When, how, and why prove theorems? A methodology for studying the perspective of geometry teachers

While every theorem has a proof in mathematics, in US geometry classrooms not every theorem is proved. How can one explain the practitioner’s perspective on which theorems deserve proof? Toward providing an account of the practical rationality with which practitioners handle the norm that every theorem has a proof we have designed a methodology that relies on representing classroom instruction using animations. We use those animations to trigger commentary from experienced practitioners. In this article we illustrate how we model instructional situations as systems of norms and how we create animated stories that represent a situation. We show how the study of those stories as prototypes of a basic model can help anticipate the response from practitioners as well as suggest issues to be considered in improving a model.     

Acoustic properties of aortic aneurysm obtained with scanning acoustic microscopy

In aortic aneurysm tissues, macrophages and their secretion of matrix metalloproteinases (MMPs) are playing important role for tissue degeneration. Some studies have shown that weakening of the mechanical properties of the degenerated tissues may progress the expansion of the aneurysm. However, actual measurement of the mechanical properties has not been investigated at microscopic level. The objective of the present study is to assess the mechanical properties of aortic aneurysm tissues by measuring acoustic properties by scanning acoustic microscopy (SAM). Twenty-one cases of aortic aneurysm including renal and common iliac aneurysm tissues were surgically excised. Each tissue was fixed by 4% formaldehyde and the specimens were treated as (1) picrosirius red staining for normal and polarized light microscopy, (2) CD68 staining for macrophage detection, and (3) no staining for acoustic microscopy. A specially developed SAM system operating in the frequency range of 100-200 MHz, was employed in the measurement. Images of amplitude and phase are obtained in a field of 2x2 mm. The intima was mainly consisted of degenerated collagen without polarization of picrosirius red staining. Macrophages stained by CD68 were observed near the degenerated collagen fibers. The sound speed was 1567 m/s in the intima, 1576 m/s in the media, 1640 m/s in the adventitia, respectively. Infiltration of macrophages showed higher values of attenuation and sound speed than the surrounding tissues. The sound speed of the intima was significantly lower than our previous measurement of atherosclerotic aorta without aneurismal change. As the tissue elasticity is closely correlated with the sound speed, the elasticity of the intima was considered to be lower in aneurysm tissues. This mechanical weakness may contribute to the expansion of the diameter of the aneurysm. Acoustic microscopy provided important data for assessing tissue mechanical properties of abdominal aneurysm.     

Étude par la fluorescence aux rayons-X du changement de coordinence de l'aluminium dans les silico-alumines armorphes

Sans résumé     

Study of S11 resonance in nuclei through (γ, η) reactions

In order to study the S₁₁(1535) resonance in the nuclear medium, total cross sections of the (γ, η) reactions on C, Al and Cu have been measured for photon energies between 680 and 1000 MeV. A broad resonance due to the excitation and decay of the S₁₁ resonance in the nucleus has been clearly observed for the first time. The apparent energy and width of the resonance are 900 and 300 MeV, respectively. Model calculations based on the quantum molecular dynamics have been performed. A comparison of the calculations with the data indicates that the S₁₁ resonance in nuclei should have a larger width; the width of about 250 MeV is required while the elementary one is about 150 MeV.     

Analysis of water molecules around GTP in Hras-GTP complex and GDP in Hras-GDP complex by molecular dynamics simulations

We investigate the structures of the Hras-GTP and the Hras-GDP complexes in water solvents in order to understand the mechanism of GTP hydrolysis in the Hras-GTP complex. We performed MD simulations of these complexes in order to study the positions and the orientations of water molecules around the guanosine nucleotides. Using trajectories we calculated the angular distribution of water molecules around the most distant phosphorus from guanosine in our previous work. It was shown that water molecules are distributed evenly in GTP, although unevenly in GDP. This suggests that the trigger of GTP hydrolysis is possibly the attack of water molecule to γ?phosphate from the appropriate direction. In this paper, in order to investigate the role of water molecules in GTP hydrolysis in detail, we calculate the orientation of water molecules. The distribution of the orientation is different between GTP and GDP. In order to investigate the cause of this difference, we examine the hydrogen bonds between water molecules and oxygen atom of the most distant phosphate from guanosine. We find that these hydrogen bonds are formed. We also find that the oxygen atom of hydrogen bond is determined by the position of the water molecule of hydrogen bond.     

Insights in quantum dynamical effects in the infrared spectroscopy of liquid water from a semiclassical study with an ab initio-based flexible and polarizable force field

The dynamical properties of liquid water play an important role in many processes in nature. In this paper, we focus on the infrared (IR) absorption spectrum of liquid water based on the linearized semiclassical initial value representation (LSC-IVR) with the local Gaussian approximation (LGA) [J. Liu and W. H. Miller, J. Chem. Phys. 131, 074113 (2009)] and an ab initio based, flexible, polarizable Thole-type model (TTM3-F) [G. S. Fanourgakis and S. S. Xantheas, J. Chem. Phys. 128, 074506 (2008)]. Although the LSC-IVR (LGA) gives the exact result for the isolated three-dimensional shifted harmonic stretching model, it yields a blueshifted peak position for the more realistic anharmonic stretching potential. By using the short-time information of the LSC-IVR correlation function; however, it is shown how one can obtain more accurate results for the position of the stretching peak. Due to the physical decay in the condensed phase system, the LSC-IVR (LGA) is a good and practical approximate quantum approach for the IR spectrum of liquid water. The present results offer valuable insight into future attempts to improve the accuracy of the TTM3-F potential or other ab initio-based models in reproducing the IR spectrum of liquid water.