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61.
In this paper we present a-posteriori KAM results for existence of d-dimensional isotropic invariant tori for n-DOF Hamiltonian systems with additional independent first integrals in involution. We carry out a covariant formulation that does not require the use of action-angle variables nor symplectic reduction techniques. The main advantage is that we overcome the curse of dimensionality avoiding the practical shortcomings produced by the use of reduced coordinates, which may cause difficulties and underperformance when quantifying the hypotheses of the KAM theorem in such reduced coordinates. The results include ordinary and (generalized) iso-energetic KAM theorems. The approach is suitable to perform numerical computations and computer assisted proofs. 相似文献
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Gold nanoparticles have unique and excellent medical and nonmedical properties and application compared with other metallic nanoparticles. Recently, they have been used for the prevention, control, and treatment of bacterial and fungal diseases. In the recent study, fresh and clean leaves of Allium noeanum Reut. ex Regel leaves have been used for the synthesis of gold nanoparticles. Also, we evaluated the cytotoxicity, antioxidant, and antibacterial properties of HAuCl4, A. noeanum, and the synthesized nanoparticles (Au NPs). These nanoparticles were analyzed by FT‐IR, UV, XRD, EDS, FE‐SEM, and TEM tests. FTIR results offered antioxidant compounds in the plant were the sources of reducing power, reducing gold ions to Au NPs. In TEM images revealed an average diameter of 10‐30 nm. At the beginning of biological experiments, DPPH free radical scavenging test was carried out to examine the antioxidant property. Also, in the bacterial part of this study, the concentration of HAuCl4, A. noeanum, and AuNPs with minimum dilution and no turbidity was considered MIC. To determine MBC, 60 μL of MIC and three preceding chambers were cultured on Muller Hinton Agar. The minimum concentration with no bacterial growth was considered MBC. Au NPs revealed excellent antioxidant potential against DPPH, non‐toxicity property against human umbilical vein endothelial cells, and antibacterial activities against Streptococcus pneumonia, Bacillus subtilis, Staphylococcus aureus, Staphylococcus saprophyticus, Salmonella typhimurium, Pseudomonas aeruginosa, Shigella flexneri, and Escherichia coli O157:H7. These findings show that the inclusion of A. noeanum extract improves the solubility of Au NPs, which led to a notable enhancement in the antioxidant and antibacterial effects. 相似文献
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