Pseudo-monotone complementarity problems in Hilbert space

In this paper, some existence results for a nonlinear complementarity problem involving a pseudo-monotone mapping over an arbitrary closed convex cone in a real Hilbert space are established. In particular, some known existence results for a nonlinear complementarity problem in a finite-dimensional Hilbert space are generalized to an infinite-dimensional real Hilbert space. Applications to a class of nonlinear complementarity problems and the study of the post-critical equilibrium state of a thin elastic plate subjected to unilateral conditions are given.This research was partially supported by the National Science Foundation Grant DMS-89-13089, Department of Energy Grant DE-FG03-87-ER-25028, and Office of Naval Research Grant N00014-89-J-1659. The authors would like to express their sincere thanks to Professor S. Schaible, School of Administration, University of California, Riverside, for his helpful suggestions and comments. They also thank the referees for their comments and suggestions that improved this paper substantially.     

平面Laplace问题的等价间接变量边界积分方程

利用变分法证明平面调和函数的外问题的确切形式；在此基础上，建立外问题的具有间接变量的等价边界积分方程；传统的外问题及边界积分方程不具有普遍适用性，本文对此进行了详细的讨论．     

Cd3Al2Ge3O12:Mn2+锗酸盐石榴石光谱性质

本文报道室温下Cd₃Al₂Ge₃O₁₂:Mn²⁺(简称CAGG:Mn²⁺)锗酸盐石榴石的漫反射光谱、激发和发射光谱.在UV光激发下,在CAGG中Mn²⁺离子发射强黄光,这是基质到Mn²⁺离子无辐射能量传递的结果.Mn²⁺的黄发射带是由一个弱的红带和一个强的绿带所组成.讨论了这两个Mn²⁺发射带的起因.     

Quantum HeisenbergS=1/2 spin glass with ferromagnetic coupling and random Dzyaloshinskii-Moriya interactions

By means of the generalized static replica symmetric spin glass theory, a quantum HeisenbergS=1/2 spin glass model with the infinite-ranged random Dzyaloshinskii-Moriya (DM) interaction and ferromagnetic coupling is investigated. The dependence of entropy, specific heat, susceptibility and the corresponding order parameters on temperature is studied numerically for different ferromagnetic interactions and fixed anisotropy. Two spin glass phases has been found including transverse and mixed spin glass phases. It has been shown that the local susceptibility exhibits double-cusp features for different ferromagnetic coupling (J ₀). Phase transition poins are found in the specific heat-temperature plane at various ferromagnetic coupling values. Additionally, the dependence of the spontaneous moment on temperature is calculated.     

光子扫描隧道显微镜的光电成像系统研究

本文论述了光子扫描隧道显微镜（ＰＳＴＭ）的显微成像机理、成像规律，针对具体的物理模型进行数值模拟计算，并得到了与实际探测相一致的场分布规律。采用自行研制的光子扫描隧道显微镜（ＰＳＴＭ）的显微实验系统对多种样品进行了表面显微成像研究，获得了关于样品表面三维立体图像信息，通过多种图像处理手段对原始图像进行后期处理，得到了更具视觉效果、更为逼真的样品表面图像。     

Equilibrium Problems with Applications to Eigenvalue Problems

In this paper, we consider equilibrium problems and introduce the concept of (S)₊ condition for bifunctions. Existence results for equilibrium problems with the (S)₊ condition are derived. As special cases, we obtain several existence results for the generalized nonlinear variational inequality studied by Ding and Tarafdar (Ref. 1) and the generalized variational inequality studied by Cubiotti and Yao (Ref. 2). Finally, applications to a class of eigenvalue problems are given.     

Polarimetric-Spectral-Sensitive Compressed Ultrafast Photography Enables Real-Time Intensity Visualization of Time-Varying Polarized Ultrafast Laser Pulses

Ultrafast laser pulses with complex spatiotemporal and polarization couplings have shown great application prospects in coherent control, particle acceleration, molecular dynamics excitation, and chiral or anisotropic detection. It is very important to observe the polarization-coupled ultrafast laser pulses for characterizing the performance of laser source and understanding the laser-matter interaction, but there is currently no detection technique that can completely characterize them, including the spatio-, spectral-, and polarimetric-temporal information. In this work, a polarimetric-spectral-sensitive has been compressed ultrafast photography (PS-CUP) to realize the real-time intensity visualization of time-varying polarized (TP) ultrafast laser pulses. PS-CUP can not only distinguish the polarization state of a TP pulse, but also realize the spatio-, spectral- and polarimetric-temporal measurement. To demonstrate the ability of polarization resolving detection, PS-CUP is used to successfully distinguish between the sinistral and dextral TP pulses and measure the angle and degree of linear polarization of a dextral TP pulse, respectively, and the experimental results are highly consistent with theoretical simulations. Owing to the unprecedented multidimensional detection ability, PS-CUP is prospected to provide a powerful tool for the diagnosis of various complex ultrafast laser pulses and the detection of ultrafast chiral optics.     

Enhanced Terahertz Phonon Polariton in Lithium Niobate Chip

Terahertz (THz) phonon polaritons, fundamental quasi-particles that couple lattice vibrations with electromagnetic fields at THz frequencies, are found in a variety of materials that offer the potential for a wide range of THz optoelectronic devices and on-chip integrated systems. However, these compact devices and on-chip systems are hampered by the absence of on-chip powerful THz phonon polariton sources. In this study, the efficient generation and amplification of THz phonon polaritons are proposed and directly visualized on a lithium niobate (LN) chip via a tilted pulsefront phase matching technique. By combining lateral pumping and phase matching schemes, two orders of magnitude are successfully attained in the interaction distance between the pump light and the LN chip, accompanied by a substantial amplification of generated THz phonon polariton. The results of this study may lead to abundant potential applications in chip scale THz photonic devices and systems based on LN materials and its integrated heterostructures.     

矩阵方程AXB=D的最小二乘Hermite解及其加权最佳逼近

本中,我们讨论了矩阵方程AXB=D的最小二乘Hermite解,通过运用广义奇异值分解(GSVD)，获得了解的通式。此外,对于给定矩阵F，也得到了它的加权最佳逼近表达式。     

TWO ENTIRE FUNCTIONS SHARING FOUR SMALL FUNCTIONS IN THE SENSE OF _(k))(β,f)=_(k))(β,g)

This paper proves a result that if two entire functions f(z) and g(z) share four small functions aj(z) (j = 1,2,3,4) in the sense of Ek)(aj, f) = Ek)(aj,g), (j = 1,2,3,4) (k ≥ 11), then there exists f(z) = g(z).