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.

EFFECT OF RICE STRAW AND NITRATE LEVELS IN SOIL SOLUTION ON NITROUS OXIDE EMISSION

Among the greenhouse gases, nitrous oxide (N2O) is considered important, in view of a global warming potential 296 times greater than that of carbon dioxide (CO2) and its dynamics strongly depend on the availability of C and mineral N in the soil. The understanding of the factors that define emissions is essential to develop mitigation strategies. This study evaluated the dynamics of N2O emissions after the application of different rice straw amounts and nitrate levels in soil solution. Pots containing soil treated with sodium nitrate rates (0, 50 and 100 g kg-1 of NO−3-N) and rice straw levels (0, 5 and 10 Mg ha-1), i.e., nine treatments, were subjected to anaerobic conditions. The results showed that N2O emissions were increased by the addition of greater NO−3 amounts and reduced by large straw quantities applied to the soil. On the 1st day after flooding (DAF), significantly different N2O emissions were observed between the treatments with and without NO−3 addition, when straw had no significant influence on N2O levels. Emissions peaked on the 4th DAF in the treatments with highest NO−3-N addition. At this moment, straw application negatively affected N2O emissions, probably due to NO−3 immobilization. There were also alterations in other soil electrochemical characteristics, e.g., higher straw levels raised the Fe, Mn and dissolved C contents. These results indicate that a lowering of NO−3 concentration in the soil and the increase of straw incorporation can decrease N2O emissions.

Effects of Pig Slurry Application and Crops on Phosphorus Content in Soil and the Chemical Species in Solution

The application of pig slurry rates and plant cultivation can modify the soil phosphorus (P) content and distribution of chemical species in solution. The purpose of this study was to evaluate the total P, available P and P in solution, and the distribution of chemical P species in solution, in a soil under longstanding pig slurry applications and crop cultivation. The study was carried out in soil columns with undisturbed structure, collected in an experiment conducted for eight years in the experimental unit of the Universidade Federal de Santa Maria (UFSM), Santa Maria (RS). The soil was an Argissolo Vermelho distrófico arênico (Typic Hapludalf), subjected to applications of 0, 20, 40, and 80 m3 ha-1 pig slurry. Soil samples were collected from the layers 0-5, 5-10, 10-20, 20-30, 30-40, and 40-60 cm, before and after black oat and maize grown in a greenhouse, for the determination of available P, total P and P in the soil solution. In the solution, the concentration of the major cations, anions, dissolved organic carbon (DOC), and pH were determined. The distribution of chemical P species was determined by software Visual Minteq. The 21 pig slurry applications increased the total P content in the soil to a depth of 40 cm, and the P extracted by Mehlich-1 and from the solution to a depth of 30 cm. Successive applications of pig slurry changed the balance between the solid and liquid phases in the surface soil layers, increasing the proportion of the total amount of P present in the soil solution, aside from changing the chemical species in the solution, reducing the percentage complexed with Al and increasing the one complexed with Ca and Mg in the layers 0-5 and 5-10 cm. Black oat and maize cultivation increased pH in the solution, thereby increasing the proportion of HPO42- and reducing H2PO4- species.

Exact solution to the exit-time problem for an undamped free particle driven by Gaussian white noise

In a recent paper [Phys. Rev. Lett. 75, 189 (1995)] we have presented the exact analytical expression for the mean exit time, T(x,v), of a free inertial process driven by Gaussian white noise out of a region (0,L) in space. In this paper we give a detailed account of the method employed and present results on asymptotic properties and averages of T(x,v).

Strong coupling solution to Schrödinger Equation: the mixing of states

In this paper we give some ideas that can be useful to solve Schrödinger equations in the case when the Hamiltonian contains a large term. We obtain an expansion of the solution in reciprocal powers of the large coupling constant. The procedure followed consists in considering that the small part of the Hamiltonian engenders a motion adiabatic to the motion generated by the large part of the same.

Soil Water Potentials and Capsicum annuum L. under Salinity

ABSTRACT Investigations into water potentials in the soil-plant system are of great relevance in environments with abiotic stresses, such as salinity and drought. An experiment was developed using bell pepper in a Neossolo Flúvico (Fluvent) irrigated with water of six levels of electrical conductivity (0, 1, 3, 5, 7 and 9 dS m-1) by using exclusively NaCl and by simulating the actual condition (using a mixture of salts). The treatments were arranged in a randomized block design, in a 6 × 2 factorial arrangement, with four replicates. Soil matric (Ψm) and osmotic (Ψo) potentials were determined 70 days after transplanting (DAT). Soil total potential was considered as the sum of Ψm and Ψo. Leaf water (obtained with the Scholander Chamber) and osmotic potentials were determined before sunrise (predawn) and at noon at 42 and 70 DAT. There were no significant differences between the salt sources used in the irrigation water for soil and plant water potentials. The supply of salts to the soil through irrigation water was the main factor responsible for the decrease in Ψo in the soil and in bell pepper leaves. The total potential of bell pepper at predawn reached values of -1.30 and -1.33 MPa at 42 and 70 DAT, respectively, when water of 9 dS m-1 was used in the irrigation. The total potential at noon reached -2.19 MPa. The soil subjected to the most saline treatment reached a water potential of -1.20 MPa at 70 DAT. There was no predawn equilibrium between the total water potentials of the soil and the plant, indicating that soil potential cannot be considered similar to that of the plant. The determination of the osmotic potential in the soil solution should not be neglected in saline soils, since it has strong influence on the calculation of the total potential.

Electrical Conductivity and Chemical Composition of Soil Solution: Comparison of Solution Samplers in Tropical Soils

ABSTRACT Soil solution samplers may have the same working principle, but they differ in relation to chemical and physical characteristics, cost and handling, and these aspects exert influence on the chemical composition of the soil solution obtained. This study was carried out to evaluate, over time, the chemical composition of solutions extracted by Suolo Acqua, with the hydrophilic membrane (HM) as a standard, using soils with contrasting characteristics, and to determine the relationship between electrical conductivity (EC) and concentration of ions and pH of soil solution samples. This study was carried out under laboratory conditions, using three soils samples with different clay and organic matter (OM) contents. Soil solution contents of F−, Cl−, NO−3, Br−, SO42−, Na+, NH4+, K+, Mg2+, Ca2+, were analyzed, as well as inorganic, organic, and total C contents, pH, and EC, in four successive sampling times. Soil solution chemical composition extracted by the Suolo Acqua sampler is similar to that collected by the HM, but the Suolo Acqua extracted more Na+ and soluble organic C than the HM solution. Solution EC, cation and anion concentrations, and soluble C levels are higher in the soil with greater clay and OM contents (Latossolo and Cambissolo in this case). Soil solution composition varied over time, with considerable changes in pH, EC, and nutrient concentrations, especially associated with soil OM. Thus, single and isolated sampling of the soil solution must be avoided, otherwise composition of the soil solution may not be correctly evaluated. Soil solution EC was regulated by pH, as well as the sum of cation and anion concentrations, and the C contents determined in the soil liquid phase.

Role of salt-inducible kinase 1 in the activation of MEF2-dependent transcription by BDNF.

Substantial evidence supports a role for myocyte enhancer factor 2 (MEF2)-mediated transcription in neuronal survival, differentiation and synaptic function. In developing neurons, it has been shown that MEF2-dependent transcription is regulated by neurotrophins. Despite these observations, little is known about the cellular mechanisms by which neurotrophins activate MEF2 transcriptional activity. In this study, we examined the role of salt-inducible kinase 1 (SIK1), a member of the AMP-activated protein kinase (AMPK) family, in the regulation of MEF2-mediated transcription by the neurotrophin brain-derived neurotrophic factor (BDNF). We show that BDNF increases the expression of SIK1 in primary cultures of rat cortical neurons through the extracellular signal-regulated kinase 1/2 (ERK1/2)-signaling pathway. In addition to inducing SIK1 expression, BDNF triggers the phosphorylation of SIK1 at Thr182 and its translocation from the cytoplasm to the nucleus of cortical neurons. The effects of BDNF on the expression, phosphorylation and, translocation of SIK1 are followed by the phosphorylation and nuclear export of histone deacetylase 5 (HDAC5). Blockade of SIK activity with a low concentration of staurosporine abolished BDNF-induced phosphorylation and nuclear export of HDAC5 in cortical neurons. Importantly, stimulation of HDAC5 phosphorylation and nuclear export by BDNF is accompanied by the activation of MEF2-mediated transcription, an effect that is suppressed by staurosporine. Consistent with these data, BDNF induces the expression of the MEF2 target genes Arc and Nur77, in a staurosporine-sensitive manner. In further support of the role of SIK1 in the regulation of MEF2-dependent transcription by BDNF, we found that expression of wild-type SIK1 or S577A SIK1, a mutated form of SIK1 which is retained in the nucleus of transfected cells, is sufficient to enhance MEF2 transcriptional activity in cortical neurons. Together, these data identify a previously unrecognized mechanism by which SIK1 mediates the activation of MEF2-dependent transcription by BDNF.

Some spectral properties of the canonical solution operator to $\bar\partial$ on weighted Fock spaces

We characterize the Schatten class membership of the canonical solution operator to $\overline{\partial}$ acting on $L^2(e^{-2\phi})$, where $\phi$ is a subharmonic function with $\Delta\phi$ a doubling measure. The obtained characterization is in terms of $\Delta\phi$. As part of our approach, we study Hankel operators with anti-analytic symbols acting on the corresponding Fock space of entire functions in $L^2(e^{-2\phi})$

The set of undominated imputations and the core: an axiomatic approach

This paper provides an axiomatic framework to compare the D-core (the set of undominatedimputations) and the core of a cooperative game with transferable utility. Theorem1 states that the D-core is the only solution satisfying projection consistency, reasonableness (from above), (*)-antimonotonicity, and modularity. Theorem 2 characterizes the core replacing (*)-antimonotonicity by antimonotonicity. Moreover, these axioms alsocharacterize the core on the domain of convex games, totally balanced games, balancedgames, and superadditive games

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.