What do multistep methods approximate?

Summary Standard analysis of multistep methods for ODE's assumes the application of an initialization routine that generates the starting points. Here ak-step method is considered directly as a mappingR ^kn R ⁿ . It is shown to approximate a mapping which is expressible directly in terms of the flow of the vector field. Some useful properties of that mapping are shown and for strictly stable methods these are applied to the question of invariant circles near a hyperbolic periodic solution.     

Convergence of Krylov methods for sums of two operators

We discuss the convergence of Krylov subspace methods for equationsx =Tx +f whereT is a sum of two operators,T =B +K, whereB is bounded andK is nuclear. Bounds are given for inf Q _k (B+K) and for inf p _k (B+K), where the infimum is over all polynomials of degreek, such thatQ _k is monic andp _k is normalized:p _k (1) = 1.     

Stability and accuracy of time discretizations for initial value problems

Summary This paper continues earlier work by the same authors concerning the shape and size of the stability regions of general linear discretization methods for initial value problems. Here the treatment is extended to cover also implicit schemes, and by placing the accuracy of the schemes into a more central position in the discussion general method-free statements are again obtained. More specialized results are additionally given for linear multistep methods and for the Taylor series method.This research has been supported by Swiss National Foundation, Grant No. 82-524.077This research has been supported by the Heinrich-Hertz-Stiftung, B 32 No. 203/79     

Mercerized cellulose biocomposites: a study of influence of mercerization on cellulose supramolecular structure, water retention value and tensile properties

In this study the effect of the mercerization degree on the water retention value (WRV) and tensile properties of compression molded sulphite dissolving pulp was evaluated. The pulp was treated with 9, 10, or 11 % aqueous NaOH solution for 1 h before compression molding. To study the time dependence of mercerization the pulp was treated with 12 wt% aqueous NaOH for 1, 6 or 48 h. The cellulose I and II contents of the biocomposites were determined by solid state cross polarization/magic angle spinning carbon 13 nuclear magnetic resonance (CP/MAS ¹³C NMR) spectroscopy. By spectral fitting of the C6 and C1 region the cellulose I and II content, respectively, could be determined. Mercerization decreased the total crystallinity (sum of cellulose I and cellulose II content) and it was not possible to convert all cellulose I to cellulose II in the NaOH range investigated. Neither increased the conversion significantly with 12 wt% NaOH at longer treatment times. The slowdown of the cellulose I conversion was suggested as being the result from the formation of cellulose II as a consequence of coalescence of anti-parallel surfaces of neighboring fibrils (Blackwell et al. in Tappi 61:71–72, 1978; Revol and Goring in J Appl Polym Sci 26:1275–1282, 1981; Okano and Sarko in J Appl Polym Sci 30:325–332, 1985). Compression molding of the partially mercerized dissolving pulps yielded biocomposites with tensile properties that could be correlated to the decrease in cellulose I content in the pulps. Mercerization introduces cellulose II and disordered cellulose and lowered the total crystallinity reflected as higher water sensitivity (higher WRV values) and poorer stiffness of the mercerized biocomposites.     

Shortcut to a Fermi-degenerate gas of molecules via cooperative association

We theoretically examine the creation of a Fermi-degenerate gas of molecules by considering a photoassociation or Feshbach resonance applied to a degenerate Bose-Fermi mixture of atoms. This problem raises interest because, unlike bosons, fermions in general do not behave cooperatively, so that the collective conversion of a degenerate gas atoms into a macroscopic number of diatomic molecules is not to be expected. Nevertheless, we find that the coupled Fermi system displays collective Rabi-like oscillations and a rapid adiabatic passage between atoms and molecules, thereby mimicking Bose-Einstein statistics. Cooperative association of a degenerate mixture of Bose and Fermi gases could therefore serve as a shortcut to a degenerate gas of Fermi molecules.     

Covalently Bound Antibody on Polystyrene Latex Beads: Formation, Stability, and Use in Analyses of White Blood Cell Populations

CD4 or CD8 antibodies were covalently bound to latex beads by reaction of activated CD4 or CD8 monoclonal antibodies with 2-μm-diameter, 1,3-diaminopropane (DAP) coupled, polystyrene aldehyde/sulfate latex beads. Spectrophotometric analyses of the filtrates of the antibody-bead conjugation mixtures for unreacted antibody allowed construction of binding curves of antibody for the polystyrene bead surface and evaluation of binding constants for association of antibody with bead, ranging from 1.5x10(7) to 1.6x10(7) M(-1) for CD4 and CD8 antibodies. The reaction of the antibody thiol group with the activated maleimide group on the bead at pH 7.2-7.3 was complete within 10-15 min. The kinetics of CD4 or CD8 monoclonal antibody displacement from the surface of covalently conjugated antibody-polystyrene latex beads was followed as a function of temperature (5, 22, and 37 degrees C) and the nature of the final diluent for the antibody-coated beads by measuring the concentration of antibody in the filtrates of conjugated beads by an ELISA (enzyme-linked immunosorbent assay). The displacement reaction showed a pseudo-zero-order dependence of the rate, with constants, k(1), ranging from 0.65x10(-17) to 270x10(-17) M s(-1). The functionality of antibody-coated beads suspended in various media was also monitored in a biological cell assay with whole blood. The cell assay depends on forming a layer of beads around targeted lymphocytes to distinguish them from nontargeted lymphocytes by differences in dc or rf conductivity or median angle light scatter. Covalently bound CD4 and CD8 antibody beads stored in one set of media at 5, 22, and 37 degrees C over a period of 16 weeks showed excellent results in the STKS assay with various blood donors, which correlated well (correlation coefficients of 0.99 for CD4 data and 0.93 for CD8 data) with reference results obtained with fluorescent markers by flow cytometry. Covalently bound CD4/CD8 beads stored for 2 weeks in BSA buffer at 5-37 degrees C performed equally well in providing accurate values of the percentage of CD4- or CD8-positive cells in the total white blood cell population, whereas the same beads stored in the 47-50 degrees C range showed some failures in performance. Comparison with antibody concentrations in filtrates of adsorbed antibody-bead suspensions showed 2- to 10-fold greater amounts of free antibody at comparable elapsed time, media, and temperature conditions. A threshold of 1-2 μg/mL of free antibody was necessary before adverse effects on the biological cell assay were noticeable. Copyright 2001 Academic Press.     

Microwave spectrum of deuterated silyl isocyanate,SiD3NCO

The microwave spectrum of SiD₃NCO has been observed and analyzed for 18 different vibrational states in the ν₁₀ manifold. Some accidental resonances have been observed and analyzed. The vibrational dependence of the rotational and l-doubling constant and centrifugal distortion constant D_JK has been successfully interpreted in terms of the two-dimensional anharmonic oscillator model.     

Quantification of a number of biogenic amines and their metabolites in brain homogenates by gas chromatography--mass spectrometry

A sensitive method is described for the assay of various biogenic amines and their metabolites from brain tissue homogenates. Based on gas chromatography-mass spectrometry and selected ion monitoring, the method allows reliable low-level quantification of the compounds of interest. By careful study of reaction conditions both in the preparation of derivatives for gas chromatography and in the synthesis of deuterated analogues for internal standard use, relatively simple procedures could be applied with good analytical efficiency. Correlation of the results with those obtained by a high-performance liquid chromatographic procedure was also investigated, and a neurologic application of the method is briefly discussed.