Bäcklund transformations and abundant exact explicit solutions of the Sharma-Tasso-Olver equation

By using an extension of the homogeneous balance method and Maple, the Bäcklund transformations for the Sharma-Tasso-Olver equation are derived. The connections between the Sharma-Tasso-Olver equation and some linear partial differential equations are found. With the aid of the transformations given here and the computer program Maple 12, abundant exact explicit special solutions to the Sharma-Tasso-Olver equation are constructed. In addition to all known solutions re-deriving in a systematic way, several entirely new and more general exact explicit solitary wave solutions can also be obtained. These solutions include (a) the algebraic solitary wave solution of rational function, (b) single-soliton solutions, (c) double-soliton solutions, (d) N-soliton solutions, (e) singular traveling solutions, (f) the periodic wave solutions of trigonometric function type, and (g) many non-traveling solutions. By using the Airy’s function and the Bäcklund transformations obtained here, the exact explicit solution of the initial value problem for the STO equation is presented. The variety of the structure of the solutions for the Sharma-Tasso-Olver equation is illustrated.     

膜结构找力分析的无矩理论和优化的复位平衡法

膜结构工程的实践和形状确定理论要求对膜结构进行找力分析。本文结合无矩理论推导了膜结构自平衡预应力确定的解析方程,研究表明膜结构自平衡预应力由膜曲面的特性和边界条件决定。根据相似原理提出了索膜结构找力分析的数值方法——复位平衡法,并且依据曲面上单元之间的关联对这种方法进行了优化。与无矩理论的计算结果比较显示优化的复位平衡法有很高的计算精度,能够应用到实际工程的精确分析中。     

Gerdjikov-Ivanov方程的精确解

研究在量子场理论、弱非线性色散水波、非线性光学等领域中出现的Gerdjikov-Ivanov方程.对Gerdjikov-Ivanov方程的研究会导出具有高次非线性项的非线性数学物理方程.选取Liénard方程作为辅助常微分方程,借助于它并根据齐次平衡原则,求解了Gerdjikov-Ivanov方程,得到了该方程的包络孤立波解和包络正弦波解. 关键词： 齐次平衡原则 F展开法 Gerdjikov-Ivanov方程 包络孤立波解     

量子点接触对单电子量子态的量子测量

研究了用介观量子点接触(QPC)对单电子两态和多态系统的量子测量问题.发现,在任意测量电压下,该测量问题不能用标准的Lindblad量子主方程描述.考虑了测量仪器和被测系统之间的能量交换对细致平衡关系的影响,对该问题提供了一个恰当的理论描述,并对未来的固态量子测量和量子反馈控制可能产生一定影响. 关键词： 量子测量 量子比特 细致平衡 退局域化     

变系数(2+1)维Broer-Kaup方程的精确解

利用齐次平衡原则,导出了变系数(2+1)维Broer-Kaup方程的B?cklund变换(BT),并由该BT,求出了(2+1)维Broer-Kaup方程的各种形式的精确解.     

Remarks on the Balance Relations for the Two-Dimensional Navier–Stokes Equation with Random Forcing

We use the balance relations for the stationary in time solutions of the randomly forced 2D Navier-Stokes equations, found in [10], to study these solutions further. We show that the vorticity ξ(t,x) of a stationary solution has a finite exponential moment, and that for any the expectation of the integral of over the level-set , up to a constant factor equals the expectation of the integral of over the same set.     

基于一种新型杂化阳极修饰层的高效有机电致发光器件

设计了基于Bphen∶LiF、Al和MoO₃的杂化电荷注入层,并将其应用于有机电致发光器件中。实验研究表明,这种杂化层作为阳极修饰层是非常有效的,它可以增加器件中载流子注入的平衡性,提高器件的性能。相对参考器件,基于杂化阳极修饰层的电致发光器件的最大电流效率和最大功率效率均提高1.3倍左右。我们对器件性能及其提高的机理进行了分析。     

Natural color low-level-light EBAPS imaging system based on three-color LCTF北大核心CSCD

The high-sensitivity electron bombarded active pixel sensor (EBAPS) not only has the characteristics of high gain and high sensitivity of vacuum imaging devices, but also has the digital characteristics of solid-state imaging devices, which greatly improves the level of night vision imaging. A natural color low-level-light EBAPS imaging system was built based on three-color liquid crystal tunable filter (LCTF). According to the characteristics of low-level-light images, the color enhancement processing such as grayscale stretching, white balance, and color correction was performed on the color images obtained by the system. The experimental results show that the system can realize the natural low-illumination color imaging that reflects the color characteristics of the scene itself, which can effectively improve the observation effect of the characteristics of the target scene at night, and can realize the color imaging under 5×10−4 lx illumination. © 2022 Editorial office of Journal of Applied Optics. All rights reserved.     

对FD-GLB-Ⅱ型新型焦利氏秤的改进

对FD-GLB-Ⅱ型新型焦利氏秤做了改进,改进后的振子质量可变,很好的满足了实验教学中对弹簧阵子简谐振动关系式的验证要求.     

Quantum-classical correspondence for motion on a plane with deficit angle

A particle constrained to move on a cone and bound to its tip by harmonic oscillator and Coulomb-Kepler potentials is considered both in the classical as well as in the quantum formulations. The SU(2) coherent states are formally derived for the former model and used for showing some relations between closed classical orbits and quantum probability densities. Similar relations are shown for the Coulomb-Kepler problem. In both cases a perfect localization of the densities on the classical solutions is obtained even for low values of quantum numbers.