or 6sigma threshold, respectively. This corresponds to a confirmation rate of approximately 30% or approximately 50%, respectively. The assay was consistent with glucocorticoid pharmacology as scaffolds with close similarity to dexamethasone were identified as active, while, for example, steroids that act as ligands to other nuclear receptors such as the estrogen receptor were found to be inactive.     

Evaluating reproducibility and similarity of mass and intensity data in complex spectra—applications to tubulin

We present a data processing approach based on the spectral dot product for evaluating spectral similarity and reproducibility. The method introduces 95% confidence intervals on the spectral dot product to evaluate the strength of spectral correlation; it is the only calculation described to date that accounts for both the non-normal sampling distribution of the dot product and the number of peaks the spectra have in common. These measures of spectral similarity allow for the recursive generation of a consensus spectrum, which incorporates the most consistent features from statistically similar replicate spectra. Taking the spectral dot product and 95% confidence intervals between consensus spectra from different samples yields the similarity between these samples. Applying the data analysis scheme to replicates of brain tubulin CNBr peptides enables a robust comparison of tubulin isotype expression and post-translational modification patterns in rat and cow brains.     

Physical and chemical properties of bio-oils from microwave pyrolysis of corn stover

This study was aimed to understand the physical and chemical properties of pyrolytic bio-oils produced from microwave pyrolysis of corn stover regarding their potential use as gas turbine and home heating fuels. The ash content, solids content, pH, heating value, minerals, elemental ratio, moisture content, and viscosity of the bio-oils were determined. The water content was approx 15.2 wt%, solids content 0.22 wt%, alkali metal content 12 parts per million, dynamic viscosity 185 mPa.s at 40 degrees C, and gross high heating value 17.5 MJ/kg for a typical bio-oil produced. Our aging tests showed that the viscosity and water content increased and phase separation occurred during the storage at different temperatures. Adding methanol and/or ethanol to the bio-oils reduced the viscosity and slowed down the increase in viscosity and water content during the storage. Blending of methanol or ethanol with the bio-oils may be a simple and cost-effective approach to making the pyrolytic bio-oils into a stable gas turbine or home heating fuels.     

Radial basis function (RBF)‐based parametric models for closed and open curves within the method of regularized stokeslets

The method of regularized Stokeslets (MRS) is a numerical approach using regularized fundamental solutions to compute the flow due to an object in a viscous fluid where inertial effects can be neglected. The elastic object is represented as a Lagrangian structure, exerting point forces on the fluid. The forces on the structure are often determined by a bending or tension model, previously calculated using finite difference approximations. In this paper, we study spherical basis function (SBF), radial basis function (RBF), and Lagrange–Chebyshev parametric models to represent and calculate forces on elastic structures that can be represented by an open curve, motivated by the study of cilia and flagella. The evaluation error for static open curves for the different interpolants, as well as errors for calculating normals and second derivatives using different types of clustered parametric nodes, is given for the case of an open planar curve. We determine that SBF and RBF interpolants built on clustered nodes are competitive with Lagrange–Chebyshev interpolants for modeling twice‐differentiable open planar curves. We propose using SBF and RBF parametric models within the MRS for evaluating and updating the elastic structure. Results for open and closed elastic structures immersed in a 2D fluid are presented, showing the efficacy of the RBF–Stokeslets method. Copyright © 2015 John Wiley & Sons, Ltd.     

DNA purification using dynamic solid-phase extraction on a rotationally-driven polyethylene-terephthalate microdevice

We report the development of a disposable polyester toner centrifugal device for semi-automated, dynamic solid phase DNA extraction (dSPE) from whole blood samples. The integration of a novel adhesive and hydrophobic valving with a simple and low cost microfabrication method allowed for sequential addition of reagents without the need for external equipment for fluid flow control. The spin-dSPE method yielded an average extraction efficiency of ∼45% from 0.6 μL of whole blood. The device performed single sample extractions or accommodate up to four samples for simultaneous DNA extraction, with PCR-readiness DNA confirmed by effective amplification of a β-globin gene. The purity of the DNA was challenged by a multiplex amplification with 16 targeted amplification sites. Successful multiplexed amplification could routinely be obtained using the purified DNA collected post an on-chip extraction, with the results comparable to those obtained with commercial DNA extraction methods. This proof-of-principle work represents a significant step towards a fully-automated low cost DNA extraction device.     

Estimation of activation energies from differential thermal analysis curves

An average activation energy ΔE3 of 31.7 ± 10.0 kcal/mole was calculated from exothermic peaks of urea nitrate differential thermal analysis (DTA) curves using the Murray and White equation and various other reaction rate equations developed by the authors. An average enthalpy of activation, ΔH3 of 30.8 ±9.7 kcal/mole was calculated from the same results. The values of ΔE3 and ΔH3 differed by a fraction of a kcal/mole indicating that ΔE3 <ΔH3 cannot be differentiated experimentally in our study. Application of the Kissinger method of calculating ΔE3 and ΔH3 produced respectively 21.6 ±7.9 and 20.7 ±8.0 kcal/mole, which are quite low. The values of ΔE3 and ΔH3 calculated thermogravimetrically were 28.1, ± 1.1 kcal/mole and 27.6 ± 1.2 kcal/mole which are close to those obtained from the Murray and White approach and the authors' approach to treatment of the DTA data. These results illustrate the pronounced effect of self heating on calculation of activation energies. The Kissinger method of calculating the reaction order developed for endothermic DTA peaks produced good results when applied to the present DTA study.     

Theoretical studies of quantum amplified isomerizations for imaging systems involving hexamethyl Dewar benzene and related systems

The ring-opening reactions of the radical cations of hexamethyl Dewar benzene (1) and Dewar benzene have been studied using density functional theory (DFT) and complete active-space self-consistent field (CASSCF) calculations. Compound 1 is known to undergo photoinitiated ring opening by a radical cation chain mechanism, termed "quantum amplified isomerization" (QAI), which is due to the high quantum yield. Why QAI is efficient for 1 but not other reactions is explained computationally. Two radical cation minima of 1 and transition states located near avoided crossings are identified. The state crossings are characterized by conical intersections corresponding to degeneracy between doublet surfaces. Ring opening occurs by formation of the radical cation followed by a decrease in the flap dihedral angle. A rate-limiting Cs transition state leads to a second stable radical cation with an elongated transannular C-C bond and an increased flap dihedral. This structure proceeds through a conrotatory-like pathway of Cs symmetry to give the benzene radical cation. The role of electron transfer was investigated by evaluating oxidation of various systems using adiabatic ionization energies and electron affinities calculated from neutral and cation geometries. Electron-transfer theory was applied to 1 to investigate the limiting effects of back-electron transfer as it is related to the unusual stability of the two radical cations. Expected changes in optical properties between reactants and products of Dewar benzene compounds and other systems known to undergo QAI were characterized by computing frequency-dependent indices of refraction from isotropic polarizabilities. In particular, the reaction of 1 shows greater contrast in index of refraction than that of the Dewar benzene parent system.     

Interspecific variation in UV defense mechanisms among temperate freshwater fishes

An important step in predicting the effects of future increases in UV radiation (UVR) is to evaluate the mechanisms that organisms use to prevent and repair DNA damage and determine how those mechanisms influence UVR sensitivity. Damage is prevented to varying degrees through photoprotection and repaired via two main pathways: nucleotide excision repair and photoenzymatic repair. At present, little is known about the generality or similarity of these defenses among temperate freshwater fishes. We used laboratory experiments to compare UVR defense mechanisms among five freshwater fish species representing four families and three orders. Purified DNA, freeze-killed larvae and live larvae were exposed to UVB radiation for 12 h in the presence or absence of photorepair radiation. After exposure, we quantified frequencies of cyclobutane pyrimidine dimers in each exposure treatment. All five species used photoprotection and proportional decreases in dimer frequency were similar for all species. Evidence of excision repair was also found for all species but proportional decreases in photoproduct frequencies varied among species. Finally, evidence of photoenzymatic repair was found for only two of the five species.