Non-Lie Symmetry Groups of (2+1)-Dimensional Nonlinear Systems

A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physics systems. Applying the modified direct method to the well-known (2 1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equation and Nizhnik-Novikov-Vesselov equation, both the Lie point symmetry groups and the non-Lie symmetry groups are obtained. The Lie symmetry groups obtained via traditional Lie approaches are only special cases. Furthermore, the expressions of the exact finite transformations of the Lie groups are much simpler than those obtained via the standard approaches.     

New Type of Conserved Quantities of Lie Symmetry for Nonholonomic Mechanical Systems in Phase Space

The new types of conserved quantities, which are directly induced by Lie symmetry of nonholonomie mechanical systems in phase space, are studied. Firstly, the criterion of the weak Lie symmetry and the strong Lie symmetry are given. Secondly, the conditions of existence of the new type of conserved quantities induced by the weak Lie symmetry and the strong Lie symmetry directly are obtained, and their form is presented. Finaily, an Appell-Hamel example is discussed to further illustrate the applications of the results.     

原子核中新的有效相互作用、新对称性及奇特核态

总结了近年来对奇特核和极端条件下核物质的研究结果,包括原子核的新有效相互作用、新对称性及奇特性质.在相对论平均场理论中,发现了反核子谱中的自旋对称性,提出了包含微观质心修正的新相互作用PK1,PK1r和PKDD?.这些新相互作用不但可以很好地描述核物质与中子星,还可以很好地给出靠近或远离β稳定线的原子核性质,包括中子滴线核与超核中的晕和巨晕现象.     

Symmetries of a (2+1)-Dimensional Toda-like Lattice

Lie group technique for solving differential-difference equations is applied to a new (2 1)-dimensional Toda-like lattice. An infinite dimensional Lie algebra and the corresponding commutation relations are obtained.     

单面完整约束力学系统的形式不变性

研究单面完整约束力学系统的形式不变性.根据运动微分方程的形式在无限小变换下的不变性，给出了单面完整约束力学系统形式不变性的定义和判据，建立了系统的形式不变性与Noether对称性、Lie对称性之间的关系，并举例说明结果的应用. 关键词： 分析力学 单面约束 形式不变性 Lie对称性 Noether对称性 守恒量     

基于量子系综的准自旋波激发的量子存贮研究

如何利用实际的物理系统存贮光子的量子信息，是当前量子计算和量子通信研究的核心问题之一，近几年来，人们从理论和实验两个方面探讨了利用自由原子系综作为量子记忆体的可能性，最近，基于固定于格点上A型“原子”系综的准自旋波激发的研究，我们提出了实现光子信息量子存贮的新方案，这个方案的目标是为了克眼自由原子系综量子存贮方案中存在的量子态漏损诱导退相干的致命问题，在研究过程中，作者发现了系综型量子记忆体中隐藏动力学的对称性和其绝热暗态演化的选择定则，为了使读者能确切地了解这个工作的意义，文章除了报道这个发表在Physical Review Letters(2003，91：147903)的研究工作外，还扼要地介绍这个方案建立的前期关于原子系综对称集体激发的系列工作。     

一类Mathieu对方程的分叉性和复杂性

用理论和数值计算方法对一类Mathieu方程进行了研究.发现该振动系统存在着广泛的周期分叉、混沌行为、对称性、“跳跃”现象、“放大”和“缩小”现象等一系列复杂的行为,并对调整系统参量以改变系统运动性态的问题作了初步的探讨.     

推广Burgers方程的对称性约化和奇性分析

将Burgers方程推广到一般形式U_1+U~(1/n)U_x十γU_(XX)=0后,我们利用Ablowita—Ramani—Segur方法研究了它的Painleve性质.该方程的所有对称性约化被得到.结果指出n=偶数和17的奇数模型的Painleve'性质需要进一步研究.     

Radial symmetry and monotonicity for an integral equation

In this paper we study radial symmetry and monotonicity of positive solutions of an integral equation arising from some higher-order semilinear elliptic equations in the whole space Rn. Instead of the usual method of moving planes, we use a new Hardy-Littlewood-Sobolev (HLS) type inequality for the Bessel potentials to establish the radial symmetry and monotonicity results.     

Influence of structural disorder on low-temperature behavior of penetration depth in electron-doped high-TC thin films

The results of Hall probe magnetic measurements in the vicinity of a DyBCO tape carrying transport or magnetization currents at 77 K were used in the inverse calculation to obtain the current distribution across the tape width. Two different methods of the inverse problem calculation were used and the results compared. The transport current applied in the absence of the external magnetic field was stepwise increased and the determined current distribution was compared with that predicted by Brandt and Indenbom. The predicted convex shape of the current distribution in the central tape section was proved. Contrary to the prediction, we have observed a drop of the current at the tape edges. This result supports the conclusions of the loss measurements in YBCO tapes [O. Tsukamoto, Supercond. Sci. Technol. 18 (5) (2005) 596]. We also mapped the magnetic field in the vicinity of the tape carrying induced magnetization currents in the absence of the transport current and determined the corresponding current distribution. Superposition of the self magnetic field and a homogeneous external magnetic field (36 mT) flattens the magnetization current distribution evidently.