In this note we determine a lower bound for the number of different configurations of monomers and dimers on the hypercubical lattice. This combinatorial problem has important applications in statistical mechanics ((1)) and solid state chemistry.

Introduction. In this note an alternative approach is presented to the problem of the scattering of small amplitude two-dimensional water waves by a fixed barrier, one edge of the barrier lying in the free surface of the water. This problem was first solved by Ursell ((1)) and generalizations of the problem have been considered by John ((2)) and Lewin ((3)).

The unsteady two-dimensional compressible boundary layers have been studied by Sarma ((5)) assuming that the Prandtl number is unity and that the wall is in an arbitrary motion, the main stream being steady. In this paper the Prandtl number is taken to be an arbitrary parameter which need not be equal to unity, and it is assumed that the main stream velocity and temperature are perturbing about a steady mean, the wall being in an arbitrary motion. Solutions are obtained in two parts, one when the temperature gradient at the wall is perturbing about a zero mean and the other when the temperature of the wall is perturbing about a steady mean. Thus in this paper the theory given in Sarma ((5)) is made still more general. Following the work of Sarma ((4)–(6)) two types of solutions are developed in each part, one for large times and the other for small times.

Consider the two-dimensional steady flow of an incompressible inviscid fluid under no body forces between two infinite horizontal planes. When an aperture is made in the lower plane, the fluid will issue as a jet bounded by free streamlines along which the pressure is constant. At infinity the flow in the jet will be uniform and parallel.

Complex variable methods are applied to derive exact solutions in closed forms for the small deflexions of uniformly loaded thin isotropic plates bounded by regular curvilinear polygonal contours having n sides. The supported boundary is either clamped or has equal boundary cross-couples. For rectilinear edges the latter conditions agree with those for a simply supported boundary. The plates taken in the z-plane are conformally mapped on the unit circle in the ζ-plane by the general mapping function

It has been shown that uncoupled surface waves of SH type can be propagated without any dispersion in an electrically conducting semi-infinite elastic medium provided a uniform magnetic field acts non-aligned to the direction of wave propagation. In general, the velocity of propagation will be slightly greater than that of plane shear waves in the medium.

Introduction. The effect of a vibrating point force on the surface of a semi-infinite elastic solid was investigated in a classic paper by Lamb ((8)). When the point force is replaced by a vibrating rigid disc the problem is more complicated, because the displacement is specified under the disc and the remainder of the surface is stress-free. This gives rise to a mixed boundary-value problem.

In this paper a fundamental problem of thermal transport in a channel-gas flow has been studied. The most general solution in terms of integral formulae has been obtained when the duct is bounded by an arbitrary closed contour, the prescribed normal temperature gradient at the wall varies arbitrarily along the periphery, and the specified additional heat generation varies in an arbitrary manner from point to point in a cross-section. The power series solution is also discussed, and is given in a separate section. One of the objects of the present study is to look forward to the qualitative as well as quantitative effects of viscous dissipation and work of compression. Several results and all the graphs of Tao ((13)) have also been corrected.