Determination of Paint Solvents by Vapour Phase Fourier Transform Infrared Spectrometry.

A fast procedure has been developed for the direct determination of paint solvents. The method is based on the injection of small volumes of untreated solvent mixtures into a heated Pyrex glass reactor in which the sample is volatilized and introduced by means of a flow of nitrogen into an IR multiple pass gas cell and the spectrum in the mid-IR region is registered as a function of time. Data found for samples are interpolated in calibration graphs obtained by injecting different volumes of pure compounds which constitute the solvent mixture. A methylisobutylketone (MIBK) toluene mixture was used as test system to develop the proposed procedure. The method provides a limit of detection of the order of 1–4 μg, a relative standard deviation of the order of 0.4 to 2% for five independent measurements, and recovery percentage values from 99.8 till 103.6 %. A commercial sample of polyurethane paint solvent has been analysed by the developed procedure.     

Unexpected reactivity of pyridinium salts toward alkynyl Fischer complexes to produce oxo‐heterocycles

The unprecedented reaction of ketone‐containing aromatic pyridinium salts 3a ‐ e and alkynyl Fischer complexes 1a ‐ f proceeds via a mild domino process to provide 4,6‐disubstituted pyran‐2‐ones 5a ‐ k and 2,3,5‐trisubstituted furans 6a ‐ h (45‐97%). According of the results of isotopic labeling experiments, a mechanism involving an initial Michael addition appears to be the key step, obtaining a mesomeric structure responsible for the formation of both products.     

Montecrinanes A–C: Triterpenes with an Unprecedented Rearranged Tetracyclic Skeleton from Celastrus vulcanicola. Insights into Triterpenoid Biosynthesis Based on DFT Calculations

Three new triterpenoids with an unprecedented 6/6/6/6‐fused tetracyclic carbon skeleton, montecrinanes A–C ( 1 – 3 ), were isolated from the root bark of Celastrus vulcanicola, along with known D:B‐friedobaccharanes ( 4 – 6 ), and lupane‐type triterpenes ( 7 – 12 ). The stereostructures of the new metabolites were elucidated based on spectroscopic (1D and 2D NMR) and spectrometric (HR‐EIMS and HR‐ESIMS) techniques. Their absolute configurations were determined by both NMR spectroscopy, with (R)‐(?)‐α‐methoxyphenylacetic acid as a chiral derivatizing agent, and biogenetic considerations. Biogenetic pathways for montecrinane and D:B‐friedobaccharane skeletons were proposed and studied by DFT methods. The theoretical results support the energetic feasibility of the putative biogenetic pathways, in which the 1,2‐methyl shift from the secondary baccharenyl cation represents a novel and key reaction step for a new montecrinane skeleton.     

Pedagogical challenges in making mathematics relevant for Indigenous Australians

After the invasion and occupation of their land by Europeans, Indigenous Australians were expected to benefit from a Western education system based on that of the dominant Europeans. Gradually educators realized that Aboriginal children learn differently and that Indigenous culture and pedagogy has validity and strength. Of course, educators also need to be acutely aware of the diversity of Indigenous cultures in Australia and that there is not a monolithic sense of Aboriginal identity or Aboriginal pedagogy. Dispossession and alienation, poor health and few employment opportunities must also affect educational interest, attendance, application and performance. In this paper the characteristics of Indigenous learners are examined and pedagogical strategies to assist in both students' learning and teachers' delivery are explored. The message conveyed in this paper has particular relevance for teaching mathematics to Aboriginal learners. It is also of considerable value in teaching mathematics to nonAboriginal students, in Australia and elsewhere.     

Wide binaries as a critical test of classical gravity

Modified gravity scenarios where a change of regime appears at acceleration scales a<a ₀ have been proposed. Since for 1M _⊙ systems the acceleration drops below a ₀ at scales of around 7000 AU, a statistical survey of wide binaries with relative velocities and separations reaching 10⁴ AU and beyond should prove useful to the above debate. We apply the proposed test to the best currently available data. Results show a constant upper limit to the relative velocities in wide binaries which is independent of separation for over three orders of magnitude, in analogy with galactic flat rotation curves in the same a<a ₀ acceleration regime. Our results are suggestive of a breakdown of Kepler’s third law beyond a≈a ₀ scales, in accordance with generic predictions of modified gravity theories designed not to require any dark matter at galactic scales and beyond.     

One-Step Generalized Estimating Equations With Large Cluster Sizes

Medical studies increasingly involve a large sample of independent clusters, where the cluster sizes are also large. Our motivating example from the 2010 Nationwide Inpatient Sample (NIS) has 8,001,068 patients and 1049 clusters, with average cluster size of 7627. Consistent parameter estimates can be obtained naively assuming independence, which are inefficient when the intra-cluster correlation (ICC) is high. Efficient generalized estimating equations (GEE) incorporate the ICC and sum all pairs of observations within a cluster when estimating the ICC. For the 2010 NIS, there are 92.6 billion pairs of observations, making summation of pairs computationally prohibitive. We propose a one-step GEE estimator that (1) matches the asymptotic efficiency of the fully iterated GEE; (2) uses a simpler formula to estimate the ICC that avoids summing over all pairs; and (3) completely avoids matrix multiplications and inversions. These three features make the proposed estimator much less computationally intensive, especially with large cluster sizes. A unique contribution of this article is that it expresses the GEE estimating equations incorporating the ICC as a simple sum of vectors and scalars.     

Optimisation of sensor positions in random linear arrays based on statistical relations between geometry and performance

Due to the widespread use of acoustic arrays, optimisation techniques for array design, focused on improving array performance, have been widely published. This paper exploits the statistical relation between different measures of sidelobe levels and the spacing of elements in random linear arrays made up of a small number of sensors. This paper defines the methodology to obtain maximum probability functions, associating array geometry and performance. These maximum probability functions allow a pre-selection of those array geometries that are more likely to be associated to specified sidelobe level values. This pre-selection results in a significantly reduced computational burden.     

Simplified model for mass diffusivity estimation based on dynamic pendant drop volume analysis

We present a simplified correlation for calculating the dissolved gas moles in a pendant drop during the diffusion time, for several drop shapes. After this correlation is determined, the Yang and Gu (Ind Eng Chem Res 44:4474–4483, 2005) dynamic pendant drop volume analysis (DPDVA) method for calculation of mass diffusivity from the pendant drop volume variation against time can be used. We solved the differential equation in cylindrical coordinates for the mass transfer model of the gas diffusion into the liquid inside the pendant drop, using a different characteristic length (L_C), instead of the outer radius of the syringe needle (r_n) used in Yang and Gu (Ind Eng Chem Res 44:4474–4483, 2005) for defining the dimensionless variables. L_C is the relationship between the pendant drop volume and its mass transfer surface area at the initial conditions. The generalized correlation saves time, simplifies the method application and the deviations in the diffusion coefficient calculation respect to the complete Yang and Gu model are below 6%.     

Relation between structure and enthalpy for stacking interactions of aromatic molecules

An approximately linear correlation has been found between the enthalpy of complexation and the area of overlap of the chromophores using published structural and thermodynamical data on the self- and hetero-association of aromatic molecules measured under similar solution conditions. This finding is consistent with the assumption that short-range van-der-Waals forces dominate over other contributions to the enthalpy of stacking of aromatic molecules. It provides a ‘model-independent’ approach for a priori estimation of the enthalpy of aromatic–aromatic stacking interactions from knowledge of the structural properties or vice versa.     

Exploring the Effect of Ligand Structural Isomerism in Langmuir–Blodgett Films of Chiral Luminescent EuIII Self‐Assemblies

Here we have investigated the influence of the antenna group position on both the formation of chiral amphiphilic Eu^III‐based self‐assemblies in CH₃CN solution and, on the ability to form monolayers on the surface of quartz substrates using the Langmuir–Blodgett technique, by changing from the 1‐naphthyl ( 2(R) , 2(S) ) to the 2‐naphthyl ( 1(R) , 1(S) ) position. The evaluation of binding constants of the self‐ assemblies in CH₃CN solution was achieved using conventional techniques such as UV/Visible and luminescence spectroscopies along with more specific circular dichroism (CD) spectroscopy. The binding constants obtained for EuL , EuL₂ and EuL₃ species in the case of 2‐naphthyl derivatives were comparable to those obtained for 1‐naphthyl derivatives. The analysis of the changes in the CD spectra of 1(R) and 1(S) upon addition of Eu^III not only allowed us to evaluate the values of the binding constants but the resulting recalculated spectra may also be used as fingerprints for assignment of the chiral self‐assembly species formed in solution. The obtained monolayers were predominantly formed from EuL₃ (≈85 %) with the minor species present in ≈15 % EuL₂ .