Representation of Integers by Ternary Quadric Forms

In this paper we give a formula for the number of representations of some square-free integers by certain ternary quadratic forms and estimate the lower bound of the 2-power appearing in this number. Supported by NSFC and RFDP.     

Molecular engineering leading to better processability of conjugated chromophores: The optical properties of new soluble copolymers containing alternative oligo-octylthiophene and oligo-methylene blocks

A series of conjugated/non-conjugated copolymers and their corresponding oligomers were prepared and their optical and physical properties were investigated for understanding the merit of blocking the conjugated chromophores with non-conjugated spacers. It was found that compared to the oligomers, copolymers have the advantages of amorphous nature, high thermal stability, and good thin film processability without sacrificing the quantum efficiency and purity of the emission color. Furthermore, based on the optical data of these copolymers and oligomers, the conjugation length of the polyoctylthiophene was estimated to be extended over 23-31 octylthiophene rings.     

Morphology manipulation of α-Fe2O3 in the mixed solvent system

By using simple mixed solvents, the morphologies of hematite (α-Fe₂O₃) particles could be manipulated, and the spherical, mulberry-like, nanospherical and top-like products could be controllably obtained. The as-obtained products were characterized by X-ray diffraction, scanning electron microscopy, and vibrating sample magnetometer. The results indicated that the morphology manipulation could be achieved by systematically adjusting the polarity of the mixed solvent via the ratio control. And the magnetic properties of the products were critically affected by their grain size and assembly morphologies.     

Quantum computation based on a quantum switch in cavity QED

A feasible scheme for constructing quantum logic gates is proposed on the basis of quantum switches in cavity QED. It is shown that the light field which is fed into the cavity due to the passage of an atom in a certain state can be used to manipulate the conditioned quantum logical gate. In our scheme, the quantum information is encoded in the states of Rydberg atoms and the cavity mode is not used as logical qubits or as a communicating “bus”; thus, the effect of atomic spontaneous emission can be neglected and the strict requirements for the cavity can be relaxed.     

GaAs中电子g因子的温度和能量依赖性的飞秒激光吸收量子拍研究

采用时间分辨椭圆偏振光抽运-探测光谱研究磁场作用下本征GaAs中电子自旋弛豫动力学，观察到吸收量子拍现象.这种吸收量子拍起源于电子自旋的拉莫尔进动，因而其拍频成为高精度测量电子g因子的一种新方法.利用这种新方法研究了本征GaAs中电子g因子的温度和能量依赖特性，发现g因子随电子的温度和能量增加而增加，但与k·p理论预测相差甚大.基于实验结果拟合，我们给出了一个g因子的温度和能量依赖的经验公式. 关键词： 椭圆偏振光抽运-探测光谱 自旋量子拍 g因子 GaAs     

Existence of nonzero solutions for a class of generalized variational inequalities

The existence of nonzero solutions for a class of generalized variational inequalities is studied by topological degree theory for multi-valued mappings in finite dimensional spaces and reflexive Banach space. One of the mappings concerned here is nonlinear with coercive or monotone and other is set-contractive or upper semi-continuous. Under some suitable assumptions, some existence theorems of nonzero solutions for this generalized variational inequalities are obtained. This work was supported by the Young Talent Foundation of Zhejiang Gongshang University and the Foundation of Department of Education of Zhejiang Province No. 20070628.