Rings of integral quaternions

A quaternion order derived from an integral ternary quadratic form f = Σa_ijx_ix_j of discriminant d = 4 det (a_ij) is m-maximal if m is not divisible by any prime p such that p² | d, or p 6; d and c_p = 1. If R is m-maximal and m is a product p₁ … p_r of primes, then any primitive element α of R has unique right-divisor ideals of each norm p₁ … p_k (k = 1, …, r). This generalizes Lipschitz's ninety-year-old theorem. We characterize m-maximal orders, study their ideals, and show how the preceding result yields formulas for the number of representations of integers by certain quaternary quadratic forms.     

Oscillatory disruptions in the Alcator C tokamak

Periodic disruptions were observed which persisted for as long as 400 ms during plasma discharges. Soft X-ray emissions, T_e, n_e, impurity radiation and plasma position showed the pulsations. The abrupt collapse in X-ray signal (1–2 ms; period ∽10 ms) encompassed a large fraction of the plasma cross section. Plasma conditions associated with the onset of this pattern are examined.     

Symmetry classification of states in high temperature superconductors

The symmetry classification of possible singlet and also triplet states in the case of the 2-dim square lattice, and 3-dim tetragonal and orthorhombic lattices is examined. If particle-hole symmetry is present then an additional symmetry classification is possible. However in the lower symmetry crystal structures that actually occur, no distinction on symmetry grounds can be drawn between usuals-wave, extendeds-wave and some of thed-wave states.