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21.
When trains of impulse controls are present on the right-hand side of a system of ordinary differential equations, the solution
is no longer smooth and contains jumps which can accumulate at several points in the time interval. In technological and physical
systems the sum of the absolute value of all the impulses is finite and hence the total variation of the solution is finite.
So the solution at best belongs to the space BV of vector functions with bounded variation. Unless variable node methods are
used, the loss of smoothness of the solution would a priori make higher-order methods over a fixed mesh inactractive. Indeed
in general the order of -convergence is and the nodal rate is . However in the linear case -convergence rate remains but the nodal rate can go up to by using one-step or multistep scheme with a nodal rate up to when the solution belongs to . Proofs are given of error estimates and several numerical experiments confirm the optimality of the estimates.
Received March 15, 1996 / Revised version received January 3, 1997 相似文献
22.
23.
H. Schmid E. Burkhardt E. Walker W. Brixel M. Clin J. -P. Rivera J. -L. Jorda M. François K. Yvon 《Zeitschrift für Physik B Condensed Matter》1988,72(3):305-322
The ferroelastic domains of the orthorhombic phase of YBa2Cu3O7- have been observed in polarized light on ceramics and single crystals. By combining polarized light microscopy with the X-ray precession technique, the correlation of the orientation of the orthorhombica- andb-axes with that of thea-b-plane bireflectance, reflection dichroism, transmission dichroism (at a thickness of about 1m), reflection tints generated with compensators and upon uncrossing of polars, as well as the orientation of etch pits has been realized on ferroelastic single domains, bi-domains and more complicated domain patterns. Four ferroelastic orthorhombic domain states have been identified, at variance with former group theoretical considerations, predicting only two states. Ensembles of lamellar domains beyond optical resolution generate strong bireflectance with principal axes rotated by 45° relative to the truea, b-directions. 相似文献
24.
Eric Cancès Renaud Keriven François Lodier Andreas Savin 《Theoretical chemistry accounts》2004,111(2-6):373-380
Efficient formulas for computing the probabilities of finding exactly electrons in an arbitrarily chosen volume 3 for Hartree–Fock wavefunctions are presented. These formulas allow the use of shape optimization techniques, such as level set methods, for optimizing with respect to various criteria involving such probabilities. The criterion defined as the difference between the Hartree–Fock and the independent-particle model probabilities of finding electrons in stresses the quantum effects due to the Pauli principle. We have implemented a 2D level set method for optimizing this criterion in order to study spatial separation of electron pairs in linear molecules. The method is described and the illustrative example of the BH molecule is reported.Contribution to the Jacopo Tomasi Honorary Issue 相似文献
25.
A highly flexible method for direct and quantitative determination of surface Br?nsted acidity of solids in terms of number, type and strength of the acid sites based on quantitative H/D exchange kinetics between the acid solid and gaseous D2O has been developed and applied to materials covering the whole range of acidity. 相似文献
26.
The formation of complexes between tin(IV) and o-diphenols, and o-hydroxyquinones, has been studied spectrophotometrically. Simple o-hydroxyquinones do not react with tin(IV), chloranilic acid gives an SnR2 complex, and o-diphenols give SnR3 complexes. The reactions of tin(IV) with hydroxyxanthene dyes to give coloured products were considered for their possible analytical utility: the pH range, absorption spectrum, solubility and composition of the complexes were investigated, and the stability constants determined. Analytical procedures have been developed for tin and checked for precision and sensitivity: gallein and hydroxyhydroquinonephthalein (dihydroxyfluorescein) are to be recommended. 相似文献
27.
Nicole Fietkau Fran?ois G Chevallier Li Jiang Timothy G J Jones Richard G Compton 《Chemphyschem》2006,7(10):2162-2167
The size of a glass sphere positioned in the center of a microdisk electrode is determined by using a simple electrochemical procedure and is confirmed, additionally, by a microscopical measurement of the sphere at the time of the electrochemical measurement. The cyclic voltammetric response of the naked electrode and of the electrode with the sphere positioned in its center is recorded over a wide range of scan rates (0.002-1.5 V s(-1)). The size of the sphere is then determined by comparison of the experimental voltammogram with simulations for each individual scan rate. 相似文献
28.
Ohne Zusammenfassung
Enzymatic detection of toxic impurities in butonate formulations after separation by thin-layer chromatography相似文献
29.
30.
Thierry Boulanger Daniel P. Vercauteren Guy Evrard François Durant 《Journal of chemical crystallography》1987,17(5):561-573
The crystal structure of 2-(carboxy-3-propyl)-3-amino-6-cyclohexylpyridazinium bromide has been determined by single-crystal X-ray diffraction techniques and refined by full-matrix least squares. The compound crystallized in the tri-clinic space groupP ¯1 witha=10.275(1),b=11.215(1),c=7.082(1) Å,=91.84(1),=102.21(1), =106.77(1)°, andZ=2. FinalR-factor is 0.045. The main structural results are very similar to the ones observed for the 6-phenyl analog. These two compounds are GABA-A antagonists.Ab initio molecular orbital calculations, with STO-3G and 4-31G basis sets, suggest that the exocyclic nitrogen accurately mimics the nitrogen atom of GABA. 相似文献