On the iterative solution of the algebraic equations in fully implicit Runge-Kutta methods

This paper deals with the iterative solution of stage equations which arise when some fully implicit Runge-Kutta methods, in particular those based on Gauss, Radau and Lobatto points, are applied to stiff ordinary differential equations. The error behaviour in the iterates generated by Newton-type and, particularly, by single-Newton schemes which are proposed for the solution of stage equations is studied. We consider stiff systems y'(t) = f(t,y(t)) which are dissipative with respect to a scalar product and satisfy a condition on the relative variation of the Jacobian of f(t,y) with respect to y, similar to the condition considered by van Dorsselaer and Spijker in [7] and [17]. We prove new convergence results for the single-Newton iteration and derive estimates of the iteration error that are independent of the stiffness. Finally, some numerical experiments which confirm the theoretical results are presented. This revised version was published online in June 2006 with corrections to the Cover Date.     

On the convergence of multipoint Padé-type approximants and quadrature formulas associated with the unit circle

We study the convergence of rational interpolants with prescribed poles on the unit circle to the Herglotz-Riesz transform of a complex measure supported on [–, ]. As a consequence, quadrature formulas arise which integrate exactly certain rational functions. Estimates of the rate of convergence of these quadrature formulas are also included.This research was performed as part of the European project ROLLS under contract CHRX-CT93-0416.     

Procedure for verification of sound source coverage over façades according to the International Standard ISO 140–5

This paper presents a new verification procedure for sound source coverage according to ISO 140–5 requirements. The ISO 140–5 standard applies to the measurement of façade insulation and requires a sound source able to achieve a sufficiently uniform sound field in free field conditions on the façade under study. The proposed method involves the electroacoustic characterisation of the sound source in laboratory free field conditions (anechoic room) and the subsequent prediction by computer simulation of the sound free field radiated on a rectangular surface equal in size to the façade being measured. The loudspeaker is characterised in an anechoic room under laboratory controlled conditions, carefully measuring directivity, and then a computer model is designed to calculate the acoustic free field coverage for different loudspeaker positions and façade sizes. For each sound source position, the method provides the maximum direct acoustic level differences on a façade specimen and therefore determines whether the loudspeaker verifies the maximum allowed level difference of 5 dB (or 10 dB for façade dimensions greater than 5 m) required by the ISO standard. Additionally, the maximum horizontal dimension of the façade meeting the standard is calculated and provided for each sound source position, both with the 5 dB and 10 dB criteria. In the last section of the paper, the proposed procedure is compared with another method used by the authors in the past to achieve the same purpose: in situ outdoor measurements attempting to recreate free field conditions. From this comparison, it is concluded that the proposed method is able to reproduce the actual measurements with high accuracy, for example, the ground reflection effect, at least at low frequencies, which is difficult to avoid in the outdoor measurement method, and it is fully eliminated with the proposed method to achieve the free field requisite.     

Asymptotic properties of local polynomial regression with missing data and correlated errors

The main objective of this work is the nonparametric estimation of the regression function with correlated errors when observations are missing in the response variable. Two nonparametric estimators of the regression function are proposed. The asymptotic properties of these estimators are studied; expresions for the bias and the variance are obtained and the joint asymptotic normality is established. A simulation study is also included.     

Mechanically Interlocked Single‐Wall Carbon Nanotubes

Extensive research has been devoted to the chemical manipulation of carbon nanotubes. The attachment of molecular fragments through covalent‐bond formation produces kinetically stable products, but implies the saturation of some of the C? C double bonds of the nanotubes. Supramolecular modification maintains the structure of the SWNTs but yields labile species. Herein, we present a strategy for the synthesis of mechanically interlocked derivatives of SWNTs (MINTs). In the key rotaxane‐forming step, we employed macrocycle precursors equipped with two π‐extended tetrathiafulvalene SWNT recognition units and terminated with bisalkenes that were closed around the nanotubes through ring‐closing metathesis (RCM). The mechanically interlocked nature of the derivatives was probed by analytical, spectroscopic, and microscopic techniques, as well as by appropriate control experiments. Individual macrocycles were observed by HR STEM to circumscribe the nanotubes.     

Development and validation of a high-performance liquid chromatographic method using fluorimetric detection for the determination of the diarrhetic shellfish poisoning toxin okadaic acid without chlorinated solvents

A modification of the high-performance liquid chromatographic method with fluorimetric detection method for the determination of diarrhetic shellfish poisoning toxins was developed to completely avoid the use of dangerous chlorinated solvents. The method was validated for the toxin okadaic acid (OA) over a period of 6 months where 12 calibrations were performed and 72 samples were analyzed. Analysis of toxic and non-toxic mussels, clams and scallops demonstrated its selectivity. Linearity was observed in the tested range of interest for monitoring purposes of edible shellfish, from the limit of detection (0.3 microg OA/g hepatopancreas) to 13 microg OA/g hepatopancreas. Intra-assay precision of the method was 7% RSD at the quantification limit (0.97 microg OA/g hepatopancreas at S/N=10). Accuracy was tested in triplicate recovery experiments from OA-spiked shellfish where recovery ranged from 92 to 106% in the concentration range of 0.8 to 3.6 microg OA/g hepatopancreas. Useful information on critical factors affecting calibration and reproducibility is also reported. Good correlation (R=0.87) was observed between the results of the method and those of the method of Lee, after the analysis of 45 samples of mussels from the galician rias.     

Supercritical fluid extraction of polycyclic aromatic hydrocarbons from liver samples and determination by HPLC-FL

An extraction/clean-up procedure by SFE was developed for isolating PAHs from liver samples for subsequent HPLC-FL determination of ten PAHs in the enriched extract. Recoveries (90-115%) and RSD % (< or =7.7) were satisfactory. When applied to 11 samples of bird of prey (Tyto alba) protected species and classified of special interest, from the Galicia (Northwest to Spain), benzo[ghi]perylene and indeno[1,2,3-cd]pyrene were undetectable; chrysene and benzo[a]pyrene are only detected in one sample; benzo[a]anthracene and benzo[k]fluoranthene are only quantified in one sample and benzo[b]fluoranthene in two samples. The other PAHs, anthracene, fluoranthene and pyrene are present in almost all the samples.     

Monitoring of substrate and product concentrations in acetic fermentation processes for onion vinegar production by NIR spectroscopy: value addition to worthless onions

Wastes and by-products of the onion-processing industry pose an increasing disposal and environmental problem and represent a loss of valuable sources of nutrients. The present study focused on the production of vinegar from worthless onions as a potential valorisation route which could provide a viable solution to multiple disposal and environmental problems, simultaneously offering the possibility of converting waste materials into a useful food-grade product and of exploiting the unique properties and health benefits of onions. This study deals specifically with the second and definitive step of the onion vinegar production process: the efficient production of vinegar from onion waste by transforming onion ethanol, previously produced by alcoholic fermentation, into acetic acid via acetic fermentation. Near-infrared spectroscopy (NIRS), coupled with multivariate calibration methods, has been used to monitor the concentrations of both substrates and products in acetic fermentation. Separate partial least squares (PLS) regression models, correlating NIR spectral data of fermentation samples with each kinetic parameter studied, were developed. Wavelength selection was also performed applying the iterative predictor weighting–PLS (IPW-PLS) method in order to only consider significant spectral features in each model development to improve the quality of the final models constructed. Biomass, substrate (ethanol) and product (acetic acid) concentration were predicted in the acetic fermentation of onion alcohol with high accuracy using IPW-PLS models with a root-mean-square error of the residuals in external prediction (RMSEP) lower than 2.5% for both ethanol and acetic acid, and an RMSEP of 6.1% for total biomass concentration (a very satisfactory result considering the relatively low precision and accuracy associated with the reference method used for determining the latter). Thus, the simple and reliable calibration models proposed in this study suggest that they could be implemented in routine applications to monitor and predict the key species involved in the acetic fermentation of onion alcohol, allowing the onion vinegar production process to be controlled in real time.     

Quantum dynamics study of the K+HF(v=0-2,j=0)-->KF+H reaction and comparison with quasiclassical trajectory results

Extensive quantum real wave packet calculations within the helicity decoupling approximation are used to analyze the influence of the HF vibrational excitation on the K+HF(v=0-2,j=0)-->KF+H reaction. Quantum reaction probabilities P and reaction cross sections sigma are compared with corresponding quasiclassical trajectory (QCT) results. Disregarding threshold regions for v=0 and 1 (v=2 has no threshold), both approaches lead to remarkably similar results, particularly for sigma, validating the use of the QCT method for this system. When moving from v=0 to v=1 there is a large increase in P and sigma, as expected for a late barrier system. For v=2 the reaction becomes exoergic and P approximately 0.95 (with the exception of large total angular momenta where centrifugal barriers play a role). While substantial vibrational enhancement of the reactivity is thus seen, it is still quite less than that inferred from experimental data in the intermediate and high collision energy ranges. The origin of this discrepancy is unclear.     

A simple helical macrocyclic polyazapyridinophane as a stereoselective receptor of biologically important dicarboxylates under physiological conditions

The interaction of a synthetic enantiopure azamacrocyclic receptor (L) with biologically important chiral dicarboxylates (A, 1-7) has been studied by means of potentiometric titrations in 0.15 M NaCl aqueous solution in a wide pH range. This macrocycle forms strong complexes of the type [HnLA](n-2) (with n = 0-5). As a general trend, the binding is much tighter at basic or neutral pH than in acidic medium. Interestingly, nonprotected excitatory amino acids (Asp and Glu) are strongly bound even at acidic pH. Regarding selectivity, the receptor showed stereoselective binding toward those substrates bearing an H-bonding donor at Calpha, being S-selective in most of the cases, except for glutamic acid. Thus, L displayed an excellent enantioselectivity for (S)-malate dianion (KS/KR = 11.50 at pH 10.0 and KS/KR = 6.86 at pH 7.0) and exhibited moderate enantiopreference for (S,S)-tartrate (KSS/KRR = 3.01 at pH 10 and KSS/KRR = 1.70 at pH 7.0). For this last anion, a very good diastereopreference was also observed (KSS/KRS = 8.46 at pH 10 and KSS/KRS = 4.99 at pH 7.0). On the contrary, L is smoothly R-selective toward (R)-Glu (KR/KS = 3.22 at pH 10 and KR/KS = 2.05 at pH 7.0) due to its longer and more flexible molecular structure. The stereoselectivity of the corresponding complexes decreased when decreasing pH values. For the hydroxy derivatives, mass spectrometry also reflected the trends observed by potentiometry and confirmed the receptor:dicarboxylate 1:1 stoichiometry of the supramolecular complexes. Additional experimental techniques were used to study the most stereoselective example. Solution studies by NMR suggested a good geometrical complementarity between the malate dianion and the receptor, which showed a predominant helical conformation in solution. Besides, self-diffusion rates (PGSE) of the diastereomeric complexes with malate also agree with binding data. Circular dichroism was also used in this case at different pH values, showing a very good correlation between the helical content of the receptor and the stereoselectivity of the molecular recognition process.