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We address the evaluation of highly oscillatory integrals,with power-law and logarithmic singularities.Such problems arise in numerical methods in engineering.Notably,the evaluation of oscillatory integrals dominates the run-time for wave-enriched boundary integral formulations for wave scattering,and many of these exhibit singularities.We show that the asymptotic behaviour of the integral depends on the integrand and its derivatives at the singular point of the integrand,the stationary points and the endpoints of the integral.A truncated asymptotic expansion achieves an error that decays faster for increasing frequency.Based on the asymptotic analysis,a Filon-type method is constructed to approximate the integral.Unlike an asymptotic expansion,the Filon method achieves high accuracy for both small and large frequency.Complex-valued quadrature involves interpolation at the zeros of polynomials orthogonal to a complex weight function.Numerical results indicate that the complex-valued Gaussian quadrature achieves the highest accuracy when the three methods are compared.However,while it achieves higher accuracy for the same number of function evaluations,it requires signi cant additional cost of computation of orthogonal polynomials and their zeros. 相似文献
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Moses S Brewer SH Lowe LB Lappi SE Gilvey LB Sauthier M Tenent RC Feldheim DL Franzen S 《Langmuir : the ACS journal of surfaces and colloids》2004,20(25):11134-11140
Single- and double-stranded deoxy ribonucleic acid (DNA) molecules attached to self-assembled monolayers (SAMs) on gold surfaces were characterized by a number of optical and electronic spectroscopic techniques. The DNA-modified gold surfaces were prepared through the self-assembly of 6-mercapto-1-hexanol and 5'-C(6)H(12)SH -modified single-stranded DNA (ssDNA). Upon hybridization of the surface-bound probe ssDNA with its complimentary target, formation of double-stranded DNA (dsDNA) on the gold surface is observed and in a competing process, probe ssDNA is desorbed from the gold surface. The competition between hybridization of ssDNA with its complimentary target and ssDNA probe desorption from the gold surface has been investigated in this paper using X-ray photoelectron spectroscopy, chronocoulometry, fluorescence, and polarization modulation-infrared reflection absorption spectroscopy (PM-IRRAS). The formation of dsDNA on the surface was identified by PM-IRRAS by a dsDNA IR signature at approximately 1678 cm(-)(1) that was confirmed by density functional theory calculations of the nucleotides and the nucleotides' base pairs. The presence of dsDNA through the specific DNA hybridization was additionally confirmed by atomic force microscopy through colloidal gold nanoparticle labeling of the target ssDNA. Using these methods, strand loss was observed even for DNA hybridization performed at 25 degrees C for the DNA monolayers studied here consisting of attachment to the gold surfaces by single Au-S bonds. This finding has significant consequence for the application of SAM technology in the detection of oligonucleotide hybridization on gold surfaces. 相似文献
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Two novel 25,27-dihydroxy-26,28-bis(3-phenylthiapropxy)-calix[4]arene(3) and 25,27-dihydroxy-26,28-bis(3-phenylthiapropoxy)-5,11,17,23-tetra-tert-butylcalix[4] arene (4) were synthesized for the evaluation of their ion-selectivity in ion-selective electrodes(ISEs).ISEs based on 3 and 4 as neutral ionophores were prepared,and their selectivity coefficients for Ag^ (lg KAg,M^pot)were investigated against other alkali metal,alkaline-earth metal,aluminum,thallium(Ⅰ),Lead and some transition metal ions using the separate solution method (SSM).These ISEs showed excellent Ag^ seletivity over most of the interfering cations examined,except for Hg^2 and Fe^2 having relative smaller interference(lg KAg,M^pot≤-2.1). 相似文献
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Takahashi K Kodama R Tanaka KA Hashimoto H Kato Y Mima K Weber FA Barbee TW Da Silva LB 《Physical review letters》2000,84(11):2405-2408
A laser self-focused channel formation into overdense plasmas was observed using a soft x-ray laser probe system with a grid image refractometry (GIR) technique. 1.053 &mgr;m laser light with a 100 ps pulse duration was focused onto a preformed plasma at an intensity of 2x10(17) W/cm (2). Cross sections of the channel were obtained which show a 30 &mgr;m diameter in overdense plasmas. The channel width in the overdense region was kept narrow as a result of self-focusing. Conically diverging density ridges were also observed along the channel, indicating a Mach cone created by a shock wave due to the supersonic propagation of the channel front. 相似文献
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ThetheoryofnonlinearpolymerizationwasinitiatedbyFlory[1]andStockmayer[2].Forsimplifyingtheevaluationofaveragepolymerquantities,manyotherstatisticalmethodssuchastheprobabilityofgeneratingfunctionmethod[3],thelawoftotalprobabilitymethod[4,5]andtheothermethods[6… 相似文献
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Celliers PM Collins GW Da Silva LB Gold DM Cauble R Wallace RJ Foord ME Hammel BA 《Physical review letters》2000,84(24):5564-5567
Simultaneous measurements of shock velocity and optical reflectance at 1064, 808, and 404 nm of a high pressure shock front propagating through liquid deuterium show a continuous increase in reflectance from below 10% and saturating at approximately (40-60)% in the range of shock velocities from 12 to 20 &mgr;m/ns (pressure range 17-50 GPa). The high optical reflectance is evidence that the shocked deuterium reaches a conducting state characteristic of a metallic fluid. Above 20 &mgr;m/ns shock velocity (50 GPa pressure) reflectance is constant indicating that the transformation is substantially complete. 相似文献
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