This paper aims to study the asymptotic behavior of a fast-slow stochastic dynamical system with singular coefficients, where the fast motion is given by a continuous diffusion process while the slow component is driven by an α-stable noise with α ∈ [1, 2). Using Zvonkin’s transformation and the technique of the Poisson equation, we have that both the strong and weak convergences in the averaging principle are established, which can be viewed as a functional law of large numbers. Then we study the small fluctuations between the original system around its average. We show that the normalized difference converges weakly to an Ornstein-Uhlenbeck type Gaussian process, which is a form of the functional central limit theorem. Furthermore, sharp rates for the above convergences are also obtained, and these convergences are shown to not depend on the regularities of the coefficients with respect to the fast variable, which reflect the effects of noises on the multi-scale systems.
By combined power evolution laws of the spectral parameter and the initial constants of integration,a new differential-difference hierarchy is presented from the Toda spectral problem.The hierarchy contains the classic Toda lattice equation,the nonisospectral Toda lattice equation and the mixed Toda lattice equation as reduced cases.The evolution of the scattering data in the inverse scattering transform is analyzed in detail and exact soliton solutions are computed through the corresponding inverse scattering transform. 相似文献
As an effective and universal acaricide, amitraz is widely used on beehives against varroasis caused by the mite Varroajacobsoni. Its residues in honey pose a great danger to human health. In this study, a sensitive, rapid, and environmentally friendly surface-enhanced Raman spectroscopy method (SERS) was developed for the determination of trace amount of amitraz in honey with the use of silver nanorod (AgNR) array substrate. The AgNR array substrate fabricated by an oblique angle deposition technique exhibited an excellent SERS activity with an enhancement factor of ∽107. Density function theory was employed to assign the characteristic peak of amitraz. The detection of amitraz was further explored and amitraz in honey at concentrations as low as 0.08 mg/kg can be identified. Specifically, partial least square regression analysis was employed to correlate the SERS spectra in full-wavelength with Camitraz to afford a multiple-quantitative amitraz predicting model. Preliminary results show that the predicted concentrations of amitraz in honey samples are in good agreement with their real concentrations. Compared with the conventional univariate quantitative model based on single peak’s intensity, the proposed multiple-quantitative predicting model integrates all the characteristic peaks of amitraz, thus offering an improved detecting accuracy and anti-interference ability. 相似文献
The rational design of nanozymes with superior activities is essential for improving bioassay performances. Herein, nitrogen and boron co-doped graphene nanoribbons(NB-GNRs) are prepared by a hydrothermal method using urea as the nitrogen source and boric acid as the boron source, respectively.The introduction of co-doped and edge structures provides high defects and active sites. The resultant NB-GNRs nanozymes show superior peroxidase-like activities to nitrogen-doped and boron-doped counterpa... 相似文献