一类复常微分方程组的亚纯解

本文应用值分布论,对一类复常微分方程组亚纯解的可能形式进行了研究,推广了[4]中的结果。     

半线性热方程的一个反问题

讨论了无界区域上半线性热方程确定未知数偶（ｕ，ｐ）的反问题。设计了一种独特的迭代方法，给出了该问题整体解的存在惟一性和稳定性。     

在整体色对称模型下的夸克囚禁势

在整体色对称模型框架下，基于已经确定好的双定域场，推导了等效的夸克夸克相互作用势．结果表明除了通常的单π及单σ交换项外，自动出现了带有屏蔽因子的囚禁势．     

原子-键电负性均衡融合进分子力场对CoCl3水溶液的分子动力学模拟研究

298．15K时运用原子-键电负性均衡融合进分子力场（ABEEM／MM）对CoCl3水溶液进行了分子动力学模拟．结果表明，ABEEM／MM力场模型可以获得体系的动态电荷，充分考虑了体系中存在的极化现象，从而及时地调节改变的静电场，真实地模拟了溶液的微观结构；并且CoCl3溶液中钴离子更倾向于和氯离子配位，而使钴离子与水分子的配位能力降低．     

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.     

可控增长条件下一类椭圆型方程弱解的局部极值原理

研究二阶非线性椭圆型偏微分方程－ｄｉｖＡ（ｘ，ｕ， ｕ）＋ Ｂ（ｘ，ｕ，ｕ）＝μ，在可控增长结构条件－Ａ（ｘ，ｚ，η）·η≥λ｜η｜ｐ－Ａ｜η｜ｐ＊－１，Ｄ｜Ａ（ｘ，ｚ，η）｜＜Ａ１（｜η｜~(ｐ－１)十｜ｚ｜ｐ＊（１－１／ｐ）．｜Ｂ（ｘ，ｚ，η）｜≤Ａ（｜η｜ｐ（１－１／ｐ＊）＋｜ｚ｜ｐ＊－１）下，应用 Ｍｏｓｅｒ迭代法得出弱解的局部极值原理，并进一步得出弱解的内部估计和全局估计．     

Pareto/NBD模型扩展

Pareto/NBD模型是由schmittlein等(1987)提出,用于描述非契约客户关系情景下客户重复购买行为.该模型被认为是目前客户基分析中的基准模型,但其所基于的概率分布假设过于严格,且存在与常识不符的问题.针对这些问题,使用马尔可夫链蒙特卡罗方法,直接获得客户购买率和流失率的后验样本,从而使放松Pareto/NBD模型的假设成为可能.通过放松Pareto/NBD模型假设,设计了三个扩展模型,推导了相应的公式.用实际的数据集对pareto/NBD模型及其扩展进行预测效果对比,发现了预测能力明显高于Pareto/NBD模型的扩展模型.     

周期与反周期的Halanay准则

研究发展方程的周期解和反周期解的存在性, 给出了发展方程的周期与反周期的Halanay准则.