Entire functions with Julia sets of positive measure

Let f be a transcendental entire function for which the set of critical and asymptotic values is bounded. The Denjoy-Carleman-Ahlfors theorem implies that if the set of all z for which |f(z)|>R has N components for some R>0, then the order of f is at least N/2. More precisely, we have log log M(r,f) > (N/2) log r - O(1), where M(r,f) denotes the maximum modulus of f. We show that if f does not grow much faster than this, then the escaping set and the Julia set of f have positive Lebesgue measure. However, as soon as the order of f exceeds N/2, this need not be true. The proof requires a sharpened form of an estimate of Tsuji related to the Denjoy-Carleman-Ahlfors theorem.Comment: 17 page

Slow escaping points of quasiregular mappings

This article concerns the iteration of quasiregular mappings on Rd and entire functions on C. It is shown that there are always points at which the iterates of a quasiregular map tend to infinity at a controlled rate. Moreover, an asymptotic rate of escape result is proved that is new even for transcendental entire functions. Let f:Rd→Rd be quasiregular of transcendental type. Using novel methods of proof, we generalise results of Rippon and Stallard in complex dynamics to show that the Julia set of f contains points at which the iterates fn tend to infinity arbitrarily slowly. We also prove that, for any large R, there is a point x with modulus approximately R such that the growth of |fn(x)| is asymptotic to the iterated maximum modulus Mn(R,f)

Results of investigations into the groundwater response and productivity of high water use agricultural systems 1990-1997 4. TKK Engineering\u27s Catchment (Williams)

High water use vegetation systems for salinity control were trialed on a 70 ha catchment located about 15 km north of Williams, Western Australia. The catchment receives about 545 mm annual rainfall and 1870 mm annual evaporation. Development of salinity is characterised by passive discharge upslope from a dolerite dyke. Because recharge exceeds the discharge capacity of current seeps, there is potential for new seeps to develop in the mid to lower slopes

Results of investigations into the groundwater response and productivity of high water use agricultural systems 1990-1997 1. Wooldridge/Wright\u27s Catchment (Kojonup)

High water use vegetation systems for salinity control were trialed on a 170 ha catchment located 13 km north of Kojonup, Western Australia. The catchment receives about 470 mm annual rainfall and 1825 mm annual evaporation

Results of investigations into the groundwater response and productivity of high water use agricultural systems 1990-1997 5 White/Beattys\u27 Catchment (Dinninup)

High water use vegetation systems for salinity control were trialed on a 250 ha catchment located three km north-west of Dinninup, Western Australia. The catchment receives about 620 mm annual rainfall and 1500 mm annual evaporation. The catchment is characterised by slopes with gradients in excess of 5%, deep weathering (15-25 m to bedrock), active seepage in the valley (piezometric heads 204 m above ground surface) and high recharge (water table fluctuations of 1-4 m)

Results of investigations into the groundwater response and productivity of high water use agricultural systems 1990-1997 3 Hunts\u27 Catchment (Frankland)

High water use vegetation systems for salinity control were trialed on an 80 ha catchment located 12 km east of Frankland, Western Australia. The catchment receives about 510 mm annual rainfall and 1525 mm annual evaporation. Development of salinity in the catchment is concentrated in the valley floor. Here the groundwater is extremely saline (3000-4000 mS/m) and piezometric levels are between 1 m below and 1 m above the surface

Results of investigations into the groundwater response and productivity of high water use agricultural systems 1990-1997. 2. Souths\u27 Catchment (Darkan)

High water use vegetation systems for salinity control were trialed on a 90 ha catchment located 12 km north north-west of Darkan, Western Australia. The catchment receives about 560 mm annual rainfall and 1895 mm annual evaporation. The catchment is characterised by a number of actively expanding seeps which are developing under the strong geological control of quartz and dolerite dykes. Development of salinity is also influenced by high recharge rates in the free draining gravel soils of the upper slope

Results of investigations into the groundwater response and productivity of high water use agricultural systems 1990-1997 : 6. Summary of all sites

The south-western Woolbelt receives annual rainfall between 500-700 mm with long dry summers and cool wet winters. The dominant land use is grazing of Merino sheep for wool productiion, with smaller areas (5-15%) of cropping. All of the catchments selected were affected by salinity, but the extent and severity varied. In all catchments the location of the major expression of salinity was the valley floor

Effects of atmospheric pressure plasma on dye uptake by the surface of wool

A woven pure wool fabric has been exposed to atmospheric pressure plasma for 30 seconds using a pilot-scale. commercial machine. X-ray photoelectron spectral data revealed large increases in oxygen and nitrogen. and a large reduction in carbon. on the surfaces of the plasma-treated fibres. A CIN ratio of 3.55 for plasma-treated wool was consistent with removal of the covalently-bound fatty acids from the surface of the cuticle cells. resulting in exposure of the proteinaceous epicuticle. Dye staining experiments revealed that the back of the fabric had received the same, uniform level of treatment as the face, despite the fact that only the face had been directly exposed to the plasma. Dyes (1 % oww) were applied to fabric at 50&deg;C (liquor ratio =40: 1) and pH values from 3 to 6. The relatively low temperature of 50&deg;C was selected in order to accentuate the effects of plasma on the rate of dye uptake. Under these conditions, dye was adsOibed onto the fibre surfaces, with very little penetration into the fibres. Effects of the plasma treatment on the rate of dyes adsorption were dyespecific. No significant effects of plasma on the rate of dye uptake were observed with relatively hydrophobic dyes, but hydrophilic dyes were adsorbed more rapidly by the plasmatreated fabric. It would appear that for more hydrophobic dyes, hydrophobic effects are more important for the adsorption of dyes by the plasma-treated fibres, even though these fibres were quite hydrophilic. On the other hand. it is concluded that for more hydrophilic dyes, electrostatic effects are more important for adsorption by the plasma-treated fibre.<br /