We note that in the literature it is often taken for granted that for fractional-order system without delays, whenever the system trajectory reaches the equilibrium, it will stay there. In fact, this is the well-known phenomenon of finite-time stability. However, in this paper, we will prove that for fractional-order nonlinear system described by Caputo’s or Riemann–Liouville’s definition, any equilibrium cannot be finite-time stable as long as the continuous solution corresponding to the initial value problem globally exists. In addition, some examples of stability analysis are revisited and linear Lyapunov function is used to prove the asymptotic stability of positive fractional-order nonlinear systems. 相似文献
The changes in milled rice FFA content and composition and in conjugated diene (CD) content and bacterial, yeast, and mold
counts were determined at 24, 37, and 50°C and 70% RH over 50 d. There was a rapid rate of FFA formation during the first
few days of storage, which was optimal at 37°C, but that slowed after 2, 4, and 5 d at 37, 24, and 50°C, respectively. There
was a second increase in FFA after about day 12 that increased with increasing temperature, indicating nonlipase hydrolysis.
Linoleic and oleic acids were the main components of the total FFA produced on the surface of milled rice. The pattern of
CD development followed that of FFA increase. Bacterial growth correlated with increased FFA levels after 12 d of storage,
suggesting that bacterial lipase rather than bran lipase may be responsible for rice lipid hydrolysis 相似文献
The effects of platinum (Pt) and silver (Ag) metallisation in the photocatalytic oxidation of resorcinol at pH 3 ± 0.5 have been investigated. The photocatalytic degradation of resorcinol was significantly improved by Pt/TiO2, while the presence of Ag/TiO2 enhanced the initial photocatalytic degradation rate of resorcinol slightly. Likewise, the photocatalytic mineralisation of resorcinol continued to be enhanced by Pt/TiO2, but it was retarded when Ag/TiO2 was used.
The function of Pt and Ag deposits on the surface of TiO2 has been found to be markedly influenced by the interaction of resorcinol and its degradation products with the metal deposits. The presence of Pt or Ag on the surface of TiO2 altered the distribution of degradation products of resorcinol as well as the production of photoactive species for the photocatalytic oxidation of resorcinol. The X-ray photoelectron spectroscopy (XPS), zeta potential and transmission electron microscopy (TEM) analyses have indicated that the contrasting effect of Pt and Ag deposits were governed by the oxidation states and the catalytic property of metal deposits. In addition to that, it has been found that the roles of metal deposits are specific and should not be generalised. 相似文献
A methylene-interrupted C18 keto-acetylenic fatty ester (methyl 12-oxo-9-octadecynoate) was obtained from methyl ricinoleate by bromination-dehydrobromination
followed by oxidation. Reaction of methyl 12-oxo-9-octadecynoate with bis(benzonitrile) palladium(II) chloride, allyl bromide,
or methyl-allyl bromide furnished methyl 8-[5-hexyl-3-allyl-furan-2-yl]-octanoate (1, 56%) or methyl 8-[5-hexyl-3-(2-methyl-allyl)-furan-2-yl]-octanoate (2, 55%). Reaction of methyl 12-oxo-11-chloro-or 11-fluoro-9-octadeyynoate (prepared from methyl santalbate-methyl 11-E-9-octadecynoate, found in sandalwood, Santalum album, seed oil) with bis(benzonitrile) palladium(II) chloride gave methyl 8-(4-fluoro-5-hexyl-furan-2-yl)-octanoate (3, 50%) or methyl 8-(4-fluoro-5-hexyl-furan-2-yl)-octanoate (4, 50%), respectively. And when methyl 12-oxo-11-chloro- or 11-fluoro-9-octadecynoate was treated with a mixture of bis(benzonitrile)
palladium(II) chloride, allyl bromide, or methyl-allyl bromide, the reaction yielded tetrasubstituted C18 furan derivatives, viz, methyl 8-(3-allyl-4-chloro-5-hexyl-furan-2-yl)-octanoate (5, 54%), methyl 8-[4-chloro-5-hexyl-3-(2-methyl-allyl)-furan-2-yl)-octanoate (6, 54%), methyl 8-(3-allyl-4-fluoro-5-hexyl-furan-2-yl]-octanoate (7, 10%), and methyl 8-[4-fluoro-5-hexyl-3-(2-methyl-allyl)-furan-2-yl]-octanoate (8, 10%). The presence of a fluorine atom in the furan derivatives 4, 7, and 8 was readily characterized by the appearance of doublets for carbon nuclei, which were coupled to the fluorine atom
in the 13C NMR spectra. All furan fatty derivatives from this work were characterized by NMR spectroscopic and mass spectrometric analyses.
The yields of compounds 7 and 8 were very low (10%) despite attempts to improve the procedure by increasing the amounts of the reactants and catalyst. 相似文献
Microsystem Technologies - This paper reports a design and fabrication process of a micro cam system (MCS) with a flat-faced translating follower. The cam rim with cover diameter of 2.4 mm... 相似文献
In this paper, the problem of a generalized type of H∞ control is investigated for continuous‐time singular systems, which treats a mixed attenuation of exogenous inputs and initial conditions. First, a performance measure that is essentially the worst‐case norm of the regulated outputs over all exogenous inputs and initial conditions is introduced. A necessary and sufficient condition is obtained to ensure the singular system to be admissible and the performance measure to be less than a prescribed scalar. Based on the criterion a sufficient condition for the existence of a state‐feedback controller is established in terms of linear matrix inequalities. Moreover, the relationship between the performance measure and the standard H∞ norm of the system is provided. Two numerical examples are given to demonstrate the properties of the obtained results. 相似文献
Digital control of optics experiments has many advantages over analog control systems, specifically in terms of the scalability, cost, flexibility, and the integration of system information into one location. We present a digital control system, freely available for download online, specifically designed for quantum optics experiments that allows for automatic and sequential re-locking of optical components. We show how the inbuilt locking analysis tools, including a white-noise network analyzer, can be used to help optimize individual locks, and verify the long term stability of the digital system. Finally, we present an example of the benefits of digital locking for quantum optics by applying the code to a specific experiment used to characterize optical Schr?dinger cat states. 相似文献