Some direct numerical approaches to the solution of the singular nonlinear transonic integral equation

The nonlinear singular integral equation of transonic flow is examined, noting that standard numerical techniques are not applicable in solving it. The difficulties in approximating the integral term in this expression were solved by special methods mitigating the inaccuracies caused by standard approximations. It was shown how the infinite domain of integration can be reduced to a finite one; numerical results were plotted demonstrating that the methods proposed here improve accuracy and computational economy.

Water-wave scattering by two submerged plane vertical barriers-Abel integral-equation approach

The classical problem of surface water-wave scattering by two identical thin vertical barriers submerged in deep water and extending infinitely downwards from the same depth below the mean free surface, is reinvestigated here by an approach leading to the problem of solving a system of Abel integral equations. The reflection and transmission coefficients are obtained in terms of computable integrals. Known results for a single barrier are recovered as a limiting case as the separation distance between the two barriers tends to zero. The coefficients are depicted graphically in a number of figures which are identical with the corresponding figures given by Jarvis (J Inst Math Appl 7:207-215, 1971) who employed a completely different approach involving a Schwarz-Christoffel transformation of complex-variable theory to solve the problem.

Use of biomass fuels in the brick-making industries of Sudan: Implications for deforestation and greenhouse gas emission

The study focuses on the potential roles of the brick making industries in Sudan in deforestation and greenhouse gas emission due to the consumption of biofuels. The results were based on the observation of 25 brick making industries from three administrative regions in Sudan namely, Khartoum, Kassala and Gezira. The methodological approach followed the procedures outlined by the Intergovernmental Panel on Climate Change (IPCC). For predicting a serious deforestation scenario, it was also assumed that all of wood use for this particular purpose is from unsustainable sources. The study revealed that the total annual quantity of fuelwood consumed by the surveyed brick making industries (25) was 2,381 t dm. Accordingly, the observed total potential deforested wood was 10,624 m3, in which the total deforested round wood was 3,664 m3 and deforested branches was 6,961 m3. The study observed that a total of 2,990 t biomass fuels (fuelwood and dung cake) consumed annually by the surveyed brick making industries for brick burning. Consequently, estimated total annual emissions of greenhouse gases were 4,832 t CO2, 21 t CH4, 184 t CO, 0.15 t N20, 5 t NOX and 3.5 t NO while the total carbon released in the atmosphere was 1,318 t. Altogether, the total annual greenhouse gases emissions from biomass fuels burning was 5,046 t; of which 4,104 t from fuelwood and 943 t from dung cake burning. According to the results, due to the consumption of fuelwood in the brick making industries (3,450 units) of Sudan, the amount of wood lost from the total growing stock of wood in forests and trees in Sudan annually would be 1,466,000 m3 encompassing 505,000 m3 round wood and 961,000 m3 branches annually. By considering all categories of biofuels (fuelwood and dung cake), it was estimated that, the total emissions from all the brick making industries of Sudan would be 663,000 t CO2, 2,900 t CH4, 25,300 t CO, 20 t N2O, 720 t NOX and 470 t NO per annum, while the total carbon released in the atmosphere would be 181,000 t annually.

Comparative growth and biomass allocation of two varieties of cat's claw creeper, Dolichandra unguis-cati (Bignoniaceae) in Australia

Introduced as an ornamental vine, cat's claw creeper Dolichandra unguis-cati (syn. Macfadyena unguis-cati) has invaded coastal and subcoastal areas of subtropical eastern Australia. Two varieties have been indentified, one of which ('short-pod') is found throughout south-eastern Australia, while the other ('long-pod') appears to be restricted to several sites in south-eastern Queensland. We compared the growth and biomass allocation patterns of the two varieties in the field over a 22-month period to determine if a higher growth rate and/or more efficient allocation of biomass may contribute to this disparity in distribution. The long-pod variety produced greater aboveground and total biomass than the short-pod variety in both riparian and non-riparian zones. Belowground the two varieties produced a similar number of tubers and overall biomass, though the long-pod variety allocated a smaller portion of its carbon belowground. High growth rates and greater biomass allocation aboveground are characteristic of invasive species, allowing them to outcompete and crowd out existing vegetation. There was no significant site by variety interaction, an indication of consistency in variety performance across riparian and non-riparian sites. Results from our study suggest that differences in growth and biomass allocations are unlikely to have contributed to the disparity in distribution of the two varieties. Despite currently occupying a relatively small range, the long-pod variety may be a more adept invader than the short-pod variety, and could become more prevalent in the future. © 2012 CSIRO.

Stunted cotton (Gossypium hirsutum L.) fully recovers biomass and yield of seed cotton after delayed root inoculation with spores of an arbuscular mycorrhizal fungus (Glomus mosseae)

In the northern grain and cotton region of Australia, poor crop growth after long periods of fallow, called 'long-fallow' disorder, is caused by a decline of natural arbuscular-mycorrhizal fungi (AMF). When cotton was grown in large pots containing 22 kg of Vertisol from a field recently harvested from cotton in Central Queensland, plants in pasteurised soil were extremely stunted compared with plants in unpasteurised soil. We tested the hypothesis that this extreme stunting was caused by the absence of AMF and examined whether such stunted plants could recover from subsequent treatment with AMF spores and/or P fertiliser. At 42 days after sowing, the healthy cotton growing in unpasteurised soil had 48% of its root-length colonised with AMF, whereas the stunted cotton had none. After inoculation with AMF spores (6 spores/g soil of Glomus mosseae) and/or application of P fertiliser (50 mg P/kg soil) at 45 days after sowing, the stunted plants commenced to improve about 25 days after treatment, and continued until their total dry matter and seed cotton production equalled that of plants growing in unpasteurised soil with natural AMF. In contrast, non-mycorrhizal cotton grown without P fertiliser remained stunted throughout and produced no bolls and only 1% of the biomass of mycorrhizal cotton. Even with the addition of P fertiliser, non-mycorrhizal cotton produced only 64% of the biomass and 58% of the seed cotton (lint + seed) of mycorrhizal cotton plants. These results show that cotton is highly dependent on AMF for P nutrition and growth in Vertisol (even with high rates of P fertiliser), but can recover from complete lack of AMF and consequent stunting during at least the first 45 days of growth when treated with AMF spores and/or P fertiliser. This corroborates field observations in the northern region that cotton may recover from long-fallow disorder caused by low initial levels of AMF propagules in the soil as the AMF colonisation of its roots increases during the growing season.

The effects of environmental factors on biomass and microcystin production by the freshwater cyanobacterial genera Microcystis and Anabaena

Several cyanobacterial genera produce the hepatotoxins, microcystins. Microcystins are produced only in cells that have microcystin synthetase gene (mcy) clusters, which encode enzyme complexes involved in microcystin biosynthesis. Microcystin-producing and nonmicrocystin-producing genotypes of single cyanobacterial genus may occur simultaneously in situ. Previously, the effects of environmental factors on the growth and microcystin production of cyanobacteria have mainly been studied by means of isolated cyanobacteria cultures in the laboratory. Studies in the field have been difficult, owing to the lack of methods to identify and quantify the different genotypes. In this study, genus-specific microcystin synthetase E (mcyE) gene primers were designed and a method to identify and quantify the mcyE copy numbers was developed and used in situ. Microcystis and Anabaena mcyE genes were observed in two Finnish lakes. Microcystis appeared to be the most abundant microcystin producer in Lake Tuusulanjärvi and in one basin of Lake Hiidenvesi. Because the most potent microcystin-producing genus of a lake can be identified, it will be possible in the future to design genus-targeted strategies for lake restoration. Effects of P and N concentrations on the biomass of microcystin-producing and nonmicrocystin-producing Microcystis strains and an Anabaena strain were studied in cultures. P and N concentrations and their combined effect increased cyanobacterial biomass of all Microcystis strains. The biomass of microcystin-producing Microcystis was higher than that of nonmicrocystin-producing strains at high nutrient concentrations. The P concentration increased Anabaena biomass, but the effect of N concentration was statistically insignificant for growth yield, probably due to the ability of the genus to fix molecular N2. P and N concentrations and combined nutrients caused an increase in cellular microcystin concentrations of the Microcystis strain cultivated in chemostat cultures. Cyanobacteria are able to hydrolyse nutrients from organic matter through extracellular enzyme activities. Leucine aminopeptidase (LAP) activity was observed in an axenic N2-fixing Anabaena strain grown in batch cultures. The P concentration caused a statistically significant increase in LAP activity, whereas the effect of N concentration was insignificant. The highest LAP activities were observed in the most eutrophic basins of Lake Hiidenvesi. LAP activity probably originated mostly from attached heterotrophic bacteria and less from cyanobacteria.

Relations between chronic regulatory focus and future time perspective: Results of a cross-lagged structural equation model

Future time perspective - the way individuals perceive their remaining time in life - importantly influences socio-emotional goals and motivational outcomes. Recently, researchers have called for studies that investigate relationships between personality and future time perspective. Using a cross-lagged panel design, this study investigated effects of chronic regulatory focus dimensions (promotion and prevention orientation) on future time perspective dimensions (focus on opportunities and limitations). Survey data were collected two times, separated by a 3. month time lag, from 85 participants. Results of structural equation modeling showed that promotion orientation had a positive lagged effect on focus on opportunities, and prevention orientation had a positive lagged effect on focus on limitations.

More fertile florets and grains per spike can be achieved at higher temperature in wheat lines with high spike biomass and sugar content at booting

An understanding of processes regulating wheat floret and grain number at higher temperatures is required to better exploit genetic variation. In this study we tested the hypothesis that at higher temperatures, a reduction in floret fertility is associated with a decrease in soluble sugars and this response is exacerbated in genotypes low in water soluble carbohydrates (WSC). Four recombinant inbred lines contrasting for stem WSC were grown at 20/10 degrees C and 11 h photoperiod until terminal spikelet, and then continued in a factorial combination of 20/10 degrees C or 28/14 degrees C with 11 h or 16 h photoperiod until anthesis. Across environments, High WSC lines had more grains per spike associated with more florets per spike. The number of fertile florets was associated with spike biomass at booting and, by extension, with glucose amount, both higher in High WSC lines. At booting, High WSC lines had higher fixed C-13 and higher levels of expression of genes involved in photosynthesis and sucrose transport and lower in sucrose degradation compared with Low WSC lines. At higher temperature, the intrinsic rate of floret development rate before booting was slower in High WSC lines. Grain set declined with the intrinsic rate of floret development before booting, with an advantage for High WSC lines at 28/14 degrees C and 16 h. Genotypic and environmental action on floret fertility and grain set was summarised in a model.

Existence theorem for a generalized Hammerstein type equation

An existence theorem is obtained for a generalized Hammerstein type equation

Development and testing of allometric equations for estimating above-ground biomass of mixed-species environmental plantings

To quantify the impact that planting indigenous trees and shrubs in mixed communities (environmental plantings) have on net sequestration of carbon and other environmental or commercial benefits, precise and non-biased estimates of biomass are required. Because these plantings consist of several species, estimation of their biomass through allometric relationships is a challenging task. We explored methods to accurately estimate biomass through harvesting 3139 trees and shrubs from 22 plantings, and collating similar datasets from earlier studies, in non-arid (>300mm rainfallyear-1) regions of southern and eastern Australia. Site-and-species specific allometric equations were developed, as were three types of generalised, multi-site, allometric equations based on categories of species and growth-habits: (i) species-specific, (ii) genus and growth-habit, and (iii) universal growth-habit irrespective of genus. Biomass was measured at plot level at eight contrasting sites to test the accuracy of prediction of tonnes dry matter of above-ground biomass per hectare using different classes of allometric equations. A finer-scale analysis tested performance of these at an individual-tree level across a wider range of sites. Although the percentage error in prediction could be high at a given site (up to 45%), it was relatively low (<11%) when generalised allometry-predictions of biomass was used to make regional- or estate-level estimates across a range of sites. Precision, and thus accuracy, increased slightly with the level of specificity of allometry. Inclusion of site-specific factors in generic equations increased efficiency of prediction of above-ground biomass by as much as 8%. Site-and-species-specific equations are the most accurate for site-based predictions. Generic allometric equations developed here, particularly the generic species-specific equations, can be confidently applied to provide regional- or estate-level estimates of above-ground biomass and carbon. © 2013 Elsevier B.V.

Effects of externally supplied protein on root morphology and biomass allocation in Arabidopsis

Growth, morphogenesis and function of roots are influenced by the concentration and form of nutrients present in soils, including low molecular mass inorganic N (IN, ammonium, nitrate) and organic N (ON, e.g. amino acids). Proteins, ON of high molecular mass, are prevalent in soils but their possible effects on roots have received little attention. Here, we investigated how externally supplied protein of a size typical of soluble soil proteins influences root development of axenically grown Arabidopsis. Addition of low to intermediate concentrations of protein (bovine serum albumen, BSA) to IN-replete growth medium increased root dry weight, root length and thickness, and root hair length. Supply of higher BSA concentrations inhibited root development. These effects were independent of total N concentrations in the growth medium. The possible involvement of phytohormones was investigated using Arabidopsis with defective auxin (tir1-1 and axr2-1) and ethylene (ein2-1) responses. That no phenotype was observed suggests a signalling pathway is operating independent of auxin and ethylene responses. This study expands the knowledge on N form-explicit responses to demonstrate that ON of high molecular mass elicits specific responses.

Wheat biomass and yield increased when populations of the root-lesion nematode (Pratylenchus thornei) were reduced through sequential rotation of partially resistant winter and summer crops

The root-lesion nematode, Pratylenchus thornei, can reduce wheat yields by >50%. Although this nematode has a broad host range, crop rotation can be an effective tool for its management if the host status of crops and cultivars is known. The summer crops grown in the northern grain region of Australia are poorly characterised for their resistance to P. thornei and their role in crop sequencing to improve wheat yields. In a 4-year field experiment, we prepared plots with high or low populations of P. thornei by growing susceptible wheat or partially resistant canaryseed (Phalaris canariensis); after an 11-month, weed-free fallow, several cultivars of eight summer crops were grown. Following another 15-month, weed-free fallow, P. thornei-intolerant wheat cv. Strzelecki was grown. Populations of P. thornei were determined to 150 cm soil depth throughout the experiment. When two partially resistant crops were grown in succession, e.g. canaryseed followed by panicum (Setaria italica), P. thornei populations were <739/kg soil and subsequent wheat yields were 3245 kg/ha. In contrast, after two susceptible crops, e.g. wheat followed by soybean, P. thornei populations were 10 850/kg soil and subsequent wheat yields were just 1383 kg/ha. Regression analysis showed a linear, negative response of wheat biomass and grain yield with increasing P. thornei populations and a predicted loss of 77% for biomass and 62% for grain yield. The best predictor of wheat yield loss was P. thornei populations at 0-90 cm soil depth. Crop rotation can be used to reduce P. thornei populations and increase wheat yield, with greatest gains being made following two partially resistant crops grown sequentially.

Solution of a generalized Korteweg—de Vries equation

The solitary-wavelike solution of the generalized Korteweg-de Vries equation with mixed nonlinearity is obtained. Two asymptotic cases of the solution have been discussed and solitary wave solutions have been derived. ©1974 American Institute of Physics.

A note on non-separable solutions of linear partial differential equation

A method has been presented for constructing non-separable solutions of homogeneous linear partial differential equations of the type F(D, D′)W = 0, where D = ∂/∂x, D′ = ∂/∂y, Image where crs are constants and n stands for the order of the equation. The method has also been extended for equations of the form Φ(D, D′, D″)W = 0, where D = ∂/∂x, D′ = ∂/∂y, D″ = ∂/∂z and Image As illustration, the method has been applied to obtain nonseparable solutions of the two and three dimensional Helmholtz equations.