复赋范空间中的同时太阳集的最佳逼近

研究了复赋范空间中的同时太阳集对无穷序列的最佳逼近问题，得到了特征及唯一性定理．     

Dynamics of a small vibro-impact pile driver

A mathematical model is developed to study periodic-impact motions and bifurcations in dynamics of a small vibro-impact pile driver. Dynamics of the small vibro-impact pile driver can be analyzed by means of a three-dimensional map, which describes free flight and sticking solutions of the vibro-impact system, between impacts, supplemented by transition conditions at the instants of impacts. Piecewise property and singularity are found to exist in the Poincaré map. The piecewise property is caused by the transitions of free flight and sticking motions of the driver and the pile immediately after the impact, and the singularity of map is generated via the grazing contact of the driver and the pile immediately before the impact. These properties of the map have been shown to exhibit particular types of sliding and grazing bifurcations of periodic-impact motions under parameter variation. The influence of piecewise property, grazing singularities and parameter variation on the performance of the vibro-impact pile driver is analyzed. The global bifurcation diagrams for the impact velocity of the driver versus the forcing frequency are plotted to predict much of the qualitative behavior of the actual physical system, which enable the practicing engineer to select excitation frequency ranges in which stable period one single-impact response can be expected to occur, and to predict the larger impact velocity and shorter impact period of such response.     

Optimal harvesting for an age-dependent <Emphasis Type="Italic">n</Emphasis>-dimensional food chain model

This paper is concerned with optimal harvesting policy for an age-dependent n-dimensional food chain model. The existence and uniqueness of non-negative solution of the system are proved using the fixed point theorem. By Mazur＇s theorem, the existence of optimal control strategy is demonstrated and optimality conditions derived by means of normal cone.     

Numerical study of optical properties of single silver nanobowtie with anisotropic topology

Optical properties of silver nanobowtie with anisotropic topology, which is separated with nanogap that is horizontal (Y direction) and vertical (Z direction) to the line between the two constituent triangles (i.e., the bowtie axis), are studied. A discrete dipole approximation (DDA) method is used to determine the extinction efficiency and the electric field (E-field) distribution, then the corresponding enhancement factor (EF) and the full width half maximum (FWHM) of the E-field are obtained and analyzed. Our results show that the wavelength of localized surface plasmon resonance (LSPR)-induced blue-shifts and the maximum EF decrease were observed with increasing gap size for the parallel polarized (Z-polarized) excitation. It is also found that the light spot at the “hot spot” in the gap becomes larger and deviates from the rectangular pattern with the increase of the gap in the Z direction (Z-gap), and the FWHM in the Z direction of the localized E-field in the gap broadens with either an increase in the gap in the Y direction (Y-gap) or the Z-gap. These behaviors are due to the decrease of the coupling efficiency of near-field plasmon coupling. In contrast, the wavelength of the LSPR and the maximum EF excited by the perpendicularly polarized (Y-polarized) light show less dependence on the gap size than that of the Y-polarized light. PACS  73.20.Mf; 78.67.-n     

Convergence Results of the ERM Method for Nonlinear Stochastic Variational Inequality Problems

This paper considers the expected residual minimization (ERM) method proposed by Luo and Lin (J. Optim. Theory Appl. 140:103–116, 2009) for a class of stochastic variational inequality problems. Different from the work mentioned above, the function involved is assumed to be nonlinear in this paper. We first consider a quasi-Monte Carlo method for the case where the underlying sample space is compact and show that the ERM method is convergent under very mild conditions. Then, we suggest a compact approximation approach for the case where the sample space is noncompact. This work was supported in part by Project 10771025 supported by NSFC and SRFDP 20070141063 of China.     

High-power passive mode-locking of a diode pumped Yb:GdVO4 laser

Passive mode-locking of a diode pumped Yb-doped GdVO₄ crystal laser was demonstrated for the first time to our knowledge. The laser was mode-locked at the wavelength of 1019.1 nm and had an average output power of 1.01 W. The mode-locked pulse duration was 3.1 ps. The laser was end-pumped by a high-power fiber pigtailed laser diode bar and the mode-locking was enabled by a semiconductor saturable absorber mirror (SESAM).     

超导芯截面形状对Bi-2223/Ag带Jc的影响

磁光图像显示Ｂｉ－２２２３／Ａｇ带材中单根超导芯的宽面两侧边缘分布有较大的超导电流密度，Ｂｉ－２２２３单根超导芯的横截面是纺锤形的，单位宽度上的横截面面积之比与电流密度在横截面上不同部分的分布之比相当，高的电流密度在单根超导芯两则的分布可能是由单芯横截面的形状引起的。     

Optimal control for a population dynamics with age-dependent and diffusion in a periodic environment

Here we consider the optimal harvesting problem for a periodic age-dependent population dynamics with diffusion. Namely, we investigate the model with periodic vital rates and a periodic forcing term that sustains oscillations. By using Mazur’s theorem, we demonstrate existence of solutions of the optimal control problem and by the conception of normal cone, we also obtain the first order necessary conditions of optimality for the problem. Our results extend some known criteria.