Millimeter Light Curve with Abrupt Jump in Cyg X-3 2008 April-May Outburst

Cyg X-3 is a well-known microquasar with a bipolar relativistic jet. Its famous giant radio outbursts have been repeated once every several years. However, the behavior of the millimeter wave emission has remained unclear because of limitations of time resolution in previous observations. We report here millimeter wave observations of Cyg X-3 experiencing giant outbursts with one of the finest time resolutions. We find a series of short-lived flares with amplitude of 1-2 Jy in the millimeter light curve of the 2008 April-May outburst. They have flat spectra around 100 GHz. We also find abrupt and large amplitude flux density changes with e-folding time of 3.6 minutes or less. The source size of Cyg X-3 is constrained within 0.4 AU and the brightness temperature is estimated to be $T_B \gtrsim 1\times10^{11}$ K.Comment: 4 figures, PASJ, in pres

Flow-chart proofs with open problems as scaffolds for learning about geometrical proofs

AcceptedArticleCopyright © FIZ Karlsruhe 2015The final publication is available at Springer via http://dx.doi.org/10.1007/s11858-015-0712-5Recent research on the scaffolding of instruction has widened the use of the term to include forms of support for learners provided by, amongst other things, artefacts and computer-based learning environments. This paper tackles the important and under-researched issue of how mathematics lessons in lower secondary school can be designed to scaffold students’ initial understanding of geometrical proofs. In order to scaffold the process of understanding the structure of introductory proofs, we show how flow-chart proofs with multiple solutions in ‘open problem’ situations are a useful form of scaffold. We do this by identifying the ‘scaffolding functions’ of flow-chart proofs with open problems through analysis of classroom-based data from a class of Grade 8 students (aged 13-14 years old) and quantitative data from three classes. We found that using flow-chart proofs with open problems supported the students’ development of a structural understanding of proof by giving them a range of opportunities to connect proof assumptions with conclusions. The implication is that such scaffolds are useful to enrich students’ understanding of introductory mathematical proofs.Grant-in-Aid for Scientific Research, Ministry of Education, Culture, Sports, Science, and Technology, Japan

Functions of Open Flow-chart Proving in introductory lessons of formal proving

ArticleLiljedahl, P., Oesterle, S., Nicol, C., & Allan, D. (Eds.). (2014). Proceedings of the Joint Meeting of PME 38 and PME-NA 36 (Vol. 4):225-232. Vancouver, Canada: PME.conference pape

Supporting students to overcome circular arguments in secondary school mathematics : the use of the flowchart proof learning platform

ArticleProceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education．Ankara, Turkey, 2011-7-10/15, 2011, 2:353-360．conference pape

Introducing the structure of proof in lower secondary school geometry: a learning progression based on flow-chart proving

ArticleProceedings of the 12th International Congress on Mathematical Education (ICME-12)．COEX, Seoul, Korea, 2012-7-8/15, 2012, 2858-2867．conference pape

Isolated Millimeter Flares of Cyg X-3

Cygnus X-3 (Cyg X-3) is a well-known microquasar with relativistic jets. Cyg X-3 is especially famous for its giant radio outbursts, which have been observed once every few years since their first discovery. Each giant outburst presumably consists of a series of short-duration flares. The physical parameters of the flares in the giant outbursts are difficult to derive because the successive flares overlap. Here, we report isolated flares in the quiescent phase of Cyg X-3, as observed at 23, 43, and 86 GHz with the 45-m radio telescope at Nobeyama Radio Observatory. The observed flares have small amplitude (0.5--2 Jy) and short duration (1--2 h). The millimeter fluxes rapidly increase and then exponentially decay. The lifetime of the decay is shorter at higher frequency. The radio spectrum of Cyg X-3 during the flares is flat or inverted around the peak flux density. After that, the spectrum gradually becomes steeper. The observed characteristics are consistent with those of adiabatic expanding plasma. The brightness temperature of the plasma at the peak is estimated to be $T_B\gtrsim 1 \times 10^{11}$ K. The magnetic field in the plasma is calculated to be $0.2 \lesssim H \lesssim 30$ G.Comment: 2012, PASJ 64, in press. 7 pages, 2 figure

Developing a Curriculum for Explorative Proving in Lower Secondary School Geometry

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