一类差分方程正解的有界性

关于最大类型的差分方程,Ladas、Stevic等人提出了一系列公开问题,Mishev D P、Kenneths等人已解决了其中许多问题.作者研究了一个差分方程正解的有界性,证明了这个方程的每一个正解是有界的,部分回答了Ladas G、Stevic S等人在文献[1-2]中提出的公开问题,部分推广了Kenneths在文献[4]中得出的结论.     

恒向线主题直接正反解的高精度算法

为提高精度、统一算法,应用拉格朗日级数理论和计算机代数系统,推导了经线弧长和等量纬度的计算公式,提出基于墨卡托投影的恒向线主题正反算法.该算法不需要迭代,应用数学上角度的定义解决了恒向线主题反解中方位角的解算问题,且不需要进行象限判定.结果表明,该算法计算精度高,具有通用性,特别适用于电算化,对船舶的航迹计算和电子海图中的航线设计具有一定的应用价值.     

存在反应的电解质溶液相平衡研究

从应用的角度出发,对电解质溶液模型、相平衡计算的现状与发展进行了简要的回顾,并系统地介绍和讨论了作者在这方面的工作。指出对Pitzer模型和作者提出的电解质溶液水化平衡模型建立各自相应的普遍化温度关系,结合所提出的固液平衡级计算方法,可以预测工业过程所涉度的高温、高压、高浓度范围内复杂体系的热力学性质,解决此类过程集成模拟优化的瓶颈问题。此外。还介绍了离子选择性电极测定弱电解质体系热力学的方法。     

半线性二阶微分方程周期边值问题

本文利用整体反函数理论,研究了半线性二阶微分方程周期边值问题,给出了周期解存在唯一性的充分条件.     

Chen-Lee-Liu方程的精确解

研究在非线性光学等领域出现的Chen-Lee-Liu(CLL)方程的精确解.通过对CLL方程的行波约化导出一个具有高次非线性项的非线性常微分方程.为了解该非线性常微分方程,给出一个新的辅助微分方程及其精确解.借助该辅助微分方程及其精确解,并根据齐次平衡原则,得到CLL方程的包络孤立波解和包络正弦波解.所用方法可应用到其它类似方程的求解.     

一类非线性二层规划的Frank-Wolfe方法

利用下层问题的K-T最优性条件将下层为线性规划的一类非线性二层规划转化为相应的单层规划,同时取互补条件为罚项,得到该类问题的单层罚问题;然后利用Frank-Wolfe方法对单层罚问题进行求解.数值实验表明该方法是可行的.     

纤维素在ZnCl_2水溶液中的溶解性能及再生结构

比较了不同质量分数的ZnCl2水溶液溶解不同聚合度纤维素的能力,发现:质量分数为65.0%以下的ZnCl2水溶液不能溶解纤维素;当ZnCl2水溶液的质量分数达到或超过65.0%时,未被水分子饱和的Zn2+可与纤维素分子链作用,使纤维素溶解,且65.0%的ZnCl2水溶液的溶解效果最佳;随着纤维素聚合度的增大,其溶解性能下降;经ZnCl2水溶液溶解后的再生纤维素的聚合度下降.广角X-射线衍射(WAXD)分析表明再生纤维素为纤维素Ⅱ结晶变体;傅里叶变换红外光谱(FT-IR)显示ZnCl2水溶液是纤维素的非衍生化溶剂,且再生纤维素分子内的氢键减弱.     

群决策的交互式TOPSIS方法及其应用

建立了一种多轮交互逐步逼近满意解的多属性群体决策的综合方法,对决策方案采用扩展的 TOPSIS(technique for order preference by similarity to ideal solution)法进行定性评价排序,以克服一类难以建立解析模型,分析求解困难的多属性群决策问题;设计了群体满意度等软指标来分析计算,判断群体一致性的达成,最终得出群体满意的方案排序.通过应用实例,说明了该方法的有效性和可行性,初步提出了可作为建立一类实际的群决策支持系统的方法和技术框架.     

Preface

Different from traditional tax audit, supervision with self-audit is a combination of audit by the taxpayer himself and audit by the tax authority. This paper mainly studies a taxpayer’s optimal policy of tax evasion under supervision with self-audit and its related properties, in order to deduce some effective suggestions and theoretical bases to restrain tax evasion. Assuming that only a certain proportion of evaded tax can be discovered when the audit is executed, the authors first formulate a static model with self-audit. This model is divided into two stages. At the first stage, taxpayers declare their taxes, then the tax authority chooses audit objects, based on a known probability, and announces the result; if the taxpayer is chosen, he will enter the second stage, during which he has a chance to pay the evaded tax and the corresponding late fees and then is audited by the tax authority. The authors show the existence and uniqueness of the optimal amount of tax evasion at the first stage and the optimal proportion to self-expose at the second stage. The authors also discuss the related properties of the interior solution, and do elasticity analyses on some parameters. Besides, the authors extend the static model into the corresponding two-period model, and study the existence and uniqueness of the solution of the extended model. Finally, under the assumption that tax evasion can only be discovered with a certain probability when the audit is executed, the authors formulate another static model with self-audit and investigate its properties. This research is partially supported by the National Natural Science Foundation of China under Grant Nos. 60674082, 70221001, and 70731003.     

Tax Evasion: Models with Self-Audit

Different from traditional tax audit, supervision with self-audit is a combination of audit by the taxpayer himself and audit by the tax authority. This paper mainly studies a taxpayer＇s optimal policy of tax evasion under supervision with self-audit and its related properties, in order to deduce some effective suggestions and theoretical bases to restrain tax evasion. Assuming that only a certain proportion of evaded tax can be discovered when the audit is executed, the authors first formulate a static model with self-audit. This model is divided into two stages. At the first stage, taxpayers declare their taxes, then the tax authority chooses audit objects, based on a known probability, and announces the result; if the taxpayer is chosen, he will enter the second stage, during which he has a chance to pay the evaded tax and the corresponding late fees and then is audited by the tax authority. The authors show the existence and uniqueness of the optimal amount of tax evasion at the first stage and the optimal proportion to self-expose at the second stage. The authors also discuss the related properties of the interior solution, and do elasticity analyses on some parameters. Besides, the authors extend the static model into the corresponding two-period model, and study the existence and uniqueness of the solution of the extended model. Finally, under the assumption that tax evasion can only be discovered with a certain probability when the audit is executed, the authors formulate another static model with self-audit and investigate its properties.