Developing the roots of modelling conceptions: ‘mathematical modelling is the life of the world’

A study conducted with 25 Year 6 primary school students investigated the potential for a short classroom intervention to begin the development of a Modelling conception of mathematics on the way to developing a sense of mathematics as a way of thinking about life. The study documents the developmental roots of the cognitive activity, actions and conceptions of both modelling and mathematics that these beginners to modelling displayed. Understanding the conceptions of mathematics that students might hold or be developing and how these can be influenced in early schooling are essential ingredients in any plans for introducing modelling seriously into primary school classrooms. The majority of the students (22/25) were identified as displaying a developing conception of modelling as a way of problem handling. The three other students displayed the developmental roots of a way of understanding the world conception of modelling. These three students also displayed a Modelling conception of mathematics with one showing indications of developing towards a Life conception of mathematics.     

Diffusion controlled hydrogen atom abstraction from tertiary amines by the benzyloxyl radical. The importance of C-H/N hydrogen bonding

The rate constants for H-atom abstraction (k(H)) from 1,4-cyclohexadiene (CHD), triethylamine (TEA), triisobutylamine (TIBA), and DABCO by the cumyloxyl (CumO(?)) and benzyloxyl (BnO(?)) radicals were measured. Comparable k(H) values for the two radicals were obtained in their reactions with CHD and TIBA whereas large increases in k(H) for TEA and DABCO were found on going from CumO(?) to BnO(?). These differences are attributed to the rate-determining formation of BnO(?) C-H/amine N lone-pair H-bonded complexes.     

Enantiopure cis- and trans-2,5-disubstituted-2,5-dihydrofurans from d-allal- and d-galactal-derived vinyl epoxides

Upon treatment with the metal enolates of methylene active compounds (dimethyl malonate and dibenzoylmethane) (C-nucleophiles) and benzyl carbamate (N-nucleophile), d-allal- and d-galactal-derived vinyl epoxides are stereoselectively transformed, in a single step, into diastereoisomeric, highly functionalized, enantiopure cis- and trans-2,5-disubstituted-2,5-dihydrofurans.     

DNA quantitation and degradation assessment: a quantitative PCR protocol designed for small forensic genetics laboratories

For over 10 years, quantitative PCR (qPCR) for DNA quantitation has been reported in forensics. However, assays have not been described for small qPCR platforms. Thus, technological advancement is not always implemented in small forensic genetics laboratories. A duplex qPCR assay is reported, using a StepOne instrument and targeting a short and a long human DNA region. This study was performed according to international validation guidelines, including sensitivity, repeatability, reproducibility, precision, accuracy, contamination assessment, known and case-type samples, and degradation studies. Characterization of the genetic markers, species specificity, and population studies had already been conducted. Moreover, case-type samples were quantified, amplified using commercial kits and the number of alleles detected was recorded. Sensitivity was shown to be 10 pg/µL. Standard curve replicates demonstrated the assay is accurate, precise, as well as fairly repeatable and reproducible. The NGM Detect kit was shown to yield higher peaks than Identifiler Plus and NGM Select for degraded samples. Moreover, quality sensors were always present and proved useful. The quantification values of the large target showed a correlation with the number of alleles detected in the STR profiles for known and casework samples. The degradation index was shown to be informative, with a value of 10 or higher indicating dropout. It is suggested that after quantitation, samples with low or degraded DNA be amplified using newer amplification kits containing quality sensors to confirm that the low-quality profile was not affected by inhibition.     

Chemical Composition and Antibacterial and Antioxidant Activity of a Citrus Essential Oil and Its Fractions

Essential oils (EOs) from Citrus are the main by-product of Citrus-processing industries. In addition to food/beverage and cosmetic applications, citrus EOs could also potentially be used as an alternative to antibiotics in food-producing animals. A commercial citrus EO—Brazilian Orange Terpenes (BOT)—was fractionated by vacuum fractional distillation to separate BOT into various fractions: F1, F2, F3, and F4. Next, the chemical composition and biological activities of BOT and its fractions were characterized. Results showed the three first fractions had a high relative amount of limonene (≥10.86), even higher than the whole BOT. Conversely, F4 presented a larger relative amount of BOT’s minor compounds (carvone, cis-carveol, trans-carveol, cis-p-Mentha-2,8-dien-1-ol, and trans-p-Mentha-2,8-dien-1-ol) and a very low relative amount of limonene (0.08–0.13). Antibacterial activity results showed F4 was the only fraction exhibiting this activity, which was selective and higher activity on a pathogenic bacterium (E. coli) than on a beneficial bacterium (Lactobacillus sp.). However, F4 activity was lower than BOT. Similarly, F4 displayed the highest antioxidant activity among fractions (equivalent to BOT). These results indicated that probably those minor compounds that detected in F4 would be more involved in conferring the biological activities for this fraction and consequently for the whole BOT, instead of the major compound, limonene, playing this role exclusively.     

Organocatalytic,Asymmetric Eliminative [4+2] Cycloaddition of Allylidene Malononitriles with Enals: Rapid Entry to Cyclohexadiene‐Embedding Linear and Angular Polycycles

A direct aminocatalytic synthesis has been developed for the chemo‐, regio‐, diastereo‐, and enantioselective construction of densely substituted polycyclic carbaldehydes containing fused cyclohexadiene rings. The chemistry utilizes, for the first time, remotely enolizable π‐extended allylidenemalononitriles as electron‐rich 1,3‐diene precursors in a direct eliminative [4+2] cycloaddition with both aromatic and aliphatic α,β‐unsaturated aldehydes. The generality of the process is demonstrated by approaching 6,6‐, 5,6‐, 7,6‐, 6,6,6‐, and 6,5,6‐fused ring systems, as well as biorelevant steroid‐like 6,6,6,6,5‐ and 6,6,6,5,6‐rings. A stepwise reaction mechanism for the key [4+2] addition is proposed as a domino bis‐vinylogous Michael/Michael/retro‐Michael reaction cascade. The utility of the malononitrile moiety as traceless activating group of the dicyano nucleophilic substrates is demonstrated.     

Diastereo- and enantioseparation of a N-Boc amino acid with a zwitterionic quinine-based stationary phase: Focus on the stereorecognition mechanism

A chiral chromatography method enabling the simultaneous diastereo- and enantioseparation of N^α-Boc-N⁴-(hydroorotyl)-4-aminophenylalanine [Boc-Aph(Hor)-OH, 1] was optimized with a quinine-based zwitterionic stationary phase. The polar-ionic eluent system consisting of ACN:MeOH:water—49.7:49.7:0.6 (v/v/v) with formic acid (4.0 mM) and diethylamine (2.5 mM), allowed the successful separation of the four acid stereoisomers: α_d,d-/d,l-1 = 1.08; α_d,l-/l,d-1 = 1.08; α_l,d-/l,l-1 = 1.40.