Effect of electric field on the spectrum and the persistent current of a quantum ring with two electrons （II） additional effect of a charged impurity

This paper studies the effect of a charged impurity together with or without an external homogeneous electric field on a quantum ring threaded by a magnetic field B and containing two electrons. The potential caused by the impurity has been plotted which is helpful to the understanding of the electronic structures inside the ring. The deep valley appearing in the potential curve is the source of localization, which affects seriously the Aharonov-Bohm oscillation （ABO） of the energy and persistent current. It also causes the fluctuation of the total orbital angular momentum L of the pair of electrons. It is found that the appearance of the impurity reduces the domain of the fractional ABO. During the increase of B, the domain of the integral ABO may appear earlier when B is even quite small. The transition from the localized states to extended states has also been studied. Furthermore, it has deduced a set of related formulae for a transformation, by which an impurity with a charge ep placed at an arbitrary point Rp is equivalent to an impurity with a revised charge ep placed at the X-axis with a revised radial distance Rp. This transformation facilitates the calculation and make the analysis of the physical result clearer.     

H1（RN）上带限制的椭圆特征问题的三个解

用变分方法证明H~1（R~N）上一个带限制的半线性椭圆特征问题解的存在性.所获得的三个解：一个是正解,一个是负解.对于第三个解,本文只证明了它的存在性,而没有确定它是正解,负解,还是变号解.     

On an over-determined problem of free boundary of a degenerate parabolic equation

This work is concerned with the inverse problem of determining initial value of the Cauchy problem for a nonlinear diffusion process with an additional condition on free boundary. Considering the flow of water through a homogeneous isotropic rigid porous medium, we have such desire: for every given positive constants K and T ₀, to decide the initial value u ₀ such that the solution u(x, t) satisfies $\mathop {\sup }\limits_{x \in H_u (T_0 )} |x| \geqslant K$ , where H _u(T ₀) = {x, ?^N: u(x, T ₀) > 0}. In this paper, we first establish a priori estimate u _t ? C(t)u and a more precise Poincaré type inequality $\left\| \phi \right\|_{L^2 (B_\varrho )}^2 \leqslant \varrho \left\| {\nabla \phi } \right\|_{L^2 (B_\varrho )}^2 $ , and then, we give a positive constant C ₀ and assert the main results are true if only $\left\| {u_0 } \right\|_{L^2 (\mathbb{R}^N )} \geqslant C_0 $ .     

一类非线性抛物方程Cauchy问题解的存在性条件

研究了带源项的非线性抛物方程Cauchy问题解存在的必要条件以及解所应具有的性质,通过把文献中的线性算子推广到形式较一般的带源项的非线性抛物算子,利用其中处理线性问题的方法来处理非线性问题．     

具有线性脉冲的周期捕食系统的持久性

研究具有HollingIV功能性反应和脉冲的周期捕食食饵系统．找到了影响该系统动力学行为的阈值Ro．证明了当Ro〈1时,该系统的食饵灭绝周期解是局部渐近稳定的;当R0〉1时,该系统的食饵灭绝周期解变得不稳定且食饵将一致持久．     

Preparation and Fluoroimmunoassay Application of New Red-Region Fluorescent Silica Nanoparticles

This is the first report on the preparation and utilization of a novel red-region fluorescent dye (tetracarboxy aluminum phthalocyanine) doped silica nanoparticles. In these nanoparticles, the tetracarboxy aluminum phthalocyanine molecules were covalently bound to silica matrix to protect the dye leaking from nanoparticles in bio-applications. The surface of the nanoparticles was modified by amino groups and easily bioconjugated with goat anti-human IgG antibody. By employing these nanoparticles as fluorescent probe, a sensitive fluoroimmunoassay method has been developed for the determination of trace level of human IgG. The calibration graph for human IgG was linear over the range of 0–500 ng mL⁻¹ with a detection limit of 1.6 ng mL⁻¹. Compared with the corresponding system using free AlC₄Pc as a probe for determining human IgG, the sensitivity of the proposed system was notably increased. The method was applied to the analysis of human IgG in human sera with satisfactory results.     

阳离子交换树脂富集-流动注射-冷原子荧光光谱法测定环境水样中痕量汞

提出了用阳离子交换树脂富集环境水样中痕量汞,用流动注射-冷原子荧光光谱法测定其中汞的含量。对阳离子交换柱的制备、富集时间、介质及洗脱剂的酸度等分析条件做了试验并予以优化。汞的质量浓度在40 ng.L-1以内与其荧光强度呈线性关系,方法的检出限(3s)为0.13 ng.L-1。应用此法对环境水样进行分析,并以此样品为基体作回收试验,测得汞的回收率在72.5%~101.3%之间。     

‐type stability criteria in division regions for multitime‐scale networks with delays

This paper is concerned with new results on ‐type stability criteria in division regions for competitive neural networks with different time scales. Under the decomposition of state space, both the neural activity levels (the short‐term memory) and the synaptic modifications (the long‐term memory), are taken into account in constructing division regions that allow the coexistence of equilibrium points. Meanwhile, novel delay‐dependent multistability and monostability criteria are established in division regions that depend on divisions in index set of neurons and boundedness of unsupervised synaptic variables. The attained results show the effects of self‐interactions of neurons and Hebbian learning behavior on the multistable convergence of the networks. Finally, numerical simulations will illustrate multistable neuron activity and synaptic dynamics of multitime‐scale competitive networks. Copyright © 2011 John Wiley & Sons, Ltd.     

Harnack Estimates for Weak Solutions to a Singular Parabolic Equation

By an interpolation method, an intrinsic Harnack estimate and some supestimates are established for nonnegative solutions to a general singular parabolic equation.