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Pontryagin–Rodygin?s Theorem for slow and fast systems describes the slow drift during the rolling up of the trajectories around the cycles of the fast dynamics. This drift is approximated by the averaging on the cycles. The calculation of this average is generally a difficult task since it requires the knowledge of the closed orbits and their periods. We present two paradigms of three time scale systems where we can overcome this limitation. It is the case of systems the fast dynamics of which have cycles with relaxation presenting or not a canard phenomenon. We can not apply Pontryagin–Rodygin?s Theorem to these systems because their fast equation is itself singularly perturbed. We also investigate the extension of the results to unbounded time intervals. The results are stated classically and proved within the framework of nonstandard analysis. 相似文献
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Let W(Γ)be a class of not-finitely graded Lie algebras related to gener-alized Virasoro algebras with basis{Lα,i,C | α ∈ Γ,i ∈ Z+},which satisfies relations[Lα,i,Lβ,j]=(β-α)Lα+β,i+j+(j-i)Lα+β,i+j+1+δα+β,0δi+j,0α3-α/12C and[C,Lα,i]=0.In this paper,W(Γ)-modules of the intermediate series satisfying some conditions are con-structed and classified.We also obtain modules of the intermediate series over the related Lie superalgebra. 相似文献
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Wang Yue Wang Yadi Huang Lina Liu Xiangyong Hu Jun Lü Junhong 《Analytical and bioanalytical chemistry》2019,411(27):7157-7164
Analytical and Bioanalytical Chemistry - Endothelial damage is a major manifestation in many forms of heart and lung injuries induced by lipopolysaccharide (LPS), but the biochemical responses and... 相似文献
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Enantioseparation of citalopram analogues with sulfated β‐cyclodextrin by capillary electrophoresis 下载免费PDF全文
Yadi Wang Shusheng Zhang Zachary S. Breitbach Hans Petersen Peter Ellegaard Daniel W. Armstrong 《Electrophoresis》2016,37(5-6):841-848
Capillary electrophoresis methods were developed for the enantiomeric separation of 27 citalopram analogues. Sulfated β‐cyclodextrin was the most broadly selective and useful chiral selector. The separations of most of the citalopram analogue compounds reported in this work have not been reported previously. Excellent enantiomeric separations were obtained for 26 out of 27 compounds, and most of the separations were achieved within 10 min. The effects of chemical parameters such as chiral selector types, buffer types, chiral selector and buffer concentrations, buffer pH and organic modifiers on the separation were investigated. The influence of analyte structure on separation also was examined and discussed. 相似文献
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A label-free, non-derivatization chemiluminescence resonance energy transfer (CRET) detection platform has been developed for the detection of the non-fluorescent small molecule 6-mercaptopurine. This CRET process arose from a chemiluminescent (CL) donor-acceptor system in which the reaction of bis(2,4,6-trichlorophenyl)oxalate (TCPO)-H(2)O(2)-fluorescein (maximum emission at 521.6 nm) served as the donor and gold nanoparticles (AuNPs, maximum absorption at 520.0 nm) served as the acceptor. This process caused a significant decrease in the CL signal of the TCPO-H(2)O(2)-fluorescein reaction. The presence of 6-mercaptopurine induced an aggregation of AuNPs with the assistance of Cu(2+) ions through cooperative metal-ligand interactions that was accompanied by a distinct change in color and optical properties. The maximum absorption band of the AuNPs was red-shifted to 721.0 nm and no longer overlapped with the CL spectrum of the reaction; as a result, the CL signal was restored. This CRET system exhibited a wide linear range, from 9.0 nmol L(-1) to 18.0 μmol L(-1), and a low detection limit (0.62 nmol L(-1)) for 6-mercaptopurine. The applicability of the proposed CRET system was evaluated by analysis of 6-mercaptopurine in spiked human plasma samples. 相似文献
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Dr. Jianxiu Du Yadi Wang Weimin Zhang 《Chemistry (Weinheim an der Bergstrasse, Germany)》2012,18(27):8540-8546
A label‐free, non‐derivatization chemiluminescence resonance energy transfer (CRET) detection platform has been developed for the detection of the non‐fluorescent small molecule 6‐mercaptopurine. This CRET process arose from a chemiluminescent (CL) donor–acceptor system in which the reaction of bis(2,4,6‐trichlorophenyl)oxalate (TCPO)–H2O2–fluorescein (maximum emission at 521.6 nm) served as the donor and gold nanoparticles (AuNPs, maximum absorption at 520.0 nm) served as the acceptor. This process caused a significant decrease in the CL signal of the TCPO–H2O2–fluorescein reaction. The presence of 6‐mercaptopurine induced an aggregation of AuNPs with the assistance of Cu2+ ions through cooperative metal–ligand interactions that was accompanied by a distinct change in color and optical properties. The maximum absorption band of the AuNPs was red‐shifted to 721.0 nm and no longer overlapped with the CL spectrum of the reaction; as a result, the CL signal was restored. This CRET system exhibited a wide linear range, from 9.0 nmol L?1 to 18.0 μmol L?1, and a low detection limit (0.62 nmol L?1) for 6‐mercaptopurine. The applicability of the proposed CRET system was evaluated by analysis of 6‐mercaptopurine in spiked human plasma samples. 相似文献
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