Use of Complex Lie Symmetries for Linearization of Systems of Differential Equations - II: Partial Differential Equations

The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations implies the linearizability of systems of partial differential equations corresponding to those complex ordinary differential equations. The invertible complex transformations can be used to obtain invertible real transformations that map a system of nonlinear partial differential equations into a system of linear partial differential equation. Explicit invariant criteria are given that provide procedures for writing down the solutions of the linearized equations. A few non-trivial examples are mentioned.Comment: This paper along with its first part ODE-I were combined in a single research paper "Linearizability criteria for systems of two second-order differential equations by complex methods" which has been published in Nonlinear Dynamics. Due to citations of both parts I and II these are not replaced with the above published articl

Robust assessment of future changes in extreme precipitation over the Rhine basin using a GCM

Estimates of future changes in extremes of multiday precipitation sums are critical for estimates of future discharge extremes of large river basins. Here we use a large ensemble of global climate model SRES A1b scenario simulations to estimate changes in extremes of 1–20 day precipitation sums over the Rhine basin, projected for the period 2071–2100 with reference to 1961–1990. We find that in winter, an increase of order 10%, for the 99th percentile precipitation sum, is approximately fixed across the selected range of multiday sums, whereas in summer, the changes become increasingly negative as the summation time lengthens. Explanations for these results are presented that have implications for simple scaling methods for creating time series of a future climate. We show that the dependence of quantile changes on summation time is sensitive to the ensemble size and indicate that currently available discharge estimates from previous studies are based on insufficiently long time series

Soil, grain and water chemistry and human selenium imbalances in Enshi district, Hubei Province, China

Many elements which are essential to human and other animal health in small doses can be toxic if ingested in excess. Selenium (Se), a naturally occurring metalloid element is found in all natural materials on earth including rocks, soils, waters, air, plant and animal tissues. Since the early 1930’s, it has been recognised that Se toxicity causes hoof disorders and hair loss in livestock. Se was also identified as an essential trace element to humans and other animals in the late 1950’s. It forms a vital constituent of the biologically important enzyme glutathione peroxidase which acts as an anti-oxidant preventing cell degeneration. Se deficiency has been implicated in the aetiology of several diseases including cancer, muscular dystrophy, muscular sclerosis and cystic fibrosis. Se can be assimilated in humans through several pathways including food, drinking water and inhalation of Se-bearing particles from the atmosphere. In the majority of situations, food is the most important source of Se, as levels in water are very low. The narrow range between deficiency levels (<40 pg per day) and toxic levels in susceptible people (> 900 pg per day) makes it necessary to carefully control the amount of Se in the diet. In China, Se deficiency has been linked to an endemic degenerative heart disease known as Keshan Disease (KD) and an endemic osteoarthropathy which causes deformity of affected joints, known as Kaschin-Beck Disease. These diseases occur in a geographic belt stretching from Heilongjiang Province in north-east China to Yunnan Province in the south-west. In the period between 1959 and 1970, peak KD incidence rates exceeded 40 per 100 000 (approximately 8500 cases per annum) with 1400 - 3000 deaths recorded each year. Incidence rates have since fallen to less than 5 per 100 000 with approximately 1000 new cases reported annually (Levander, 1986). Se toxicity (selenosis) resulting in hair and nail loss and disorders of the nervous system in the human population, has also been recorded in Enshi District, Hubei Province and in Ziyang County, Shanxi Province. China possesses one of the best epidemiological databases in the world on Se-related diseases which has been used in conjunction with geochemical data to demonstrate a significant geochemical control on human Se exposure. However, the precise geographical areas at risk and the geochemical controls on selenium availability have yet to be established

Spreading and localization of wavepackets in disordered wires in a magnetic field

We study the diffusive and localization properties of wavepackets in disordered wires in a magnetic field. In contrast to a recent supersymmetry approach our numerical results show that the decay rate of the steady state changes {\em smoothly} at the crossover from preserved to broken time-reversal symmetry. Scaling and fluctuation properties are also analyzed and a formula, which was derived analytically only in the pure symmetry cases is shown to describe also the steady state wavefunction at the crossover regime. Finally, we present a scaling for the variance of the packet which shows again a smooth transition due to the magnetic field.Comment: 4 pages, 4 figure

European Rural Development Policy Preferences

This paper presents the results of a survey about policy preferences collected from agricultural economists at an EAAE Seminar on rural development policy experiences. It documents the diversity in rural development problems and favored tactics across Europe.Rural development, policy, preferences, Community/Rural/Urban Development,

The Forum of European Geological Surveys Geochemistry Task Group 1994-1996 inventory

The Forum of European Geological Surveys (FOREGS) includes representatives from 33 European countries and is responsible for co-ordinating Geological Survey activities in Europe. The FOREGS Geochemistry Task Group was established in 1994 to develop a strategy for the preparation of European geochemical maps following the recommendations of the International Geological Correlation Programme (IGCP) Project 259 ‘International Geochemical Mapping’ (now the International Union of Geological Sciences (IUGS) /International Association of Geochemistry and Cosmochemistry (IAGC) Working Group on Global Geochemical Baselines). The FOREGS geochemistry programme is aimed at preparing a standardised European geochemical baseline to IGCP-259 standards. The principal aims of this dataset will be for environmental purposes, as a baseline for the assessment of the extent and distribution of contaminated land in the context of variations in the natural geochemical background, but it will also have applications in resource assessment and for the development of policy for the sustainable management of metalliferous mineral and other resources. The first phase of the programme was the compilation of an inventory of geochemical data based on the results of a questionnaire completed by Geological Surveys and related organisations throughout the FOREGS community. The results show that the sample types which have been used most extensively are stream sediment (26% coverage), surface water (19% coverage) and soil (11% coverage). Stream sediments have been collected using a narrow range of mesh sizes (< 150–< 200 μm), but soil samples have been collected according to two different conventions: some surveys used a similar mesh size range to that used for stream sediments while others employed the < 1000 or < 2000 μm fractions traditionally used by soil surveys. Sample densities range from 1 sample per 0.5 km2 to 1 per 3500 km2. Various analytical methods have been used, but most of the available data have been calibrated using international reference materials, and data for the most important of the potentially harmful elements (PHEs) are available for most datasets. Systematic radiometric data are available for only a small proportion of Europe, a situation which compares very unfavourably with that in Australia, North America, the former Soviet Union and many developing countries. Recommendations are made for increasing the compatibility of geochemical methods between national geochemical surveys as a basis for the preparation of a series of European geochemical maps. The next stage of the FOREGS Geochemistry Task Group will be the collection of the Global Reference Network of samples against which to standardise national datasets according to the methods recommended in the final report of the IGCP 259 programme

Krymsk®1 (VVA-1), A dwarfing rootstock suitable for high density plum orchards in the Netherlands

Krymsk®:1 (Prunus tomentosa × Prunus cerasifera) was selected by Gennady Eremin at the Krymsk Breeding Station in Russia in 1966. Since 1994, it has been tested as a rootstock for several plum cultivars in The Netherlands. Graft compatibility was good for scion cultivars ‘Avalon’, ‘Excalibur’, ‘Jubileum’, ‘Opal’, and ‘Victoria’. Growth and production efficiency of plum on Krymsk®:1 was compared with that of plum on St. Julien A and, depending on the cultivar, also with Ferlenain, Otesani 8 and Pixy. With all cultivars, trees on rootstock Krymsk®:1 were by far the least vigorous, most precocious, and most production efficient. The production efficiency of ‘Avalon’ and ‘Excalibur’ on Krymsk®:1 grown for 10 years was 0.41 and 0.26 kg/cm² trunk cross sectional area, respectively, 3.4 and 4.3 times higher on Krymsk®:1 than on St. Julien A. With ‘Opal’ the production efficiency calculated over the first 5 years after planting was 2 to 3 times higher than on St. Julien A, but this difference became non significant after 7 years of cultivation. This was due to the much higher increase in production per tree during the 5th and 6th leaf of the trees on St. Julien A than on Krymsk®:1. Fruit size of ‘Opal’, ‘Avalon’ and ‘Excalibur’ was similar for trees grown on Krymsk®:1 and St. Julien A. With ‘Victoria’ fruit size was significantly larger (5 g) with Krymsk®:1 than with St. Julien A. Krymsk®:1 also increased the percentage of first pick by 15%, the sugar content by 9%, enhanced the development of fruit overcolour and reduced the percentage of fruits with gummosis in ‘Victoria’ plums. Dutch fruit growers show great interest in Krymsk®:1 as a rootstock for plum, as this rootstock makes high density plum orchards feasible. Growers switching to trees on Krymsk®1 have to take more care of their trees, especially in the first years after planting. Pruning, irrigation, and fertilization of the trees need much more attention in order to keep the trees vigorous and ensure good production levels. From 2002 to spring 2008, 120,000 plum trees on Krymsk®1 have been planted in The Netherlands and planting densities have increased from 830 up to 2,285 trees/ha. The main cultivar planted is ‘Victoria’

Stages of steady diffusion growth of a gas bubble in strongly supersaturated gas-liquid solution

Gas bubble growth as a result of diffusion flux of dissolved gas molecules from the surrounding supersaturated solution to the bubble surface is studied. The condition of the flux steadiness is revealed. A limitation from below on the bubble radius is considered. Its fulfillment guarantees the smallness of fluctuation influence on bubble growth and irreversibility of this process. Under the conditions of steadiness of diffusion flux three stages of bubble growth are marked out. With account for Laplace forces in the bubble intervals of bubble size change and time intervals of these stages are found. The trend of the third stage towards the self-similar regime of the bubble growth, when Laplace forces in the bubble are completely neglected, is described analytically.Comment: 22 page

On the Spectrum of the Resonant Quantum Kicked Rotor

It is proven that none of the bands in the quasi-energy spectrum of the Quantum Kicked Rotor is flat at any primitive resonance of any order. Perturbative estimates of bandwidths at small kick strength are established for the case of primitive resonances of prime order. Different bands scale with different powers of the kick strength, due to degeneracies in the spectrum of the free rotor.Comment: Description of related published work has been expanded in the Introductio