超混沌系统的控制

将反馈精确线性化的方法用于超混沌用于超混沌系统的控制。并针对超混沌Ｒｏｓｓｌｅｒ设计了控制器,使该系统实现了全局稳定（稳化）,同时还能实现对原系统的任意不稳定平衡点和周期信号的稳态跟踪。仿真结果证实了此方法的有效性,并且数值分析了闭环系统的鲁棒性。     

Design and Synthesis of Novel Chromophore with Multi-Carboxyl Groups

In order to explore the application of organic conjugated small molecules in bioimaging, a novel functional chromophore with A-π-D-π-A structure (Cr-3) was synthesized through Knoevenagel condensation reaction, consisting of carbazole unit as electron donor and cyanoacetic acid as electron acceptor groups. To improve the water solubility of this conjugated molecule, three carboxyl groups were introduced to chromophore Cr-3. Compared to the traditional D-π-A chromophores, chromophore Cr-3 showed the great improvement in water with the solubility of 2000 ppm. Also, the thermal stability of chromophore Cr-3 was also studied. The thermal decomposition temperature (Td) of Cr-3 was approximately 180°C, which was attributed to the dehydration of the carboxyl groups. Though the second harmonic generation (SHG) effect was not very high, it is large enough for the detection of SHG signal in water solution (0.28 pm/V).     

Nonlinear optomechanical detection for Majorana fermions via a hybrid nanomechanical system

The pursuit for detecting the existence of Majorana fermions is a challenging task in condensed matter physics at present. In this work, we theoretically propose a novel nonlinear optical method for probing Majorana fermions in the hybrid semiconductor/superconductor heterostructure. Our proposal is based on a hybrid system constituted by a quantum dot embedded in a nanomechanical resonator. With this method, the nonlinear optical Kerr effect presents a distinct signature for the existence of Majorana fermions. Further, the vibration of the nanomechanical resonator will enhance the nonlinear optical effect, which makes the Majorana fermions more sensitive to be detected. This proposed method may provide a potential supplement for the detection of Majorana fermions.     

输流管道含有内共振的横向受迫振动研究

利用多元L-P法研究外部周期激励下两端铰支输流管道含有内共振的非线性受迫振动问题。对于外激励作用下的流固耦合系统,当第二阶固有频率约为第一阶值的3倍,并且激励频率接近系统固有频率时,系统会发生含有强烈内部共振的主共振。利用多元L-P法求解这种振动响应,并详细分析振动中前两个模态的运动及外激励幅值对内共振的影响。数值算例揭示了系统由于内共振而发生的更加丰富而复杂的动力学行为,并且表明,随着激励幅值的增大,部分内共振的发生趋势将降低并最终消失。研究结果同时证明了多元L-P法在研究非线性动力学方面是便捷而高效的。     

混合CS算法的DE算法

为解决基本差分进化算法的缺陷,利用布谷鸟搜索（CS）算法寻优能力强的优点,在DE每次完成选择操作后,不直接进入下一次迭代,而是引入CS算法,继续进行搜索,这样就增加了粒子的搜索活力,从而得到一种新的差分进化算法。经过对6个标准测试函数的大量实验计算表明,该算法能有效克服DE算法的缺陷,使寻优精度有较大改进。将算法应用于求解非线性方程组问题,给出了数值算例。     

A sequential quadratic programming-based algorithm for optimization of gas networks

British Gas uses a complex, heavily looped network of pipes and controllable units (compressors and regulators) to transmit gas from coastal supply terminals to regional demand points. Computer algorithms are required for efficient management of the system. This paper describes an algorithm for optimal control over periods of up to a day. The problem is large scale and highly nonlinear in both objective function and constraints. The method is based on Sequential Quadratic Programming and takes account of the structure of the pipeflow equations by means of a reduced gradient technique which eliminates most of the variables from the quadratic subproblems. The latter involve only simple bound constraints, which are handled efficiently by a conjugate gradient-active set algorithm. Trust region techniques permit use of the exact Hessian, preserving sparsity. More general constraints are handled at an outer level by a truncated augmented Lagrangian method. Results are included for some realistic problems. The algorithm is generally applicable to problems with a control structure.     

一类非线性奇异摄动系统的渐近性分析

研究了一类非线性奇异摄动系统的两点优化问题，并对其在组合控制的作用下的渐近性进行了研究。组合控制是由降阶子系统的最优控制、左边界渐近稳定控制和右边界层最小能量控制三部分组成。研究表明，在该控制的作用下，系统的末状态与要求的末状态之间的误差很小，性能指标与最优控制的性能指标之间的误差也很小。以中程空地导弹的中制导系统为例进行了仿真。仿真结果表明组合控制效果良好。     

Perona-Malik模型离散格式的改进

Perona和Malik给出的离散格式是原Perona-Malik模型的近似模型的离散形式.这个离散格式用差商代替梯度,并略去了原模型的一项,本文通过理论分析发现这些简化影响了平滑的速度和效果.文中将省略的一项也加以离散,并将差商绝对值替换为梯度模,最终得到一个隐式的离散格式.实验结果表明,本文的离散格式提高了平滑速度,改进了平滑效果.     

1,3-对称取代的克酮酸衍生物光学性能研究

通过实验来研究1,3-对称取代的克酮酸衍生物的三阶非线性光学特性,计算出其分子超极化率,探讨了产生三阶非线性光学性能的原因.确定该衍生物在一定条件下具有较大的三阶非线性光学性质和较快的光学响应.     

含有一维p-Laplacian算子的非线性两点边值问题的可解性

考察了含有一维p-Laplacian算子的非线性两点边值问题：{（φp（u＇（t）））＇＋f（t,u（t）,u＇（t））=0,0≤t≤1 u＇（0）=A,u（1）=B的可解性。通过应用Schauder不动点定理,得到了这类方程的解的几个存在性定理。主要结果表明：如果非线性项在其定义域的某个有界子集上的“高度”是适当的,那么该问题必存在解或正解。