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.     

9(11)-Secoestra-11,17-dioic acids and related compounds

While hydrogenations of 2b furnished a mixture in which the rac 14α isomer 8b predominated, the rac lactone 6 was hydrogenolyzed to give the rac 14β diacid 9a. Clemmensen reduction of 6 gave the rac 14α tetrahydro compound 7a. Another route to 8 involved conversion of the d-ketoacid 11b into 23b via the cyanolactone 20b or the amidolactone 21b. Base-catalyzed elimination at 206° yielded the Δ¹⁶ diester 27 which was hydrogenated to 8c. An analogous conversion was also carried out in the ring B reduced series 13 → 20a + 21a → 23a → 25a → 26. In the 14β series, using the same sequence of reactions, the rac ketoacid 10a was transformed into the rac lactone ester 29. In distinction from the 14α series, treatment with alkali at 206° gave only partial elimination, the double bond migrating to the 14,15 position to furnish 2. Evidence is presented that amides of the ketoacid 13a exist in the hydroxylactam form 30 and can be readily O-alkylated to furnish 22. Attempts to aromatize ring B of 13a with DDQ led to lactones 15 and 16, while reaction of the ester 13b with DDQ gave the pentaene 17 and the hexaene 18, establishing that dehydrogenation proceeded stepwise in the sequence Δ⁸, Δ¹⁴ and finally Δ⁶.     

Inhomogeneous and homogeneous broadening effects onnuclear resonance experiments

Inhomogeneous broadening of resonance lines causes a reduction of absorption in nuclear resonance experiments. This is particularly devastating to the observation of the Mössbauer effect in isomers like ¹⁰⁷Ag with a half-life of 44s.It has been suggested in the literature that homogeneous broadening can provide overlap of resonance lines and thus theMössbauer effect can be recovered. The analysis presented in this paper shows that this is not the case for Mössbauer experiments, unless the radiative width Γ_Γ also increases. Although overlap occurs when the lines are homogeneously broadened to a total width Γ_{_}H which exceeds the natural width Γ, and the inhomogeneous width Δ, the Mössbauer absorption remains low because it is proportional to the factor of Γ_γ/Γ _H.     

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.     

Palm Raceme as a Promising Biomass Precursor for Activated Carbon to Promote Lipase Activity with the Aid of Eutectic Solvents

This study concerns the role of activated carbon (AC) from palm raceme as a support material for the enhancement of lipase-catalyzed reactions in an aqueous solution, with deep eutectic solvent (DES) as a co-solvent. The effects of carbonization temperature, impregnation ratio, and carbonization time on lipase activity were studied. The activities of Amano lipase from Burkholderia cepacia (AML) and lipase from the porcine pancreas (PPL) were used to investigate the optimum conditions for AC preparation. The results showed that AC has more interaction with PPL and effectively provides greater enzymatic activity compared with AML. The optimum treatment conditions of AC samples that yield the highest enzymatic activity were 0.5 (NaOH (g)/palm raceme (g)), 150 min, and a carbonization temperature of 400 °C. DES was prepared from alanine/sodium hydroxide and used with AC for the further enhancement of enzymatic activity. Kinetic studies demonstrated that the activity of PPL was enhanced with the immobilization of AC in a DES medium.     

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.