By noting that it is possible to interchange the roles of the solution vector x and the vector of Lagrange multipliers λ in the restricted least squares problem we are able to give a very efficient implementation of Clark's subset selection algorithm. Numerical results are presented for several selection heuristics.

The one-dimensional, non-linear theory of pulse propagation in large arteries is examined in the light of the analogy which exists with gas dynamics. Numerical evidence for the existence of shock-waves in current one-dimensional blood-flow models is presented. Some methods of suppressing shock-wave development in these models are indicated.

The essential aspects of the Boundary Integral Equation Method for the numerical solution of elliptic type boundary value problems are presented. A numerical example for a stress concentration problem in classical elasticity in three dimensions is given along with several examples for a class of scalar problems in elastic torsion of non-cylindrical bars. Some discussion and criticism of the method itself and in comparison with widely used field methods is also presented.

We consider infinite volume limit Gibbs states of a nonrelativistic quantum Bose gas consisting of one species of spinless particles with positive interaction potentials. The finite volume reduced density matrices are dominated by the corresponding matrices for the noninteracting gas, and as a consequence all infinite volume limit states are regular, locally normal, and analytic on the appropriate CCR algebra. For sufficiently short range repulsive two-body interactions, the cyclic vector associated with the limit state is separating for the σ-weak closure of the algebra in the associated representation.

The complete symmetry group of a forced harmonic oscillator is shown to be Sl(3, R) in the one-dimensional case. Approaching the problem through the Hamiltonian invariants and the method of extended Lie groups, the method used is that of time-dependent point transformations. The result applies equally well to the forced repulsive oscillator and a particle moving under the influence of a coordinate-free force. The generalization to na-dimensional systems is discussed.

A boundary integral procedure for the solution of an important class of problems in anisotropic elasticity is outlined. Specific numerical examples are considered in order to provide a comparison with the standard boundary integral method.

Some corrections of error bounds obtained by Chatelin and Lemordant for the first three terms of the asymptotic case of a strong approximation are given. The error bounds for the approximations of order 2 in the Galerkin method are compared with the Rayleigh quotients constructed with the eigenvectors in the Sloan method. A numerical experiment is also carried out.

The existence of stable periodic oscillatory solutions in a two species competition model with time delays is established using a combination of Hopf-bifurcation theory and the asymptotic method of Krylov, Bogoliuboff and Mitropoisky.

In the present paper the flow in the porous region bounded by confocal prolate spheroids rotating slowly about the major axis is investigated by a singularity method.

Nonlinear hydromagnetic convection in a horizontal layer of fluid rotating about the vertical axis is investigated using the mean field approximation. The boundary layer method is used assuming large Rayleigh number R for different ranges of the Chandrasekhar number Q and the Taylor number Ta. The heat flux F is determined for the value of the horizontal wave number α which maximizes F. It is shown that, for certain regions of the parameter space (R, Q, Ta), F and α change discontinuously for Ta greater than some critical value (given R and Q). Thus, for Ta about this critical value, wave numbers and heat fluxes of two different values will be predicted simultaneously. Also, for certian regions of the parameter space, the field can facilitate convection, but rotation can facilitate convection only for sufficiently large Ta.

The oscillatory squeeze film problem is solved for the simple fluid in the sense of Noll. It is shown that dynamic properties of polymeric liquids can be measured on the plastometer in the oscillatory mode. This should be useful to food and other technologists who have to deal with awkward, highly viscous materials.

The singularity subtraction technique described by Kantorovich and Krylov in [11] is designed to reduce or overcome the effect of a weakly singular kernel in the numerical solution of integral equations. First, the equation is rearranged in such a way that the singularity of the kernel is at least partially cancelled by the smoothness of the solution, and then numerical integration is applied. We present convergence results and error bounds under general conditions on the nature of the singularity and the numerical integration procedure. Numerical examples demonstrate the benefit of the singularity subtraction technique.

In this short paper, it is shown that the geodesic deviation equation admits a “constant of the motion” and so can be solved exactly. We also derive an expression for the energy E of relative motion between two freely falling test particles. We can infer that, in general, E will not be a linear superposition of kinetic and potential energies.

The minimization of signal distortion was one approach applied successfully in the theory of optimum signal detection for arrays [3]. The processors considered operated on the input as received.

In some applications it is desirable to clip the received signal before processing and the problem of optimum processing of such clipped signals then arises. Several approaches to this problem are being studied, but the present paper is concerned with that based on minimum signal distortion.

In this, the first of three papers, we examine conditions, derived previously, which specify the equilibrium solutions of an adjustment process for N players engaged in a game with continuous (in fact, continuously differentiable) payoff functions, where each player's strategy is to choose a single real number. It is equivalent to the basic form of quantity-variation competition between N firms. The conditions are related to a new optimum which takes account of the ability of firms, or coalitions of firms, to discipline another firm that tries to increase its own profit. Closely related optima are also introduced and analysed. The new optima occupy N-dimensional regions in the strategy space, and contain the optima of Cournot, Pareto, von-Neumann and Morgenstern, and Nash as special cases.

We examine the differential properties of the solution of the linear integral equation of the second kind, whose kernel depends on the difference of arguments and has an integrable singularity at the point zero. The derivatives of the solution of the equation have singularities at the end points of the domain of integration, and we derive precise estimates for these singularities.

It is shown that under some conditions a collection of continuous mappings gives rise to a set-valued dynamical system. Using this it is further shown that under some other conditions the system ẋ(t) ∈ F(x(t)) is equivalent to a set-valued dynamical system.

The extent to which an asymmetric low-aspect-ratio flat ship is wetted when planing at infinite Froude number is investigated, with emphasis placed on its relationship with the shape of the hull. Two cases are considered. First the hull is assumed to have two laterally-asymmetric leading edges and, secondly, the hull is assumed to be yawed sufficiently for one of the leading edges to become a trailing edge. In the first case, the relationship involves a pair of coupled integral equations, but in the second case there is a complication by the occurrence of hull-wake interaction.

This paper gives a theorem by which it is possible to derive in an easy way a local approximation theorem and an inverse function theorem. The latter theorems are not new. The main advantage of our paper is in giving a relatively short route to these results.

We construct collocation methods with an arbitrary degree of accuracy for integral equations with logarithmically or algebraically singular kernels. Superconvergence at collocation points is obtained. A grid is used, the degree of non-uniformity of which is in good conformity with the smoothness of the solution and the desired accuracy of the method.