Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at t = -1

We prove that the hyperelliptic Torelli group is generated by Dehn twists about separating curves that are preserved by the hyperelliptic involution. This verifies a conjecture of Hain. The hyperelliptic Torelli group can be identified with the kernel of the Burau representation evaluated at t = −1 and also the fundamental group of the branch locus of the period mapping, and so we obtain analogous generating sets for those. One application is that each component in Torelli space of the locus of hyperelliptic curves becomes simply connected when curves of compact type are added

Effective-Range Expansion of the Neutron-Deuteron Scattering Studied by a Quark-Model Nonlocal Gaussian Potential

The S-wave effective range parameters of the neutron-deuteron (nd) scattering are derived in the Faddeev formalism, using a nonlocal Gaussian potential based on the quark-model baryon-baryon interaction fss2. The spin-doublet low-energy eigenphase shift is sufficiently attractive to reproduce predictions by the AV18 plus Urbana three-nucleon force, yielding the observed value of the doublet scattering length and the correct differential cross sections below the deuteron breakup threshold. This conclusion is consistent with the previous result for the triton binding energy, which is nearly reproduced by fss2 without reinforcing it with the three-nucleon force.Comment: 21 pages, 6 figures and 6 tables, submitted to Prog. Theor. Phy

Technical and Comparative Aspects of Brain Glycogen Metabolism.

It has been known for over 50 years that brain has significant glycogen stores, but the physiological function of this energy reserve remains uncertain. This uncertainty stems in part from several technical challenges inherent in the study of brain glycogen metabolism, and may also stem from some conceptual limitations. Factors presenting technical challenges include low glycogen content in brain, non-homogenous labeling of glycogen by radiotracers, rapid glycogenolysis during postmortem tissue handling, and effects of the stress response on brain glycogen turnover. Here, we briefly review aspects of glycogen structure and metabolism that bear on these technical challenges, and discuss ways these can be overcome. We also highlight physiological aspects of glycogen metabolism that limit the conditions under which glycogen metabolism can be useful or advantageous over glucose metabolism. Comparisons with glycogen metabolism in skeletal muscle provide an additional perspective on potential functions of glycogen in brain