多维Lotka-Uolterra周期系统周期解的存在性及其全局吸引性

研究了m-维离散Lotka-Volterra竞争系统，并获得了该系统周期解的存在性及其全局吸引性.     

全对称傅里叶透镜的设计

本文研究了傅里叶透镜的设计,并叙述了一种对称型傅里时变换透镜.在相对孔径1:10时,输入面和频谱面处的象质均较好.傅里叶交换透镜的特点是必须对两对物象共轭位置(即位于前焦面处的输入面和位于后焦面处的频谱面)控制除畸变以外的全部象差.1969年后开始出现的傅里叶变换透镜,多属6～8片的对称或近似对称的四组元双远距型,本文叙述了一种严格对称型四片傅里叶交换透镜.     

High frequency forcing on nonlinear systems

High-frequency signals are pervasive in many science and engineering fields.In this work,the effect of high-frequency driving on general nonlinear systems is investigated,and an effective equation for slow motion is derived by extending the inertial approximation for the direct separation of fast and slow motions.Based on this theory,a high-frequency force can induce various phase transitions of a system by changing its amplitude and frequency.Numerical simulations on several nonlinear oscillator systems show a very good agreement with the theoretic results.These findings may shed light on our understanding of the dynamics of nonlinear systems subject to a periodic force.     

直接相位调制产生周期性线性啁啾脉冲特性研究

提出一种利用周期性抛物线调制信号对光脉冲进行相位调制以获得周期性线性啁啾脉冲的方法, 并对其进行了数值模拟与实验研究. 数值模拟结果表明: 增益饱和效应、群速度色散以及同步误差对啁啾脉冲的时间-光谱特性影响较大; 自相位调制对啁啾脉冲的影响较小. 实验获得了0.52 nm带宽的周期性线性啁啾脉冲, 与模拟结果符合较好. 实验结果同时表明装置中存在较大的偏振模色散, 导致幅频效应较大, 后续的研究中需加入对此的考虑. 模拟及实验研究表明: 直接相位调制是一种新型的可方便地获得周期性线性啁啾脉冲的方法, 其在光谱色散平滑中具有潜在应用. 关键词： 直接相位调制 周期性线性啁啾脉冲 幅频效应     

Terfenol-D/PZT磁电复合材料的磁电相位移动研究

采用粘合法制备了叠层结构的块体Terfenol-D/PZT磁电复合材料,测量了不同频率下的磁电回线,采用新的极坐标下的方式做图.从极坐标下的磁电回线中可以看出,随直流磁场的变化,非谐振频率下的磁电相位发生了轻微移动,移动幅度随频率的增加而增加;而在谐振频率下,伴随着巨磁电效应,磁电相位发生了显著移动,移动幅度达到了近90°.与粉末Terfenol-D/环氧树脂/PZT磁电复合材料对比之后表明,非谐振频率下块体Terfenol-D/PZT的磁电相位移动主要由涡流引起;而谐振频率下大幅度相位移动则主要来源于Terfenol-D的磁致弹性变化.     

Rigid geometric structures,isometric actions,and algebraic quotients

By using a Borel density theorem for algebraic quotients, we prove a theorem concerning isometric actions of a Lie group G on a smooth or analytic manifold M with a rigid A-structure σ. It generalizes Gromov’s centralizer and representation theorems to the case where R(G) is split solvable and G/R(G) has no compact factors, strengthens a special case of Gromov’s open dense orbit theorem, and implies that for smooth M and simple G, if Gromov’s representation theorem does not hold, then the local Killing fields on [(M)\tilde]{\widetilde{M}} are highly non-extendable. As applications of the generalized centralizer and representation theorems, we prove (1) a structural property of Iso(M) for simply connected compact analytic M with unimodular σ, (2) three results illustrating the phenomenon that if G is split solvable and large then π ₁(M) is also large, and (3) two fixed point theorems for split solvable G and compact analytic M with non-unimodular σ.     

Shaping of few-cycle laser pulses via a subwavelength structure

We theoretically investigate the propagation of few-cycle laser pulses in resonant two-level dense media with a sub- wavelength structure, which is described by the full Maxwell-Bloch equations without the frame of slowly varying envelope and rotating wave approximations. The input pulses can be shaped into shorter ones with a single or less than one optical cycle. The effect of the parameters of the subwavelength structure and laser pulses is studied. Our study shows that the media with a subwavelength structure can significantly shape the few-cycle pulses into a subcycle pulse, even for the case of chirp pulses as input fields. This suggests that such subwavelength structures have potential application in the shaping of few-cycle laser pulses.     

叠加态下3色场波形优化增大谐波辐射截止能量及强度

在He~+离子1s态和2s态的叠加态作为初始态时,提出一种优化3束激光场来增大谐波截止能量和强度的方法.结果表明:在叠加初始态下,谐波强度要比基态初始态下增强3个数量级以上.随后,在3色场波形优化下,谐波截止能量又得到增大,进而获得一个高强度、高光子能量的谐波光谱连续区.通过叠加光谱连续区上最后100次的谐波可以获得一个27 as的孤立阿秒脉冲.     

一种新的稳健波束形成算法及其一维搜索策略

存在条件失配时自适应波束形成器的性能急剧下降,凸优化技术的引入使稳健波束形成器的设计更加灵活,但同时带来了计算复杂度的增加和工程实现上的困难.针对上述问题,提出了一种基于最小二乘估计的稳健波束形成算法,并推导得到一种基于一维搜索的求解方法.首先利用广义旁瓣对消器的结构将标准Capon波束形成器转化为稳健最小二乘问题,并将该问题转化为二阶锥规划的形式.为了减少计算量,利用二阶锥规划问题的原始问题和对偶问题的关系,将求解过程转化为一维搜索,并利用牛顿迭代法获得最优解,从而获得与标准Capon波束形成相近的计算复杂度.仿真分析表明,该算法具有良好的抗导向矢量失配和快拍数不足的稳健性.     

Increment sizes of the principal value of Brownian local time

Let W be a standard Brownian motion, and define Y(t)= ∫₀ ^t ds/W(s) as Cauchy's principal value related to local time. We determine: (a) the modulus of continuity of Y in the sense of P. Lévy; (b) the large increments of Y. Received: 1 April 1999 / Revised version: 27 September 1999 / Published online: 14 June 2000