Some scaling solutions of a class of radially symmetric non-linear diffusion equations in an arbitrary dimension d are obtained, (A) for an initial point source with a fixed total amount of material, and (B) for a radial flux of material through a hyper-spherical surface. In this macroscopic...

The analytical solution to the parts of the boundary of the Mandelbrot set associated with cycles of order six is obtained in the form of a polynomial. The associated algebraic elimination problem is considered for cycles of general order n.

The analytical solutions to the parts of the boundary of the Mandelbrot set associated with cycles of order 7 and 8 are obtained by an arithmetic method in the form of polynomials. The “inverse orbit” method of calculating the values of cycle centres is extended to complex cases, and applied...

The boundaries of regions containing complex temperature zeros of the partition function of the two-dimensional Ising model on partially anisotropic triangular lattices are investigated in detail. A “diagonal” symmetry of one of the boundaries on lattices with one “odd” and two equal...

Special features of the complex temperature zeros of the partition function of the two-dimensional Ising model on completely anisotropic triangular lattices with all “odd” interactions, such as one with interaction ratios 5:3:1, are investigated. A bifurcation of one of the boundary lines at...

The boundaries of regions containing complex temperature zeros of the partition function of the two-dimensional Ising model on completely anisotropic triangular and quadratic lattices are investigated in detail. Numerical solutions of the boundary equations are presented for triangular lattices...

An explicit function is constructed to permit easy calculation of the asymptotic structure of the various spirals and branches around the main cardioid in the Mandelbrot set. Details of its application to “exterior” spirals are presented.

Demographic forecasts predict that over the next fifty years the proportion of people in New Zealand over the age of 65 will more than double, from 12 percent in 1999 to 26 percent in 2050. This paper reviews potential economic implications of this demographic change in the following broad...

Differences in productivity explain much of the growing income gap between Australia and New Zealand. Good policy responses rely on understanding the sources of these differences. Seventy percent of the aggregate gap in productivity between the two countries is due to underperformance of New...

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