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.     

Analysis of the globins from fast human haemoglobins by isoelectrofocusing on polyacrylamide gel rods

The globins from all fast haemoglobin (Hb) components obtainable by Bio-Rex 70 cation-exchange chromatography were examined by isoelectrofocusing on polyacrylamide gel rods with 8.0 mol/l urea. From this analysis HbA1a1 and HbA1a2 seem to be very heterogeneous components. HbA1b is separable into two components, one of which is varied in both the beta chains. Between HbA1b2 and the well-known HbA1c components two chromatographic peaks are separated, one with a noticeable percentage of glucosylated beta chain and one that probably contains HbF. HbA1c has both beta chains glucosylated, while HbA1x seems to be a beta monoglucosylated Hb form. Finally, the early part of the HbAo peak has a large amount of glucosylation on both alpha and beta chains.     

Role of spin noise in the detection of nanoscale ensembles of nuclear spins

When probing nuclear spins in materials on the nanometer scale, random fluctuations of the spin polarization will exceed the mean Boltzmann polarization for sample volumes below about (100 nm){3}. In this Letter, we use magnetic resonance force microscopy to observe nuclear spin fluctuations in real time. We show how reproducible measurements of the polarization variance can be obtained by controlling the spin correlation time and rapidly sampling a large number of independent spin configurations. This allows significant improvement in the signal-to-noise ratio for nanometer-scale magnetic resonance imaging.     

Exploring the Synthesis of a New Group of Chiral Ammonium Salts with Specific Configurations at the Stereogenic Nitrogen Centers

A group of new chiral dications with a fixed, specific configuration at the stereogenic nitrogen center was created. Stereoselective synthesis and recrystallization give the diastereomerically and enantiomerically pure dications, including a chiral amphiphile with surface‐active properties.     

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.     

Improved determination of the bisphosphonate pamidronate disodium in plasma and urine by pre-column derivatization with fluorescamine, high-performance liquid chromatography and fluorescence detection.

An improved method for the determination of 1-hydroxy-3-aminopropylidene-1,1-bisphosphonate (pamidronate) in human urine and plasma is described. The procedure is based on a co-precipitation of the bisphosphonates (pamidronate and 6-amino-1-hydroxypentilidene-bisphosphonate, used as internal standard) with calcium phosphate. After centrifugation the precipitate is redissolved in hydrochloric acid, followed by a second precipitation. Then the bisphosphonates are dissolved in ethylenediaminetetraacetic acid, derivatized with fluorescamine, and separated by high-performance liquid chromatography. Using fluorescence detection, the limit of quantitation for pamidronate was 0.8 mumol/l in plasma and 0.7 mumol/l in urine.