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1.
We discuss an error estimation procedure for the global error of collocation schemes applied to solve singular boundary value problems with a singularity of the first kind. This a posteriori estimate of the global error was proposed by Stetter in 1978 and is based on the idea of Defect Correction, originally due to Zadunaisky. Here, we present a new, carefully designed modification of this error estimate which not only results in less computational work but also appears to perform satisfactorily for singular problems. We give a full analytical justification for the asymptotical correctness of the error estimate when it is applied to a general nonlinear regular problem. For the singular case, we are presently only able to provide computational evidence for the full convergence order, the related analysis is still work in progress. This global estimate is the basis for a grid selection routine in which the grid is modified with the aim to equidistribute the global error. This procedure yields meshes suitable for an efficient numerical solution. Most importantly, we observe that the grid is refined in a way reflecting only the behavior of the solution and remains unaffected by the unsmooth direction field close to the singular point. 相似文献
2.
Sajewicz Mieczysław Hauck Heinz-E. Drabik Gabriela Namysło Ewa Głód Bronisław Kowalska Teresa 《平面色谱法杂志一现代薄层色谱法》2006,19(4):278-281
JPC – Journal of Planar Chromatography – Modern TLC - We have previously described unexpected two-dimensionality in the thin-layer chromatographic separation of pairs of enantiomers of... 相似文献
3.
Ewa Stró?yna 《Journal of Differential Equations》2003,193(1):239-259
We solve completely the problem of classification of germs of complex planar vector fields with nilpotent singularity with respect to formal orbital equivalence. 相似文献
4.
A method for the deposition of BN onto graphite and other substrates is described. Boron trichloride (BCl3) and ammonia (NH3) diluted with Ar were used as reacting gases. The deposition process was carried out at 1300 K as well as lower temperatures in an open system at pressures of 1 atm. The consequences of the introduction of hydrogen to the system were considered. It was demonstrated that the replacement of argon with hydrogen increases the efficiency of the process as well as the theoretical rate of BN deposition. However, the acceleration of the deposition seems to be unprofitable, because the resulting supersaturation leads to the formation of an amorphous phase. The modification of the experimental conditions were proposed.Dedicated to Professor Dr. rer. nat. Dr. h.c. Hubertus Nickel on the occasion of his 65th birthday 相似文献
5.
JPC – Journal of Planar Chromatography – Modern TLC - Emodin and twelve phenolic acids (ellagic, gallic, protocatechuic, homoprotocatechuic, caffeic, p-hydroxybenzoic, p-coumaric,... 相似文献
6.
Gajdek P Bober B Mej E Bialczyk J 《Journal of photochemistry and photobiology. B, Biology》2004,76(1-3):103-106
UV radiation was applied to degrade cyanobacterial hepatotoxin, microcystin-LR in the presence of phycocyanin as a model natural sensitiser. The concentrations of both the toxin and the pigment used in the experiments were higher by several orders of magnitude than found in the environment. The photoreaction parameters were optimised. The process was found to be of limited use for water treatment due to its low efficacy. Additionally, pronounced UV-induced bleaching of the pigment significantly reducing the photoreaction rates of the toxin was observed for the highest UV radiation intensities applied. 相似文献
7.
The mechanism of the indium electrodeposition on gold from acidic KBr solutions has been investigated by means of the rotating ring-disc electrode technique. The measurements showed that the overall electrode reaction In(III) + 3 e In consists of two successive charge transfer steps, i.e. In(III) + 2 e In(I) and In(I) + e In, with soluble monovalent indium as an intermediate. The current efficiency for In(I) generation under steady-state conditions is 100% in the case of low disc current densities. The disproportionation of In(I) in the bulk of solution occurs in slightly acidified solutions,pH=2, in addition to the In(I) electrochemical reduction. Based on the ring current transients, it was established that the two-electron transfer step is preceded by the formation of a thin passive film of indium metal.
Untersuchung der elektrochemischen Reduktion von In(III)-Ionen an Gold in sauren Bromidlösungen mit der rotierenden Ring-Scheiben-Elektrode
Zusammenfassung Mit Hilfe der rotierenden Ring-Scheiben-Elektrode wurde der Mechanismus der kathodischen Abscheidung von Indium auf Gold in sauren KBr-Lösungen untersucht. Aus den Messungen folgt, daß die Bruttoreaktion In(III) + 3e In über zwei aufeinanderfolgende Durchtrittsreaktionen, In(III) + 2 e In(I) und In(I) + e In, mit löslichem einwertigem Indium als Zwischenprodukt abläuft. Bei kleinen Stromdichten werden die In(I)-Ionen mit 100%iger Stromausbeute erzeugt. In schwächer sauren Lösungen (pH=2) konnte außer der elektrochemischen Reduktion von In(I) zusätzlich dessen Disproportionierung innerhalb der Lösung ermittelt werden. Auf Grund der Ringstrom-Zeit-Kurven wurde auch festgestellt, daß die Bildung von einer dünnen In-Metallschicht, die ein passives Verhalten aufweist, dem Zweielektronenübergang vorangegangen ist.相似文献
8.
Summary Complexation equilibria of the Tl(I) ion with 18-crown-6 and dibenzo-18-crown-6 were studied polarographically in 10 nonaqueous solvents. The stability of the complexes is strongly influenced by the nature of solvents and varies with their Lewis basicities. It has been found that the logK
s value (K
s is the stability constant of the complex) can be well described by empirical relation logK
s=a DN+b, whereDN stands for the Gutmann donor number anda andb mark the regression coefficient. Addition of the second explanatory parameter, the acceptor number, is not statistically significant. This result is in agreement with the predominant role of Tl(I) ion solvation.
Elektrochemische Untersuchungen von Tl(I)-Kronenetherkomplexen in nichtwäßrigen Medien
Zusammenfassung Es wurden die Komplexierungsgleichgewichte des Tl(I)-Ions mit 18-Krone-6 und Dibenzo-18-krone-6 polarographisch in 10 nichtwäßrigen Lösungsmitteln untersucht. Die Stabilität der Komplexe wird sehr stark vom Solvens beeinflußt, wobei eine starke Abhängigkeit von der Lewis-Basizität beobachtet wird. Es wurde festgestellt, daß die logK s-Werte (K s ist die Komplexstabilitätskonstante) gut mit der empirischen Beziehung logK s=a DN+b beschrieben werden können, wobeiDN die Gutmann'sche Donorzahl unda undb die Regressionskonstanten bedeuten. Hinzunahme der Akzeptorzahl als zweiten Parameter bleibt statistisch insignifikant. Dieses Ergebnis stimmt mit dem dominierenden Einfluß der Tl(I)-Ionensolvatation überein.相似文献
9.
Ewa Dabek-Zlotorzynska Maria Piechowski Fang Liu Scott Kennedy Joseph F. Dlouhy 《Journal of chromatography. A》1997,770(1-2):349-359
Capillary electrophoresis (CE) with indirect UV detection utilizing a pyromellitate-based electrolyte was used for the routine analysis of major anions in atmospheric aerosols collected on filters with high-volume (Hi-Vol) samplers. The long-term reliability of the CE system was checked over an 8-month period during which over 2900 samples were analyzed. In addition, approximately 1100 samples were analyzed in parallel by ion chromatography (IC). It has been shown that acceptable analytical performance can be routinely obtained. The agreement between the CE and IC results is good, generally better than 20% at concentrations larger than 1 mg l−1. 相似文献
10.
Aquation of [Cr(pic)3]0 and [Cr(pic)2(OH)]2
0 in aqueous HClO4 solutions leads to formation of the common product – [Cr(pic)2(H2O)2]+. The first, reversible stage, the ring opening via Cr—N bond breaking in [Cr(pic)3]0 is followed by the second, rate-determining step – one-end bonded pic ligand liberation. In the case of the [Cr(pic)2(OH)]2
0 complex, the first faster stage produces the singly bridged dimer, which undergoes cleavage into the parent monomers in the second, much slower step. The subsequent aquation of [Cr(pic)2(H2O)2]+ is extremely slow and leads to [Cr(pic)(H2O)4]2+ formation, which practically does not undergo further ligand substitution under the conditions applied. Kinetics of the first aquation stage for [Cr(pic)3]0 and of the second step for [Cr(pic)2(OH)]2
0 were studied spectrophotometrically in the 0.1–1.0 M HClO4 range at I = 1.0 M. The observed pseudo-first order rate constant for [Cr(pic)3]0 decreases with [H+] increase according to the rate law: k
obs = k
1 + k
–1
Q
1/[H+], where k
1 and k
–1 are the rate constants of the forward and the reverse processes in the unprotonated substrate and Q
1 is the protonation constant of the pyridine nitrogen atom. In the case of the [Cr(pic)2(OH)]2
0 complex, the rate for the singly bridged dimer cleavage does not depend on [H+]. The activation parameters for the chelate-ring opening in [Cr(pic)3]0 and for the singly bridged dimer cleavage have been determined and discussed. Some kinetic data of the slow, second aquation stage for the [Cr(pic)3]0 complex and of the fast, first aquation stage for the doubly bridged dimer have been studied; for both reactions the rate increases linearly with the increase in [H+]. 相似文献