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.     

Compact groups of positive operators on Banach lattices

In this paper, we study groups of positive operators on Banach lattices. If a certain factorization property holds for the elements of such a group, the group has a homomorphic image in the isometric positive operators which has the same invariant ideals as the original group. If the group is compact in the strong operator topology, it equals a group of isometric positive operators conjugated by a single central lattice automorphism, provided an additional technical assumption is satisfied, for which we have only examples. We obtain a characterization of positive representations of a group with compact image in the strong operator topology, and use this for normalized symmetric Banach sequence spaces to prove an ordered version of the decomposition theorem for unitary representations of compact groups. Applications concerning spaces of continuous functions are also considered.     

Equivalence after extension and Schur coupling coincide for inessential operators

In recent years the coincidence of the operator relations equivalence after extension (EAE) and Schur coupling (SC) was settled for the Hilbert space case. For Banach space operators, it is known that SC implies EAE, but the converse implication is only known for special classes of operators, such as Fredholm operators with index zero and operators that can in norm be approximated by invertible operators. In this paper we prove that the implication EAE $?$ SC also holds for inessential Banach space operators. The inessential operators were introduced as a generalization of the compact operators, and include, besides the compact operators, also the strictly singular and strictly co-singular operators; in fact they form the largest ideal such that the invertible elements in the associated quotient algebra coincide with (the equivalence classes of) the Fredholm operators.     

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.     

Synthesis and conformation of some 2,4-dioxa- and 2,4-dioxa-3-silabicyclo[3.3.1]nonanes

The conformation of the title compounds established by ¹³C and ¹H NMR spectroscopy shows that replacement of the 2- and 4-methylene groups in bicyclo[3.3.1]nonane by ether oxygen atoms strongly destablizes the cc conformation: in 2-oxabicyclo[3.3.1]-nonane the cc and the bc conformers are about equally populated, whereas in 2,4-dioxabicyclo[3.3.1]nonane the bc conformation predominates. The 2,4-dioxa-3-silabicyclo[3.3.1]nonanes also occur predominantly inthe bc conformation. As in the carbocyclic bicyclo[3.3.1]nonanes both wings are strongly flattened. A stereoselective synthesis of 3-methylbicyclo[3.3.1]nonane, an important model compound in this study, is described.     

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.     

The electron impact induced fragmentations of some 7-alkyl-3-oxabicyclo[3.3.1]nonanes

The mass spectra of a series of 7-alkyl substituted 3-oxabicyclo[3.3.1]nonanes are recorded. The fragmentation has been studied by the use of the metastable DADI and defocussing techniques. The character of the alkyl group is found to influence the fragmentation pattern. Stereoselective fragmentations for the 7-t-butyl derivatives are observed. In the endo-isomer, in contrast to the exo-isomer, a transannular hydrogen transfer plays a role.