Dynamic polarizability of two‐electron ions under Debye screening

The effect of plasma screening on the dynamic dipole polarizability (DPP) of two‐electron ions Be²⁺, B³⁺, and C⁴⁺ has been investigated using highly correlated exponential wave functions within the framework of pseudostate summation technique and Debye screening concept. Plasma‐screening effect on the oscillator strengths (OS) of the ultraviolet and visible series has also been investigated for the systems Li⁺, Be²⁺, B³⁺, C⁴⁺. The DPP are reported as functions of screening parameters. The OS for S‐P transitions are also reported for various screening parameters. The OS and dynamic polarizability show interesting behavior with increasing screening strength and nuclear charge. © 2015 Wiley Periodicals, Inc.     

Revisiting the extrapolation of correlation energies to complete basis set limit

The extrapolation scheme of correlation energy is revisited to evaluate the complete basis set limit from double‐zeta (DZ) and triple‐zeta levels of calculations. The DZ level results are adjusted to the standard asymptotic behavior with respect to the cardinal number, observed at the higher levels of basis sets. Two types of adjusting schemes with effective scaling factors, which recover errors in extrapolations with the DZ level basis set, are examined. The first scheme scales the cardinal number for the DZ level energy, while the second scheme scales the prefactor of the extrapolation function. Systematic assessments on the Gaussian‐3X and Gaussian‐2 test sets reveal that these calibration schemes successfully and drastically reduce errors without additional computational efforts. © 2015 Wiley Periodicals, Inc.     

煤催化气化条件下不同煤种煤灰烧结行为研究

选取9类典型煤种,利用压差法测定烧结温度的实验装置,结合灰渣的XRD分析结果,考察了添加K基碱金属催化剂、不同煤种灰成分对烧结温度的影响。结果表明,碳酸钾催化剂的添加,明显降低高铁钙含量的WJT煤的灰熔点及烧结温度,碱金属K化合物极易同煤中Fe、Ca的矿物质反应生成低温共融物进而加剧煤灰的熔融结渣。不同煤种烧结温度的差异与煤灰中硅、铝、铁、钙含量密切相关。铝、硅含量高的煤灰烧结温度较高,而铁、钙含量高的煤灰烧结温度相对较低。碱金属K催化剂的添加加剧了煤灰的烧结结渣,而钙、铁的存在会加速硅铝酸盐间的反应生成低温共融物进而加速灰熔融。各煤种烧结温度的变化与其灰成分在CaO-SiO₂-Al₂O₃、FeO-SiO₂-Al₂O₃三元相图上的位置相吻合。     

A UV‐Cleavable Bottlebrush Polymer with o‐Nitrobenzyl‐Linked Side Chains

An ultraviolet (UV)‐cleavable bottlebrush polymer is synthesized using the “grafting‐onto” strategy by combining living radical polymerization and copper‐catalyzed azide‐alkyne cycloaddition (CuAAC). In this approach, reversible addition‐fragmentation chain transfer polymerization is used to prepare a poly(methylacrylate) backbone with azide side groups, while atom transfer radical polymerization is employed to prepare polystyrene (PS) side chains end‐functionalized with o‐nitrobenzyl (UV‐cleavable) propargyl groups. CuAAC is then used to graft PS side chains onto the polymer backbone, producing the corresponding bottlebrush polymers with UV‐cleavable PS side chains. The formation of the bottlebrush polymer is characterized by ¹H nuclear magnetic resonance spectroscopy, gel permeation chromatography (GPC), and Fourier transform infrared spectroscopy. The cleavage behavior of the bottlebrush polymer is monitored in tetrahydrofuran solution under UV irradiation by GPC and viscosity measurements.

     

Optimal investment strategies for participating contracts

Participating contracts are popular insurance policies, in which the payoff to a policyholder is linked to the performance of a portfolio managed by the insurer. We consider the portfolio selection problem of an insurer that offers participating contracts and has an S-shaped utility function. Applying the martingale approach, closed-form solutions are obtained. The resulting optimal strategies are compared with portfolio insurance hedging strategies (CPPI and OBPI). We also study numerical solutions of the portfolio selection problem with constraints on the portfolio weights.     

Erdélyi-type integrals for generalized hypergeometric functions with integral parameter differences

In this paper, we extend one of Erdélyi's classical integrals for the Gauss hypergeometric functions to a special class of generalized hypergeometric functions in which certain pairs of numerator and denomiator parameters differ by positive integers. Our main results are achieved by applying the fractional integration by parts and series manipulation technique. Some special cases are also pointed out which includes a new extension of a Thomae-type transformation.     

Numerical solution of a singular integral equation arising in a cruciform crack problem

A singular integral equation arising in a cruciform crack problem is investigated in the present paper. Based on the convex technique, the piecewise Taylor-series expansion method is extended by introducing a weight parameter. An approximate solution of the singular integral equation is constructed and its convergence and error estimate are made. The variations of the approximate solutions associating with stress intensity factors are analyzed by considering internal pressures of power and sine functions, respectively. By comparing with the known methods, the observations reveal that a good approximation can be achieved using less derivative times, less discretization points, and a suitable weight parameter. The obtained results show that the crack growth is dependent on applied mechanical loadings.     

Mixed two‐grid finite difference methods for solving one‐dimensional and two‐dimensional Fitzhugh–Nagumo equations

The aim of this paper is to propose mixed two‐grid finite difference methods to obtain the numerical solution of the one‐dimensional and two‐dimensional Fitzhugh–Nagumo equations. The finite difference equations at all interior grid points form a large‐sparse linear system, which needs to be solved efficiently. The solution cost of this sparse linear system usually dominates the total cost of solving the discretized partial differential equation. The proposed method is based on applying a family of finite difference methods for discretizing the spatial and time derivatives. The obtained system has been solved by two‐grid method, where the two‐grid method is used for solving the large‐sparse linear systems. Also, in the proposed method, the spectral radius with local Fourier analysis is calculated for different values of h and Δt. The numerical examples show the efficiency of this algorithm for solving the one‐dimensional and two‐dimensional Fitzhugh–Nagumo equations. Copyright © 2016 John Wiley & Sons, Ltd.     

DSMC approach to nonstationary Mach reflection of strong incoming shock waves using a smoothing technique

The direct simulation Monte Carlo (DSMC) method is applied to simulation of nonstationary Mach reflection of strong shock waves. Normally the DSMC method is very time consuming in solving unsteady flow field problems especially for high Mach numbers, because of the necessity of iterative calculations to eliminate the inherent statistical fluctuation caused by a finite sample size. A central weighted smoothing technique is introduced to process the DSMC results, so that the iteration time can be significantly reduced. In spite of some relaxations of the shock wave structure, the smoothing technique is verified to be useful to estima te the flow fields qualitatively and even quantitatively by using a relatively small sample size. The comparison between the present approach and the kineticmodel approach (Xu et al. 1991a, 1991b) on the application to unsteady rarefied flow fields was also carried out.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.