The local ultraconvergence of high‐order finite element method for second‐order elliptic problems with constant coefficients over a rectangular partition

In this article, we will discuss the local ultraconvergence of high‐degree finite element method based on a rectangular partition for the second‐degree elliptic problem with constant coefficients in Ω ? ?² , u( y ) = 0 on ?Ω . Based on suitable regularity, ultraconvergence of the displacement of the extrapolated kth (k ≥ 3) degree finite element solution has been obtained by an extrapolation technique. Finally, numerical experiments are applied to demonstrate our theoretical findings.     

Bilevel convex programming models

Bilevel convex models are studied after being cast into a parametric programming form. This form has a lexicographic inner-outer structure where the optimal value of the outer model is optimized on the set of optimal solutions of the inner model. Optimal solutions are characterized using a Lagrangian saddle-point approach and a marginal value formula is given for the outer model. These are used to formulate a general method for finding an optimal solution by input optimization.     

Local defect structures and EPR studies on (FeO6)9− and (FeO4)5− clusters in YGG: Fe3+ system

The octahedral (FeO₆)^9? and tetrahedral (FeO₄)^5? clusters in yttrium gallium garnet (YGG): Fe³⁺ system are investigated based on the 252 × 252 complete energy matrices for d⁵ configuration ions in trigonal and tetragonal ligand fields, moreover, the EPR and optical spectra are made unified calculation. The results indicate that the defect structures around Fe³⁺ centres display expansion effects at different temperatures 4.2 and 295 K, and which are close to those in YIG garnet, respectively. Simultaneously, the defect structure parameters for Fe³⁺ centres in YGG are determined, and the relationship between the defect structure and the temperature has been discussed.     

Temperature‐dependent local atomic structures in the traditional Fe65Ni35 Invar alloy by X‐ray fluorescence holography

Fe and Ni Kα X‐ray fluorescence holography measurements were conducted on a single crystal Fe₆₅Ni₃₅ Invar alloy at 100 and 300 K to investigate the temperature dependence of the 3‐dimensional local structures around the Fe and Ni atoms, respectively. Local structural information was obtained by detailed analyses using a L₁‐regularized linear regression for the experimental data. At 100 K, the local atomic arrangements around both the elements show fcc structures. At 300 K, however, only the image around Fe shows a bcc‐like neighboring arrangement. From these X‐ray fluorescence holography data, we propose a model that with increasing temperature, an Fe atom with the low‐spin state enters at the central position of the fcc lattice and is stabilized. And then, large angular positional fluctuations are induced for the atoms at the face‐centered positions around the central Fe atom only.     

New simple exact penalty function for constrained minimization

By adding one variable to the equality-or inequality-constrained minimization problems, a new simple penalty function is proposed. It is proved to be exact in the sense that under mild assumptions, the local minimizers of this penalty function are precisely the local minimizers of the original problem, when the penalty parameter is sufficiently large.     

局部方差在图像质量评价中的应用

将灰度图像的局部方差分布（QLS）作为表征图像结构信息的一个重要特征,对局部方差分布矩阵进行奇异值分解,计算得到相应的奇异值特征向量;通过计算降质图像与原参考图像局部方差矩阵奇异值特征向量的夹角大小度量两图像的结构相似度,实现了对降质图像的质量评价。实验结果表明：局部方差分布更能突出图像的结构特征,评价结果优于传统的均方误差（MSE）、峰值信噪比（PSNR）、结构相似度（SSIM）以及直接评价图像像素分布的奇异值分析（SVD）等方法,与人眼视觉感知效果的一致性较好。     

Zhiber-Shabat方程的多辛几何和多辛隐式格式研究

Zhiber-Shabat方程,描述许多重要的物理现象,是一类重要的非线性方程,有着许多广泛的应用前景.本文给出Zhiber-Shabat方程的多辛几何结构和多辛Fourier拟谱方法.数值算例结果表明多辛离散格式具有较好的长时间的数值稳定性.     

Identification of mechanisms of toxic action for skin sensitisation using a SMARTS pattern based approach

Skin sensitisation is a key endpoint under REACH as it is costly and its assessment currently has a high dependency on animal testing. In order to reduce both the cost and the numbers of animals tested, it is likely that (quantitative) structure–activity relationships ((Q)SAR) and read-across methods will be utilised as part of intelligent testing strategies. The majority of skin sensitisers elicit their effect via covalent bond formation with skin proteins. These reactions have been understood in terms of well defined nucleophilic–electrophilic reaction chemistry. Thus, a first step in (Q)SAR analysis is the assignment of a chemical's potential mechanism of action enabling it to be placed in an appropriate reactivity domain. The aim of this study was to design a series of SMARTS patterns capable of defining these reactivity domains. This was carried out using a large database of local lymph node assay (LLNA) results that had had potential mechanisms of action assigned to them using expert knowledge. A simple algorithm was written enabling the SMARTS patterns to be used to screen a database of SMILES strings. The SMARTS patterns were then evaluated using a second, smaller, test set of LLNA results which had also had potential mechanisms of action assigned by experts. The results showed that the SMARTS patterns provided an excellent method of identifying potential electrophilic mechanisms. The findings are supported, in part, by molecular orbital calculations which confirm assignment of reactive mechanism of action. The ability to define a chemical's potential reaction mechanism is likely to be of significant benefit to regulators and risk assessors as it enables category formation and subsequent read-across to be performed.