Von Neumann-Morgenstern solution and convex descompositions of TU games

We study under which conditions the core of a game involved in a convex decomposition of another game turns out to be a stable set of the decomposed game. Some applications and numerical examples, including the remarkable Lucas¿ five player game with a unique stable set different from the core, are reckoning and analyzed.

Simultaneous multielement extraction with the Mehlich-1 solution for Southern Brazilian soils determined by ICP-OES and the effects on the nutrients recommendations to crops

The amounts of macro (P, K, Ca and Mg) and micronutrients (Cu and Zn) extracted with the Mehlich-1 (M1) solution, by the 1.0 mol L-1 KCl (KCl) and with the 0.1 mol L-1 HCl (HCl) for representative soil types of the Rio Grande do Sul state (Brazil) were compared with those extracted with the Mehlich-1 solution determined with the inductively coupled plasma optical emission spectroscopy (ICP). The amounts of nutrients extracted by the different methods showed high correlation coefficients. On average, the Mehlich-1 solution extracted similar amounts of P, determined with colorimetric and ICP methods, and, K determined with emission and ICP. The amounts of Ca and Mg extracted with the Mehlich-1 solution, determined by ICP, were similar to those extracted with the KCl solution determined by the atomic absorption spectrophotometry. The amounts of Cu and Zn extracted with the Mehlich-1 solution, determined by the ICP, were higher than those extracted with the 0.1 mol L-1 HCl determined by the atomic absorption spectrophotometry. The results indicate that the Mehlich-1 solution and ICP can be used for simultaneous multielement extraction and determination for Southern Brazilian soils. However, a conversion factor for values interpretation is needed. The use of the conversion factor to determine the K availability index in soils is adequate and does not affect the K recommendations for crops in southern Brazilian soils.

Nitrate and ammonium in soil solution in tobacco management systems

Tobacco farmers of southern Brazil use high levels of fertilizers, without considering soil and environmental attributes, posing great risk to water resources degradation. The objective of this study was to monitor nitrate and ammonium concentrations in the soil solution of an Entisol in and below the root zone of tobacco under conventional tillage (CT), minimum tillage (MT) and no-tillage (NT). The study was conducted in the small-watershed Arroio Lino, in Agudo, State of Rio Grande do Sul, Brazil. A base fertilization of 850 kg ha-1 of 10-18-24 and topdressing of 400 kg ha-1 of 14-0-14 NPK fertilizer were applied. The soil solution was sampled during the crop cycle with a tension lysimeter equipped with a porous ceramic cup. Ammonium and nitrate concentrations were analyzed by the distillation and titration method. Nitrate concentrations, ranging from 8 to 226 mg L-1, were highest after initial fertilization and decreased during the crop cycle. The average nitrate (N-NO3-) concentration in the root zone was 75 in NT, 95 in MT, and 49 mg L-1 in CT. Below the root zone, the average nitrate concentration was 58 under NT, 108 under MT and 36 mg L-1 under CT. The nitrate and ammonium concentrations did not differ significantly in the management systems. However, the nitrate concentrations measured represent a contamination risk to groundwater of the watershed. The ammonium concentration (N-NH4+) decreased over time in all management systems, possibly as a result of the nitrification process and root uptake of part of the ammonium by the growing plants.

Attributes of irrigated rice and soil solution as affected by salinity levels of the water layer

In the State of Rio Grande do Sul, Brazil, flooded rice fields using Patos Lagoon as the source of water for irrigation are subject to be damaged by salinity, since this source is bound to the sea on its southern end. The sensitivity of rice is variable during plant development, being higher in the seedling and reproductive periods. However, there is not enough information about the behavior of plants under salt stress during the course of its development, especially in the vegetative stage. This study evaluated the effect of different levels of salinity of irrigation water on the salinity of soil solution over time and on some plant attributes, during the vegetative stage of rice. The study was conducted in a greenhouse, where seeds of the variety IRGA 424 were sown in pots and irrigated with water with electrical conductivity (ECi) levels of: 0.3, 0.75, 1.5, 3.0 and 4.5 dS m-1; from the tillering initiation (V4) until the panicle initiation (PI). The evaluations made were the electrical conductiviy of soil solution (ECe), the dry biomass of plants and stems, tillering, height and the transpiration of plants. The ECe increased with the ECi over time, and was determined by water transpiration flux in pots. The ECe values at the end of the experiment were high and, in most cases, higher than the critical values for flooded rice. The growth attributes of rice were negatively affected from ECi of 2.0 dS m-1 and ECe of 4.0 dS m-1.

Rice grown in nutrient solution with doses of manganese and silicon

Although silicon is not recognized as a nutrient, it may benefit rice plants and may alleviate the Mn toxicity in some plant species. The dry matter yield (root, leaf, sheaths and leaf blade) and plant architecture (angle of leaf insertion and leaf arc) were evaluated in rice plants grown in nutrient solutions with three Mn doses, with and without Si addition. The treatments were arranged in a 2 x 3 factorial [with and without (2 mmol L-1) Si; three Mn doses (0.5; 2.5 and 10 µmol L-1)], in a randomized block design with 4 replications. The experimental unit was a 4 L plastic vase with 4 rice (Metica-1 cultivar) plants. Thirty nine days after keeping the seedlings in the nutrient solution the plant dry matter yield was determined; the angle of leaf insertion in the sheath and the leaf arc were measured; and the Si and Mn concentrations in roots, sheaths and leaves were determined. The analysis of variance (F test at 5 and 1 % levels) and the regression analysis (for testing plant response to Mn with the Si treatments) were performed. The Si added to the nutrient solution increased the dry matter yield of roots, sheaths and leaf blades and also decreased the angle of leaf blade insertion into the sheath and the foliar arc in the rice plant. Additionally, it ameliorated the rice plant architecture which allowed an increase in the dry matter yield. Similarly, the addition of Mn to the solution improved the architecture of the rice plants with gain in dry matter yield. As Si was added to the nutrient solution, the concentration of Mn in leaves decreased and in roots increased thus alleviating the toxic effects of Mn on the plants.

Effect of NPK fertilization on production and leaf nutrient content of eucalyptus minicuttings in nutrient solution

Adequate nutrient levels in plants vary according to the species or clone, age and management practice. Therefore, adjustments of the nutrient solution are often necessary according to the plant material for multiplication. This study aimed to evaluate the influence of NPK fertilization on production and leaf nutrient contents of eucalyptus cuttings in nutrient solution. The study was conducted from November 2008 to January 2009 in a greenhouse. The experimental design was completely randomized fractional factorial (4 x 4 x 4)½, with a total of 32 treatments with three replications. The treatments consisted of four doses of N (50, 100, 200 and 400 mg L-1) as urea, P (7.5, 15, 30 and 60 mg L-1) in the form of phosphoric acid and K (50, 100, 200 and 400 mg L-1) in the form of potassium chloride in the nutrient solution. Only the effect of N alone was significant for the number and dry weight of minicuttings per ministump, with a linear decreasing effect with increasing N levels. The highest number of cuttings was obtained at a dose of 50, 7.5 and 50 mg L-1 of N, P and K, respectively.

Zenith angle distributions at Super-Kamiokande and SNO and the solution of the solar neutrino problem

We have performed a detailed study of the zenith angle dependence of the regeneration factor and distributions of events at SNO and SK for different solutions of the solar neutrino problem. In particular, we discuss the oscillatory behavior and the synchronization effect in the distribution for the LMA solution, the parametric peak for the LOW solution, etc. A physical interpretation of the effects is given. We suggest a new binning of events which emphasizes the distinctive features of the zenith angle distributions for the different solutions. We also find the correlations between the integrated day-night asymmetry and the rates of events in different zenith angle bins. The study of these correlations strengthens the identification power of the analysis.

Deficiency symptoms and uptake of micronutrients by castor bean grown in nutrient solution

Castor bean is a nutrient-demanding species, but there is still little information on its micronutrient requirements. The objectives of this study were to evaluate the effects of levels of B (2.5, 12.5 and 25.0 µmol L-1), Cu (0.05, 0.25 and 0.50 µmol L-1), Mn (0.2, 1.0 and 2.0 µmol L-1) and Zn (0.2, 1.0 and 2.0 µmol L-1) in a nutrient solution on plant B, Cu, Mn and Zn concentrations and uptake, vegetative growth and fruit yield of castor bean "Iris", grown in greenhouse. The experiment was arranged in a completely randomized block design with three replicates. The first deficiency symptoms were observed for B, followed by Zn, Cu and Mn. The main changes in the cell ultrastructure due to lack of B were thickening of the cell walls and middle lamellae, distorted chloroplasts and tightly stacked thylakoids, besides the absence of starch grains. The Mn, Zn and Cu deficiencies led to disruption of chloroplasts, disintegration of thylakoids and absence of amyloplasts. The concentration and uptake of B, Cu, Mn, and Zn in castor bean plants increased with micronutrient supply in the solution. Fruit yield was drastically reduced by B and Mn deficiencies. On the other hand, the dry matter yield of the shoot and root of castor bean plants was not. In the treatment with full nutrient solution, the leaves accumulated 56 and 48 % of the total B and Mn taken up by the plants, respectively, and the seeds and roots 85 and 61 % of the total Cu and Zn taken up, respectively. This shows the high demand of castor bean Iris for B and Mn for fruit yield.

Dynamics of ammonium and pH in the solution of soils with different salinity levels, growing irrigated rice

Rice in Rio Grande do Sul State is grown mostly under flooding, which induces a series of chemical, physical and biological changes in the root environment. These changes, combined with the presence of rice plants, affect the availability of exchangeable ammonium (NH4+) and pH of soil solution, whereas the dynamics of both variables can be influenced by soil salinity, a common problem in the coastal region. This study was conducted to evaluate the dynamics of exchangeable NH4+ and pH in the soil solution, and their relation in the solution of Albaqualf soils with different salinity levels, under rice. Four field experiments were conducted with soils with exchangeable Na percentage (ESP) of 5.6, 9.0, 21.2, and 32.7 %. Prior to flooding, soil solution collectors were installed at depths of 5, 10 and 20 cm. The soil solution was collected weekly, from 7 to 91 days after flooding (DAF), to analyze exchangeable NH4+ and pH in the samples. Plant tissue was sampled 77 DAF, to determine N uptake and estimate the contribution of other N forms to rice nutrition. The content of exchangeable NH4+ decreased over time at all sites and depths, with a more pronounced reduction in soils with lower salinity levels, reaching values close to zero. A possible contribution of non-exchangeable NH4+ forms and N from soil organic matter to rice nutrition was observed. Soil pH decreased with time in soils with ESP 5.6 and 9.0 %, being positively correlated with the decreasing NH4+ levels at these sites.

Nutrition, dry matter accumulation and partitioning and phosphorus use efficiency of potato grown at different phosphorus levels in nutrient solution

High rates of phosphate fertilizers are applied to potato (Solanum tuberosum L.), which may cause antagonistic interactions with other nutrients and limit crop yields when over-supplied. The purpose of this study was to evaluate the influence of phosphorus (P) levels in nutrient solution on P use efficiency, nutritional status and dry matter (DM) accumulation and partitioning of potato plants cv. Ágata. The experiment was carried out in a greenhouse, arranged in a completely randomized block design with four replications. Treatments consisted of seven P levels in nutrient solution (0, 2, 4, 8, 16, 31, and 48 mg L-1). Plants were harvested after 28 days of growth in nutrient solution, and separated in roots, stems and leaves for evaluations. The treatment effects were analyzed by regression analysis. Phosphorus levels of up to 8 mg L-1 increased the root and shoot DM accumulation, but drastically decreased the root/shoot ratio of potato cv. Ágata. Higher P availability increased P concentration, accumulation and absorption efficiency, but decreased P use efficiency. Higher P levels increased the N, P, Mg, Fe, and Mn concentrations in roots considerably and decreased K, S, Cu, and Zn concentrations. In shoot biomass, N, P, K, and Ca concentrations were significantly increased by P applied in solution, unlike Mg and Cu concentrations. Although higher P levels (> 8 mg L-1) in nutrient solution increased P concentration, accumulation and absorption efficiency, the DM accumulation and partitioning of potato cv. Ágata were not affected.

A Rotating black ring solution in five dimensions

The vacuum Einstein equations in five dimensions are shown to admit a solution describing a stationary asymptotically flat spacetime regular on and outside an event horizon of topology S1S2. It describes a rotating black ring. This is the first example of a stationary asymptotically flat vacuum solution with an event horizon of nonspherical topology. The existence of this solution implies that the uniqueness theorems valid in four dimensions do not have simple five-dimensional generalizations. It is suggested that increasing the spin of a spherical black hole beyond a critical value results in a transition to a black ring, which can have an arbitrarily large angular momentum for a given mass.

Exact solution to the mean exit time problem for free inertial processes driven by Gaussian white noise

We obtain the exact analytical expression, up to a quadrature, for the mean exit time, T(x,v), of a free inertial process driven by Gaussian white noise from a region (0,L) in space. We obtain a completely explicit expression for T(x,0) and discuss the dependence of T(x,v) as a function of the size L of the region. We develop a new method that may be used to solve other exit time problems.

Continued fraction solution for the radiative transfer equation in three dimensions

Starting from the radiative transfer equation, we obtain an analytical solution for both the free propagator along one of the axes and an arbitrary phase function in the Fourier-Laplace domain. We also find the effective absorption parameter, which turns out to be very different from the one provided by the diffusion approximation. We finally present an analytical approximation procedure and obtain a differential equation that accurately reproduces the transport process. We test our approximations by means of simulations that use the Henyey-Greenstein phase function with very satisfactory results.

Solution to telegrapher's equation in the presence of reflecting and partly reflecting broundaries

We show that the reflecting boundary condition for a one-dimensional telegraphers equation is the same as that for the diffusion equation, in contrast to what is found for the absorbing boundary condition. The radiation boundary condition is found to have a quite complicated form. We also obtain exact solutions of the telegraphers equation in the presence of these boundaries.