In this paper we consider the effect of the passage of shallow water waves over vertical walled objects on a flat seabed. The effect of reflections at the successive walls is taken into account when determining the place of breaking of the wave. The results are obtained by the introduction of special reflection and transmission coefficients at each wall and recurrence relations are formulated connecting their values at successive walls. The effect of this is to reduce the calculation of the place of breaking of the wave over a stepped seabed to an equivalent one for a wave over a flat seabed, the result of which is well known.

1-Nitro-, 1-bromo-, and 1-acetamidofluoranthene undergo bromination to yield 4,9-dibrominated products. 1-Acetamidofluoranthene also yields 1-acetamido-4,8,9-tribrofluoranthene and as a side product 1-acetamido-4,8,9,x-tetrabromofluoranthene, from the former of which 1,4,8,9-tetrabromofluoranthene is obtained and found to be identical with the product resulting from the interaction of 1-bromofluoranthene with three molecules of bromine.

It is the purpose of this paper to make a study of the solutions of the following k-formally self-adjoint differential equations

where ar, br), r = 1, 2, …, k, denote k semi-open intervals in which ar is finite and br is arbitrary and the λs, s = 1, 2, …, k, are spectral parameters.

The main theme of the paper is that of extending the Hermann Weyl limit-point, limit-circle theory to the multi-parameter case. That is we consider under which circumstances there exist, for each r, one or two solutions yr(xr) of (*) which are square integrable in a suitably defined Hilbert space Hr. This is then generalised to consider the problem of investigating the possibility of the product

of solutions of (*) being square integrable in H, the tensor product of the separate spaces Hr. The analyticky of the corresponding generalised Hermann Weyl coefficients mr(λ1, λ2,…, λk), r = 1,…, k, is also investigated. Some examples illustrating the theory are given and an alternative formulation of the problem is suggested.

There is now strong evidence, from observations of directional correlation between the α-particles and neutrons of fission, for the release of 5He as a neutron-unstable light particle with a frequency of a few per 104 low-energy fission events (Cheifetz et al. 1972).

Because the energy spectrum of the neutrons liberated in the disintegration of 5He particles travelling with a fixed kinetic energy is a rectangular spectrum (assuming isotropy of disintegration directions in the centre-of-mass space), it is in principle possible to deduce the kinetic energy spectrum characterising the 5He particles of ternary fission at the moment of disintegration from the energy spectrum of the liberated neutrons.

Detailed calculations have been made in relation to the limitations of actual experimental arrangements with regard to this possibility. These limitations are shown to be severe—not least in respect of statistical accuracy. Indeed, it is shown that considerable difficulty attaches to the ‘simple’ evaluation of the 5He/4He ratio (which Cheifetz et al. estimate as 1 :(8 ± 2) for 252Cf, for α-particles of energy greater than 9 MeV).

An instrumental cause is suggested for the maximum reported by Cheifetz et al. in the energy spectrum ascribed to the 5He disintegration neutrons.

The first part of this paper is concerned with the elastic response of an isotropie infinite plane containing a central circular inhomogeneity to a deformation such that in the homogeneous infinite plane the associated elastic displacement is the gradient of a harmonic function. Based upon the Papkovich stress-function approach, it is shown that it is possible to represent all solutions to such problems by means of only one family of equations. The second part of the paper is concerned with the elastokinetics of two bonded dissimilar half-planes subjected to any uniformly moving body force. It is again shown that there exist simple relations between components of the elastic field in the composite plane and those of a particular field in the homogeneous infinite plane.

A way is suggested of modifying the kernel of an integral equation of the second kind so that truncation of the algebraic system of equations corresponding to the new kernel is subject to less error than that for the original kernel. A computable bound for the error is derived.