一种求解非线性无约束优化问题的充分下降的共轭梯度法

共轭梯度法是一类具有广泛应用的求解大规模无约束优化问题的方法. 提出了一种新的非线性共轭梯度(CG)法,理论分析显示新算法在多种线搜索条件下具有充分下降性. 进一步证明了新CG算法的全局收敛性定理. 最后,进行了大量数值实验,其结果表明与传统的几类CG方法相比,新算法具有更为高效的计算性能.     

Alternative difference analysis scheme combining R‐space EXAFS fit with global optimization XANES fit for X‐ray transient absorption spectroscopy

Time‐resolved X‐ray absorption spectroscopy (TR‐XAS), based on the laser‐pump/X‐ray‐probe method, is powerful in capturing the change of the geometrical and electronic structure of the absorbing atom upon excitation. TR‐XAS data analysis is generally performed on the laser‐on minus laser‐off difference spectrum. Here, a new analysis scheme is presented for the TR‐XAS difference fitting in both the extended X‐ray absorption fine‐structure (EXAFS) and the X‐ray absorption near‐edge structure (XANES) regions. R‐space EXAFS difference fitting could quickly provide the main quantitative structure change of the first shell. The XANES fitting part introduces a global non‐derivative optimization algorithm and optimizes the local structure change in a flexible way where both the core XAS calculation package and the search method in the fitting shell are changeable. The scheme was applied to the TR‐XAS difference analysis of Fe(phen)₃ spin crossover complex and yielded reliable distance change and excitation population.     

线性半向量二层规划问题的全局优化方法

研究了线性半向量二层规划问题的全局优化方法. 利用下层问题的对偶间隙构造了线性半向量二层规划问题的罚问题, 通过分析原问题的最优解与罚问题可行域顶点之间的关系, 将线性半向量二层规划问题转化为有限个线性规划问题, 从而得到线性半向量二层规划问题的全局最优解. 数值结果表明所设计的全局优化方法对线性半向量二层规划问题是可行的.     

Global Analysis of Response in the Piezomagnetoelastic Energy Harvester System under Harmonic and Poisson White Noise Excitations

The piezomagnetoelastic energy harvester system subjected to harmonic and Poisson white noise excitations is studied by using the generalized cell mapping method. The transient and stationary probability density functions (PDFs) of response based on the global viewpoint are obtained by the matrix analysis method. Monte Carlo simulation results verify the accuracy of this method. It can be observed that evolutionary direction of transient and stationary PDFs is in accordance with the unstable manifold for this system, and a stochastic P-bifurcation occurs as the intensity of Poisson white noise increases. This study presents an efficient numerical tool to solve the stochastic response of a three-dimensional dynamical system and provides a new idea to analyze the energy harvester system.     

威尔霍斯特型偏微分方程人口模型解的存在惟一性

讨论了威尔霍斯特型偏微分方程人口模型解的整体存在惟一性及关于初值的连续依赖性和C1光滑性.     

Investigation of nanostructured Fe3O4 polypyrrole core-shell composites by X-ray absorbtion spectroscopy and X-ray diffraction using synchrotron radiation

In this article, we focus on the structural peculiarities of nanosized Fe₃O₄ in the core-shell nanocomposites obtained by polymerization of conducting polypyrrole shell around Fe₃O₄ nanoparticles. The local structure of Fe atoms was determined from the Extended X-ray Absorption Fine Structure analysis using our own package computer programs. An X-ray diffraction method that is capable to determine average particle size, microstrains, as the particle size distribution of Fe₃O₄ nanoparticles is presented. The method is based on the Fourier analysis of a single X-ray diffraction profile using a new fitting method based on the generalized Fermi function facilities. The crystallites size obtained by X-ray diffraction spectra analysis was estimated between 3.2 and 10.3 nm. Significant changes in the first and the second Fe coordination shell in comparison with standard bulk were observed. The global and local structure of the nanosized Fe₃O₄ are correlated with the synthesis conditions of the core-shell polypyrrole nanocomposites.     

参外联合激励复合非线性振子的分岔分析

讨论了参外联合激励复合非线性振子的动力学行为.对其定常解在一阶近似下的方程进行了局部分岔分析,给出了简单分岔和Hopf分岔发生的条件,并通过对近似方程和原系统的数值模拟加以验证.分析了多种参数对该振子动力学行为演化过程的影响.根据全局分岔理论探讨了该振子在不同条件下发生同宿、异宿分岔的必要条件,其结论与数值计算的结果大致符合. 关键词： 复合非线性振子 局部分岔 全局分岔 混沌     

一个全球气候非线性振荡模型的近似解

研究了一个全球气候的非线性模型. 利用摄动理论和方法, 构造了相关问题解的渐近展开式, 该问题解的渐近展开式具有较高的近似度. 摄动渐近方法是一个解析方法, 得到的解还能够继续进行解析运算. 关键词： 非线性 摄动 全球气候     

Global Synchronization of Directed Networks with Fast Switching Topologies

Global synchronization of a class of directed dynamical networks with switching topologies is investigated. It is found that if there is a directed spanning tree in the fixed time-average of network topology and the time-average is achieved sufficiently fast, then the network will reach global synchronization for sufficiently large coupling strength.     

OPERATIONAL MODAL ANALYSIS SCHEMES USING CORRELATION TECHNIQUE

For some large-scale engineering structures in operating conditions, modal parameters estimation must base itself on response-only data. This problem has received a considerable amount of attention in the past few years. It is well known that the cross-correlation function between the measured responses is a sum of complex exponential functions of the same form as the impulse response function of the original system. So this paper presents a time-domain operating modal identification global scheme and a frequency-domain scheme from output-only by coupling the cross-correlation function with conventional modal parameter estimation. The outlined techniques are applied to an airplane model to estimate modal parameters from response-only data.