N‐dimensional switch function for energy conservation in multiprocess reaction dynamics

The MReaDy program was designed for studying Multiprocess Reactive Dynamic systems, that is, complex chemical systems involving different and concurrent reactions. It builds a global potential energy surface integrating a variety of potential energy surfaces, each one of them representing an elementary reaction expected to play a role in the chemical process. For each elementary reaction, energy continuity problems may happen in the transition between potential energy surfaces due to differences in the functional form for each of the fragments, especially if built by different authors. A N‐dimensional switch function is introduced in MReaDy in order to overcome such a problem. As an example, results of a collision trajectory calculation for H₂ + OH → H₃O are presented, showing smooth transition in the potential energy, leading to conservation in the total energy. Calculations for a hydrogen combustion system from 1000 K up to 4000 K shows a variation of 0.012% when compared to the total energy of the system. © 2016 Wiley Periodicals, Inc.     

Barzilai–Borwein method with variable sample size for stochastic linear complementarity problems

A smoothing method for solving stochastic linear complementarity problems is proposed. The expected residual minimization reformulation of the problem is considered, and it is approximated by the sample average approximation (SAA). The proposed method is based on sequential solving of a sequence of smoothing problems where each of the smoothing problems is defined with its own sample average approximation. A nonmonotone line search with a variant of the Barzilai–Borwein (BB) gradient direction is used for solving each of the smoothing problems. The BB search direction is efficient and low cost, particularly suitable for nonmonotone line search procedure. The variable sample size scheme allows the sample size to vary across the iterations and the method tends to use smaller sample size far away from the solution. The key point of this strategy is a good balance between the variable sample size strategy, the smoothing sequence and nonmonotonicity. Eventually, the maximal sample size is used and the SAA problem is solved. Presented numerical results indicate that the proposed strategy reduces the overall computational cost.     

非线性Black-Scholes模型下几何平均亚式期权定价

在非线性Black-Scholes模型下,本文研究了几何平均亚式期权定价问题.首先利用单参数摄动方法,将亚式期权适合的偏微分方程分解成一系列常系数抛物方程.其次通过计算这些常系数抛物型方程的解,给出了几何平均亚式期权的近似定价公式.最后利用Green函数分析了近似结论的误差估计.     

具有相依结构离散时间模型破产概率的上界

研究两类具有相依结构的离散时间风险模型的破产概率问题.其中,索赔和利率过程假设为2个不同的自回归移动平均模型.利用更新递归技巧,首先得到了该模型下破产概率所满足的递归方程.然后,根据该递归方程得到了破产概率的上界估计.最后对两类风险模型的破产概率的上界进行了比较.     

带有相依利率和保费的离散时间模型的破产问题

考虑一类具有相依结构的离散时间风险过程,其中利率和保费收入过程为两个不同的自回归移动平均模型.利用更新递归方法,得到了破产前盈余与破产后赤字的联合分布和破产持续时间分布的递归计算公式.     

The average norm of polynomials of fixed height

Let be any integer and let

be the set of all polynomials of height 1 and degree . Let

Here is the power of the norm on the boundary of the unit disc. So is the average of the power of the norm over

In this paper we give exact formulae for for various values of . We also give a variety of related results for different classes of polynomials including polynomials of fixed height H, polynomials with coefficients and reciprocal polynomials. The results are surprisingly precise. Typical of the results we get is the following.

Theorem 0.1. For , we have

and

     

高效液相色谱法测定盐酸羟甲唑啉滴鼻剂的稳定性

The stability of oxymetazoline hydrochloride nasal solution was determined by HPLC and the initialaverage rate method. The procedure was carripd out on a 250mm×4. 6mm column with 5μm ODS using wa-ter-methanol-sodium acetate solution(lmol/L)-glacil acetic acid-triethylamine as mobile phase,with UV de-tection at 280nm. The elution was performed at the flow rate of lmL/min. The results show that the expirydate of this preparation is about three years at room temperature.