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A Markov observation model with dividend is defined and the interpretation of the practical significance is given. We try to use an irreducible and homogeneous discrete-time Markov chain to modulate the inter-observation times and embed a dividend strategy. In the Markov observation model with dividend, a system of liner equations for the expected discounted value of dividends until ruin time is derived. Moreover, an explicit expression is obtained and proved. Finally, some interesting properties are illustrated by numerical analysis and by comparing with the complete compound binomial model with dividend.     

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A cured model is a useful approach for analysing failure time data in which some subjects could eventually experience and others never experience the event of interest. All subjects in the test belong to one of the two groups: the susceptible group and the non-susceptible group. There has been considerable progress in the development of semi-parametric models for regression analysis of time-to-event data. However, most of the current work focuses on right-censored data, especially when the population contains a non-ignorable cured subgroup. In this paper, we propose a semi-parametric cure model for current status data. In general, treatments are developed to both increase the patients' chances of being cured and prolong the survival time among non-cured patients. A logistic regression model is proposed for whether the subject is in the susceptible group. An accelerated failure time regression model is proposed for the event time when the subject is in the non-susceptible group. An EM algorithm is used to maximize the log-likelihood of the observed data. Simulation results show that the proposed method can get efficient estimations.     

稳健残差控制图的构建及在金融时序中的应用

对于呈现自相关和波动族聚性并存的受控过程,通常采用残差控制图对其进行监控。但异常点的存在会对自相关或波动族聚性模型的拟合产生重要影响,使得基于该模型的残差并非独立同分布导致常规残差控制图监控失效。为解决这类问题,本文提出稳健残差控制图。即建立稳健的ARMA模型解决自相关问题从而得到无自相关的残差序列,用稳健的GARCH模型来构建控制图的上下限。模拟和实证研究表明,本文提出的稳健残差控制图具有很好的抗异常点能力并能更好的对金融时间序列的异常现象进行监控。     

Global X2A′ potential energy surface of Li2H and quantum dynamics of H + Li2 (X1Σg+) → Li + LiH (X1Σ+) reaction

A global potential energy surface (PES) for the electronic ground state of Li₂H system is constructed over a large configuration space. About 30 000 ab initio energy points have been calculated by MRCI‐F12 method with aug‐cc‐pVTZ basis set. The neural network method is applied to fit the PES and the root mean square error of the current PES is only 1.296 meV. The reaction dynamics of the title reaction has been carried out by employing time‐dependent wave packet approach with second order split operator on the new PES. The reaction probability, integral cross section and thermal rate constant are obtained from the dynamics calculation. In most of the collision energy regions, the integral cross sections are in well agreement with the results reported by Gao et al. The rate constant calculated from the new PES increases in the temperature range of present investigation.     

Dielectric relaxation of Tripropylene glycol–water mixture using time domain reflectometry

The complex permittivity spectra of tripropylene glycol and water solutions have been obtained by time domain reflectometry (TDR) technique in the frequency range from 10 MHz to 30 GHz and the temperature range 20°C–05°C. The dielectric relaxation parameters such as static dielectric constant and relaxation time were obtained by using the non-linear least square fit method. The intermolecular hydrogen bonding of tripropylene glycol–water has been discussed using the Kirkwood correlation factor and thermodynamic parameters. The activation energy decreases with increase in water content in the mixture as expected in the Arrhenius behaviour. The dielectric constant for mixtures has been fitted to the Bruggeman mixture formula in the non-linear case.     

Morphological evolution of Ge islands on the Si(100) surface: from huts to pits

The morphological evolution on the size and shape of Ge island on the Si(100) surface by depositing and subsequent annealing processes is studied in situ by using scanning tunneling microscopy at ultrahigh vacuum environment. A slower growth rate is maintained when the islands grow to larger sizes beyond the wetting layers. While at room temperature, the epitaxial strain is relieved by the formation of three‐dimensional islands (so‐called ‘hut’ clusters). When the sample is annealed at 200 °C, the strain is relieved by forming pits, having the circular cone shape but with their apex pointing down, with Ge clusters formed at the rim of pits. Copyright © 2016 John Wiley & Sons, Ltd.     

Compression stress relaxation in carbon black reinforced HNBR at low temperatures

Findings of a study of stress relaxation behaviour of hydrogenated nitrile butadiene rubber (HNBR) at nominal compressive strains up to 0.4 and temperatures above and below the glass transition temperature T_g are reported. Two formulations of a model HNBR with 36% acrylonitrile content and carbon black (CB) loading of 0 and 50 phr were investigated. The relaxation function of HNBR is found to be independent of strain at temperatures right above the T_g or at times longer than 10⁻³ s for the deformations employed. CB imparts higher long-term stiffness and also larger relaxation strength at times longer than 10⁻⁴ s to the HNBR, but it does not affect the relaxation behaviour of the rubber in the time span from 10⁻³ – 10⁴ s. In addition, the relationship between the strain energy function of HNBR and temperature is demonstrated to have a complex concave-downward shape which is affected by two competing contributions of entropy elasticity and the stress relaxation.     

Theoretical approaches for predicting the color of rigid dyes in solution

Aiming at developing an affordable and easily implementable computational protocol for routine prediction of spectral properties of rigid molecular dyes, density functional theory, and time‐dependent density functional theory were used in conjunction with a vibronic coupling scheme for band shape estimate. To predict the perceived color of molecules in solution, a model has been setup linking the UV‐vis spectra predicted at ab initio level to the L *a *b * colorimetric parameters. The results show that a mixed protocol, implying the use of a global hybrid functional for the prediction of adiabatic energy differences and a range separated hybrid for the prediction of potential energy curvature, allows perceived colors to be quantitatively predicted, as demonstrated by the comparison of L *a *b * colorimetric parameters obtained from computed and experimental spectra. © 2017 Wiley Periodicals, Inc.     

[Cu6(NGuaS)6]2+ and its oxidized and reduced derivatives: Confining electrons on a torus

The hexanuclear thioguanidine mixed‐valent copper complex cation [Cu₆(NGuaS)₆]⁺² (NGuaS = o‐SC₆H₄NC(NMe₂)₂) and its oxidized/reduced states are theoretically analyzed by means of density functional theory (DFT) (TPSSh + D3BJ/def2‐TZV (p)). A detailed bonding analysis using overlap populations is performed. We find that a delocalized Cu‐based ring orbital serves as an acceptor for donated S p electrons. The formed fully delocalized orbitals give rise to a confined electron cloud within the Cu₆S₆ cage which becomes larger on reduction. The resulting strong electrostatic repulsion might prevent the fully reduced state. Experimental UV/Vis spectra are explained using time‐dependent density functional theory (TD‐DFT) and analyzed with a natural transition orbital analysis. The spectra are dominated by MLCTs within the Cu₆S₆ core over a wide range but LMCTs are also found. The experimental redshift of the reduced low energy absorption band can be explained by the clustering of the frontier orbitals. © 2017 Wiley Periodicals, Inc.