Synthesis of benzothiazoles via ipso substitution of ortho-methoxythiobenzamides

An efficient route to the synthesis of benzothiazoles from ortho-methoxythiobenzamides via the ipso substitution of an aromatic methoxy group is presented, and the mechanism of the Jacobson synthesis of benzothiazoles is further investigated.     

Single-beam and enhanced two-beam second-harmonic generation from silicon nanocrystals by use of spatially inhomogeneous femtosecond pulses

Optical second-harmonic generation (SHG) is used as a noninvasive probe of the interfaces of Si nanocrystals (NCs) embedded uniformly in an SiO2 matrix. Measurements of the generated SH mode verify that the second-harmonic polarization has a nonlocal dipole form proportional to (E x Delta inverted) E that depends on inhomogeneities in the incident field E, as proposed in recent models based on a locally noncentrosymmetric dipolar response averaged over the spherical NC interfaces. A two-beam SHG geometry is found to enhance this polarization greatly compared to single-beam SHG, yielding strong signals useful for scanning, spectroscopy, and real-time monitoring. This configuration provides a general strategy for enhancing the second-order nonlinear response of centrosymmetric samples, as demonstrated here for both Si nanocomposites and their glass substrates.     

Propagation of intense laser pulses through inhomogeneous ionizinggas profiles

By simultaneously and self-consistently solving Maxwell's equations, the Ammosov-Delone-Krainov (ADK) field ionization equation, and the relativistic cold plasma equations, we have investigated the propagation of intense, ultrashort laser pulses through spatially inhomogeneous longitudinal gas gradients. Along with highly accurate calculations of the spatial and temporal beam profiles of the pulse at the end of various gradients, we have also determined simple scaling rules for the location of the vacuum-gas interface in order to minimize the pulse distortion at the focus. We show the benefits of using either preionized or low-Z gases, and we discuss the implications of this work for plasma-channel laser wakefield acceleration     

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.     

Femtosecond carrier-induced screening of dc electric-field-induced second-harmonic generation at the Si(001) SiO(2) interface

Carrier-induced screening of the dc electric field at the Si(001)-SiO(2) interface is observed by intensity-dependent and femtosecond-time-resolved second-harmonic spectroscopy. The screening occurs on a time scale of ~?(p)(-1) , the reciprocal plasma frequency of the generated carriers.