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.     

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.     

Error estimates for space–time discontinuous Galerkin formulation based on proper orthogonal decomposition

In this study, proper orthogonal decomposition (POD) method is applied to diffusion–convection–reaction equation, which is discretized using space–time discontinuous Galerkin (dG) method. We provide estimates for POD truncation error in dG-energy norm, dG-elliptic projection, and space–time projection. Using these new estimates, we analyze the error between the dG and the POD solution, and the error between the exact and the POD solution. Numerical results, which are consistent with theoretical convergence rates, are presented.     

On the stability of Timoshenko-type systems with internal frictional dampings and discrete time delays

In this paper, we consider a vibrating system of Timoshenko-type in a bounded one-dimensional domain under Dirichlet–Dirichlet or Dirichlet–Neumann boundary conditions with one or two discrete time delays and one or two internal frictional dampings. First, we show that the system is well posed in the sens of semigroup theory. Second, we prove the exponential stability regardless to the speeds of wave propagation of the system if the weights of the time delays are smaller than the ones of the corresponding dampings, respectively. However, when the weight of one time delay is not smaller than the one of the corresponding damping, we prove the exponential stability in case of equal-speed wave propagation, and the polynomial stability in the opposite case.     

Pseudo‐differential operators in a Gelfand–Shilov setting

We introduce some general classes of pseudodifferential operators with symbols admitting exponential type growth at infinity and we prove mapping properties for these operators on Gelfand–Shilov spaces. Moreover, we deduce composition and certain invariance properties of these classes.     

On the distribution of cumulative Parisian ruin

We introduce the concept of cumulative Parisian ruin, which is based on the time spent in the red by the underlying surplus process. Our main result is an explicit representation for the distribution of the occupation time, over a finite-time horizon, for a compound Poisson process with drift and exponential claims. The Brownian ruin model is also studied in details. Finally, we analyse for a general framework the relationships between cumulative Parisian ruin and classical ruin, as well as with Parisian ruin based on exponential implementation delays.