Dimension Theory for Invariant Measures of Endomorphisms

We establish the exact dimensional property of an ergodic hyperbolic measure for a C ² non-invertible but non-degenerate endomorphism on a compact Riemannian manifold without boundary. Based on this, we give a new formula of Lyapunov dimension of ergodic measures and show it coincides with the dimension of hyperbolic ergodic measures in a setting of random endomorphisms. Our results extend several well known theorems of Barreira et al. (Ann Math 149:755–783, 1999) and Ledrappier and Young [Commun Math Phys 117(4):529–548, 1988] for diffeomorphisms to the case of endomorphisms.     

Rich dynamical behaviours for predator–prey model with weak Allee effect

The weak Allee effect on the predator is introduced into the classic predator–prey model of Lotka–Volterra type. Global qualitative and bifurcation analyses are combined to determine the global dynamics of the model. It is shown that the weak Allee effect can bring rich and complicated dynamics to the previous simple model, such as the saddle–node bifurcation, subcritical and supercritical Hopf bifurcations, and Bogdanov–Takens bifurcations, implying that weak Allee effect can be one of the simple reasons for many complicated behaviours in the predator–prey communities.     

Synthesis and characterization of ZnxHg1?xSeyS1?y quantum dots

This article describes the synthesis of highly water-soluble Zn _x Hg_1−x Se _y S_1−y quantum dots (QDs) in aqueous solution through a simple photo-assisted reaction between ZnSe QDs and mercury(I) nitrate dihydrate [Hg₂(NO₃)₂·2H₂O]. In order to deduce the optimal synthesis conditions, we varied several parameters, including the concentrations of mercaptosuccinic acid (MSA) and Hg₂(NO₃)₂·2H₂O, the illumination time, and the reaction temperature. When irradiated at temperatures below 80 °C, the ZnSe QDs reacted with the S²⁻ ions formed rapidly from MSA and the Hg²⁺ ions formed from Hg₂ ²⁺ ions to form Zn _x Hg_1−x Se _y S_1−y QDs through a process of photo-etching and surface combination. Under different conditions, we prepared a series of Zn _x Hg_1−x Se _y S_1−y QDs that emit fluorescence at the maximum wavelengths ranging from 405 to 760 nm. Inductively coupled plasma-mass spectrometry and transmission electron microscopy/energy dispersive spectrometry revealed that the content of Hg in the Zn _x Hg_1−x Se _y S_1−y QDs was greater when the synthesis was conducted at higher temperature. The Zn_0.88Hg_0.12Se_0.44S_0.56 QDs exhibit improved photostability than crude ZnSe QDs and possess long lifetimes (τ₁ ~ 38 ns and τ₂ ~ 158 ns).     

Numerical and experimental study of excited light and auto-fluorescence diffusion in teeth

Excited light and corresponding intrinsic fluorescence diffusion inside teeth tissue are an essential problem for light-based carious lesion detection. Based on finite element numerical analysis of diffusion equation, the photon density distribution of both excited light and autofluorescence of 2D premolar teeth model is obtained. The dependence of excited light and autofluorescence density distribution inside the teeth model on the scattering coefficient of enamel (5–25 mm⁻¹) and dentine (100–140 mm⁻¹) is numerically simulated and analyzed. The fitted results reveal that fluorescence intensity decreases exponentially. Optical penetration depth and fluorescence relative depth declined with the increment of scattering coefficient of enamel. And the dentine had the opposite effect. Finally, the experiment of measurement of fluorescence intensity on the teeth surface is conducted and the result is compared with the numerical computation.     

Sono-assisted preparation of highly-efficient peroxidase-like Fe3O4 magnetic nanoparticles for catalytic removal of organic pollutants with H2O2

Fe₃O₄ magnetic nanoparticles (Fe₃O₄ MNPs) with much improved peroxidase-like activity were successfully prepared through an advanced reverse co-precipitation method under the assistance of ultrasound irradiation. The characterizations with XRD, BET and SEM indicated that the ultrasound irradiation in the preparation induced the production of Fe₃O₄ MNPs possessing smaller particle sizes (16.5 nm), greater BET surface area (82.5 m² g^?1) and much higher dispersibility in water. The particle sizes, BET surface area, chemical composition and then catalytic property of the Fe₃O₄ MNPs could be tailored by adjusting the initial concentration of ammonia water and the molar ratio of Fe²⁺/Fe³⁺ during the preparation process. The H₂O₂-activating ability of Fe₃O₄ MNPs was evaluated by using Rhodamine B (RhB) as a model compound of organic pollutants to be degraded. At pH 5.4 and temperature 40 °C, the sonochemically synthesized Fe₃O₄ MNPs were observed to be able to activate H₂O₂ and remove ca. 90% of RhB (0.02 mmol L^?1) in 60 min with a apparent rate constant of 0.034 min^?1 for the RhB degradation, being 12.6 folds of that (0.0027 min^?1) over the Fe₃O₄ MNPs prepared via a conventional reverse co-precipitation method. The mechanisms of the peroxidase-like catalysis with Fe₃O₄ MNPs were discussed to develop more efficient novel catalysts.     

Nonparametric estimation of quantiles for a class of stationary processes

We study smoothed quantile estimator for a class of stationary processes. We obtain the convergency rates and the Bahadur representation, as well as the asymptotic normality for this estimator by the method of m-dependent approximation. Our results can be used in the study of the estimation of value-at-risk(Va R) and applied to many time series which have important applications in econometrics.     

一类SEI传染病扩散模型及其移动边沿

该文研究一类SEI传染病模型,其中病毒在潜伏期和感染期具有感染性.首先研究固定区域上SEI偏微分方程组,考虑平衡解的局部稳定性和全局稳定性.然后重点研究相应的自由边界问题,其中自由边界表示病毒的移动边沿。给出了该问题解的全局存在性、唯一性,讨论了自由边界的性质,证明了病毒要么蔓延,要么消退.还给出了蔓延和消退的充分条件,结果表明:当有效接触率很小或平均潜伏期较短,且初始染病区域小时,疾病消退;而当有效接触率大或平均潜伏期较长,且初始染病区域大时,疾病蔓延.