Sufficient conditions are obtained for the existence of a unique linearly asymptotically stable positive periodic solution of an ecosystem model of two species competition in a periodic environment with time lags in interspecific interactions. It is shown that if the self-regulating intraspecific interaction effects are strong enough and act without time delays then time delays of any length in the interspecific interactions cannot destabilise an otherwise stable ecosystem in a periodic environment.

By erecting a co-ordinate system tailored to the geometry of a cosmic string and examining the properties of the near gravitational field, it is possible to distinguish two types of gravitational waves supported by a general string metric. The first type, travelling waves, are completely decoupled from the curvature of the world sheet, whereas the second type, which I choose to call curvature waves, are generated in response to any non-trivial geometric structure on the string.

The endemicity of infectious diseases is investigated from a deterministic viewpoint. Sustained oscillation of infectives is often due to seasonal effects which may be related to climatic changes. For example the transmission of the measles virus by droplets is enhanced in cooler, more humid seasons. In many countries the onset of cooler, more humid weather coincides with the increased aggregation of people and the seasonal effect can be exacerbated. In this paper we consider non-autonomous compartmental epidemiological models and demonstrate that the critical community size phenomenon may be associated with the seasonal variation in the disease propagation. This approach is applicable to both the prevaccination phenomenon of critical community size and the current goal of worldwide elimination of measles by vaccination.

The perturbation of the eigenvalues of a regular Sturm–Liouville problem in normal form which results from a small perturbation of the coefficient function is known to be uniformly bounded. For numerical methods based on approximating the coefficients of the differential equation, this result is used to show that a better bound on the error is obtained when the problem is in normal form. A method having a uniform error bound is presented, and an extension of this method for general Sturm–Liouville problems is proposed and examined.

The change of impedance per unit length in a single or double conductor line situated parallel to an infinitely long two-layered metallic circular cylinder is found (within the quasistatic approximation) in the form of an infinite series. The cylinder consists of an inner core and an outer annulus. The properties of the inner core are assumed to be constant. The relative magnetic permeability, μ(r) = rα and the conductivity, σ(r) = σ(0)rκ, of the outer annulus vary with respect to the radial coordinate, r, and α and κ are arbitrary real numbers. Numerical results are presented in the form of figures and tables.

The classic problem, first treated by Taylor [18], of the dispersion of inert soluble matter in fluid flow continues to attract attention from researchers describing the approach to the asymptotic state [5, 17]. The present article considers some of the complications caused when the solute is chemically active, Dispersing chemically active solutes occur in diverse fields such as chromatography, chemical engineering and environmental fluid mechanics.

The asymptotic large-time analysis of Chatwin [5] is re-worked to handle the case of reactive solutes dispersing in parallel flow. Matching between moderate and large-time solutions requires consideration of the integral moments of the reactive contaminant could, and the Aris method of moments is therefore invoked and modified for reaction effects. The results are applied in detail to the outstanding paractical example—the chemical flow reactor (a device used to measure reaction rates for chemical reactions taking place between fluids). For this case, the paper provides a practical alternative to recent variable diffusion coefficient studies [6, 7, 15], and presents further results for the concentration distribution and for the limiting behaviour under weak and vigorous recactions at the boundary of the flow.

Using a mixed-type Fourier transform of a general form in the case of water of infinite depth and the method of eigenfunction expansion in the case of water of finite depth, several boundary-value problems involving the propagation and scattering of time harmonic surface water waves by vertical porous walls have been fully investigated, taking into account the effect of surface tension also. Known results are recovered either directly or as particular cases of the general problems under consideration.

A local description of space and time in which translations are included in the group of gauge transformations is studied using the formalism of fibre bundles. It is shown that the flat Minkowski space–time may be obtained from a non-flat connection in a de Sitter structured fibre bundle by choosing at least two different cross-sections. The interaction terms in the covariant derivative of a Dirac wave function that correspond to translations may be interpreted as the mass term of the Dirac equation, and then the two cross-sections (gauges) correspond to the description of a fermion and antifermion respectively.

Increase in dimensionality of the signal space for a fixed bandwidth leads to exponential growth in the number of different signals which must be encoded. In this paper we determine the best subspace of orthogonal functions which can be used to minimise the worst ratio of peak power to RMS power. A mathematical formulation of this problem has been made and it has been found that the Fourier basis satisfies the required constraints of optimality in terms of form factor (peak/RMS ratio).

Sufficient conditions for the controllability of nonlinear neutral Volterra integrodifferential systems with implicit derivative are established. The results are a generalisation of the previous results, through the notions of condensing map and measure of noncompactness of a set.

Necessary and sufficient conditions for optimality in the control of linear differential systems ẋ = Ax + Bu with Stieltjes boundary conditions , where ν is an r × n matrix valued measure of bounded variation, are obtained, Feedback-like control is given in the case of quadratic performance.

The resolution of many problems in probability depends on being able to provide sufficiently good upper or lower bounds to certain moments of distributions. A striking example from the literature of a result that can offer such bounds was given by Pó1ya over sixty years ago as the following theorem (see [7, Vol. II, p. 144] and [7, Vol. I, p. 94]).

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 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.

A new version of Jensen's inequality is established for probability distributions on the non-negative real numbers which are characterized by moments higher than the first. We deduce some new sharp bounds for Laplace-Stieltjes transforms of such distribution functions.

In the absence of surface tension, the problem of determining a travelling surface pressure distribution that displaces a portion of the free surface in a prescribed manner has been solved by several authors, and this “planing-surface” problem is reasonably well understood. The effect of inclusion of surface tension is to change, in a dramatic way, the singularity in the integral equation that describes the problem. It is now necessary in general to allow for isolated impulsive pressure, as well as a smooth distribution over the wetted length. Such pressure points generate jump discontinuities in free-surface slope. Numerical results are obtained here for a class of problems in which there is a single impulse located at the leading edge of the planing surface and detachment with continuous slope at the trailing edge. These results do not appear to approach the classical results in the limit as the surface tension approaches zero, a paradox that is resolved in Part II, which follows.

A simple eigenvalue and a corresponding wavefunction of a Schrödinger operator is initially approximated by the Galerkin method and by the iterated Galerkin method of Sloan. The initial approximation is iteratively refined by employing three schemes: the Rayleigh-Schrödinger scheme, the fixed point scheme and a modification of the fixed point scheme. Under suitable conditions, convergence of these schemes is established by considering error bounds. Numerical results indicate that the modified fixed point scheme along with Sloan's method performs better than the others.

Sufficient conditions are obtained for the existence of a globally attracting positive periodic solution of the mutualism model

where ri, Ki, αi ∈ C(R, R+) and αi > Ki, i = 1, 2, τi, σi ∈ C(R, R+), i = 1, 2, and ri, Ki, αi, τi, σi (i = 1, 2) and functions of period ω > 0.