Higher-Dimensional KdV Equations and Their Soliton Solutions

A (2+1)-dimensional KdV equation is obtained by use of Hirota method, which possesses N-soliton solution, specially its exact two-soliton solution is presented. By employing a proper algebraic transformation and the Riccati equation, a type of bell-shape soliton solutions are produced via regarding the variable in the Riccati equation as the independent variable. Finally, we extend the above (2+1)-dimensional KdV equation into (3+1)-dimensional equation, the two-soliton solutions are given.     

PS_(3000)-b-PAA_(5000)球形胶束温度效应的原位小角X射线散射技术研究

应用小角X射线散射技术(SAXS)对两亲嵌段共聚物聚苯乙烯聚丙烯酸(PS-b-PAA)胶束形貌的温度影响进行了原位表征.SAXS结果表明:随着水含量的增加,粒子尺寸相应增加;对于水含量10%的PS_(3000)-b-PAA_(5000)胶束溶液,发现了明显的SAXS双峰现象;双峰的位置不随着温度的变化而改变,但是peak 1和peak 2的相对强度随着温度发生了减弱和增强的交错变化;相邻的SAXS双峰说明在PS_(3000)-b-PAA_(5000)胶束溶液中最初形成的粒子尺寸并不是均匀的,主要分为尺寸极其相近的两种球形粒子;随着温度的升高,粒径大小不同的两种粒子存在着一种消融和生长的过程,并且保持着一个相同的归一化动态平衡速率.     

Can contributions to B_s→l＋l-γ from the magnetic-penguin operator with real photons in the standard model be neglected？

Using the Bs meson wave function extracted from non-leptonic Bs decays, we reevaluate the rare decays Bs→l＋l- γ,（l=e,μ） in the Standard Model, including two kinds of contributions from the magnetic-penguin operator with virtual and real photons. We find that contributions to the exclusive decays from the magnetic-penguin operator b→sγ with real photons, which were regarded as negligible in the previous literature, are large and the branching ratios Bs→l＋l-γ are enhanced by a factor of almost 2. With the predicted branching ratios of the order of 10-8, it is expected that these radiative dileptonic decays will be detected in LHC-b and B factories in the near future.     

New 3-mode bosonic operator realization of SU（2） Lie algebra： From the point of view of squeezing

We consider the quantum mechanical SU(2) transformation e2λ JzJ± e-2λJz= e±2λJ± as if the meaning of squeezing with e±2λbeing squeezing parameter. By studying SU(2) operators(J±,Jz) from the point of view of squeezing we find that(J±,Jz) can also be realized in terms of 3-mode bosonic operators. Employing this realization, we find the natural representation(the eigenvectors of J+ or J-) of the 3-mode squeezing operator e2λ Jz. The idea of considering quantum SU(2) transformation as if squeezing is liable for us to obtain the new bosonic operator realization of SU(2) and new squeezing operators.     

锁相检测式二维小角度测量装置

介绍了一种新型的二维小角度检测装置。由于该装置采用了光电自准直结构,以高灵敏度的四象限硅光电探测器作为检测元件,采用交流调制,锁相放大的方法对信号进行了处理,所以有效地消除了直流漂移的影响,提高了稳定性和测试精度。分析了光斑的形状和大小对测试结果的影响,研制了专门的标定装置。首先由高精度的光电自准直仪标定测量角度与输出信号的关系,并将相关数据存入单片机,然后由软件拟合出关系曲线。测量时,既可自动显示角度的大小,同时也可以与计算机相连。该测试系统结构小巧,具有较高的测量精度。     

A class of nonlinear relativistic partial differential equations in elementary particle theory

In mathematical approaches to elementary particle theory, the equation [² - ²/t²]=m² ;+g ³ has been of interest [1,2]; it describes a quartically self-coupled neutral scalar meson field. This paper applies the decomposition method [3-6] to obtain accurate non-perturbative timedevelopment of the field for this equation, or variations involving other nonlinear interactions, without the use of cutoff functions or truncations.     

Geometric phase as a simple closed-form integral

For a general evolution of a quantal system, the geometric phase measured with reference to a given initial state is derived as an integral of a function of the pure state density operator by invoking the Pancharatnam connection continuously.     

Oh型分子三重简并态Hamiltonian算符的研究

本文应用群论原理及不可约张量性质，详细推导了Ｏｈ型分子三重简并态Ａｍａｔ－Ｎｉｅｌｓｅｎ方案中精确到四级的Ｈａｍｉｌｔｏｎｉａｎ算符，为Ｏｈ型分子精细结构理论和光谱的进一步研究做了数学上的准备。     

The Ablowitz–Ladik hierarchy integrability analysis revisited: the vertex operator solution representation structure

A regular gradient-holonomic approach to studying the Lax type integrability of the Ablowitz–Ladik hierarchy of nonlinear Lax type integrable discrete dynamical systems in the vertex operator representation is presented. The relationship to the Lie-algebraic integrability scheme is analyzed and the connection with the τ-function representation is discussed.     

对《对重整热力学第二定律理论体系的不同看法》一文的补正

对笔者在《大学物理》2002年第8期上发表的《对重整热力学第二定律理论体系的不同看法》一文的错误之处进行了补正.