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.     

Hypercomplex analysis and integration of systems of ordinary differential equations

We review the theory of hypercomplex numbers and hypercomplex analysis with the ultimate goal of applying them to issues related to the integration of systems of ordinary differential equations (ODEs). We introduce the notion of hypercomplexification, which allows the lifting of some results known for scalar ODEs to systems of ODEs. In particular, we provide another approach to the construction of superposition laws for some Riccati‐type systems, we obtain invariants of Abel‐type systems, we derive integrable Ermakov systems through hypercomplexification, we address the problem of linearization by hypercomplexification, and we provide a solution to the inverse problem of the calculus of variations for some systems of ODEs. Copyright © 2016 John Wiley & Sons, Ltd.     

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。     

共形空间${\mathbb Q}^{n+1}_1$中类空超曲面的拼挤问题

通过对第二共形基本形式的模长平方作拼挤,给出Clifford超柱面的一个共形特征.     

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.     

DFT in a nutshell

The purpose of this short essay is to introduce students and other newcomers to the basic ideas and uses of modern electronic density functional theory, including what kinds of approximations are in current use, and how well they work (or not). The complete newcomer should find it orients them well, while even longtime users and aficionados might find something new outside their area. Important questions varying in difficulty and effort are posed in the text, and are answered in the Supporting Information. © 2012 Wiley Periodicals, Inc.     

Local Hartree–Fock orbitals using a three‐level optimization strategy for the energy

Using the three‐level energy optimization procedure combined with a refined version of the least‐change strategy for the orbitals—where an explicit localization is performed at the valence basis level—it is shown how to more efficiently determine a set of local Hartree–Fock orbitals. Further, a core–valence separation of the least‐change occupied orbital space is introduced. Numerical results comparing valence basis localized orbitals and canonical molecular orbitals as starting guesses for the full basis localization are presented. The results show that the localization of the occupied orbitals may be performed at a small computational cost if valence basis localized orbitals are used as a starting guess. For the unoccupied space, about half the number of iterations are required if valence localized orbitals are used as a starting guess compared to a canonical set of unoccupied Hartree–Fock orbitals. Different local minima may be obtained when different starting guesses are used. However, the different minima all correspond to orbitals with approximately the same locality. © 2013 Wiley Periodicals, Inc.