Superconvergence of a two‐grid method for fourth‐order dispersive‐dissipative wave equations

In this paper, the superconvergence analysis of a two‐grid method (TGM) with low‐order finite elements is presented for the fourth‐order dispersive‐dissipative wave equations for a second order fully discrete scheme. The superclose estimates in the H¹‐norm on the two grids are obtained by the combination technique of the interpolation and Ritz projection. Then, with the help of the interpolated postprocessing technique, the global superconvergence properties are deduced. Finally, numerical results are provided to show the performance of the proposed TGM for conforming bilinear element and nonconforming element, respectively. It shows that the TGM is an effective method to the problem considered of our paper compared with the traditional Galerkin finite element method (FEM).     

A Unified Approach to Local Quantum Uncertainty and Interferometric Power by Metric Adjusted Skew Information

Local quantum uncertainty and interferometric power were introduced by Girolami et al. as geometric quantifiers of quantum correlations. The aim of the present paper is to discuss their properties in a unified manner by means of the metric adjusted skew information defined by Hansen.     

Effects of graded porous structure on local strain distribution under compression in silicone rubber

Silicone rubber samples with gradually changing pore sizes within the range of 70–610 μm are produced using an improved spacer method. The samples are scanned using an X‐ray computed tomography to evaluate their graded structure as compared to uniform rubber. A compressive test reveals that graded porous silicone rubber has characteristic stress–strain curves whose slope changes within a specific strain range depending on the porous structure. Analysis results of local strain based on a digital image correlation of the graded porous silicone rubber under compression demonstrate that the characteristic stress–strain properties are caused by shifts in the main deformation region in the graded structure. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1033–1042     

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。