It was proved by J. Williamson (1) that when C is any circulant matrix of order n and Ω is a certain diagonal matrix then

where ∥ C ∥ is the determinant of C and I is the unit matrix of order n. A simpler proof was given by U. Wegner (2), and later the characteristic equation of ΩC was discussed independently by L. Toscano (3). In the present note we prove the more general theorem that there corresponds to any matrix A of order n with simple elementary divisors a solution X of the equation (AX)n = ∥ A ∥ I. The theorem has a simple geometrical interpretation; the proof is almost immediate.

Equipment has been designed and constructed for the interruption of the ion beam in a high-voltage accelerating tube and for the detection and measurement of the period of short-lived radioactive elements. This method has been applied to the measurement of the half-life of 12B which has been found to be 27 ± 2 msec. The reaction 15N(n, α)12B has been detected.

Let ξ and η be two independent and normal random variables, with zero means and with standard deviations each equal to ½ Put

The joint distribution of X, Y, Z is a particular case of the Wishart distribution (1). It may be defined by the generating function of its cumulants (c.g.f.)

The flow past a wedge which is moving with supersonic velocity into a gas at rest has been treated by a number of investigators. In the analysis of the problem given in the present note, the condition for the detachment of the shock wave is examined, and an error in a previous treatment by Epstein is corrected.

The purpose of this note is to show that Peng's (1) method of approximation is not practicable in the case of quadrilinear interaction (i.e. Fermi's (2) original theory of β-decay), and that it does not remove the infinite self-energy of a nucleon in interaction with a charged scalar meson field. The two examples do not, however, provide a serious argument against Peng's theory, since both refer to field theories which have been abandoned for physical reasons. The principal failure of Peng's method to cope with quadrilinear interactions could even be interpreted in such a way as to mean that interactions of this sort do not exist—a statement which would be equivalent to the assumption that Fermi particles can only interact by means of a Bose field. (2n + 1) linear interaction terms must contain one Bose quantity at least, since Fermi field quantities are not observable and therefore can only enter the interaction term in bilinear form.