Simulation model for shapiro time delay and light deflection experiments

The time delay experiment proposed by I.I. Shapiro in 1964 and conducted in the seventies was the most precise experiment of general relativity until that time. Further experimentation has improved the accuracy level of both the time delay and the light deflection experiments. A simulation model is proposed that involves only a simple mass and time transformation factor involving velocity of light. The light deflection and the time delay experiments are numerically simulated using this model that does not use the general relativistic equations. The computed values presented in this paper compare well with recent levels of accuracy of their respective experimental results.     

Determination of lead in drinking waters by hydride generation and atomic-absorption spectroscopy, and three other methods

Simultaneous presence of copper and nickel in potable waters interferes with the determination of lead at trace levels by the hydride-atomic-absorption spectrophotometric method. This interference is eliminated by co-precipitating lead with manganese dioxide from acidic solution. The precipitate is dissolved in 0.85% nitric acid and analysed by the automated hydride-atomic-absorption method. This method has been applied to 22 representative water samples and results compared with those obtained by using differential pulse anodic-stripping voltammetry, flame atomic-absorption and graphite-furnace atomic-absorption spectrophotometry. The precision of the three methods is reported and their accuracy checked by the analysis of reference standard water samples. The sensitivity of the three methods is of the order of 1 mug/l., compared to 100 mug/l. for flame atomic-absorption. The merits of each method are discussed.     

In situ Raman studies on lithiated single-wall carbon nanotubes in liquid ammonia

The charge transfer induced lithiation of single-wall carbon nanotubes (SWNTs) was investigated by in situ monitoring by Raman spectroscopy as lithium was added incrementally to a dispersion of SWNTs in liquid ammonia. Charge transfer from liquid ammonia solvated lithium to the SWNTs led to intercalation of lithium into the SWNT ropes, as well as to the semi-covalent lithiation of the SWNTs. Raman spectra of the SWNTs recorded as lithium was added showed a 30 wavenumber downshift of the G band (1594 cm⁻¹) with the concomitant appearance of a new peak at 1350 cm⁻¹ that was assigned as the signature of the lithiated SWNTs. Addition of 1-iodododecane to the lithiated SWNTs resulted in the covalent attachment of dodecyl groups. The intercalation of lithium throughout the SWNT ropes led to complete dodecylation of all individual SWNTs.     

Carbon nanotube salts. Arylation of single-wall carbon nanotubes

[reaction: see text] Carbon nanotube salts prepared by treating single-wall carbon nanotubes (SWNTs) with lithium in liquid ammonia react readily with aryl iodides to give SWNTs functionalized by aryl groups.     

Mass spectra of sterically crowded trialkylsilyl derivatives of nucleosides

The electron impact mass spectra of tert-butyldimethylsilyl-, cyclo-tetramethylene-tert-butylsilyl and cyclo-tetramethylene-isopropylsilyl- ether derivatives of ribo- and 2′-deoxyribonucleosides are described in detail. The interpretation of fragmentation pathways of full and mixed derivatives was aided by metastable ion decomposition studies, precise mass and deuterium labelling measurements, and spectra of mixed derivatives containing the ‘passive’ (in these spectra) trimethylsilyl group. The sterically crowded silyl groups have a powerful fragmentation directing effect. Elimination of a bulky radical, R˙ (tert-butyl or isopropyl), from the molecular ion produces the siliconium ion [M? R]⁺, which is the precursor for most of the other prominent ions in the spectra. These arise from ‘siliconium ion rearrangements’ resulting from the interaction of the positively charged siliconium ion center with electron dense regions (i.e. oxygens) in the molecule, to form cyclic silyloxonium ions which subsequently decompose. Since the interacting oxygen and silicon must be sterically accessible, the fragment ion types and their abundances are very dependent upon structure. Consequently, [M? R]⁺ ions formed from 2′, 3′ or 5′-O-silyl groups give rise to different sets of daughter ions which, for the most part, are not found, or have very low abundances, in the mass spectra of underivatized or trimethylsilylated nucleosides. Detailed information on sugar and base moieties and isomeric substitution is readily obtained.     

Sampled-Data Nash Equilibria in Differential Games with Impulse Controls

Journal of Optimization Theory and Applications - We study a class of deterministic two-player nonzero-sum differential games where one player uses piecewise-continuous controls to affect the...     

Schur complement preconditioners for anisotropic problems

We present two new variants of Schur complement domain decompositionpreconditioners suitable for 2D anisotropic problems. Thesevariants are based on adaptations of the probing idea, describedby Chan et al (1992 Fifth Int. Symp. on Domain DecompositionMethods for Partial Differential Equations, Philadelphia: SIAM,pp 236-249), used in conjunction with a coarse grid approximationas introduced by Bramble et al (1986 Math. Comput. 47, 103-134).The new methods are specifically designed for situations wherethe coupling between neighbouring interfaces is stronger thanthe coupling within an interface. Taking into account this strongcoupling, one variant uses a multicolour probing technique toavoid distortion in the probe approximations that appear whenusing the method proposed by Chan et al. The second techniqueuses additional probe matrices to approximate not only the couplingwithin the interfaces but also the coupling between interfacepoints across the subdomains. This latter procedure looks somewhatlike an alternating line relaxation method for anisotropic problems,see Brandt (1977 Math. Comput.. 31, 333-390). To assess therelevance of the new preconditioners, we compare their numericalbehaviour with well known robust preconditioners such as thebalanced Neumann-Neumann method proposed by Mandel (1993 Commun.Numer. Methods Eng.. 9, 233-241).     

A Predictive Approach Using Fractal Analysis for Analyte-Receptor Binding and Dissociation Kinetics for Surface Plasmon Resonance Biosensor Applications

A predictive approach using fractal analysis is presented for analyte-receptor binding and dissociation kinetics for biosensor applications. Data taken from the literature may be modeled, in the case of binding using a single-fractal analysis or a dual-fractal analysis. The dual-fractal analysis represents a change in the binding mechanism as the reaction progresses on the surface. A single-fractal analysis is adequate to model the dissociation kinetics in the examples presented. Predictive relationships developed for the binding and the affinity (k(diss)/k(bind)) as a function of the analyte concentration are of particular value since they provide a means by which the binding and the affinity rate coefficients may be manipulated. Relationships are also presented for the binding and the dissociation rate coefficients and for the affinity as a function of their corresponding fractal dimension, D(f), or the degree of heterogeneity that exists on the surface. When analyte-receptor binding or dissociation is involved, an increase in the heterogeneity on the surface (increase in D(f)) leads to an increase in the binding and in the dissociation rate coefficient. It is suggested that an increase in the degree of heterogeneity on the surface leads to an increase in the turbulence on the surface owing to the irregularities on the surface. This turbulence promotes mixing, minimizes diffusional limitations, and leads subsequently to an increase in the binding and in the dissociation rate coefficient. The binding and the dissociation rate coefficients are rather sensitive to the degree of heterogeneity, D(f,bind) (or D(f1)) and D(f,diss), respectively, that exists on the biosensor surface. For example, the order of dependence on D(f,bind) (or D(f1)) and D(f2) is 6.69 and 6.96 for k(bind,1) (or k(1)) and k(2), respectively, for the binding of 0.085 to 0.339 μM Fab fragment 48G7(L)48G7(H) in solution to p-nitrophenyl phosphonate (PNP) transition state analogue immobilized on a surface plasmon resonance (SPR) biosensor. The order of dependence on D(f,diss) (or D(f,d)) is 3.26 for the dissociation rate coefficient, k(diss), for the dissociation of the 48G7(L)48G7(H)-PNP complex from the SPR surface to the solution. The predictive relationships presented for the binding and the affinity as a function of the analyte concentration in solution provide further physical insights into the reactions on the surface and should assist in enhancing SPR biosensor performance. In general, the technique is applicable to other reactions occurring on different types of biosensor surfaces and other surfaces such as cell-surface reactions. Copyright 2000 Academic Press.