The existence and the properties of the solutions of a nonlinear differential system describing a diffusion system with concentration-dependent diffusion coefficients are investigated. It is shown that there exists at least one solution which is monotonie decreasing and asymptotically tends to the prescribed value.

The asymptotic behaviour of double integrals over a portion of the plane is investigated when the integrand contains an exponential factor with a large parameter. The exponent can have a stationary point which may or may not be close to the boundary of the domain of integration. Results are first derived for a rectangular region with a particularly simple exponent in the integrand and shown to be uniformly valid under certain conditions. In some circumstances the asymptotic terms can be evaluated by means of a universal function. The theory is then generalised to cover more complicated exponents and arbitrary wedge-shaped domains; it is found that the asymptotic behaviour can still be expressed in terms of the same universal function.

In this paper we discuss the structure semigroup of the L1-algebra of an Arens-Singer semigroup. Arising from this study we provide a complete and rather unexpected description of a nontrivial structure semigroup. We then link the above ideas with that of the almost periodic compactification of the semigroup.

The curve Γ common to two quadric surfaces has 24 principal chords; they are the sides of six skew quadrilaterals each of which has for its two diagonals a pair of opposite edges of that tetrahedron S which is self-polar for both quadrics. These three pairs of quadrilaterals serve to identify the three pairs of quadrics through Γ that are mutually apolar.

The vertices of the quadrilaterals lie four on each edge of S. Both nodes of the plane projection of Γ from such a vertex are biflecnodes.

It is shown that, from an operational point of view, the production and detection of spin-polarised electrons by Mott scattering is equivalent to the performance of a Stern-Gerlach type experiment with heavy spin-one-half particles. The argument is based on standard quantum mechanical formalism using density matrices and Stokes vectors for the description of polarised assemblies of particles.

This paper is concerned with the asymptotic properties of the eigenvalues and eigenfunctions of the boundary value problem

With suitable restrictions placed on the real-valued coefficient q the spectrum of this problem, with respect to the eigenvalue parameter λ, is discrete; let {λn; n = 1, 2, …} and {ψn; n = 1, 2, …} be the eigenvalues and associated eigenfunctions. Asymptotic formulae are obtained for N(λ), the number of eigenvalues not exceeding the real number λ, and for ψn(x) as n→∞ where x is a fixed, positive real number.

The existence of a work by Aristotle on the constitution of Athens is attested by the historians Philochorus, writing before 306 B.C., and Timaeus, writing about 300 B.C. No trace of such a work was known until 1891, when the almost complete text of one was recovered from the sands of Egypt by F. G. Kenyon of the British Museum. It was then recognised that two small and much damaged sheets found ten years before also contained parts of this work.