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This paper obtains solitons as well as other solutions to a few nonlinear evolution equations that appear in various areas of mathematical physics. The two analytical integrators that are applied to extract solutions are tan–cot method and functional variable approaches. The soliton solutions can be used in the further study of shallow water waves in (1+1) as well as (2+1) dimensions. 相似文献
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The oxidation of clean polycrystalline aluminium foil was performed in a previously described anaerobic cell and studied by core level and valence band X-ray photoelectron spectroscopy. Oxide free sample surfaces were exposed under inert atmosphere at room temperature to increasingly oxidative environments of water vapor and liquid water beginning with an oxide free metal foil each time. Minor oxidative environments were found to produce a film of boehmite with a thinner outer film of gibbsite. Harsher oxidation in liquid water resulted in an oxide film much thicker than that found on the as received sample which contained an inner composition of gamma alumina with an outer film of gibbsite. As expected, the oxide film observed for ultra high purity polycrystalline aluminiurm foil in the as received state was gibbsite. The valence band of the cleaned metal is discussed in terms of residual surface species. The evaluation and determination of these residual surface species is evaluated following an analysis of two different band structure calculations which use different d orbital exponents. It is found that while the density of states is almost unaltered by changes in the d exponent, the predicted spectrum is substantially changed. The work makes extensive use of valence band X-ray photoelectron spectroscopy. 相似文献
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Dussault PH Lee IQ Lee HJ Lee RJ Niu QJ Schultz JA Zope UR 《The Journal of organic chemistry》2000,65(25):8407-8414
The Lewis acid-mediated reaction of alkene nucleophiles with peroxyacetals provides an effective route for the synthesis of homologated peroxides and hydroperoxides. In the presence of Lewis acids such as TiCl(4), SnCl(4), and trimethylsilyl triflate, peroxyacetals and peroxyketals undergo reaction with allyltrimethylsilane, silyl enol ethers, and silyl ketene acetals to afford homoallyl peroxides, 3-peroxyketones, and 3-peroxyalkanoates, respectively. Reactions of peroxyacetals are Lewis acid dependent; TiCl(4) promotes formation of ethers while SnCl(4) and trimethylsilyl triflate promote formation of peroxides. Lewis acid-promoted reactions of silylated hydroperoxyacetals furnish silylated hydroperoxides, which can be deprotected to homologated hydroperoxides. Hydroperoxyketals undergo Lewis acid-mediated allylation to furnish 1,2-dioxolanes via attack of hydroperoxide on the intermediate carbocation. Lewis acid-mediated cyclization of unsaturated peroxyacetals furnishes 1,2-dioxanes, 1,2-dioxepanes, and 1,2-dioxacanes through 6-endo/exo, 7-endo/endo, and 8-endo/endo pathways. The corresponding reactions involving 6-endo/endo and 5-endo/exo pathways were unsuccessful. 相似文献
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