Learning to Make Sense of Division of Fractions: One K–8 Preservice Teacher's Perspective

Current reform documents in mathematics education recommend that teachers help students develop both conceptual and procedural understandings. However, teachers often do not possess the in-depth mathematical reasoning necessary to accomplish this goal. The purpose of this article is to provide one way in which preservice teachers can come to better understand the mathematics they will teach.     

A probability metrics approach for reducing the bias of optimality gap estimators in two-stage stochastic linear programming

Monte Carlo sampling-based estimators of optimality gaps for stochastic programs are known to be biased. When bias is a prominent factor, estimates of optimality gaps tend to be large on average even for high-quality solutions. This diminishes our ability to recognize high-quality solutions. In this paper, we present a method for reducing the bias of the optimality gap estimators for two-stage stochastic linear programs with recourse via a probability metrics approach, motivated by stability results in stochastic programming. We apply this method to the Averaged Two-Replication Procedure (A2RP) by partitioning the observations in an effort to reduce bias, which can be done in polynomial time in sample size. We call the resulting procedure the Averaged Two-Replication Procedure with Bias Reduction (A2RP-B). We provide conditions under which A2RP-B produces strongly consistent point estimators and an asymptotically valid confidence interval. We illustrate the effectiveness of our approach analytically on a newsvendor problem and test the small-sample behavior of A2RP-B on a number of two-stage stochastic linear programs from the literature. Our computational results indicate that the procedure effectively reduces bias. We also observe variance reduction in certain circumstances.     

An Air‐Stable Semiconducting Polymer Containing Dithieno[3,2‐b:2′,3′‐d]arsole

Arsole‐containing conjugated polymers are a practically unexplored class of materials despite the high interest in their phosphole analogues. Herein we report the synthesis of the first dithieno[3,2‐b;2′,3′‐d]arsole derivative, and demonstrate that it is stable to ambient oxidation in its +3 oxidation state. A soluble copolymer is obtained by a palladium‐catalyzed Stille polymerization and demonstrated to be a p‐type semiconductor with promising hole mobility, which was evaluated by field‐effect transistor measurements.     

Development of a competitive ELISA for the quantification of F5 conjugate in HER2-targeted STEALTH immunoliposome doxorubicin in plasma samples

HER2 (human epidermal growth factor receptor 2, erbB2, or neu) is overexpressed by a large number of tumor types and has been identified as an important target for cancer therapy. F5 is a single-chain human antibody fragment that recognizes HER2 receptor and is covalently conjugated to PEGylated lipid to form F5 conjugate (F5CG) in the product HER2 targeted STEALTH immunoliposome doxorubicin. Here we described the method development of a competitive enzyme-linked immunosorbent assay (ELISA) for the determination of total concentration of F5 conjugate in plasma samples. The method involved the biotinylation of F5CG, detergent treatment of plasma sample to solubilize F5CG into monomeric form, and competitive ELISA for solubilized F5CG competitively binding to anti-F5CG antibody with biotinylated F5CG for the determination of total F5CG in plasma. The detection range of this method was from 0.2 ng/mL to 125 ng/mL for F5CG in plasma. The lower limit of quantification (LLOQ) was 0.2 ng/mL. This method was established and used for the measurement of F5CG concentration to provide information about F5CG circulation after the administration of immunoliposome in preclinical studies.      

Adiabatic and nonadiabatic dynamics in the CH3(CD3)+HCl reaction

The scattering dynamics leading to the formation of Cl (2P(3/2)) and Cl* (2P(1/2)) products of the CH(3)+HCl reaction (at a mean collision energy =22.3 kcal mol(-1)) and the Cl (2P(3/2)) products of the CD(3)+HCl reaction (at =19.4 kcal mol(-1)) have been investigated by using photodissociation of CH(3)I and CD(3)I as sources of translationally hot methyl radicals and velocity map imaging of the Cl atom products. Image analysis with a Legendre moment fitting procedure demonstrates that, in all three reactions, the Cl/Cl* products are mostly forward scattered with respect to the HCl in the center-of-mass (c.m.) frame but with a backward scattered component. The distributions of the fraction of the available energy released as translation peak at f(t)=0.31-0.33 for all the reactions, with average values that lie in the range =0.42-0.47. The detailed analysis indicates the importance of collision energy in facilitating the nonadiabatic transitions that lead to Cl* production. The similarities between the c.m.-frame scattering and kinetic energy release distributions for Cl and Cl* channels suggest that the nonadiabatic transitions to a low-lying excited potential energy surface (PES) correlating to Cl* products occur after passage through the transition state region on the ground-state PES. Branching fractions for Cl* are determined to be 0.14+/-0.02 for the CH(3)+HCl reaction and 0.20+/-0.03 for the CD(3)+HCl reaction. The difference cannot be accounted for by changes in collision energy, mass effects, or vibrational excitation of the photolytically generated methyl radical reagents and instead suggests that the low-frequency bending modes of the CD(3)H or CH(4) coproduct are important mediators of the nonadiabatic couplings occurring in this reaction system.     

Photosystem I/molecular wire/metal nanoparticle bioconjugates for the photocatalytic production of H2

Photosystem I (PS I) is a robust photosynthetic complex that adeptly captures photons to create a charge-separated state with a quantum efficiency that approaches 1.0. This charge-separated state is stable for approximately 100 ms, and the low-potential reductant that is produced is poised at a redox potential favorable for H2 evolution. PS I has been covalently linked to Pt and Au nanoparticle surfaces by 1,6-hexanedithiol which serves as a molecular wire to both connect PS I to the particles and transfer electrons from the terminal electron transfer cofactor of PS I, FB, to the nanoparticle. Illumination of these Photosystem I/molecular wire/nanoparticle bioconjugates is able to catalyze the reaction: 2H+ + 2e(-)--> H2. Transfer of the electrons from PS I to the nanoparticle through the molecular wire is not rate-limiting for H2 evolution. Supplying the system with more efficient donor-side electron donating species results in a 5-fold increase in the rate of H2 evolution.     

Recent Advances in Asymmetric Catalysis Using p-Block Elements

The development of new methods for enantioselective reactions that generate stereogenic centres within molecules are a cornerstone of organic synthesis. Typically, metal catalysts bearing chiral ligands as well as chiral organocatalysts have been employed for the enantioselective synthesis of organic compounds. In this review, we highlight the recent advances in main group catalysis for enantioselective reactions using the p-block elements (boron, aluminium, phosphorus, bismuth) as a complementary and sustainable approach to generate chiral molecules. Several of these catalysts benefit in terms of high abundance, low toxicity, high selectivity, and excellent reactivity. This minireview summarises the utilisation of chiral p-block element catalysts for asymmetric reactions to generate value-added compounds.     

Efficacy and Limitations of Chemically Diverse Small-Molecule Enzyme-Inhibitors against the Synergistic Coagulotoxic Activities of Bitis Viper Venoms

Snakebite remains a significant public health burden globally, disproportionately affecting low-income and impoverished regions of the world. Recently, researchers have begun to focus on the use of small-molecule inhibitors as potential candidates for the neutralisation of key snake venom toxins and as potential field therapies. Bitis vipers represent some of the most medically important as well as frequently encountered snake species in Africa, with a number of species possessing anticoagulant phospholipase A₂ (PLA₂) toxins that prevent the prothrombinase complex from inducing clot formation. Additionally, species within the genus are known to exert pseudo-procoagulant activity, whereby kallikrein enzymatic toxins cleave fibrinogen to form a weak fibrin clot that rapidly degrades, thereby depleting fibrinogen levels and contributing to the net anticoagulant state. Utilising well-validated coagulation assays measuring time until clot formation, this study addresses the in vitro efficacy of three small molecule enzyme inhibitors (marimastat, prinomastat and varespladib) in neutralising these aforementioned activities. The PLA₂ inhibitor varespladib showed the greatest efficacy for the neutralisation of PLA₂-driven anticoagulant venom activity, with the metalloproteinase inhibitors prinomastat and marimastat both showing low and highly variable degrees of cross-neutralisation with PLA₂ anticoagulant toxicity. However, none of the inhibitors showed efficacy in neutralising the pseudo-procoagulant venom activity exerted by the venom of B. caudalis. Our results highlight the complex nature of snake venoms, for which single-compound treatments will not be universally effective, but combinations might prove highly effective. Despite the limitations of these inhibitors with regards to in vitro kallikrein enzyme pseudo-procoagulant venom activity, our results further support the growing body of literature indicating the potential use of small molecule inhibitors to enhance first-aid treatment of snakebite envenoming, particularly in cases where hospital and thus antivenom treatment is either unavailable or far away.