Single determinant N‐representability and the kernel energy method applied to water clusters

The Kernel energy method (KEM) is a quantum chemical calculation method that has been shown to provide accurate energies for large molecules. KEM performs calculations on subsets of a molecule (called kernels) and so the computational difficulty of KEM calculations scales more softly than full molecule methods. Although KEM provides accurate energies those energies are not required to satisfy the variational theorem. In this article, KEM is extended to provide a full molecule single‐determinant N‐representable one‐body density matrix. A kernel expansion for the one‐body density matrix analogous to the kernel expansion for energy is defined. This matrix is converted to a normalized projector by an algorithm due to Clinton. The resulting single‐determinant N‐representable density matrix maps to a quantum mechanically valid wavefunction which satisfies the variational theorem. The process is demonstrated on clusters of three to twenty water molecules. The resulting energies are more accurate than the straightforward KEM energy results and all violations of the variational theorem are resolved. The N‐representability studied in this article is applicable to the study of quantum crystallography. © 2017 Wiley Periodicals, Inc.     

Banach空间中寻求(α,β)-适度混合集值映像吸引点的一般迭代格式

引入（α，β）-适度混合集值映像与条件I^*的概念，提出了用于寻求（α，β）-适度混合集值映像吸引点的一般迭代法.在一致凸Banach空间中，利用条件I^*与半紧性质，建立了所提（α，β）-适度混合集值映像的迭代格式的强收敛性.结论改进与修正了之前文献中已发布的相应结果.     

An optimal perturbation bound

Cai and Zhang establish separate perturbation bounds for distances with spectral and Frobenius norms (Cai T, Zhang A. Rate‐optimal perturbation bounds for singular subspaces with applications to high‐dimensional statistics. The Annals of Statistics. 2018; Vol. 46, No. 1: 60?89). We extend their theorem to each unitarily invariant norm. It turns out that our estimation is optimal as well.     

Classical Backfitting for Smooth-Backfitting Additive Models

Smooth backfitting has been shown to have better theoretical properties than classical backfitting for fitting additive models based on local linear regression. In this article, we show that the smooth backfitting procedure in the local linear case can be alternatively performed as a classical backfitting procedure with a different type of smoother matrices. These smoother matrices are symmetric and shrinking and some established results in the literature are readily applicable. The connections allow the smooth backfitting algorithm to be implemented in a much simplified way, give new insights on the differences between the two approaches in the literature, and provide an extension to local polynomial regression. The connections also give rise to a new estimator at data points. Asymptotic properties of general local polynomial smooth backfitting estimates are investigated, allowing for different orders of local polynomials and different bandwidths. Cases of oracle efficiency are discussed. Computer-generated simulations are conducted to demonstrate finite sample behaviors of the methodology and a real data example is given for illustration. Supplementary materials for this article are available online.     

Solvent‐free inkjet printing process for the fabrication of conductive,transparent, and flexible ionic liquid‐polymer gel structures

A new and solvent‐free process for the fabrication of inkjet printed ionic liquid‐polymer gel microstructures with high‐resolution (line widths of ～40 μm), good electrical conductivity (5–30 mS cm^?1), optical transparency, and mechanical flexibility is presented. Carrying out the printing and polymerization process in nitrogen atmosphere eliminates the inhibiting influence of oxygen and guarantees homogeneously gelled structures. Careful selection and combination of ionic liquids (ILs) and unsaturated monomers makes it possible to achieve low viscosities which are printable with commercially available inkjet printers and printheads without adding extra solvents. By using different types and amounts of ILs and monomers the resulting properties of the printed IL‐polymer gels can be controlled in terms of ionic conductivity, optical transmission, and mechanical flexibility. Higher conductivities are possible by using a bifunctional instead of a monofunctional monomer, which allows one to lower the amount of monomer without loss in mechanical strength. Cast samples make it possible to obtain data of transmission (～90% for 170‐μm thick films) and mechanical flexibility (E = 0.02–0.23 MPa) of bulk material. Comparing electrical conductivity of printed and cast samples, the higher values of printed samples indicate the conductivity enhancing influence of moisture absorbed from the surrounding atmosphere after the fabrication process. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Hidden Markov models revealing the stress field underlying the earthquake generation

The application of the hidden Markov models (HMMs) is attempted for revealing key features for the earthquake generation which are not accessible to direct observation. Considering that the states of the HMM correspond to levels of the stress field, our objective is to identify these states. The observations are considered after grouping earthquake magnitudes and the cases of different number of states are examined. The problems of HMMs theory are solved and the ensuing HMMs are compared on the basis of Akaike and Bayesian information criteria. A new insight on the evaluation of future seismic hazard is given by calculating the mean number of steps for the first visit to a particular state, along with the respective variance. We further calculate an estimator of the mean number of steps for the first visit to a particular state and we construct its confidence interval. Additionally, a second approach to the problem is followed by assuming a different determination of observations. The HMMs applied to both approaches, contribute significantly to seismic hazard assessment via revealing the number of the stress levels as well as the way in which these levels are associated with certain earthquake occurrence.     

Relationship between liquid crystalline phase stability and ingredient composition in liquid crystal oil–water emulsion

In this study, we postulated that the optical retardation magnitude could be used to evaluate the stability of the LC phase through the Mueller matrix polarimeter method in LC emulsion. In addition, we found that the increase of cetearyl alcohol concentration induced the more periodic dense lattice structure in crystalline phase of LC lamellae and the sorbitan olivate was relatively more responsible for higher ordering in LC phase compared to C12–20 alkyl glucoside in terms of molecular parallel packing on the basis of the optical retardation magnitude. Furthermore, it was confirmed that the LC emulsion had higher skin barrier function owing to lower TEWL and higher reflectance than ordinary emulsion on human skin and maintained a uniform phase without phase separation for 8 weeks.     

Flexible active matrix addressed displays manufactured by printing and coating techniques

A flexible electrochromic active matrix addressed display, including 8 × 8 pixels, is demonstrated by using solution processing based on standard printing and coating manufacturing techniques. Each organic electrochromic display (OECD) pixel and its corresponding organic electrochemical transistor (OECT) are located on different sides of the flexible PET substrate. Electronic vias generated through the plastic substrate connects each OECD pixel with one addressing OECT. When comparing this display with actively addressed OECDs with all its components located on the same side, the present approach based on this electronic via substrate provides an enhanced pixel resolution and a relatively more simplified manufacturing process. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

周期系数线性系统的稳定性

利用柯西矩阵的性质,讨论了周期系数线性矩阵的稳定性问题.将矩阵稳定的条件减弱为拟稳定,利用矩阵的不等式运算性质,得到了各种周期系统平凡解稳定的判据,所得结论,推广了现有文献的结论.最后,利用Matlab模拟仿真,验证了所得结果的可行性.