Extension of a Recent Method for Obtaining Exact Solutions of the Bruce and Klute Equation

A method based on a specific power-law relationship between the hydraulic head and the Boltzmann variable was recently presented. We generalized this relationship to a range of powers and extended the solution to include the saturated zone. As a result, the new solution satisfies the Bruce and Klute equation exactly.

The generalized log-gamma mixture model with covariates: local influence and residual analysis

In a sample of censored survival times, the presence of an immune proportion of individuals who are not subject to death, failure or relapse, may be indicated by a relatively high number of individuals with large censored survival times. In this paper the generalized log-gamma model is modified for the possibility that long-term survivors may be present in the data. The model attempts to separately estimate the effects of covariates on the surviving fraction, that is, the proportion of the population for which the event never occurs. The logistic function is used for the regression model of the surviving fraction. Inference for the model parameters is considered via maximum likelihood. Some influence methods, such as the local influence and total local influence of an individual are derived, analyzed and discussed. Finally, a data set from the medical area is analyzed under the log-gamma generalized mixture model. A residual analysis is performed in order to select an appropriate model.

New Analytic Solution Related to the Richards, Philip, and Green-Ampt Equations for Infiltration

Based on physical laws of similarity, an analytic solution of the soil water potential form of the Richards equation was derived for water infiltration into a homogeneous sand. The derivation assumes a similarity between the soil water retention function and that of the soil water content profiles taken at fixed times. The new solution successfully described soil water content profiles experimentally measured for water infiltrating downward, upward, and horizontally into a homogeneous sand and agrees with that presented by Philip in 1957. The utility of this analysis is still to be verified, but it is expected to hold for soils that have a narrow pore-size distribution before wetting and that manifest a sharp increase of water content at the wetting front during infiltration. The effect of van Genuchten`s parameters alpha and n on the application of the solution to other porous media was investigated. The solution also improves and provides a more realistic description of the infiltration process than that pioneered by Green and Ampt in 1911.

A generalized modified Weibull distribution for lifetime modeling

A four parameter generalization of the Weibull distribution capable of modeling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone as well as non-monotone failure rates, which are quite common in lifetime problems and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the Weibull, extreme value, exponentiated Weibull, generalized Rayleigh and modified Weibull distributions, among others. We derive two infinite sum representations for its moments. The density of the order statistics is obtained. The method of maximum likelihood is used for estimating the model parameters. Also, the observed information matrix is obtained. Two applications are presented to illustrate the proposed distribution. (C) 2008 Elsevier B.V. All rights reserved.

New Analytic Solution of Boltzmann Transform for Horizontal Water Infiltration into Sand

The use of the Boltzmann transform function, lambda(theta), to solve the Richards equation when the diffusivity, D, is a function of only soil water content,., is now commonplace in the literature. Nevertheless, a new analytic solution of the Boltzmann transform lambda(h) as a function of matric potential for horizontal water infiltration into a sand was derived without invoking the concept or use of D(theta). The derivation assumes that a similarity exists between the soil water retention function and the Boltzmann transform lambda(theta). The solution successfully described soil water content profiles experimentally measured for different infiltration times into a homogeneous sand and agrees with those presented by Philip in 1955 and 1957. The applicability of this solution for all soils remains open, but it is anticipated to hold for soils whose air-filled pore-size distribution before wetting is sufficiently narrow to yield a sharp increase of water content at the wetting front during infiltration. It also improves and provides a versatile alternative to the well-known analysis pioneered by Green and Ampt in 1911.

The exponentiated generalized gamma distribution with application to lifetime data

A four-parameter extension of the generalized gamma distribution capable of modelling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone and non-monotone failure rate functions, which are quite common in lifetime data analysis and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the exponentiated Weibull, exponentiated generalized half-normal, exponentiated gamma and generalized Rayleigh, among others. We derive two infinite sum representations for its moments. We calculate the density of the order statistics and two expansions for their moments. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is obtained. Finally, a real data set from the medical area is analysed.

Double generalized linear model for tissue culture proportion data: a Bayesian perspective

Joint generalized linear models and double generalized linear models (DGLMs) were designed to model outcomes for which the variability can be explained using factors and/or covariates. When such factors operate, the usual normal regression models, which inherently exhibit constant variance, will under-represent variation in the data and hence may lead to erroneous inferences. For count and proportion data, such noise factors can generate a so-called overdispersion effect, and the use of binomial and Poisson models underestimates the variability and, consequently, incorrectly indicate significant effects. In this manuscript, we propose a DGLM from a Bayesian perspective, focusing on the case of proportion data, where the overdispersion can be modeled using a random effect that depends on some noise factors. The posterior joint density function was sampled using Monte Carlo Markov Chain algorithms, allowing inferences over the model parameters. An application to a data set on apple tissue culture is presented, for which it is shown that the Bayesian approach is quite feasible, even when limited prior information is available, thereby generating valuable insight for the researcher about its experimental results.

Distribution and storage characterization of soil solution for drip irrigation

The increased use of marginal quality water with drip irrigation requires sound fertigation practices that reconcile environmental concerns with viable crop production objectives. We conducted experiments to characterize dynamics and patterns of soil solution within wet bulb formed by drip irrigation. Time-domain reflectometry probes were used to monitor the distribution of potassium nitrate (KNO(3)) and water distribution from drippers discharging at constant flow rates of 2, 4 and 8 L h(-1) in soil-filled containers. Considering results from different profiles, we observed greater solute storage near the dripper decreasing gradually towards the wetting front. About half of the applied KNO(3) solution (48%) was stored in the first layer (0-0.10 m) for all experiments, 29% was stored in the next layer (0.10-0.20 m). Comparing different dripper flow rates, we observed higher solution storage for 4 L h(-1), with 45, 53 and 47% of applied KNO(3) solution accumulating in the first layer (0-0.10 m) for dripper flow rates of 2, 4 and 8 L h(-1), respectively. The results suggest that based on the volume and frequency used in this experiment, it would be advantageous to apply small amounts of solution at more frequent intervals to reduce deep percolation losses of applied water and solutes.

Nickel adsorption in two Oxisols and an Alfisol as affected by pH, nature of the electrolyte, and ionic strength of soil solution

Background, aim, and scope The retention of potentially toxic metals in highly weathered soils can follow different pathways that variably affect their mobility and availability in the soil-water-plant system. This study aimed to evaluate the effects of pH, nature of electrolyte, and ionic strength of the solution on nickel (Ni) adsorption by two acric Oxisols and a less weathered Alfisol. Materials and methods The effect of pH on Ni adsorption was evaluated in surface and subsurface samples from a clayey textured Anionic `Rhodic` Acrudox ( RA), a sandy-clayey textured Anionic `Xantic` Acrudox (XA), and a heavy clayey textured Rhodic Kandiudalf (RK). All soil samples were equilibrated with the same concentration of Ni solution (5.0 mg L(-1)) and two electrolyte solutions (CaCl(2) or NaCl) with different ionic strengths (IS) (1.0, 0.1 and 0.01 mol L(-1)). The pH of each sample set varied from 3 to 10 in order to obtain sorption envelopes. Results and discussion Ni adsorption increased as the pH increased, reaching its maximum of nearly pH 6. The adsorption was highest in Alfisol, followed by RA and XA. Competition between Ni(2+) and Ca(2+) was higher than that between Ni(2+) and Na(+) in all soil samples, as shown by the higher percentage of Ni adsorption at pH 5. At pH values below the intersection point of the three ionic strength curves (zero point of salt effect), Ni adsorption was generally higher in the more concentrated solution (highest IS), probably due to the neutralization of positive charges of soil colloids by Cl(-) ions and consequent adsorption of Ni(2+). Above this point, Ni adsorption was higher in the more diluted solution (lowest ionic strength), due to the higher negative potential at the colloid surfaces and the lower ionic competition for exchange sites in soil colloids. Conclusions The effect of ionic strength was lower in the Oxisols than in the Alfisol. The main mechanism that controlled Ni adsorption in the soils was the ionic exchange, since the adsorption of ionic species varied according to the variation of pH values. The ionic competition revealed the importance of electrolyte composition and ionic strength on Ni adsorption in soils from the humid tropics. Recommendations and perspectives The presence of NaCl or CaCl(2) in different ionic strengths affects the availability of heavy metals in contaminated soils. Therefore, the study of heavy metal dynamics in highly weathered soils must consider this behavior, especially in soils with large amounts of acric components.

Novel and facile solution-phase synthesis of 2,5-diketopiperazines and O-glycosylated analogs

This work describes the synthesis in Solution of a series of related diketopiperazines with potential biological activities: cyclo(L-Pro-L-Ser), cyclo(L-Phe-L-Ser), cyclo(D-Phe-L-Ser) and the corresponding glycosylated analogs of the latter, cyclo[D-Phe-L-Ser(alpha GlcNAc)] and cyclo[D-Phe-L-Ser(beta GlcNAc)]. The synthetic approach involved coupling reactions of -OH or O-glycosylated serine benzyl esters with NFmoc-protected amino acids (Pro or Phe), followed by one-pot deprotection-cyclization reaction in the presence of 20% piperidine in DMF. (C) 2009 Elsevier Ltd. All rights reserved.

Computationally efficient solution techniques for adsorption problems involving steep gradients in bidisperse particles

A piecewise uniform fitted mesh method turns out to be sufficient for the solution of a surprisingly wide variety of singularly perturbed problems involving steep gradients. The technique is applied to a model of adsorption in bidisperse solids for which two fitted mesh techniques, a fitted-mesh finite difference method (FMFDM) and fitted mesh collocation method (FMCM) are presented. A combination (FMCMD) of FMCM and the DASSL integration package is found to be most effective in solving the problems. Numerical solutions (FMFDM and FMCMD) were found to match the analytical solution when the adsorption isotherm is linear, even under conditions involving steep gradients for which global collocation fails. In particular, FMCMD is highly efficient for macropore diffusion control or micropore diffusion control. These techniques are simple and there is no limit on the range of the parameters. The techniques can be applied to a variety of adsorption and desorption problems in bidisperse solids with non-linear isotherm and for arbitrary particle geometry.

Analytical solution of forced convection in a duct of rectangular cross-section saturated by a porous medium

A theoretical analysis is presented to investigate fully developed (both thermally and hydrodynamically) forced convection in a duct of rectangular cross-section filled with a hyper-porous medium. The Darcy-Brinkman model for flow through porous media was adopted in the present analysis. A Fourier series type solution is applied to obtain the exact velocity and temperature distribution within the duct. The case of uniform heat flux on the walls, i.e. the H boundary condition in the terminology of Kays and Crawford [1], is treated. Values of the Nusselt number and the friction factor as a function of the aspect ratio, the Darcy number, and the viscosity ratio are reported.

Sampling phylogenetic tree space with the generalized Gibbs sampler

The generalized Gibbs sampler (GGS) is a recently developed Markov chain Monte Carlo (MCMC) technique that enables Gibbs-like sampling of state spaces that lack a convenient representation in terms of a fixed coordinate system. This paper describes a new sampler, called the tree sampler, which uses the GGS to sample from a state space consisting of phylogenetic trees. The tree sampler is useful for a wide range of phylogenetic applications, including Bayesian, maximum likelihood, and maximum parsimony methods. A fast new algorithm to search for a maximum parsimony phylogeny is presented, using the tree sampler in the context of simulated annealing. The mathematics underlying the algorithm is explained and its time complexity is analyzed. The method is tested on two large data sets consisting of 123 sequences and 500 sequences, respectively. The new algorithm is shown to compare very favorably in terms of speed and accuracy to the program DNAPARS from the PHYLIP package.

Exact solution of the A(n-1)((1)) trigonometric vertex model with non-diagonal open boundaries

The A(n-1)((1)) trigonometric vertex model with generic non-diagonal boundaries is studied. The double-row transfer matrix of the model is diagonalized by algebraic Bethe ansatz method in terms of the intertwiner and the corresponding face-vertex relation. The eigenvalues and the corresponding Bethe ansatz equations are obtained.

Superconducting Correlations in Metallic Nanoparticles: Exact Solution of the BCS Model by the Algebraic Bethe Ansatz

Superconducting pairing of electrons in nanoscale metallic particles with discrete energy levels and a fixed number of electrons is described by the reduced Bardeen, Cooper, and Schrieffer model Hamiltonian. We show that this model is integrable by the algebraic Bethe ansatz. The eigenstates, spectrum, conserved operators, integrals of motion, and norms of wave functions are obtained. Furthermore, the quantum inverse problem is solved, meaning that form factors and correlation functions can be explicitly evaluated. Closed form expressions are given for the form factors and correlation functions that describe superconducting pairing.