AN ESTIMATE ON THE DISTRIBUTION AND MOMENTS OF THE LAST EXIT TIME OF AN ELLIPTIC DIFFUSION PROCESS

Let LB be the last exit time from a compact set B of an elliptic diffusion process X. A moderate estimate for the distribution of LB is obtained, and the sufficient and necessary condition for Ex(LBk)<∞is proved.     

复合结构丝中的电流密度分布和巨磁阻抗效应

提出了由中间为高电导率的非铁磁性金属丝外面包裹一层铁磁材料组成的复合结构丝的电流 密度分布和巨磁阻抗(GMI)效应模型，并对Cu/FeCoNi复合丝进行了数值模拟. 结果表明：在 相同的磁性材料几何尺寸和磁特性时，Cu/FeCoNi复合丝铁磁层内的电流随频率的升高比匀 质FeCoNi铁磁丝内的电流更趋于表面分布，而且开始出现趋肤效应时对应的频率明显降低. 当在比较低的频率下就可以观察到明显的MI变化时，复合结构丝中的电阻和电抗变化主要是 由趋肤效应引起，趋肤效应仍然是引起复合结构材料(包括多层薄膜结构) 关键词： 电流密度 巨磁阻抗效应 趋肤效应     

Ab initio calculations of accurate dissociation energy and analytic potential energy function for the second excited state B1∏ of 7LiH

The reasonable dissociation limit of the second excited singlet state B¹∏ of ⁷LiH molecule is obtained. The accurate dissociation energy and equilibrium geometry of the B¹\Pi state are calculated using a symmetry-adapted-cluster configuration--interaction method in full active space. The whole potential energy curve for the B¹∏ state is obtained over the internuclear distance ranging from about 0.10nm to 0.54nm, and has a least-square fit to the analytic Murrell--Sorbie function form. The vertical excitation energy is calculated from the ground state to the B¹∏ state and compared with previous theoretical results. The equilibrium internuclear distance obtained by geometry optimization is found to be quite different from that obtained by single-point energy scanning under the same calculation condition. Based on the analytic potential energy function, the harmonic frequency value of the B¹∏ state is estimated. A comparison of the theoretical calculations of dissociation energies, equilibrium interatomic distances and the analytic potential energy function with those obtained by previous theoretical results clearly shows that the present work is more comprehensive and in better agreement with experiments than previous theories, thus it is an improvement on previous theories.     

动态广义球对称含荷黑洞的统计熵

利用改进了的brickwall膜模型,计算了动态广义球对称含荷黑洞的熵,研究结果表明,对于动态黑洞,将黑洞熵表示为与视界面积成正比时,则比例系数总与动态黑洞的视界速度有关 关键词： 广义球对称黑洞 黑洞熵 brick-wall膜模型 WKB近似     

Kerr介质中"耦合双原子-单模光场"模型的反聚束效应

利用全量子理论,研究了在Kerr介质中,耦合二能级双原子与单模光场相互作用过程的反聚束效应,着重讨论了Kerr介质对场的二阶相干度的影响,并揭示了初始场强及原子间耦合系数的变化与场的二阶相干度的关系。     

分离变量法与等腰直角三角形波导的边值问题

根据叠加原理，讨论等腰直角三角形波导边值问题的IE波解和TM波解，纠正有关文献中的错误解法，指出分离变量法的适用条件。     

A remark on the mild solutions of non-local evolution equations

We provide a counterexample to some recent publications concerning the existence of the mild solutions of the non-local evolution equations, and indicate that in the study of the non-local evolution equations, the operators from which the mild solutions may be derived are in general not compact, thus those fixed point theorems requiring the compactness of the operators are not applicable.     

Synthesis,Functionalization, and Bioconjugation of Monodisperse,Silica‐Coated Gold Nanoparticles: Robust Bioprobes

Herein, we report an efficient process for preparing monodisperse Au@SiO₂ nanoparticles using homogeneous shaking and without the use of surface‐coupling silane agents or large stabilizers. The resulting pure‐silica surface of the Au@SiO₂ nanoparticles is very important for straightforward surface functionalization with different functional groups via well‐established silica surface chemistry. Subsequent covalent bioconjugation of the aldehyde‐functionalized Au@SiO₂ nanoparticles with various biomolecules is successfully employed to make robust nanoprobes for fast, colorimetric DNA and protein detection based on the sequence‐specific hybridization properties of DNA and the specific binding affinity between proteins, respectively.     

Photorefractive shearing interferometer

A novel method of obtaining shearing interferogram by slightly moving the crystal in a photorefractive interferometer is proposed. This method can measure the phase of an object itself instead of its diffraction field, and it is easy to realize continuously changeable shearing distance in any lateral direction and introduce carrier fringes at the same time. Both the theoretical analysis and experimental verification are given.     

一类具无穷时滞泛函微分方程的周期解

讨论具有无穷时滞中立型泛函微分方程$ \frac{\rm d}{{\rm d}t}\left(x(t)-\int_{-\infty}^{0}g(s,x(t+s)){\rm d}s\right) =A(t,x(t))x(t)+f(t,x_t)$的周期解问题,利用重合度理论中的延拓定理得到了周期解的存在性和唯一性条件;特别地,当$g(s,x)\equiv 0, A(t,x)=A(t)$时, 给出了存在唯一稳定周期解的条件.