Narrow Results

The aim of this paper is to show that fermion and boson random point processes naturally appear from representations of CAR and CCR which correspond to gauge invariant generalized free states (also called quasi-free states). We consider particle density operators ρ(x), x ∈ ℝ^d, in the representation of CAR describing an infinite free Fermi gas of finite density at both zero and finite temperature [6], and in the representation of CCR describing an infinite free Bose gas at finite temperature [5]. We prove that the spectral measure of the smeared operators ρ(f) = ∫ dx f(x) ρ(x) (i.e., the measure μ which allows to realize the ρ(f)'s as multiplication operators by <·, f> in L²(dμ)) is a well-known fermion, respectively boson process on the space of all locally finite configurations in ℝ^d

Let (X, 0) be the germ of a normal space of dimension n+1 with an isolated singularity at 0 and let f be a germ of holomorphic function with an isolated regularity at 0. We prove that the meromorphic extension of the current

We prove that a complex curve charged by a local Ahlfors current is either a disk or an annulus.

As a historical remark the similarities are pointed out between a form of chiral action introduced by Schwinger and the formalism used in the noncommutative extensions of electromagnetism.

The dynamics which control the spread of tracers in the N.W. European Shelf Seas are reviewed. The perspective of this review is to allow a comparison with the vastly different regimes found in Australian waters. Whilst these N.W. European Shelf Seas are dominated by the influence of the M₂ semi-diurnal tide, the Gulfs off South Australia have significant diurnal constitutents and a peculiar near equality of M₂ and S₂—producing ‘dodge’ tides. Nevertheless, generalised expressions for both the annual mean and the seasonal amplitude of sea surface temperature (derived from North Atlantic data) are generally applicable.

The greater sensitivity of diurnal tidal constituents to bed friction coupled with the proximity to the related inertial latitude suggests that tidal propagation models may require more tuning of the bed stress coefficient. However the greatest contrast is for ‘estuaries’ where the excess of evaporation over precipitation and river flow produces ‘inverse estuaries’ unknown in Europe. Whilst flushing time concepts can be used in similar fashions, the extraction of tracers from such estuaries occurs close to the bed via ‘inverse’ salt wedges. This contrast with mean surface extraction in European estuaries will have significant influences on the related ecology.

A ‘Future Work’ section describes recent developments and plans to extend marine forecasting via Operational Oceanography. Whilst Australian requirements will differ considerably, the need to maintain awareness and adopt common practices is important to fulfill the wider goals of GOOS—the Global Ocean Observing System.

A three-dimensional hydrodynamic-numeric computer program to compute sea levels and currents caused by tides, winds and surges at the open boundary was applied to Boston Bay, South Australia to calculate near-surface and near-bottom currents during the tuna mortalities of April 1996. A particle tracking computer program, based on a Lagrangian–Stochastic procedure, using these currents as input was then applied to the lower part of the water column to compute the movement of suspended sediment near the sea floor. When compared with cumulative tuna deaths, a significant connection between suspended sediment concentrations and mortality percentages at tuna farm locations is evident if a three to five day time lag is assumed.