Zero-point spin reduction in a two-dimensional Heisenberg antiferromagnet Cu(HCOO)2 · 4H2O

The copper NMR in a two-dimensional Heisenberg antiferromagnet Cu(HCOO)₂ ·4H₂O (T_N = 17 K) was observed using a standard spin- echo method at liquid He temperatures. The field-dependence of the ⁶³Cu NMR frequency was measured for H₀ (? 56 kOe) | b-axis. The result was interpreted by taking into account a zero-point spin reduction of about 35% in addition to the rotation of the antiferromagnetic spin axis. The amount of the observed spin reduction is in good agreement with the prediction of spin-wave theory.     

Product of matrical discs

We determine the matrical disc with minimal radius for the set of products XY when X and Y run over a (possibly distinct) matrical disc, respectively. Also we determine the union of the numerical ranges W(XY).     

Synthesis and complexation of a novel cyclophane

A novel cyclophane, 17, 17, 40, 40-tetramethyl-7, 30-dinitro-1, 10, 24, 33-tetraoxa[2.2.1.2.2.1] metaparaparametaparaparacyclophane, was synthesized by 2:2 cyclization of 3,5-bis(bromomethyl)nitrobenzene, derived from 3,5-dimethylnitrobenzene, and bisphenol A. The cyclophane was found to form 1:1 complex with benzene.     

Experiments on plasma heating in the lower hybrid frequency range

Experimental results of lower hybrid heating in a small tokamak are described. When rf power is applied, a high energy tail of ions is produced, whether or not there is a lower hybrid resonance layer (LHR layer) in the plasma column, though bulk ion heating is not observed. The electron temperature in the plasma surface increases, while the electrons in the center lose their energy, which is related to an impurity ion flux diffusing from the outside of the plasma.