Local field distribution and configuration of CO molecules adsorbed on the nanostructure platinum surface

This paper shows that the local electric field distribution near the nanostructure metallic surface is obtained by solving the Laplace equation, and furthermore, the configuration of CO molecules adsorbed on a Pt nanoparticle surface is obtained by using Monte Carlo simulation. It is found that the uneven local electric field distribution induced by the nanostructure surface can influence the configuration of carbon monoxide (CO) molecules by a force, which drags the adsorbates to the poles of the nanoparticles. This result, together with our results obtained before, may explain the experimental results that the nanostructure metallic surface can lead to abnormal phenomena such as anti-absorption infrared effects.     

关于一类拟线性退化抛物方程

对拟线性退化抛物方程θ_(xx)u uθ_yu-θ_tu=f(·,u)进行了研究,得到了在[O,T]×Ω上的初边值问题解的存在唯—性,这里要求T充分小．     

Numerical Simulations of femtosecond-laser-induced dynamic alignment of molecules in the high-frequency off-resonance regime

The motion equation for ? between the molecular axis and laser polarization direction in a high-frequency off-resonance femtosecond laser field is deduced while simultaneously examining the effects of a permanent dipole moment and field-induced polarizability and hyperpolarizability to molecular rotation. Femtosecond-laser-induced dynamic alignment of CO, N₂, and Br₂ molecules are investigated by numerically solving the obtained rotation equation for the angle ?. The effects of the molecular permanent dipole moment and the field-induced polarizability and hyperpolarizability on the degree of alignment are presented at different intensities. Our computational results show that the dynamic alignment of molecules is primarily determined by field-induced polarizability and the second hyperpolarizability for the laser intensity range from 5 × 10¹⁴ to 5 × 10¹⁶ W/cm². The contributions of higher order correction terms to molecular alignment can usually be neglected. The polarizability-field interaction makes the angular distributions of a molecule have a maximum along the polarization axis and a minimum perpendicular to it. The role of the second hyperpolarizability keeps the molecular counts maximum along the laser polarization direction but minimum at an angle of 45° between the molecular axis and the polarization direction. There is also a second maximum of molecular counts perpendicular to the polarization axis. For CO, N₂, and Br₂ molecules, the dependences of laser-induced dynamic alignment on laser intensity exhibit completely different characteristics.     

A NEW APPROACH TO SOLVE PERTURBED NONLINEAR EVOLUTION EQUATIONS THROUGH LIE-BACKLUND SYMMETRY METHOD

A new method based on Lie-Backlund symmetry method to solve the perturbed nonlinear evolution equations is presented. New approximate solutions of perturbed nonlinear evolution equations stemming from the exact solutions of unperturbed equations are obtained. This method is a generalization of Burde＇s Lie point symmetry technique.     

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.