Existence theorem for a generalized Hammerstein type equation

An existence theorem is obtained for a generalized Hammerstein type equation

The transient response of certain third-ordernon-linear systems

In this paper a method of solving certain third-order non-linear systems by using themethod of ultraspherical polynomial approximation is proposed. By using the method of variation of parameters the third-order equation is reduced to three partial differential equations. Instead of being averaged over a cycle, the non-linear functions are expanded in ultraspherical polynomials and with only the constant term retained, the equations are solved. The results of the procedure are compared with the numerical solutions obtained on a digital computer. A degenerate third-order system is also considered and results obtained for the above system are compared with numerical results obtained on the digital computer. There is good agreement between the results obtained by the proposed method and the numerical solution obtained on digital computer.

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.

Identifying risk-efficient strategies using stochastic frontier analysis and simulation: An application to irrigated cropping in Australia

In irrigated cropping, as with any other industry, profit and risk are inter-dependent. An increase in profit would normally coincide with an increase in risk, and this means that risk can be traded for profit. It is desirable to manage a farm so that it achieves the maximum possible profit for the desired level of risk. This paper identifies risk-efficient cropping strategies that allocate land and water between crop enterprises for a case study of an irrigated farm in Southern Queensland, Australia. This is achieved by applying stochastic frontier analysis to the output of a simulation experiment. The simulation experiment involved changes to the levels of business risk by systematically varying the crop sowing rules in a bioeconomic model of the case study farm. This model utilises the multi-field capability of the process based Agricultural Production System Simulator (APSIM) and is parameterised using data collected from interviews with a collaborating farmer. We found sowing rules that increased the farm area sown to cotton caused the greatest increase in risk-efficiency. Increasing maize area also improved risk-efficiency but to a lesser extent than cotton. Sowing rules that increased the areas sown to wheat reduced the risk-efficiency of the farm business. Sowing rules were identified that had the potential to improve the expected farm profit by ca. $50,000 Annually, without significantly increasing risk. The concept of the shadow price of risk is discussed and an expression is derived from the estimated frontier equation that quantifies the trade-off between profit and risk.

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.

Kinetics of vapour phase oxidation of furfural on vanadium catalyst

Vapour phase oxidation of furfural over vanadium pentoxide catalyst was studied using an isothermal flow reactor in the temperature range of 220–280°C. Maleic anhydride and carbon dioxide are found to be formed from furfural by a parallel reaction scheme. The following rate equation based on the two-stage redox mechanism—the substance to be oxidized reduces the catalyst which in turn is reoxidized by oxygen from the feed—is found to explain the data satisfactorily.The reoxidation of the reduced catalyst was found to be the rate controlling step.

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.

Reduced withdrawal and failure rates of accelerated nursing students enrolled in pharmacology is associated with a supportive intervention

Background To reduce nursing shortages, accelerated nursing programs are available for domestic and international students. However, the withdrawal and failure rates from these programs may be different than for the traditional programs. The main aim of our study was to improve the retention and experience of accelerated nursing students. Methods The academic background, age, withdrawal and failure rates of the accelerated and traditional students were determined. Data from 2009 and 2010 were collected prior to intervention. In an attempt to reduce the withdrawal of accelerated students, we set up an intervention, which was available to all students. The assessment of the intervention was a pre-post-test design with non-equivalent groups (the traditional and the accelerated students). The elements of the intervention were a) a formative website activity of some basic concepts in anatomy, physiology and pharmacology, b) a workshop addressing study skills and online resources, and c) resource lectures in anatomy/physiology and microbiology. The formative website and workshop was evaluated using questionnaires. Results The accelerated nursing students were five years older than the traditional students (p < 0.0001). The withdrawal rates from a pharmacology course are higher for accelerated nursing students, than for traditional students who have undertaken first year courses in anatomy and physiology (p = 0.04 in 2010). The withdrawing students were predominantly the domestic students with non-university qualifications or equivalent experience. The failure rates were also higher for this group, compared to the traditional students (p = 0.05 in 2009 and 0.03 in 2010). In contrast, the withdrawal rates for the international and domestic graduate accelerated students were very low. After the intervention, the withdrawal and failure rates in pharmacology for domestic accelerated students with non-university qualifications were not significantly different than those of traditional students. Conclusions The accelerated international and domestic graduate nursing students have low withdrawal rates and high success rates in a pharmacology course. However, domestic students with non-university qualifications have higher withdrawal and failure rates than other nursing students and may be underprepared for university study in pharmacology in nursing programs. The introduction of an intervention was associated with reduced withdrawal and failure rates for these students in the pharmacology course.

Kinetics of vapour phase oxidation of furfural on vanadium catalyst

Vapour phase oxidation of furfural over vanadium pentoxide catalyst was studied using an isothermal flow reactor in the temperature range of 220–280°C. Maleic anhydride and carbon dioxide are found to be formed from furfural by a parallel reaction scheme. The following rate equation based on the two-stage redox mechanism—the substance to be oxidized reduces the catalyst which in turn is reoxidized by oxygen from the feed—is found to explain the data satisfactorily. The reoxidation of the reduced catalyst was found to be the rate controlling step.

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.

Surface Discharge Studies with Uniform Field Electrodes at Low Pressures

An investigation of power frequency (50 Hz) surface partial discharges in dry air, using 21r/3 Rogowski profile electrodes in the low pressure range of 0.067 to 91.333 kPa, shows that for the discharges occurring symmetrically around the electrodes and just outside the uniform field region, the breakdown voltages are 20 to 30% lower than those accounted for by the usual Paschen values. Emphasis, therefore, has been given to modified values of breakdown voltages for any useful calculations. The effect of reduced pressure on inception voltage has been discussed and an attempt has been made to explain the difference between the observed and calculated values on the basis of a pressure-dependent secondary ionization coefficient. It is shown that increasing the insulation thickness in a critical pressure range (0.067 to 0.400 kPa) does not allow any significant increase in the discharge free working stress of the insulation system. At higher pressures (>0.400 kPa) the increase in inception voltage with thickness and pressure follows an equation which is expected to hold for other insulating materials as well.

A note on the analysis of the dispersion equation for surface magnetoplasmons in the Faraday configuration

The analysis of the dispersion equation for surface magnetoplasmons in the Faraday configuration for the degenerate case of decaying constants being equal is given from the point of view of understanding the non-existence of the “degenerate modes”. This analysis also shows that there exist well defined “degenerate points” on the dispersion curve with electromagnetic fields varying linearly over small distances taken away from the interface.