Finite element approximation of nonlinear transient magnetic problems involving periodic potential drop excitations

This paper deals with the computation of nonlinear 2D transient magnetic fields when the data concerning the electric current sources involve potential drop excitations. In the first part, a mathematical model is stated, which is solved by an implicit time discretization scheme combined with a finite element method for space approximation. The second part focuses on developing a numerical method to compute periodic solutions by determining a suitable initial current which avoids large simulations to reach the steady state. This numerical method leads to solve a nonlinear system of equations which requires to approximate several nonlinear and linear magnetostatic problems. The proposed methods are first validated with an axisymmetric example and sinusoidal source having an analytical solution. Then, we show the saving in computational effort that this methodology offers to approximate practical problems specially with pulse-width modulation (PWM) voltage supply.     

Symbolic computation of the Birkhoff normal form in the problem of stability of the triangular libration points

The problem of stability of the triangular libration points in the planar circular restricted three-body problem is considered. A software package, intended for normalization of autonomous Hamiltonian systems by means of computer algebra, is designed so that normalization problems of high analytical complexity could be solved. It is used to obtain the Birkhoff normal form of the Hamiltonian in the given problem. The normalization is carried out up to the 6th order of expansion of the Hamiltonian in the coordinates and momenta. Analytical expressions for the coefficients of the normal form of the 6th order are derived. Though intermediary expressions occupy gigabytes of the computer memory, the obtained coefficients of the normal form are compact enough for presentation in typographic format. The analogue of the Deprit formula for the stability criterion is derived in the 6th order of normalization. The obtained floating-point numerical values for the normal form coefficients and the stability criterion confirm the results by Markeev (1969) and Coppola and Rand (1989), while the obtained analytical and exact numeric expressions confirm the results by Meyer and Schmidt (1986) and Schmidt (1989). The given computational problem is solved without constructing a specialized algebraic processor, i.e., the designed computer algebra package has a broad field of applicability.     

基于定向爬山的遗传算法

爬山法是一种局部搜索能力相当好的算法,主要是因为它是通过个体的优劣信息来引导搜索的。而传统的遗传算法作为一种全局搜索算法,在搜索过程中却没有考虑个体间的信息,而仅依靠个体适应度来引导搜索,使得算法的收敛性受到限制。将定向爬山机制应用于遗传算法,提出了一种基于定向爬山的遗传算法（OHCGA）。该算法结合了爬山法与遗传算法的优点,通过比较个体的优劣,使用定向爬山操作引导算法向更优秀的解区域进行搜索。实验结果表明,与传统遗传算法（TGA）相比,OHCGA较大地提高了算法的收敛速度和搜索最优解的能力。     

抗强剪切攻击的四元数彩色图像零水印算法

针对现有彩色图像零水印算法对存在信息量丢失的各种攻击(如剪切、行列移除、 涂抹等)的不足,提出一种基于非负矩阵分解(NMF)和四元数实矩阵的彩色图像零水印算法。该 算法首先提取彩色图像的3 个分量(R、G、B)并将各分量进行NMF 分解;其次将分解后的各系 数矩阵在版权中心进行注册,同时将原始彩色图像使用四元数实矩阵来表征,并计算实数字矩 阵的Krawtchouk 不变矩;最后,在版权中心注册Krawtchouk 不变矩特征向量;由剩余未剪切 部分的彩色图像和注册的系数矩阵共同恢复出完整的原始图像。实验结果表明：在彩色图像剪 切或涂抹面积超过80%时,水印信息仍可以正确地被提取;使用四元数彩色图像整体法表征图 像在图像类聚以及水印误检率方面的性能都要优于彩色图像三通道分别处理或直接灰度化实现 的效果。     

Effects of solution pH and Cl on electrochemical behaviour of an Aermet100 ultra-high strength steel in acidic environments

In this work, the effects of solution pH and Cl⁻ on the electrochemical behaviour of an Aermet100 ultra-high strength steel in 0.5 M (Na₂SO₄ + H₂SO₄) solution were studied by polarization curve and electrochemical impedance spectroscopy (EIS) measurements, combined with scanning electron microscopy (SEM) and X-ray photoelectron spectroscopy (XPS) characterization. The results show that, when solution pH is below 4, the steel is in the active dissolution state, and corrosion current decreases with the increase of pH. There exists a critical pH value, above which the steel is passivated. Moreover, the oxides and hydroxides of Fe, Co, Ni and Cr are the primary components of the passive film. With addition of Cl⁻, pits are initiated on the steel electrode.     

M-矩阵性质的注记

首先利用M-矩阵的基本性质,讨论了M-矩阵乘积及凸组合特性,获得关于M-矩阵乘积及凸组合的相关结论;随后通过比较矩阵及非负矩阵的性质,探讨了矩阵的逆及行列式性质,推导出了M-矩阵的不等式关系.     

一类 p-Kirchhoff 方程无穷多解的存在性

研究一类带有凹凸非线性项的 p‐Kirchhoff 方程无穷多解的存在性。在Kirchhoff 函数 M以及权函数 f 满足更弱的假设下（即 M无正下界,权函数 f 不定号）,利用RN 中两个重要的不等式证明能量泛函 J满足（PS ）c条件。结合喷泉定理,得到该方程的无穷多解的存在性,并且获得了一列能量无界的正能量解。拓展了 p‐Kirchhoff方程解的多重性结果。     

On the sizing of a solar thermal electricity plant for multiple objectives using evolutionary optimization

Design, implementation and operation of solar thermal electricity plants are no more an academic task, rather they have become a necessity. In this paper, we work with power industries to formulate a multi-objective optimization model and attempt to solve the resulting problem using classical as well as evolutionary optimization techniques. On a set of four objectives having complex trade-offs, our proposed procedure first finds a set of trade-off solutions showing the entire range of optimal solutions. Thereafter, the evolutionary optimization procedure is combined with a multiple criterion decision making (MCDM) approach to focus on preferred regions of the trade-off frontier. Obtained solutions are compared with a classical generating method. Eventually, a decision-maker is involved in the process and a single preferred solution is obtained in a systematic manner. Starting with generating a wide spectrum of trade-off solutions to have a global understanding of feasible solutions, then concentrating on specific preferred regions for having a more detailed understanding of preferred solutions, and then zeroing on a single preferred solution with the help of a decision-maker demonstrates the use of multi-objective optimization and decision making methodologies in practice. As a by-product, useful properties among decision variables that are common to the obtained solutions are gathered as vital knowledge for the problem. The procedures used in this paper are ready to be used to other similar real-world problem solving tasks.     

基于NSCT域改进型NMF的图像融合方法

针对多传感器图像融合问题,提出一种基于非下采样轮廓波变换域改进型非负矩阵分解的图像融合方法.首先,采用非下采样轮廓波变换对源图像进行多尺度、多方向稀疏分解;然后对低频子图像采用改进型非负矩阵分解方法进行融合,该过程无需对W和H进行随机化便可快速生成低频融合图像,高频子图像则采用自适应unit-fast-linking脉冲耦合神经网络模型进行融合;最后利用非下采样轮廓波逆变换合成各子图像即可得到最终融合图像.仿真实验验证了该方法的有效性.