Rethinking the discovery function of proof within the context of proofs and refutations

Proof and proving are important components of school mathematics and have multiple functions in mathematical practice. Among these functions of proof, this paper focuses on the discovery function that refers to invention of a new statement or conjecture by reflecting on or utilizing a constructed proof. Based on two cases in which eighth and ninth graders engaged in proofs and refutations, we demonstrate that facing a counterexample of a primitive statement can become a starting point of students’ activity for discovery, and that a proof of the primitive statement can function as a useful tool for inventing a new conjecture that holds for the counterexample. An implication for developing tasks by which students can experience this discovery function is mentioned.     

Self‐Assembly of Metal–Organic Frameworks into Monolithic Materials with Highly Controlled Trimodal Pore Structures

We present a two‐step template‐free approach toward monolithic materials with controlled trimodal porous structures with macro‐, meso‐, and micropores. Our method relies on two ordering processes in discrete length scales: 1) Spontaneous formation of macroporous structures in monolithic materials by the sol–gel process through the short‐range ordered self‐assembly of metal–organic frameworks (MOFs), and 2) reorganization of the framework structures in a mediator solution. The Zr‐terephthalate‐based MOF (UiO‐66‐NH₂) was adopted as a proof of concept. The self‐assembly‐induced phase separation process offered interconnected macropores with diameters ranging from 0.9 to 1.8 μm. The subsequent reorganization process converted the microporous structure from low crystalline framework to crystalline UiO‐66. The resultant mesopore size within the skeletons was controlled in the range from 9 to 21 nm. This approach provides a novel way of designing spaces from nano‐ to micrometer scale in network‐forming materials.     

Development of non-destructive isotopic analysis methods using muon beams and their application to the analysis of lead

Journal of Radioanalytical and Nuclear Chemistry - Elemental isotopic ratios are measured in various research fields and provide useful information regarding age, origin, geological and biological...     

Promotion of Cell Migration into a Hydrophobically modified Alaska Pollock Gelatin‐Based Hydrogel

In situ chemically cross‐linkable hydrogels composed of hexyl group–modified Alaska pollock–derived gelatin (C6‐ApGltn) and poly(ethylene glycol)‐based four‐armed cross‐linker is developed. Water droplets are quickly absorbed into the C6‐ApGltn hydrogel in the first 10 s compared with original ApGltn (Org‐ApGltn), and the final contact angle on C6‐ApGltn is significantly lower than that on Org‐ApGltn. Using a fluorescent probe, an increase in fluorescence intensity on C6‐ApGltn compared to that on Org‐ApGltn is found, indicating the formation of a hydrophobic pocket. Moreover, the promotion of cell migration into the C6‐ApGltn hydrogel is observed in vitro and in vivo compared with Org‐ApGltn hydrogel, despite no significant difference in elastic modulus. Therefore, the C6‐ApGltn hydrogel could potentially be used as a supporting material for cell transplantation and tissue/organ engineering.     

Fiber-optic distributed measurement of polarization beat length using slope-assisted Brillouin optical correlation-domain reflectometry

Optical Review - We demonstrate distributed measurement of the polarization beat length along single-mode optical fibers (SMFs) using slope-assisted Brillouin optical correlation-domain...     

Regioselective protection of sugars catalyzed by dimethyltin dichloride

The first catalytic process for protection of hydroxyl groups in sugars has been developed. Highly regioselective protection was accomplished along with high chemical yield. The regioselectivity of the benzoylation was realized as an intrinsic character of sugars based on a stereorelationship among their hydroxyl groups. Furthermore, complete protection of alpha-methyl glucoside and beta-methyl xyloside was accomplished.     

Synthesis of syn‐2,4‐Dimercapto‐1,3,2,4‐dithiadigermetane and Its Application to Ge2PdS4 Cluster Synthesis

The sulfurization of DmpGeH₃ (Dmp=2,6‐dimesitylphenyl) afforded the trinuclear germanium sulfide [DmpGe(μ‐S)]₂(μ‐S)₂Ge(SH)‐Dmp and a series of polythiadigermabicyclo[x.1.1]alkanes (x=3, 4, 5). The reduction of the S? S bonds of these germabicycloalkanes by NaBH₄ at 0 °C afforded the dinuclear mercaptogermane syn‐[DmpGe(SH)(μ‐S)₂Ge(SH)‐Dmp] ( 5 ) in good yield. The reaction of [Pd(dppe)Cl₂] (dppe=1,2‐bis(diphenylphosphanyl)ethane) and the dilithium salt of 5 prepared in situ by the addition of nBuLi (2 equiv) gave the Ge₂PdS₄ cluster [DmpGe(μ‐S)]₂[(μ‐S)₂Pd(dppe)], in which the dithiadigermetanedithiolate is bound to the Pd atom at the two thiolato sulfur atoms. The same reaction with [Pd(PPh₃)₂Cl₂] gave another Ge₂PdS₄ cluster, [DmpGe(μ‐S)]₂[(μ‐S)₂Pd(PPh₃)], but with the dithiadigermetanedithiolate and the Pd center conjoined through a μ‐S atom between the two germanium atoms in addition to the two thiolato sulfur atoms to form a highly distorted cluster core. The formation of two different types of Ge₂PdS₄ clusters represents the usefulness of 5 in the synthesis of various polynuclear complexes composed of germanium and transition metals.     

Facile unidirectional alignment of mesochannels in a mesoporous silica film on a freshly cleaved mica surface

The alignment of mesochannels in a mesoporous silica film on a freshly cleaved mica surface, prepared by an evaporation-induced self-assembly process, is unexpectedly found to be unidirectional with the narrowest directional distribution.     

Construction of L‐Lysine Sensor by Layer‐by‐Layer Adsorption of L‐Lysine 6‐Dehydrogenase and Ferrocene‐Labeled High Molecular Weight Coenzyme Derivative on Gold Electrode

A ferrocene‐labeled high molecular weight coenzyme derivative (PEI‐Fc‐NAD) and a thermostable NAD‐dependent L ‐lysine 6‐dehydrogenase (LysDH) from thermophile Geobacillus stearothermophilus were used to fabricate a reagentless L ‐lysine sensor. Both LysDH and PEI‐Fc‐NAD were immobilized on the surface of a gold electrode by consecutive layer‐by‐layer adsorption (LBL) technique. By the simple LBL method, the reagentless L ‐lysine sensor, with co‐immobilization of the mediator, coenzyme, and enzyme was obtained, which exhibited current response to L ‐lysine without the addition of native coenzyme to the analysis system. The amperometric response of the sensor was dependent on the applied potential, bilayer number of PEI‐Fc‐NAD/LysDH, and substrate concentration. A linear current response, proportional to L ‐lysine concentration in the range of 1–120 mM was observed. The response of the sensor to L ‐lysine was decreased by 30% from the original activity after one month storage.     

Polymer-like polyphenols of black tea and their lipase and amylase inhibitory activities

Lipase and amylase inhibitory activities of black tea were examined. After solvent partitioning of a black tea extract with the ethyl acetate and n-butanol, the two soluble fractions showed comparable inhibitory activities. Activity in the ethyl acetate fraction was mainly attributable to polyphenols with low-molecular weights, such as theaflavin gallates. On the other hand, the active substance in the n-butanol layer was ascertained to be a polymer-like substance. 1H- and 13C-NMR spectra showed signals arising from the flavan A-ring and galloyl groups, although signals due to flavan B-rings were not detected, suggesting that the polymer-like substances were generated by oxidative condensation of flavan B-rings, a result which was previously deduced from our results of in vitro catechin oxidation experiments. Enzymatic oxidation of epicatechin 3-O-gallate produced a similar polymer-like substance and suggested that condensation between a B-ring and galloyl groups was involved in the polymerization reaction.