Optimal Convergence Rates of Classical Solutions for Vlasov-Poisson-Boltzmann System

The dynamics of charged dilute particles can be modeled by the two species Vlasov-Poisson-Boltzmann system when the particles interact through collisions in the self-induced electric field. By constructing the compensating function for multi-species particle system, the optimal time decay of global classical solutions to this system near a global Maxwellian is obtained through a refined energy method.     

Synthesis of water-dispersible photoluminescent silicon nanoparticles and their use in biological fluorescent imaging

Water-dispersible silicon nanoparticles (Si-NPs) are desirable for applications in biological techniques. A simplified method to synthesize such particles is reported here. The resulting Si-NPs are water-dispersible and luminescent. Under the excitation of UV light, the Si-NPs emit strong red light with a peak maximum at 606 nm and a quantum yield of 6%. They are highly stable, and remain so over several weeks. Fourier Transform Infrared (FTIR) spectroscopy shows a visible Si–CH₂ scissoring vibration mode. Furthermore, the surface chemical bondings were confirmed by X-ray photoelectron spectroscopy (XPS). In the Si2p and C1s core levels, Si–C components are observed. The diameters of the synthesized Si-NPS as measured by atomic force microscope (AFM) are approximately 5 nm. Furthermore, the nanoparticles can be taken up by cultured cells. Fluorescence images of Si-NPs within MCF-7 human breast cancer cells show they are distributed throughout the cell tissue.     

An attractor for the singularly perturbed Kirchhoff equation with supercritical nonlinearity

We consider a quasilinear wave equation of Kirchhoff type

?_utt−(1+‖∇u‖²)Δu+_ut+f(u)=g(x),$?u_{tt}-(1+{\Vert \mathrm{\nabla }u\Vert }^2)\mathrm{\Delta }u+u_t+f(u)=g(x),$

where ?>0$?>0$ is a small parameter. Without any growth restrictions on the nonlinearity f(u)$f(u)$, we prove the existence of a finite-dimensional global attractor on an appropriate (bounded) phase space. The key step is the estimate of the difference between the solutions of a quasilinear dissipative hyperbolic equation of Kirchhoff type and the corresponding quasilinear parabolic equation.     

塑化剂迁移量测定和迁移模型研究进展

综述国内外塑化剂迁移量测定和迁移模型研究进展,从创新实验测定方法和实验误差分析的角度简要评述了迁移量测定的研究成果;从数学模型的角度对微分方程模型、统计模型和计算机模拟3类重要迁移模型进行评述。最后指出,测定实验和迁移模型相结合来研究塑化剂迁移问题是未来一个值得重视的方法。     

特大容积滑冰馆的扩声

介绍一个体积约３６００００ｍ＾３左右，８０００－１００００座的特大型滑冰馆的扩声设计及竣工测量结果。     

Design and application of feedback-sustained target waves in excitable medium

In this paper, we present a formulas of rational ratios between the frequency of external stimulus and its paced target waves, considering the existence of the absolute refractory period and the relative refractory period. Based on this, we design a self-sustained high-frequency target waves by feeding back few periphery field points to the center to responsibly play the role of source for pacemaker. Such constructed target waves, to all appearances, are shown as a repetition of their initial condition. We explore further in application that those feedback-sustained targets can eliminate both a freely rotating spiral waves and a pinned ones only if frequencies, feedback lengths and radius of obstacles are appropriately chosen. After feedback stimuli are removed, the system eventually returns to the rest state.     

一类带有非线性源并以有限Borel测度为初值的非线性双曲方程的BV解

主要考虑以有限Borel测度为初值的非线性双曲方程的Cauchy问题ut (um)x=up,其中0＜m＜1,0＜p≤m是给定常数.特别地,得到了上述问题BV解的存在性.     

Mathematica软件在函数图形绘制及特性分析中的应用

函数图形绘制及其特性分析在科学研究中具有重要的地位,利用Mathematica软件强大的绘图功能,从多元函数的极限、梯度场、重积分的定义、重积分计算中的定限、柱面坐标系和球面坐标系的几何解释等方面探讨利用Mathematica软件平台进行三维图形绘制和特性分析的方法,有助于提高数学分析能力和解决综合应用问题的能力。