Invention of new statements for counterexamples

ArticleLiljedahl, P., Oesterle, S., Nicol, C., & Allan, D. (Eds.). (2014). Proceedings of the Joint Meeting of PME 38 and PME-NA 36 (Vol. 4):17-24 . Vancouver, Canada: PME.conference pape

Proof validation and modification by example generation: A classroom-based intervention in secondary school geometry

ArticleProceedings of the 13th International Congress on Mathematical Education (ICME-13). Hamburg, Germany, 2016-7-24/31, ICME. (2016)journal articl

Lakatos’ heuristic rules as a framework for proofs and refutations in mathematical learning: Local-counterexample and modification of proof

ArticleProceedings of the 12th International Congress on Mathematical Education (ICME-12). COEX, Seoul, Korea, 2012-7-8/15, ICME. 2838-2847 (2012)conference pape

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.ArticleInternational Journal of Mathematical Education in Science and Technology. 45(7):1053-1067 (2014)journal articl

Proof problems with diagrams: An opportunity for experiencing proofs and refutations

It has become gradually accepted that proof and proving are essential at all grades of mathematical learning. Among the various aspects of proof and proving, this study addresses proofs and refutations described by Lakatos, in particular a part of increasing content by deductive guessing, to introduce an authentic process into mathematics classrooms. This paper analyzes proof problems with diagrams as an appropriate task for this mathematical action, and illustrates, with a sequence of three lessons in the eighth grade, that a certain type of such problems can provide students with an opportunity to engage in this action.ArticleFor the Learning of Mathematics. 34(1):36-42 (2014)journal articl

A Case of Dominant Dystrophic Epidermolysis Bullosa with a G2043R Mutation in the Type VII Collagen Gene

Dystrophic epidermolysis bullosa (DEB) is a subepidermal bulla, characterized by severe itching, lichenoid or nodular prurigo-like lesions, skin erosion, scars, milia, and nail dystrophy, resulting from COL7A1 mutation. Herein, we report a case of dominant DEB with a G2043R mutation in COL7A1

Organosilica nanoparticles containing sodium borocaptate (BSH) provide new prospects for boron neutron capture therapy (BNCT): efficient cellular uptake and enhanced BNCT efficacy

Boron neutron capture therapy (BNCT), a method based on the fission of boron-10 upon neutron irradiation, has emerged as an attractive option for radiation therapy. To date, the main drugs used in BNCT are 4-boronophenylalanine (BPA) and sodium borocaptate (BSH). While BPA has been extensively tested in clinical trials, the use of BSH has been limited, mainly due to its poor cellular uptake. Here, we describe a novel type of mesoporous silica-based nanoparticle containing BSH covalently attached to a nanocarrier. Synthesis and characterization of these nanoparticles (BSH-BPMO) are presented. The synthetic strategy involves a click thiol–ene reaction with the boron cluster, providing hydrolytically stable linkage with the BSH in four steps. The BSH-BPMO nanoparticles were efficiently taken up into cancer cells and accumulated in the perinuclear region. Inductively coupled plasma (ICP) measurements of boron uptake in cells highlight the important role of the nanocarrier in the enhancement of boron internalization. BSH-BPMO nanoparticles were also taken up and distributed throughout tumour spheroids. BNCT efficacy was examined by the neutron exposure of the tumour spheroids. BSH-BPMO loaded spheroids were completely destroyed upon neutron irradiation. In contrast, neutron irradiation of tumour spheroids loaded with BSH or BPA resulted in significantly less spheroid shrinkage. The significant difference in BNCT efficacy of the BSH-BPMO was correlated with the improved boron uptake via the nanocarrier. Overall, these results demonstrate the critical role of the nanocarrier in BSH internalization and the enhanced BNCT efficacy of the BSH-BPMO compared with BSH and BPA, two drugs used in BNCT clinical trials

Contrasting life-history responses to climate variability in eastern and western North Pacific sardine populations

大洋の東西で異なるマイワシの環境応答 --耳石が示すグローバル生存戦略の鍵--. 京都大学プレスリリース. 2022-10-17.Massive populations of sardines inhabit both the western and eastern boundaries of the world’s subtropical ocean basins, supporting both commercial fisheries and populations of marine predators. Sardine populations in western and eastern boundary current systems have responded oppositely to decadal scale anomalies in ocean temperature, but the mechanism for differing variability has remained unclear. Here, based on otolith microstructure and high-resolution stable isotope analyses, we show that habitat temperature, early life growth rates, energy expenditure, metabolically optimal temperature, and, most importantly, the relationship between growth rate and temperature are remarkably different between the two subpopulations in the western and eastern North Pacific. Varying metabolic responses to environmental changes partly explain the contrasting growth responses. Consistent differences in the life-history traits are observed between subpopulations in the western and eastern boundary current systems around South Africa. These growth and survival characteristics can facilitate the contrasting responses of sardine populations to climate change

Cool core disturbed: Observational evidence for coexistence of sub-sonic sloshing gas and stripped shock-heated gas around the core of RX J1347.5-1145

RXJ1347.5-1145 (z = 0.451) is one of the most luminous X-ray galaxy clusters, which hosts a prominent cool core and exhibits a signature of a major merger. We present the first direct observational evidence for sub-sonic nature of sloshing motion of the cool core. We find that a residual X-ray image from the Chandra X-ray Observatory after removing the global emission shows a clear dipolar pattern characteristic of gas sloshing, whereas we find no significant residual in the Sunyaev-Zel'dovich effect (SZE) image from the Atacama Large Millimeter/submillimeter Array (ALMA). We estimate the equation of state of perturbations in the gas from the X-ray and SZE residual images. The inferred velocity is 420 +310 -420 km s-1, which is much lower than the adiabatic sound speed of the intracluster medium in the core. We thus conclude that the perturbation is nearly isobaric, and gas sloshing motion is consistent with being in pressure equilibrium. Next, we report evidence for gas stripping of an infalling subcluster, which likely shock-heats gas to high temperature well in excess of 20 keV. Using mass distribution inferred from strong lensing images of the Hubble Space Telescope (HST), we find that the mass peak is located away from the peak position of stripped gas with statistical significance of > 5{\sigma}. Unlike for the gas sloshing, the velocity inferred from the equation of state of the excess hot gas is comparable to the adiabatic sound speed expected for the 20 keV intracluster medium. All of the results support that the southeast substructure is created by a merger. On the other hand, the positional offset between the mass and the gas limits the self-interaction cross section of dark matter to be less than 3.7 h-1 cm2 g-1 (95% CL).Comment: 18 pages, 10 figures, accepted for publication in Ap

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.ArticleInternational Journal of Mathematical Education in Science and Technology. 45(7):1053-1067 (2014)journal articl