Elements Aij Research Articles

Effects of Small Changes in the Elements Aij on the Zeros of |Aij|

A Method is presented for determining approximately the effects of small changes in the characteristics of a dynamical system on its free motion. Successive factorisations of the determinantal equation, as the system is altered, are avoided at the expense of accuracy, but the influence of the small changes on, for example, the stability of the system, are quite easily determined.

Note on the Relation between certain Forbidden Beta Transitions and the Nuclear Spin Orbit Interaction

The second-forbidden beta decay matrix element Aij is given in terms of the nuclear spin orbit potential strength u and another second-forbidden beta decay matrix element Rij. The result is used, together with the predictions of the Mayer shell model for the single particle configurations, to obtain an estimate of u from the decay of 99Tc for two types of space dependence of the spin orbit potential. The result is in reasonable agreement with that found from a study of the stationary states of 5He.

Powers of a matrix over a lattice

Let M==jaijjJ be an nXn matrix with elements in a lattice in which meet, join, and inclusion are denoted by ab, a+b, and aCb, respectively. Two nXn lattice matrices M and M' are said to be equal if aij=a', i, j= 1, 2, , n, and if aijCa', i, j= 1, 2, , n, then we shall write MCM'. The n2 elements of M will be called independent provided P1C Ek.=2 Pk, where P1, P2, * * *, P, are any products of elements aij of M, implies P1CPm for some mn such that 2 <m<r.