Crystal Structure,Magnetism, 89Y Solid State NMR,and 121Sb Mössbauer Spectroscopic Investigations of YIrSb

The ternary antimonide YIrSb was synthesized from the binary precursor YIr and elemental antimony by a diffusion controlled solid‐state reaction. Single crystals were obtained by a flux technique with elemental bismuth as an inert solvent. The YIrSb structure (TiNiSi type, space group Pnma) was refined from single‐crystal X‐ray diffractometer data: a = 711.06(9), b = 447.74(5), c = 784.20(8) pm, wR₂ = 0.0455, 535 F² values, 20 variables. ⁸⁹Y solid state MAS NMR and ¹²¹Sb Mössbauer spectra show single resonance lines in agreement with single‐crystal X‐ray data. YIrSb is a Pauli paramagnet.     

Complete reducibility and Steinberg endomorphisms

Let G be a connected reductive algebraic group defined over an algebraically closed field of positive characteristic. We study a generalization of the notion of G-complete reducibility in the context of Steinberg endomorphisms of G. Our main theorem extends a special case of a rationality result in this setting.     

Single-particle relaxation time of the two-dimensional electron gas in Si/SiGe: Many-body effects

The single-particle relaxation time of the two-dimensional electron gas in SiGe/Si/SiGe quantum wells is calculated. Many-body effects beyond the random-phase approximation become important at low electron density. For charged impurity scattering (remote doped), the importance of these many-body effects as functions of the electron density and spacer width is analyzed. Induced by many-body effects, a strong reduction of the single-particle relaxation time at low electron densities is predicted. The relation with the transport scattering time is described, multiple-scattering effects are commented, and the determination of many-body effects in existing samples is discussed.     

Home to School: Numeracy Practices and Mathematical Identities

Drawing on a perspective of mathematics as situated social practice, we focus on 4 children in an urban preschool classroom and follow those children between home and school sites to shed light on urban children's persistent underachievement in mathematics. In this article, we describe the ways in which numeracy practices travel with children between home and school and, within those contexts, shape complex and sometimes limited social identities for children. We found that school imperatives, such as assessments and socialization curricula, often obscure teachers' views of children's mathematical practices. Deficit assumptions about family and community support for children, and limited interaction between caregivers and teachers, further contribute to the tendency of school personnel to overlook the mathematical practices that children bring with them to school. We further suggest that vignettes drawn from ethnographic-type research such as this have potential for professional development for classroom teachers.