The reduction of an important class of triple integral equations to a pair of simultaneous Fredholm equations has been carried out by Cooke [1]. In this paper, Cooke's equations are transformed to new uncoupled Fredholm equations which, for certain important cases, are shown to be simpler than Cooke's and also superior for the purposes of solution by iteration.

Within the scope of Eringen's linearised micropolar theory, this note outlines a solution for the stress concentration around an elliptic hole in an infinite plate under axial tension.

The recent work of Cheng and Stokes on the processing of clipped signals from two or three receivers is extended and generalised by removing a number of restrictions. In particular, there is no restriction on the number of receivers and the restrictions on the statistical properties of the signal and noise processes have been considerably relaxed.

Mathematically—Plackett's result is used to expand the orthant proabilities involved in increasing powers of the input signal to noise ratio.

The Pontryagin theory of optimal control is modified by assuming a positive cost associated with switching control from one discrete value to another. The resulting new theory permits a general existence theorem. Pontryagin's maximum principle is replaced by an “indifference principle”.

We consider a programming problem in which the objective function is the sum of a differentiable function and the p norm of Sx, where S is a matrix and p > 1. The constraints are inequality constraints defined by differentiable functions. With the aid of a recent transposition theorem of Schechter we get a duality theorem and also a converse duality theorem for this problem. This result generalizes a result of Mond in which the objective function contains the square root of a positive semi-definite quadratic function.

One of the most succesful algorithims for nonlinear least squares calculations is that associated with the names of Levenberg, Marquardt, and Morrison. This algorithim gives a method which depends nonlinearly on a parameter γ for computing the correction to the current point. In this paper an attempt is made to give a rule for choosing γ which (a) permits a satisfactory convergence theorem to be proved, and (b) is capable of satisfactory computer implementation. It is beleieved that the stated aims have been met with reasonable success. The convergence theorem is both simple and global in character, and a computer code is given which appears to be at least competitive with existing alternatives.

The local properties of non-linear differential-difference equations are investigated by considering the location of the roots of the eigen-equation derived from the lineraised approximation of the original model. A general linear system incorporating one time delay is considered and local stability results are obtained for cases in which the coefficient matrices satisfy certain assumptions. The results have applications to recent Biological and Economic models incorporating time lags.

The paper investigates the effect of a static magnetic field on the helical flow of an incompressible cholestenc liquid crystal with director of unit magnitude between two coaxial circular cylinders rotating with different angular velocities about their common axis and moving with different axial velocities. At low shear rates with a weak magnetic field in the axial direction, the axial velocity, the angular velocity and the orientation of molecules between the two cylinders have been obtained. It is found that the magnetic field has influenced the orientation of molecules while the axial velocity and the angular velocity remain uneffected by the magnetic field.

It is shown that the necessary and sufficient condition for the transposition invariance of the field equations derivable from an Einstein-Kaufman variational action principle is the vanishing of xythe vector Γλ. When this condition is satisfied, the field equations become the so-called strong field equations of Einstein. In this sense, the latter can be claimed to follow from the same action principle.