The development of children's understanding of mathematical patterns through mathematical activities

In this paper we report how children (aged 8) developed their mathematical understanding through number tasks based on the Fibonacci sequence (Bamboo numbers) used in the context of a Substantial Learning Environment (SLE), which is designed to be mathematically rich, have a clear purpose and give opportunities to utilise mathematical thinking. The flexible nature of the SLEs makes it possible for teachers and children to explore various mathematical patterns. To capture children's activities when working within SLEs, we make particular reference to Pegg and Tall's work in 2005, and consider a theoretical framework based on the SOLO taxonomy (Biggs and Collis 1982) and the developmental process of understanding mathematical concepts. It was found that the key progression to be made through learning using our Bamboo number-based SLEs is from Multi-structural to Relational levels. It was also suggested that it is difficult for many children to understand the structural aspects of number patterns.     

Bifurcations and chaos in register transitions of excised larynx experiments

Experimental data from an excised larynx are analyzed in the light of nonlinear dynamics. The excised larynx provides an experimental framework that enables artificial control and direct observation of the vocal fold vibrations. Of particular interest in this experiment is the coexistence of two distinct vibration patterns, which closely resemble chest and falsetto registers of the human voice. Abrupt transitions between the two registers are typically accompanied by irregular vibrations. Two approaches are presented for the modeling of the excised larynx experiment; one is the nonlinear predictive modeling of the experimental time series and the other is the biomechanical modeling (three-mass model) that takes into account basic mechanisms of the vocal fold vibrations. The two approaches show that the chest and falsetto vibrations correspond to two coexisting limit cycles, which jump to each other with a change in the bifurcation parameter. Irregular vibrations observed at the register jumps are due to chaos that exists near the two limit cycles. This provides an alternative mechanism to generate chaotic vibrations in excised larynx experiment, which is different from the conventionally known mechanisms such as strong asymmetry between the left and right vocal folds or excessively high subglottal pressure.     

Multicomponent QM study on the reaction of HOSO + NO2 with H2O: Nuclear quantum effect on structure and reaction energy profile

The hydrogen transfer reaction in the reaction of HOSO + NO₂ with and without H₂O have been investigated using multicomponent quantum-mechanics method, which can directly take nuclear quantum effect (NQE) of light nuclei into account. For the case of the reaction without H₂O, our calculation reveals that the reaction leading to trans-HONO is preferred. For the reaction with H₂O, water-non-mediated and water-mediated (hydrogen-relay) hydrogen transfer mechanism are investigated. The NQE of hydrogen nucleus lowers the relative energy of the stationary point structures and reduces the activation barrier of the reactions. The largest stabilization is found in the transition state structure of the hydrogen-relay type reaction. H/D isotope effects for the reactions are also analyzed. In particular, H/D isotope effect on the activation barrier is analyzed in detail with the aid of the active strain model.     

Chemical Interactions of Cryptic Actinomycete Metabolite 5‐Alkyl‐1,2,3,4‐tetrahydroquinolines through Aggregate Formation

Organisms often produce secondary metabolites as a mixture of biosynthetically related congeners. However, why are metabolites with minor chemical variations produced simultaneously? 5‐Alkyl‐1,2,3,4‐tetrahydroquinolines (5aTHQs) are small, lipophilic metabolites produced by Streptomyces nigrescens HEK616 when cultured with Tsukamurella pulmonis TP‐B0596. A mixture of 5aTHQs forms aggregates that show enhanced membrane affinity and biological activity. The ability to form aggregates and membrane‐binding activity is regulated by the length of the alkyl chains. Aggregates with long alkyl chains were too stable to fuse with lipid membranes. However, if inactive 5aTHQ congener was mixed with active congener, the mixture showed increased membrane affinity, enabling cellular entry and biological activity. Therefore, it is shown that sloppiness in a biosynthetic pathway, by which minor structural variations can be produced, is functionally rational, as the metabolites show synergistic action.     

Zirconia-based planar NO2 sensor using ultrathin NiO or laminated NiO–Au sensing electrode

The nanostructured thin NiO films with the thicknesses of 30–180 nm were examined as a sensing electrode (SE) for the planar mixed-potential-type yttria-stabilized zirconia (YSZ)-based NO₂ sensor. The sensing characteristics were examined in the temperature range of 600–800 °C under the wet condition (5 vol.% water vapor). Among the NiO-SEs tested, the 60 nm-thick NiO-SE sintered at 1,000 °C was found to give the highest NO₂ sensitivity in the NO₂ concentration range of 50–400 ppm accompanying with fast response/recovery at the operating temperatures of 600–700 °C. The high NO₂ sensitivity was attributed to the high catalytic activity for both electrochemical reactions of O₂ and NO₂ at the interface of NiO-SE/YSZ. The ultrathin gold layer with the thickness of about 60 nm was additionally formed on the 60 nm-thick NiO-SE to fabricate the laminated-type (60 nm NiO/60 nm Au)-SE. It was demonstrated that the use of this laminated (NiO–Au)-SE improved both the sensitivity and the selectivity to NO₂.     

Biosynthesis of Indole Diterpene Lolitrems: Radical-Induced Cyclization of an Epoxyalcohol Affording a Characteristic Lolitremane Skeleton

Lolitrems are tremorgenic indole diterpenes that exhibit a unique 5/6 bicyclic system of the indole moiety. Although genetic analysis has indicated that the prenyltransferase LtmE and the cytochrome P450 LtmJ are involved in the construction of this unique structure, the detailed mechanism remains to be elucidated. Herein, we report the reconstitution of the biosynthetic pathway for lolitrems employing a recently established genome-editing technique for the expression host Aspergillus oryzae. Heterologous expression and bioconversion of the various intermediates revealed that LtmJ catalyzes multistep oxidation to furnish the lolitrem core. We also isolated the key reaction intermediate with an epoxyalcohol moiety. This observation allowed us to establish the mechanism of radical-induced cyclization, which was firmly supported by density functional theory calculations and a model experiment with a synthetic analogue.     

Ab initio study of NMR spectra of Li2S–SiS2 glass system

We obtained the chemical shielding constants of ²⁹Si in Li₂S–SiS₂ glass system on the basis of molecular orbital calculations. The relative chemical shieldings calculated at the HF/6-31G* level is −16.1 and −23.8 ppm for E(1) and E(0), respectively. These calculations are in good agreement with the previous NMR study: σ(E(2))>σ(E(1))>σ(E(0)). It is found theoretically that incorporation of Li₂S into SiS₂ does not influence the ²⁹Si chemical shift, while incorporation of Li₂O into SiO₂ does to a significant extent. It is also found that the existence of oxygen in Li₂S–SiS₂ glasses increases the chemical shielding of ²⁹Si by about 25 ppm, which is in good agreement with the experimental result.     

Structure revision of spiroleucettadine, a sponge alkaloid with a bicyclic core meager in H-atoms

Our 2004 disclosure of the amino hemiketal-containing spiroleucettadine was met with keen interest by the natural products and synthetic communities. As repeated efforts to synthesize spiroleucettadine failed and questions regarding the original structure elucidation process arose, evidence mounted against the validity of the proposed structure. The low ratio of H/C in the core of spiroleucattadine complicated the original structure elucidation process. Speculation prompted a reisolation of spiroleucettadine from an untouched portion of the original Luecetta collection and a thorough analysis of analytical data. In addition, a systematic analysis of candidate structures was performed via density functional theory (DFT) calculations; a favored high scoring structure 1b was ultimately confirmed to be spiroleucettadine via X-ray analysis of crystalline spiroleucettadine and reinforced the validity of DFT calculations in structure elucidation. We present the revised structure of spiroleucettadine, a bicyclic sponge alkaloid with a scarcity of H-atoms in its core.     

Total Biosynthesis of Melleolides from Basidiomycota Fungi: Mechanistic Analysis of the Multifunctional GMC Oxidase Mld7

Mushroom terpenoids are biologically and chemically diverse fungal metabolites. Among them, melleolides are representative sesquiterpenoids with a characteristic protoilludane skeleton. In this study, we applied a recently established hot spot knock-in method to elucidate the biosynthetic pathway leading to 1α-hydroxymelleolide. The biosynthesis of the sesquiterpene core involves the cytochrome P450 catalyzing stepwise hydroxylation of the Δ⁶-protoilludene framework and a stereochemical inversion process at the C5 position catalyzed by short-chain dehydrogenase/reductase family proteins. The highlight of the biosynthesis is that the flavoprotein Mld7 catalyzes an oxidation-triggered double-bond shift accompanying dehydration and acyl-group-assisted substitution with two different nucleophiles at the C6 position to afford the Δ⁷-protoilludene derivatives, such as melleolide and armillarivin. The complex reaction mechanism was proposed by DFT calculations. Of particular importance is that product distribution is regulated by interaction with the cell membrane.