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Introduction Editorial Note HYDRODYNAMICS Non-linear problems in the theory of fluid motion with free boundaries. Operator methods in the theory of compressible fluids. An existence theorem in two-dimensional gas dynamics. Recent developments in free boundary theory. Theory of the propagation of shock waves from cylindrical charges of explosive. The method of characteristics in the three-dimensional stationary supersonic flow of a compressible gas. The numerical solution of the turbulence problem. On the stability of transonic flows. Stability of the laminar boundary layer in a compressible fluid. Remarks on the spectrum of turbulence. Two-dimensional compressible flows. Polygonal approximation method in the hodograph plane. The boundary layer of yawed cylinders. On shock-wave phenomena: Interaction of shock waves in gases. The breaking of waves in shallow water. On Hamilton's principle for perfect compressible fluids. ELASTICITY AND PLASTICITY The foundations of the theory of elasticity. On dynamic structural stability. Stress-strain relations for strain hardening materials: Discussion and proposed experiments. The edge effect in bending and buckling with large deflections. Numerical methods in the solution of problems of non-linear elasticity. Large deflection theory for rectangular plates. Discontinuous solutions in the theory of plasticity. On finite deflections of circular plates.