Score vectors of tournaments

A tournament T on any set X is a dyadic relation such that for any x, y ∈ X (a) (x, x) ? T and (b) if x ≠ y then (x, y) ∈ T iff (y, x) ? T. The score vector of T is the cardinal valued function defined by R(x) = |{y ∈ X : (x, y) ∈ T}|. We present theorems for infinite tournaments analogous to Landau's necessary and sufficient conditions that a vector be the score vector for some finite tournament. Included also is a new proof of Landau's theorem based on a simple application of the “marriage” theorem.     

Nuclear magnetic relaxation study of the establishment of order in the ammonium halides

The temperature dependence and thermal hysteresis of proton and deuteron spin—lattice relaxation times at high fields and a study of the recovery of the proton and deuteron magnetizations in ammonium halides are reported. The anomalies occurring near the order—disorder phase transition are related to structural, dielectric and Raman data. The hysteresis effect and the establishment of long range order are shown to be related.     

An improved solid-state perchlorate-selective electrode

A solid-state perchlorate sensitive electrode, based upon a radical-ion salt derived from N-ethylbenzothiazole-2,2'-azine. has been prepared. Its response characteristics and high apparent selectivity for perchlorate over many common anions show marked improvements with respect to similar systems which were studied earlier. The general electrode properties observed suggest that it may be considered an acceptable practical alternative to existing liquid-membrane sensors for perchlorate.