Three-bedroom townhouses, Air Niugini Staff Housing, Papua New Guinea

Street elevation, carports below entry balconies.

Two-bedroom townhouses, Air Niugini Staff Housing, Papua New Guinea

As seen from road.

Three-bedroom townhouse, Air Niugini Staff Housing, Papua New Guinea

Side elevation, showing upper level bedroom windows.

Burrundulla Garden Housing at Kambah, Canberra

View to rear of townhouses with enclosed garden, shed and clothes line.

Burrundulla Garden Housing at Kambah, Canberra

View to flats with townhouses beyond.

Burrundulla Garden Housing at Kambah, Canberra

View of flats from internal street.

Burrundulla Garden Housing at Kambah, Canberra

View to townhouses with individual front porch and paired carports.

Burrundulla Garden Housing at Kambah, Canberra

View to front elevation of flats from internal street.

Burrundulla Garden Housing at Kambah, Canberra

View through internal street with townhouses on left and flats on left.

Burrundulla Garden Housing at Kambah, Canberra

View to townhouses and carports from east.

Burrundulla Garden Housing at Kambah, Canberra

View to development with townhouses in foreground and flats beyond.

Burrundulla Garden Housing at Kambah, Canberra

View of townhouses from exterior.

Gauge P-representations for quantum-dynamical problems: Removal of boundary terms

P-representation techniques, which have been very successful in quantum optics and in other fields, are also useful for general bosonic quantum-dynamical many-body calculations such as Bose-Einstein condensation. We introduce a representation called the gauge P representation, which greatly widens the range of tractable problems. Our treatment results in an infinite set of possible time evolution equations, depending on arbitrary gauge functions that can be optimized for a given quantum system. In some cases, previous methods can give erroneous results, due to the usual assumption of vanishing boundary conditions being invalid for those particular systems. Solutions are given to this boundary-term problem for all the cases where it is known to occur: two-photon absorption and the single-mode laser. We also provide some brief guidelines on how to apply the stochastic gauge method to other systems in general, quantify the freedom of choice in the resulting equations, and make a comparison to related recent developments.

Existence of Multiple Solutions for Second Order Boundary Value Problems

We give conditions on f involving pairs of lower and upper solutions which lead to the existence of at least three solutions of the two point boundary value problem y" + f(x, y, y') = 0, x epsilon [0, 1], y(0) = 0 = y(1). In the special case f(x, y, y') = f(y) greater than or equal to 0 we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and of Lakshmikantham et al.