“Mathematicians Would Say It This Way”: An Investigation of Teachers' Framings of Mathematicians

Although popular media often provides negative images of mathematicians, we contend that mathematics classroom practices can also contribute to students' images of mathematicians. In this study, we examined eight mathematics teachers' framings of mathematicians in their classrooms. Here, we analyze classroom observations to explore some of the characteristics of the teachers' framings of mathematicians in their classrooms. The findings suggest that there may be a relationship between a teachers' mathematics background and his/her references to mathematicians. We also argue that teachers need to be reflective about how they represent mathematicians to their students, and that preservice teachers should explore their beliefs about what mathematicians actually do.     

Phomosines H-J, novel highly substituted biaryl ethers, isolated from the endophytic fungus Phomopsis sp. from Ligustrum vulgare

From the endophytic fungus Phomosis sp., four known phomosines A-D (1-4) and three new phomosines H-J (5-7) have been isolated. The structures of the new compounds were determined on the basis of their spectroscopic data analysis (1H, 13C, 1H-1H COSY, HMQC, and HMBC NMR, as well as mass spectrometry). The structures of phomosine H (5) and J (7) were also confirmed by semisynthesis from phomosine A (1). The remaining four known compounds [phomosines A-D (1-4)] were identified by comparing their spectroscopic data with those reported in the literature. The four known metabolites were biologically active. Of the novel metabolites, only 6 was antifungal and antibacterial.     

Sol–gel derived dye-bridged hybrid materials for white luminescence

Novel yellow and blue emissive dyes have been synthesized using 2,5-diamino-3,6-dicyanopyrazine and various alkoxysilanes and they are covalently bridged to cycloaliphatic epoxy functional oligosiloxane via non-hydrolytic sol–gel reaction. Dye-bridged hybrid materials (DBH) are fabricated by thermal curing the dye-bridged oligosiloxane. Structure and formation of dyes and siloxane network is studied using analysis method. Four components of red, yellow, green and blue emitting DBH cover entire visible range and white luminescence with high color rendering index is realized by controlling their combinations. We have ensured superior thermal stability DBH at 120 °C for 200 h caused by covalently bridged structure and robust siloxane matrix.     

Thermo- and pH-Responsiveness of Emulsions Stabilized with Acidic Thermosentive Polymers

A temperature- and pH-responsive polymeric surfactant was prepared by copolymerizing N-isopropylacrylamide, methacrylic acid, and octadecylacrylate. Poly(N-isopropylacrylamide-co-methacrylic acid-co-octadecylacrylate) (P(NIPAM-MAA-ODA) was used as an emulsifier for the preparation of water-in-oil emulsions. The mean droplet size at room temperature was almost constant for 50 hours at pH 5.0, 7.0, and 9.0. However, the size markedly increased for 50 hours at pH 3.0, possibly because of the low hydrophilicity of the copolymer and the small interfacial area one molecule of the copolymer can stabilize at a low pH value. The droplet size markedly decreased from 4.7 to 1.8 µm, when the pH of medium increased from 5.0 to 9.0 with the temperature kept constant. This may be ascribed to that the hydrophilicity of the copolymer and the interfacial area one molecule of copolymer can stabilize will be higher at a higher pH value. When the temperature increased over 35°C with the pH kept constant, the droplet size significantly increased probably because the NIPAM segment of the copolymer becomes hydrophobic with increasing the temperature so the copolymer would poorly act as an emulsifier.     

Emulsions Stabilized with poly(Hydroxyethyl Acrylate-co-Coumaryl Acrylate-co-2-Ethylhexyl acrylate)

Thermo- and photo-responsive emulsions were prepared using mineral oil as an oil phase and a thermo- and-photo-sensitive polymer as an emulsifier. Hydroxyethyl acrylate (HEA) was copolymerized with Coumaryl acrylate (CA) and 2-Ethylhexyl acrylate (EHA) by a free radical reaction with the content of CA in the reaction mixture being varied (0, 0.5, 1, 2, 3 mol%) and the content of EHA being kept constant (2 mol%). CA was used as a photo-responsive comonomer and EHA was used as a hydrophobic comonomer to endow the copolymer with amphiphilicity. The copolymers prepared using the HEA/CA/EHA mixture where CA content was 1, 2, 3 mol% exhibited a phase transition in the range of 20°C– 45°C, and the phase transition temperature decreased with increasing the content. The CA of the copolymers was readily dimerized under the irradiation of UV (365 nm. 400 W) and the dimerization degree was 27%–47% in 60 min. The droplet size of emulsions significantly increased with increasing the temperature from 27°C- 50°C, possibly due to the thermal contraction of the copolymers. Also, the size markedly increased by 60 min-irradiation of the UV light, possibly because of the photo collapse of the copolymers.     

Real-time TEM imaging of the formation of crystalline nanoscale gaps

We present real-time transmission electron microscopy of nanogap formation by feedback controlled electromigration that reveals a remarkable degree of crystalline order. Crystal facets appear during feedback controlled electromigration indicating a layer-by-layer, highly reproducible electromigration process avoiding thermal runaway and melting. These measurements provide insight into the electromigration induced failure mechanism in sub-20 nm size interconnects, indicating that the current density at failure increases as the width decreases to approximately 1 nm.