On the complete integrability of the discrete Nahm equations

The discrete Nahm equations, a system of matrix valued difference equations, arose in the work of Braam and Austin on half-integral mass hyperbolic monopoles. We show that the discrete Nahm equations are completely integrable in a natural sense: to any solution we can associate a spectral curve and a holomorphic line-bundle over the spectral curve, such that the discrete-time DN evolution corresponds to walking in the Jacobian of the spectral curve in a straight line through the line-bundle with steps of a fixed size. Some of the implications for hyperbolic monopoles are also discussed

Household wealth and adolescents' social-emotional functioning in schools.

This study attempts a two-part shift in educational research narrowly fixated on the socioeconomic determinants of student test-score performance. First, we focus on variations in how to measure wealth. Second, we move beyond achievement and focus on the wealth determinants of adolescents' social-emotional competencies. Using data from a nationally-representative sample of US eighth graders, we find that the correlation between wealth and social-emotional competencies varies according to how the partitions among the upper class, the middle and working classes, and the poor are defined. By emphasizing wealth in the production of classed social-emotional competencies not captured by test scores, our findings suggest that the growth of household wealth has a more salient effect for lower- and middle-class adolescents than the highest class which appears to have the least to gain, in terms of social-emotional competencies, from an increase in household wealth

A note on color neutrality in NJL-type models

By referring to the underlying physics behind the color charge neutrality condition in quark matter, we discuss how this condition should be properly imposed in NJL-type models in a phenomenologically meaningful way. In particular, we show that the standard assumption regarding the use of two color chemical potentials, chosen in a very special way, is not justified in general. When used uncritically, such an approach leads to wrong or unphysical conclusions.Comment: 4 pages, no figure; v2: minor clarifications, references adde