三角代数上的零点Lie高阶可导映射

研究了三角代数上在零点Lie高阶可导映射的结构,证明了三角代数上的每一个零点Lie高阶可导映射可表示为高阶导子与中心值映射之和.     

一类空间中高阶微分的性质

 对具有Schauder基的无穷维Banach空间上的映射定义高阶偏导数,讨论其高阶微分与高阶偏导数的关系,并讨论映射的像所在空间为具有Schauder基的无穷维Banach空间时,这一映射与其坐标映射在高阶可微方面的关系.     

—简单非线性量子系统的WKB解

本文利用WKB方法导出了量子双共振系统的共振系数的解析式,其中正确选取量子化条件起到了重要作用。     

三角代数上Lie积为平方零元的非线性Jordan高阶可导映射

设U是一个 2-无挠的三角代数,D ={d_n}_n∈N是U上一个Lie积为平方零元的非线性Jordan高阶可导映射。证明了三角代数U上的每一个Lie积为平方零元的非线性Jordan高阶可导映射都是高阶导子。作为结论的应用,得到套代数或 2-无挠的上三角分块矩阵代数上的每一个Lie积为平方零元的非线性Jordan高阶可导映射都是高阶导子。     

三角代数上的零点(m,n)-高阶可导映射

用矩阵分解的方法证明了|mn(m+n)(m-n)|-无挠的三角代数上的每一个零点(m,n)-高阶可导映射都是高阶导子。作为此结论的应用,得到套代数或|mn(m+n)(m-n)|-无挠的上三角分块矩阵代数上的每一个零点(m,n)-高阶可导映射都是高阶导子。     

非线性高阶共振非局部边值问题

针对一类新的非线性n阶共振非局部边值问题,运用Mawhin重合度理论,研究了边值问题解的若干存在性结论.结果表明:通过建立Sobolev空间和Banach空间,构造指标为零的Fredholm算子和满足适当条件的线性连续映射及其格林函数,当非线性项满足线性增长性条件时,同样可以得到共振边值问题解的存在性.该结果丰富了非线性高阶共振边值问题定解理论的相关成果,为工程实际问题提供了理论依据.     

高能电子与磁场波纹共振作用的研究

托卡马克装置中逃逸电子的产生伴有很高能量的释放,有损装置第一壁材料的性能和寿命。在高能电子和磁场波纹发生共振的作用下,可发现在弱的电场下逃逸电子可以和高阶谐波发生共振从而将逃逸电子的能量极限限制在一定的低能量安全范围内。     

超光速RX模电磁波与磁层电子的二阶共振作用

扩展了现有的一阶波-粒相互作用的相对论模型.计算了一阶特别是二阶共振作用对电子的随机加速趋势:对于二阶回旋共振,RX模能有效地把电子能量从～10keV加速到～MeV的量级,其加速范围可涵盖磁层的大部分区域和波的大传播角.相反,对于一阶回旋共振,RX模对电子的加速效应有限,且局限于小传播角范围,如<10°.这表明:对于非平行RX模,一阶以上高阶回旋共振作用对电子的随机加速起着重要作用.     

高阶多点边值问题共振情况下正解的存在性

针对高阶多点共振边值问题研究较少的情况,利用Leggett—Williams型迭合度理论,探讨一类高阶微分方程多点边值问题共振情况下正解的存在性。通过合理的假设,得到了存在正解的充分性条件,并举例说明了结论的可行性。     

高阶振型对结构动力分析的影响

本文的目的在于分析高阶振型对结构动力分析的影响,分析舍去非共振高阶振型所产生的误差,并提出消除此误差的方法和措施。最后应用文中提出的公式,对具体结构进行了计算分析,得出了必须考虑高阶振型影响的结论。     

关于Hilbert空间上随机微分方程的稳定性问题

沿用经典的Liapunov直接法建立随机稳定性理论,其核心工作在于引进非负C~2-类函数V(t,x)及应用停止过程的It(?)公式(参看胡宣达[4]).我们尝试建立起Hilbert空间上停止过程的It(?)公式,并将随机稳定性理论推广到Hilbert空间上的随机微分方程上去.     

平行双量点中的Fano-Kondo

通过么正变换得到了平行双量子点有间库仑作用时的Fano—Anderson哈密顿量，并用格林函数运动方程的方法济南市出了与实验观测量密切相关的推迟和量子分布格林函数。借助于新得到的哈密顿量和格林函数，可以研究Kondo和Fano共振的关联效应。     

Banach空间中随机元的强收敛性

本文讨论了Hiibert空间中两两独立同分布随机元的Marcinkiewicz强大数律(SLLN),并把一维欧氏空间中的Hajek—Renyi不等式推广到p—型Banach空间中,由此得出若干结论。最后用几个例子说明,空间的几何结构对其收敛速度有很大影响。     

Chaotic electron diffusion through stochastic webs enhances current flow in superlattices

Understanding how complex systems respond to change is of fundamental importance in the natural sciences. There is particular interest in systems whose classical newtonian motion becomes chaotic as an applied perturbation grows. The transition to chaos usually occurs by the gradual destruction of stable orbits in parameter space, in accordance with the Kolmogorov-Arnold-Moser (KAM) theorem--a cornerstone of nonlinear dynamics that explains, for example, gaps in the asteroid belt. By contrast, 'non-KAM' chaos switches on and off abruptly at critical values of the perturbation frequency. This type of dynamics has wide-ranging implications in the theory of plasma physics, tokamak fusion, turbulence, ion traps, and quasicrystals. Here we realize non-KAM chaos experimentally by exploiting the quantum properties of electrons in the periodic potential of a semiconductor superlattice with an applied voltage and magnetic field. The onset of chaos at discrete voltages is observed as a large increase in the current flow due to the creation of unbound electron orbits, which propagate through intricate web patterns in phase space. Non-KAM chaos therefore provides a mechanism for controlling the electrical conductivity of a condensed matter device: its extreme sensitivity could find applications in quantum electronics and photonics.     

空间映射与响应面法相结合的结构优化

应用空间映射与响应面方法实现了由低保真模型到高保真模型的响应面映射,在原有空间映射方法的基础上将一类结构优化问题构造为标准二次规划模型,有利于高保真模型的优化求解,且解决了空间映射方法中低保真模型设计变量更新困难的问题。此方法可大大减少应用序列RSM方法进行结构多学科优化时的重分析计算量。数值算例表明此方法可获得较好的求解效率和精度。     

Quantum plasmon resonances of individual metallic nanoparticles

The plasmon resonances of metallic nanoparticles have received considerable attention for their applications in nanophotonics, biology, sensing, spectroscopy and solar energy harvesting. Although thoroughly characterized for spheres larger than ten nanometres in diameter, the plasmonic properties of particles in the quantum size regime have been historically difficult to describe owing to weak optical scattering, metal-ligand interactions, and inhomogeneity in ensemble measurements. Such difficulties have precluded probing and controlling the plasmonic properties of quantum-sized particles in many natural and engineered processes, notably catalysis. Here we investigate the plasmon resonances of individual ligand-free silver nanoparticles using aberration-corrected transmission electron microscope (TEM) imaging and monochromated scanning TEM electron energy-loss spectroscopy (EELS). This technique allows direct correlation between a particle's geometry and its plasmon resonance. As the nanoparticle diameter decreases from 20 nanometres to less than two nanometres, the plasmon resonance shifts to higher energy by 0.5 electronvolts, a substantial deviation from classical predictions. We present an analytical quantum mechanical model that describes this shift due to a change in particle permittivity. Our results highlight the quantum plasmonic properties of small metallic nanospheres, with direct application to understanding and exploiting catalytically active and biologically relevant nanoparticles.     

具有质量的刚杆连接的双摆运动

建立了用具有质量的刚杆连接的双摆运动方程,并将重力作为扰动,利用KAM定理研究了双摆的运动规律．当重力能量与总能量相比很小时,KAM不变闭曲线的存在表明无重力系统的“总动量“守恒的特点．     

Kondo physics in carbon nanotubes

The connection of electrical leads to wire-like molecules is a logical step in the development of molecular electronics, but also allows studies of fundamental physics. For example, metallic carbon nanotubes are quantum wires that have been found to act as one-dimensional quantum dots, Luttinger liquids, proximity-induced superconductors and ballistic and diffusive one-dimensional metals. Here we report that electrically contacted single-walled carbon nanotubes can serve as powerful probes of Kondo physics, demonstrating the universality of the Kondo effect. Arising in the prototypical case from the interaction between a localized impurity magnetic moment and delocalized electrons in a metallic host, the Kondo effect has been used to explain enhanced low-temperature scattering from magnetic impurities in metals, and also occurs in transport through semiconductor quantum dots. The far greater tunability of dots (in our case, nanotubes) compared with atomic impurities renders new classes of Kondo-like effects accessible. Our nanotube devices differ from previous systems in which Kondo effects have been observed, in that they are one-dimensional quantum dots with three-dimensional metal (gold) reservoirs. This allows us to observe Kondo resonances for very large electron numbers (N) in the dot, and approaching the unitary limit (where the transmission reaches its maximum possible value). Moreover, we detect a previously unobserved Kondo effect, occurring for even values of N in a magnetic field.     

基于汉字字频向量的中文文本自动分类系统

提出了一种根据汉字统计特性和基于实例映射的中文文本自动分类方法。该方法采用汉字字频向量作为文本的表示方法。它的显著特点是引入线性最小二乘方估计（ＬｉｎｅａｒＬｅａｓｔＳｑｕａｒｅＦｉｌ，ＬＬＳＦ）技术建立文本分类器模型，通过对训练集语料的手工分类标引以及对文本和类别间的相关性判定的学习，实现了基于全局最小错误率的汉字———类别两个向量空间的映射函数，并用该函数对测试文本进行分类