Product Integration Rules at Clenshaw-Curtis and Related Points: A Robust Implementation

Product integration rules generalizing the Fej?r, Clenshaw-Curtis,and Filippi quadrature rules respectively are derived for integralswith trigonometric and hyperbolic weight factors. The Chebyshevmoments of the weight functions are found to be given by well-conditionedexpressions, in terms of hypergeometric functions ₀F₁. An a priori error estimator is discussed which is shown bothto avoid wasteful invocation of the integration rule and toincrease significantly the robustness of the automatic quadratureprocedure. Then, specializing to extended Clenshaw-Curtis (ECC) rules,three types of a posteriori error estimates are considered andthe existence of a great risk of their failure is demonstratedby large scale validation tests. An empirical error estimator,superseding them for slowly varying integrands, is found toresult in a spectacular increase in the output reliability. Finally, enhancements in the control of the interval subdivisionstrategy aiming at increasing code robustness is discussed.Comparison with the code DQAWO of QUADPACK, with about a hundredthousand solved integrals, is illustrative of the increasedrobustness and error estimate reliability of our computer codeimplementation of the ECC rules.     

Thermodynamic Complexation of Dopamine with Zinc(II) in Media with Different Dielectric Constants

The complexation of zinc(II) with dopamine has been investigated by spectrophotometric measurements in mixed solvent system at an ionic strength of 0.2 mol•dm－3 sodium chloride, employed at at (15±0.1), (25±0.1), (35±0.1) ℃ at inin a pH range of ca. 6 to ca. 7 with a high ratio of ligand to metal. The effect of solvent systems on protonation and complexation are was was discussed. Linear relationships are werewere observed by plotting lg K versus 1/D, where K and D show stability and dielectric constants, respectively.     

Lattice Boltzmann simulation of natural convection in nanofluid-filled 2D long enclosures at presence of magnetic field

In this paper, the effects of a magnetic field on natural convection flow in filled long enclosures with Cu/water nanofluid have been analyzed by lattice Boltzmann method. This study has been carried out for the pertinent parameters in the following ranges: the Rayleigh number of base fluid, Ra = 10³–10⁵, the volumetric fraction of nanoparticles between 0 and 6 %, the aspect ratio of the enclosure between A = 0.5 and 2. The Hartmann number has been varied from Ha = 0 to 90 with interval 30 while the magnetic field is considered at inclination angles of θ = 0°, 30°, 60° and 90°. Results show that the heat transfer decreases by the increment of Hartmann number for various Rayleigh numbers and the aspect ratios. Heat transfer decreases with the growth of the aspect ratio but this growth causes the effect of the nanoparticles to increase. The magnetic field augments the effect of the nanoparticles at high Rayleigh numbers (Ra = 10⁵). The effect of the nanoparticles rises for high Hartmann numbers when the aspect ratio increases. The rise in the magnetic field inclination improves heat transfer at aspect ratio of A = 0.5.     

1H NMR‐based metabolomics exploring urinary biomarkers correlated with proteinuria in focal segmental glomerulosclerosis: a pilot study

Focal segmental glomerulosclerosis (FSGS) is a common glomerulonephritis, and its rates of occurrence are increasing worldwide. Proteinuria is a clinical defining feature of FSGS which correlates with the severity of podocyte injury in patients with nephrotic‐range protein excretion. Metabolite biomarkers corresponding with the level of proteinuria could be considered as non‐invasive complementary prognostic factors to proteinuria. The urine samples of 15 patients (n = 6 women and n = 9 men) with biopsy‐proven FSGS were collected and subjected to nuclear magnetic resonance (NMR) analysis for metabolite profiling. Multivariate statistical analyses, including principal component analysis and orthogonal projection to latent structure discriminant analysis, were applied to construct a predictive model based on patients with proteinuria >3000 mg/day and <3000 mg/day. In addition, random forest was performed to predict differential metabolites, and pathway analysis was performed to find the defective pathways responsible for proteinuria. Ten metabolites, significant in both statistical methods (orthogonal projection to latent structure discriminant analysis and random forest), were considered as prognostic biomarkers for FSGS: citrulline, dimethylamine, proline, acetoacetate, alpha‐ketoisovaleric acid, valine, isobutyrate, D‐Palmitylcarnitine, histidine, and N‐methylnicotinamide. Pathway analysis revealed impairment of the branched‐chain amino acid degradation pathways in patients with massive proteinuria. This study shows that metabolomics can reveal the molecular changes corresponding with disease progression in patients with FSGS and provide a new insight for pathogenic pathways. Copyright © 2016 John Wiley & Sons, Ltd.     

Higher derivatives in quantum cosmology: (I). The isotropic case

This paper is the first in a series that investigates the effects on cosmology of curvature-squared terms which are bound to appear in the effective action whether or not gravity is perturbatively finite, is cut off by nonperturbative effects, or is made renormalisable by the addition of curvature squared terms to the bare action. We examine how these terms affect the recent proposal that the quantum state of the universe is defined by a path integral over compact metrics. In this paper we consider a simple minisuperspace model of an isotropic universe. In such a model the C-squared term in the action plays no role while the R-squared term behaves like a massive scalar field. The wave function of the universe can be interpreted as corresponding in the classical limit to a family of solutions that start out with a long period of exponential expansion and then go over to a matter dominated era.     

Efficient recovery of rare earth elements from coal based resources: a bioleaching approach

Rare earth element (REE) resources in coal-related materials are vast. Assuming a coal production rate of 600 million short tons per year with an average REE content of 200 ppm, the potential REE resource is 120,000 tons per year, which is similar to the annual global production of REEs. Most of those resources that are associated with coal-related materials are found in association with the gangue or ash-based content from the coal ore. Under normal coal plant operation, the REEs often end up in refuse piles or tailings impoundments. In many cases, these REEs can be recovered at low cost using appropriate coal preparation, heap leaching, solvent extraction and/or selective precipitation, followed by subsequent separation and purification of individual REEs. In the present research, the processing approach uses a natural pyrite stream, which was removed during coal cleaning and used to enhance leaching. Bio-oxidation has been used commercially to accelerate leaching, and this approach has been applied to coal-based materials. The ferric ions generated from bio-oxidation oxidize sulfide minerals such as pyrite, which generates acid. Both acid and ferric ions are helpful for leaching REEs, as well as for removing residual sulfides, thereby preventing future acid mine drainage and related liabilities. It can be seen that, recovery of REEs from coal waste materials can enable coal producers to use untapped REEs resources to produce revenue and extend resource life while simultaneously reducing future environmental issues and costs.     

Influence of absorbed pump profile on the temperature distribution within a diode side-pumped laser rod

In this paper, an analytical model for temperature distribution of the side-pumped laser rod is extracted. This model can be used for side-pumped laser rods whose absorbed pump profile is a Gaussian profile. Then, it is validated by numerical results which exhibit a good agreement with the analytical results. Afterwards, by considering a general expression for super-Gaussian and top-hat profiles, and solving the heat equation, the influence of profile width and super-Gaussian exponent of the profile on temperature distribution are investigated. Consequently, the profile width turns out to have a greater influence on the temperature compared to the type of the profile.     

An experimental investigation of the structural response of reactor fuel plates

In some reactors, thin fuel plates are cooled by water flowing through thin channels on either side of the plates. There is a need to know the amount of deformation in the fuel plates due to the coolant flow so that failures can be avoided. A verifiable solution to this problem in the past has not been available. An experimental-analytical solution to this problem for design purposes has been developed and is herein presented.