On positive solutions of nonlinear elliptic equations involving concave and critical nonlinearities

We study the existence of nonnegative solutions of elliptic equations involving concave and critical Sobolev nonlinearities. Applying various variational principles we obtain the existence of at least two nonnegative solutions.

Investigations of growth processes in Y-Ba-Cu-O materials by microstructural examination of quenched samples

Y-Ba-Cu-O samples with additions of Y2O3 and CeO2 were quenched during seeded isothermal melt processing and examined by optical microscopy and scanning electron microscopy. Large YBa2Cu3O7-y (Y123) particles in the starting powder were found to form a distinct type of melt during heating, which was unaffected by the Y2O3 or CeO2 additives. This type of melt later formed regions with a low concentration of Y2BaCuO5 (Y211) particles in the Y123 matrix. The maximum growth rate of Y123 that could be sustained in the sample was found to be lower in the melt formed from large Y123 particles, and this may lead to growth accidents and subgrains in some samples.

Growth of subtropical ECM fungi with different nitrogen sources using a new floating culture technique

Eight species of ectomycorrhizal (ECM) fungi in the genera Amanita. Gymnoboletus, Lactarius, and Russula were isolated from subtropical plant communities in eastem Australia. Two species were isolated from each of rainforest, Nothofagus forest, Eucalyptus forest, and Eucalyptus dominated wallum (heath) forest. These communities differ strongly in their soluble soil nitrogen (N) composition. The ability of the fungi to use inorganic (nitrate, ammonium) and organic (amide, peptide, protein) nitrogen sources was determined. As the fungi did not grow in liquid culture, a 'floating culture' technique was devised that allows hyphal growth on a screen floating on liquid medium. With some exceptions, fungal biomass production in floating culture closely reflected fungal growth on solid media assessed by total colony glucosamine content. Most isolates grown in floating culture had similar glucosamine concentrations on all N sources, with isolate specific concentrations ranging from 6 to 12 mug glucosamine g(-1) DW. However, Russula spp. had up to 1.7-fold higher glucosamine concentrations when growing with glutamine or ammonium compared to nitrate, glutathione or protein. Floating cultures supplied with 0.5, 1.5. 4.5, or 10 mm N mostly produced greatest biomass with 4.5 mM N. In vitro nitrate reductase activity (NRA) ranged from very low (0.03 mumol NO2- g(-1) fw h(-1)) in Russula sp. (wallum) to high (2.16 mumol NO2- g(-1) fw h(-1)) in Gymnoboletus sp. (rainforest) and mirrored the fungi's ability to use nitrate as a N source. All Russula spp. (wallum, Nothofagus and Eucalyptus forests), Lactarills sp, (rainforest) and.4manita sp. (wallum) utilized ammonium and glutamine but had little ability to use other N sources. In contrast,Amanita species (Nothofagus and Eucalyptus forests) grew on all N sources but produced most biomass with ammonium and glutamine. Only Gymnoboletus sp. (rainforest) showed similar growth with nitrate and ammonium as N sources. Fungal N source use was not associated with taxonomic groups, but is discussed in the context of soil N sources in the different habitats.

Boundary value problems for systems of difference equations associated with systems of second-order ordinary differential equations

We study difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order ordinary differential equations. We formulate conditions which guarantee a priori bounds on first differences of solutions to the discretized problem. We establish existence results for solutions to the discretized boundary value problems subject to nonlinear boundary conditions. We apply our results to show that solutions to the discrete problem converge to solutions of the continuous problem in an aggregate sense. (C) 2002 Elsevier Science Ltd. All rights reserved.

Existence of multiple solutions for second-order discrete boundary value problems

We give conditions on f involving pairs of discrete lower and discrete upper solutions which lead to the existence of at least three solutions of the discrete two-point boundary value problem yk+1 - 2yk + yk-1 + f (k, yk, vk) = 0, for k = 1,..., n - 1, y0 = 0 = yn,, where f is continuous and vk = yk - yk-1, for k = 1,..., n. In the special case f (k, t, p) = f (t) greater than or equal to 0, we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and Peterson and are in the spirit of our results for the continuous analogue. (C) 2002 Elsevier Science Ltd. All rights reserved.

Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations

We study the continuous problem y"=f(x,y,y'), xc[0,1], 0=G((y(0),y(1)),(y'(0), y'(1))), and its discrete approximation (y(k+1)-2y(k)+y(k-1))/h(2) =f(t(k), y(k), v(k)), k = 1,..., n-1, 0 = G((y(0), y(n)), (v(1), v(n))), where f and G = (g(0), g(1)) are continuous and fully nonlinear, h = 1/n, v(k) = (y(k) - y(k-1))/h, for k =1,..., n, and t(k) = kh, for k = 0,...,n. We assume there exist strict lower and strict upper solutions and impose additional conditions on f and G which are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. We show that the discrete approximation also has solutions which approximate solutions of the continuous problem and converge to the solution of the continuous problem when it is unique, as the grid size goes to 0. Homotopy methods can be used to compute the solution of the discrete approximation. Our results were motivated by those of Gaines.

Productivity growth in Australian manufacturing sector: some new evidence

This article examines the productivity performance of Australia's manufacturing sector by decomposing its output growth into input growth, technological progress and gains in technical efficiency. This three-way decomposition is done with an improved version of the stochastic frontier model using eight, two-digit industry level data from 1968/9 to 1994/5. Empirical evidence shows that input growth fueled output growth from 1968/9 to 1973/4, but since then, total factor productivity (TFP) growth has been the main contributor of output growth. While the trend of TFP growth was found to be promising for most industries with positive and increasing technological progress, the negative gains from technical efficiency over time is however cause for concern.

Supersymmetric t-J Gaudin models and KZ equations

Supersymmetric t-J Gaudin models with open boundary conditions are investigated by means of the algebraic Bethe ansatz method. Off-shell Bethe ansatz equations of the boundary Gaudin systems are derived, and used to construct and solve the KZ equations associated with sl (2\1)((1)) superalgebra.

Urbanization, population transition, and growth

This paper analyzes a dual economy consisting of urban market areas and less developed rural areas with or without local markets. Urban areas have better opportunities for earnings and education than rural areas. Rural families choose whether to move to urban areas at costs that differ from location to location. As per capita output grows relative to the moving cost, urbanization proceeds, leading to lower fertility, more investments in human and physical capital per child relative to output per worker, and faster economic growth. These impacts are stronger if rural areas have no access to markets.

Simulating growth, development, and yield of tillering pearl millet. III. Biomass accumulation and partitioning

Pearl millet landraces from Rajasthan, India, yield significantly less than improved cultivars under optimum growing conditions, but not under stressed conditions. To successfully develop a simulation model for pearl millet, capable of capturing such genotype x environment (G x E) interactions for grain yield, we need to understand the causes of the observed yield interaction. The aim of this paper is to quantify the key parameters that determine the accumulation and partitioning of biomass: the,light extinction coefficient, radiation use efficiency (RUE), pattern of dry matter allocation to the leaf blades, the determination of grain number, and the rate and duration of dry matter accumulation into individual grains. We used data on improved cultivars and landraces, obtained from both published and unpublished sources collected at ICRISAT, Patancheru, India. Where possible, the effects of cultivar and axis (main shoot vs. tillers) on these parameters were analysed, as previous research suggested that G x E interactions for grain yield are associated with differences in tillering habit. Our results indicated there were no cultivar differences in extinction coefficient, RUE, and biomass partitioning before anthesis, and differences between axes in biomass partitioning were negligible. This indicates there was no basis for cultivar differences in the potential grain yield. Landraces, however, produced consistently less grain yield for a given rate of dry matter accumulation at anthesis than did improved cultivars. This was caused by a combination of low grain number and small grain size. The latter was predominantly due to a lower grain growth rate, as genotypic differences in the duration of grain filling were relatively small. Main shoot and tillers also had a similar duration of grain filling. The low grain yield of the landraces was associated with profuse nodal tillering, supporting the hypothesis that grain yield was below the potential yield that could be supported by assimilate availability. We hypothesise this is a survival strategy, which enhances the prospects to escape the effects of stress around anthesis. (C) 2002 E.J. van Oosterom. Published by Elsevier Science B.V. All rights reserved.

Productivity growth in pre-1990 Mongolian agriculture: Spiralling disaster or emerging success?

The reasons for the spectacular collapse of so many centrally-planned economies are a source of ongoing debate. In this paper, we use detailed farm-level data to measure total factor productivity (TFP) changes in Mongolian grain and potato farming during the 14-year period immediately preceding the 1990 economic reforms. We measure TFP growth using stochastic frontier analysis (SFA) and data envelopment analysis (DEA) methods. Our results indicate quite poor overall performance, with an average annual TFP change of - 1.7% in grain and 0.8% in potatoes, over the 14-year period. However, the pattern of TFP growth changed substantially during this period, with TFP growth exceeding 7% per year in the latter half of this period. This suggests that the new policies of improved education, greater management autonomy, and improved incentives, which were introduced in final two planning periods in the 1980s, were beginning to have a significant influence upon the performance of Mongolian crop farming. Crown Copyright (C) 2002 Published by Elsevier Science B.V. All rights reserved.

An assessment of maturity from anthropometric measurements

Purpose: The range of variability between individuals of the same chronological age (CA) in somatic and biological maturity is large and especially accentuated around the adolescent growth spurt. Maturity assessment is an important consideration when dealing with adolescents, from both a research perspective and youth sports stratification. A noninvasive, practical method predicting years from peak height velocity (a maturity offset value) by using anthropometric variables is developed in one sample and cross-validated in two different samples. Methods: Gender specific multiple regression equations were calculated on a sample of 152 Canadian children aged 8-16 yr (79 boys; 73 girls) who were followed through adolescence from 1991 to 1997, The equations included three somatic dimensions (height, sitting height, and leg length), CA, and their interactions. The equations were cross-validated on a Combined sample of Canadian (71 boys, 40 girls measured from 1964 through 1973) and Flemish children (50 boys, 48 girls measured from 1985 through 1999). Results: The coefficient of determination (R2) for the boys' model was 0.92 and for the girls' model 0.91 the SEEs were 0.49 and 0.50, respectively, Mean difference between actual and predicted maturity offset for the verification samples was 0.24 (SD 0.65) yr in boys and 0,001 (SD 0.68) yr in girls. Conclusion: Although the cross-validation meets statistical standards or acceptance, caution 1, warranted with regard to implementation. It is recommended that maturity offset be considered as a categorical rather than a continuous assessment. Nevertheless, the equations presented are a reliable, noninvasive and a practical solution for the measure of biological maturity for matching adolescent athletes.