Approximate solutions of Fredholm integral equations of the second kind

This note is concerned with the problem of determining approximate solutions of Fredholm integral equations of the second kind. Approximating the solution of a given integral equation by means of a polynomial, an over-determined system of linear algebraic equations is obtained involving the unknown coefficients, which is finally solved by using the least-squares method. Several examples are examined in detail. (c) 2009 Elsevier Inc. All rights reserved.

Light scattering studies on solutions of chlorinated rubber

Measurements have been made of the depolarisation factors \sigma u ,\sigma v ,\sigma h, and the intensity of scattering in the horizontal transverse direction, in the case of solutions of four different samples of chlorinated rubber in carbon tetrachloride. The size, shape and molecular weight of the micelles have been deduced by the application of the light scattering theories of Gans, Vrklajan and Katalinic and Debye. The extent to which the degradation of the rubber molecule occurs on chlorination has also been assessed.

Genetic analysis of resistance to root-lesion nematode (Pratylenchus thornei) in wheat

The inheritance of resistance to root-lesion nematode was investigated in five synthetic hexaploid wheat lines and two bread wheat lines using a half-diallel design of F1 and F2 crosses. The combining ability of resistance genes in the synthetic hexaploid wheat lines was compared with the performance of the bread wheat line 'GS50a', the source of resistance to Pratylenchus thornei used in Australian wheat breeding programmes. Replicated glasshouse trials identified P. thornei resistance as polygenic and additive in gene action. General combining ability (GCA) of the parents was more important than specific combining ability (SCA) effects in the inheritance of P. thornei resistance in both F1 and F2 populations. The synthetic hexaploid wheat line 'CPI133872' was identified as the best general combiner, however, all five synthetic hexaploid wheat lines possessed better GCA than 'GS50a'. The synthetic hexaploid wheat lines contain novel sources of P. thornei resistance that will provide alternative and more effective sources of resistance to be utilized in wheat breeding programmes

Rhizoctonia crown and root rot of the pasture legume, sulla (Hedysarum coronarium)

Rhizoctonia solani AG-2-2 was isolated from wilting and dying plants of sulla (Hedysarum coronarium), which is currently being assessed in eastern and southern Australia for its potential as a pasture and forage legume. Infected plants in the field had extensive rotting of the taproot, lateral roots and crown. Koch's postulates were fulfilled using three inoculation methods. The disease may pose a considerable threat to the potential use of H. coronarium in the dryland, grazing farming systems of Australia, with resistance offering the most viable option for minimising its impact.

Closed-form solutions for low-rank non-rigid reconstruction

Recovering the motion of a non-rigid body from a set of monocular images permits the analysis of dynamic scenes in uncontrolled environments. However, the extension of factorisation algorithms for rigid structure from motion to the low-rank non-rigid case has proved challenging. This stems from the comparatively hard problem of finding a linear “corrective transform” which recovers the projection and structure matrices from an ambiguous factorisation. We elucidate that this greater difficulty is due to the need to find multiple solutions to a non-trivial problem, casting a number of previous approaches as alleviating this issue by either a) introducing constraints on the basis, making the problems nonidentical, or b) incorporating heuristics to encourage a diverse set of solutions, making the problems inter-dependent. While it has previously been recognised that finding a single solution to this problem is sufficient to estimate cameras, we show that it is possible to bootstrap this partial solution to find the complete transform in closed-form. However, we acknowledge that our method minimises an algebraic error and is thus inherently sensitive to deviation from the low-rank model. We compare our closed-form solution for non-rigid structure with known cameras to the closed-form solution of Dai et al. [1], which we find to produce only coplanar reconstructions. We therefore make the recommendation that 3D reconstruction error always be measured relative to a trivial reconstruction such as a planar one.

Impacts of sodic soil amelioration on deep drainage

Groundwater tables are rising beneath irrigated fields in some areas of the Lower Burdekin in North Queensland, Australia. The soils where this occurs are predominantly sodic clay soils with low hydraulic conductivities. Many of these soils have been treated by applying gypsum or by increasing the salinity of irrigation water by mixing saline groundwater with fresh river water. While the purpose of these treatments is to increase infiltration into the surface soils and improve productivity of the root zone, it is thought that the treatments may have altered the soil hydraulic properties well below the root zone leading to increased groundwater recharge and rising water tables. In this paper we discuss the use of column experiments and HYDRUS modelling, with major ion reaction and transport and soil water chemistry-dependent hydraulic conductivity, to assess the likely depth, magnitude and timing of the impacts of surface soil amelioration on soil hydraulic properties below the root zone and hence groundwater recharge. In the experiments, columns of sodic clays from the Lower Burdekin were leached for extended periods of time with either gypsum solutions or mixed cation salt solutions and change s in hydraulic conductivity were measured. Leaching with a gypsum solution for an extended time period, until the flow rate stabilised, resulted in an approximately twenty fold increase in the hydraulic conductivity when compared with a low salinity, mixed cation solution. HYDRUS modelling was used to high light the role of those factors which might influence the impacts of soil treatment, particularly at depth, including the large amounts of rain during the relatively short wet season and the presence of thick low permeability clay layers.

Approximate closed-form solutions of realistic true proportional navigation guidance using the Adomian decomposition method

Approximate closed-form solutions of the non-linear relative equations of motion of an interceptor pursuing a target under the realistic true proportional navigation (RTPN) guidance law are derived using the Adomian decomposition method in this article. In the literature, no study has been reported on derivation of explicit time-series solutions in closed form of the nonlinear dynamic engagement equations under the RTPN guidance. The Adomian method provides an analytical approximation, requiring no linearization or direct integration of the non-linear terms. The complete derivation of the Adomian polynomials for the analysis of the dynamics of engagement under RTPN guidance is presented for deterministic ideal case, and non-ideal dynamics in the loop that comprises autopilot and actuator dynamics and target manoeuvre, as well as, for a stochastic case. Numerical results illustrate the applicability of the method.

Resistance of selected strawberry cultivars to root-knot nematode species (Meloidogyne spp.)

Strawberry runner production areas in Queensland are assessed for the presence of Pratylenchus vulnus (lesion nematode) and Meloidogyne hapla (root-knot nematode) as part of the approval process for sites used in runner production under the approved runner scheme. M. hapla is known to infest strawberry. The ability of three other Meloidogyne species occurring in Queensland to infest this host was investigated. The species M. arenaria, M. incognita and M. javanica, in addition to M. hapla, were able to reproduce on strawberry roots of the cultivar 'Joy', which sustained higher nematode reproduction rates than 'Jewel' and 'Sweet Charlie'. The ability of species other than M. hapla to infest strawberry needs to be recognised in site selection for runner production, and in screening cultivars for resistance to nematodes.

Note on the Similarity Solutions of Unsteady Jets in Rotating Fluids

The structure of time dependent jets in rotating fluids using similarity transformations is studied theoretically for which exact solutions are discussed. Approximate solution using a modified yon Mises transformation is also explored.

Resistance of Brassicaceae plants to root-knot nematode (Meloidogyne spp.) in northern Australia

Brassicaceae plants have the potential as part of an integrated approach to replace fumigant nematicides, providing the biofumigation response following their incorporation is not offset by reproduction of plant-parasitic nematodes on their roots. Forty-three Brassicaceae cultivars were screened in a pot trial for their ability to reduce reproduction of three root-knot nematode isolates from north Queensland, Australia: M. arenaria (NQ1), M. javanica (NQ2) and M. arenaria race 2 (NQ5/7). No cultivar was found to consistently reduce nematode reproduction relative to forage sorghum, the current industry standard, although a commercial fodder radish (Raphanus sativus) and a white mustard (Sinapis alba) line were consistently as resistant to the formation of galls as forage sorghum. A second pot trial screened five commercially available Brassicaceae cultivars, selected for their biofumigation potential, for resistance to two nematode species, M. javanica (NQ2) and M. arenaria (NQ5/7). The fodder radish cv. Weedcheck, was found to be as resistant as forage sorghum to nematode reproduction. A multivariate cluster analysis using the resistance measurements, gall index, nematode number per g of root and multiplication for two nematode species (NQ2 and NQ5/7) confirmed the similarity in resistance between the radish cultivar and forage sorghum. A field trial confirmed the resistance of the fodder radish cv. Weedcheck, with a similar reduction in the number of Meloidogyne spp. juveniles recovered from the roots 8 weeks after planting. The use of fodder radish cultivars as biofumigation crops to manage root-knot nematodes in tropical vegetable production systems deserves further investigation.

Root-lesion nematodes (Pratylenchus thornei and P. neglectus): A review of recent progress in managing a significant pest of grain crops in northern Australia

Two species of root-lesion nematode (predominantly Pratylenchus thornei but also P. neglectus) are widespread pathogens of wheat and other crops in Australia's northern grain belt, a subtropical region with deep, fertile clay soils and a summer-dominant rainfall pattern. Losses in grain yield from P. thornei can be as high as 70% for intolerant wheat cultivars. This review focuses on research which has led to the development of effective integrated management programs for these nematodes. It highlights the importance of correct identification in managing Pratylenchus species, reviews the plant breeding work done in developing tolerant and resistant cultivars, outlines the methods used to screen for tolerance and resistance, and discusses how planned crop sequencing with tolerant and partially resistant wheat cultivars, together with crops such as sorghum, sunflower, millets and canaryseed, can be used to reduce nematode populations and limit crop damage. The declining levels of soil organic matter in cropped soils are also discussed with reference to their effect on soil health and biological suppression of root-lesion nematodes.

Multinomial solutions of the beach equation

Exact multinomial solutions of the beach equation for shallow water waves on a uniformly sloping beach are found and related to solution of the same equation found earlier by other investigators, using integral transform techniques. The use of these solutions for a general initialvalue problem for the equation under investigation is briefly discussed.

Genotypic variation in seedling root architectural traits and implications for drought adaptation in wheat (Triticum aestivum L.)

Root system characteristics are of fundamental importance to soil exploration and below-ground resource acquisition. Root architectural traits determine the in situ space-filling properties of a root system or root architecture. The growth angle of root axes is a principal component of root system architecture that has been strongly associated with acquisition efficiency in many crop species. The aims of this study were to examine the extent of genotypic variability for the growth angle and number of seminal roots in 27 current Australian and 3 CIMMYT wheat (Triticum aestivum L.) genotypes, and to quantify using fractal analysis the root system architecture of a subset of wheat genotypes contrasting in drought tolerance and seminal root characteristics. The growth angle and number of seminal roots showed significant genotypic variation among the wheat genotypes with values ranging from 36 to 56 (degrees) and 3 to 5 (plant-1), respectively. Cluster analysis of wheat genotypes based on similarity in their seminal root characteristics resulted in four groups. The group composition reflected to some extent the genetic background and environmental adaptation of genotypes. Wheat cultivars grown widely in the Mediterranean environments of southern and western Australia generally had wider growth angle and lower number of seminal axes. In contrast, cultivars with superior performance on deep clay soils in the northern cropping region, such as SeriM82, Baxter, Babax, and Dharwar Dry exhibited a narrower angle of seminal axes. The wheat genotypes also showed significant variation in fractal dimension (D). The D values calculated for the individual segments of each root system suggested that, compared to the standard cultivar Hartog, the drought-tolerant genotypes adapted to the northern region tended to distribute relatively more roots in the soil volume directly underneath the plant. These findings suggest that wheat root system architecture is closely linked to the angle of seminal root axes at the seedling stage. The implications of genotypic variation in the seminal root characteristics and fractal dimension for specific adaptation to drought environment types are discussed with emphasis on the possible exploitation of root architectural traits in breeding for improved wheat cultivars for water-limited environments.

A fuzzy logic based dynamic wave model inversion algorithm for canal regulation

A fuzzy logic based centralized control algorithm for irrigation canals is presented. Purpose of the algorithm is to control downstream discharge and water level of pools in the canal, by adjusting discharge release from the upstream end and gates settings. The algorithm is based on the dynamic wave model (Saint-Venant equations) inversion in space, wherein the momentum equation is replaced by a fuzzy rule based model, while retaining the continuity equation in its complete form. The fuzzy rule based model is developed on fuzzification of a new mathematical model for wave velocity, the derivational details of which are given. The advantages of the fuzzy control algorithm, over other conventional control algorithms, are described. It is transparent and intuitive, and no linearizations of the governing equations are involved. Timing of the algorithm and method of computation are explained. It is shown that the tuning is easy and the computations are straightforward. The algorithm provides stable, realistic and robust outputs. The disadvantage of the algorithm is reduced precision in its outputs due to the approximation inherent in the fuzzy logic. Feed back control logic is adopted to eliminate error caused by the system disturbances as well as error caused by the reduced precision in the outputs. The algorithm is tested by applying it to water level control problem in a fictitious canal with a single pool and also in a real canal with a series of pools. It is found that results obtained from the algorithm are comparable to those obtained from conventional control algorithms.

Phase relations between Al2O3---Cr2O3 and FeAl2O4---FeCr2O4 solid solutions at 1823 K

Tie-lines between the corundum and spinel solid solutions have been determined experimentally at 1823 K. Next, activities of FeCr2O4 and FeAl2O4 in the spinel solid solution were determined by combining the tie-line data with literature values for the activities of Cr2O3 and Al2O3 in the corundum phase. Activities and the Gibbs energy of mixing for the spinel solid solution were also obtained from a model based on cation distribution between nonequivalent crystallographic sites in the oxide lattice. The difference between the Gibbs energy of mixing obtained experimentally and from the model has been attributed to a strain enthalpy term which is relatively unchanged in magnitude from the reported at 1373 K. The integral enthalpy of mixing obtained from experimental data at 1373 and 1823 K using the second law is compared with the model result.