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Suppose that a consistent one-step numerical method of orderr is applied to a smooth system of ordinary differential equations.Given any integer m 1, the method may be shown to be of orderr + m as an approximation to a certain modified equation. Ifthe method and the system have a particular qualitative propertythen it is important to determine whether the modified equationsinherit this property. In this article, a technique is introducedfor proving that the modified equations inherit qualitativeproperties from the method and the underlying system. The techniqueuses a straightforward contradiction argument applicable toarbitrary one-step methods and does not rely on the detailedstructure of associated power series expansions. Hence the conclusionsapply, but are not restricted, to the case of Runge-Kutte methods.The new approach unifies and extends results of this type thathave been derived by other means: results are presented forintegral preservation, reversibility, inheritance of fixed points.Hamiltonian problems and volume preservation. The techniquealso applies when the system has an integral that the methodpreserves not exactly, but to order greater than r. Finally,a negative result is obtained by considering a gradient systemand gradient numerical method possessing a global property thatis not shared by the associated modified equations. 相似文献
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Much is known about the connection between the growth and decayof subharmonic functions. The results indicate that there isa general principle: asubharmonic function cannot decay toofast relative to its growth.Three theorems are provedwhich, together with work previously published elsewhere, givea fairly complete account of how this principle works out fora subharmonic function having extremal decay along a ray. 1991Mathematics Subject Classification: 30D20, 31A05. 相似文献
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Saib F. Touahra F. Azoudj Y. Chebout R. Lerari D. Bachari K. Abdi A. Trari M. 《Journal of Solid State Electrochemistry》2022,26(3):607-619
Journal of Solid State Electrochemistry - Ca2Co2O5 was successfully synthesized from nitrate precursors. It crystallizes in the brownmillerite structure and exhibits semiconducting properties. The... 相似文献
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Dahbi S Azzi M Saib N de la Guardia M Faure R Durand R 《Analytical and bioanalytical chemistry》2002,374(3):540-546
The ability of bone charcoal to remove Cr(III) from aqueous solutions by adsorption has been investigated. The adsorbent used was first characterised and then the adsorption was studied as a function of time and amount of charcoal. Tests were carried out with synthetic solutions whose Cr concentrations (500 mg L(-1)) were similar to those found in some effluents of Moroccan tannery industries. Cr removal efficiencies higher than 90% were obtained at pH 3.5 using 3 g of bone charcoal and a stirring time of about 30 min. Results of Cr removal by all sieved fractions of bone charcoal had shown the same interesting capabilities for Cr(III) retention. The cross interference with other elements was also investigated. Pre-treatment of bone charcoal by nitric acid led to an increase in its specific surface area but induced a drastic reduction in its Cr elimination abilities. Adsorption tests were also carried out using calcinated bone charcoal. The results obtained showed a similar percentage of Cr retention to those found with untreated bone charcoal. On the other hand, a double treatment of bone charcoal with HCl and NaOH provided an enhancement of Cr(III) retention. The role played by the mineral fraction of the solid phase of bone was thus evidenced. 相似文献
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Handzy DO Bauer W Daffin FC Gaff SJ Gelbke CK Glasmacher T Gualtieri E Hannuschke S Huang MJ Kunde GJ Lacey R Li T Lisa MA Llope WJ Lynch WG Martin L Montoya CP Pak R Peaslee GF Pratt S Schwarz C Stone N Tsang MB Vander Molen AM Westfall GD Yee J Yennello SJ 《Physical review letters》1995,75(16):2916-2919