复微分方程组的超越解

利用最大模原理,讨论了复代数微分方程组的超越亚纯解存在性问题,得到了在一定条件下,该方程组的超越解为代数解的一个结果.例子表明这个结果是精确的.     

Mixed eigenvalues of discrete p-Laplacian

This paper deals with the principal eigenvalue of discrete p-Laplacian on the set of nonnegative integers. Alternatively, it is studying the optimal constant of a class of weighted Hardy inequalities. The main goal is the quantitative estimates of the eigenvalue. The paper begins with the case having reflecting boundary at origin and absorbing boundary at infinity. Several variational formulas are presented in different formulation： the difference form, the single summation form, and the double summation form. As their applications, some explicit lower and upper estimates, a criterion for positivity （which was known years ago）, as well as an approximating procedure for the eigenvalue are obtained. Similarly, the dual case having absorbing boundary at origin and reflecting boundary at presented at the end of Section 2 to infinity is also studied. Two examples are illustrate the value of the investigation.     

表面活性剂CMC值的测定研究

发现表面活性物质正丁醇的吸附量Γ随浓度c的不断上升最终会下降,这与吉布斯吸附公式的推导结果不符。对此,深入研究了其临界胶束浓度(CMC)与Γ的关系,最终分析得出Γ下降区段对应的浓度是没有意义的,即吉布斯吸附公式的推导使用只在浓度不超过CMC时才有意义。     

类氖氩离子能级及碰撞强度的计算

利用扭曲波波恩近似方法及AUTOSTRUCTURE (AS)程序，快速精确地计算了类氖Ar8+离子2s22p6、2s22p53s、2s22p53p、2s22p53d、2s2p63s、2s2p63p和2s2p63d组态的能级以及当电子碰撞能量为75.0、125.0、175.0、250.0 (Ry)时，从j能态到i能态的碰撞强度.并且与已有的研究成果进行了对比.结果表明，采用扭曲波波恩近似并结合AUTOSTRUCTURE (AS)程序的研究方法，可以成为研究原子或离子碰撞强度的有效途径。     

A corresponding-state approach to quark-cluster matter

The state of super-dense matter is essential for us to understand the nature of pulsars; however, non- perturbative quantum chromodynamics makes it very difficult to make direct calculations of the state of cold matter at realistic baryon number densities inside compact stars. Nevertheless, from an observational point of view, it is conjectured that pulsars could be made up of quark clusters since the strong coupling between quarks might render the quarks to be grouped in clusters. In this paper, we attempt to find an equation of state of condensed quark-cluster matter in a phenomenological way. Supposing that the quark-clusters could be analogized to inert gases, we apply here the corresponding-state approach to derive the equation of state of quark-cluster matter, as was similarly demonstrated for nuclear and neutron-star matter in the 1970s. According to the calculations that we have presented, the quark-cluster stars, which are composed of quark-cluster matter, could have a high maximum mass that is consistent with observations and, in turn, further observations of pulsar mass could also place a constraint on the properties of quark-cluster matter. We will also briefly discuss the melting heat during the solid-liquid phase conversion and its related astrophysical consequences.     

中国进口食品安全风险评估的统计学方法

近年来,随着对外贸易的快速发展和人民生活水平的不断提高,我国已经成为食品进口大国。运用科学的方法优化检验资源配置,强化对进口食品安全的风险管理,是一个关系到人民福社的重大问题。国际上通行的做法是对不同种类的食品和检测项目的潜在风险进行评估,并根据评估结果制定有针对性的监督抽检计划,使得更多的检验资源可以投入到对高风险产品和项目的监管中去。我国在这方面的管理实践才刚刚起步,急需建立一套符合我国食品进口自身特点和管理需求的风险评价模型和相应的估计方法。本文借鉴了其它国家的相关做法,并结合我国进口食品的管理需求和历史检测数据的特点,制定了一套完整的风险评价和估计方法。     

三维Zakharov-Kuznetsov方程解的衰减性

考虑三维Zakharov-Kuznetsov方程的初值问题,证明了该初值问题解的指数衰减性.这个性质与加权Sobolev空间中解的持久性及该问题解的唯一连续性相关.     

非线性Black-Scholes模型下算术平均亚式期权定价问题

在非线性Black-Scholes模型下,研究了算术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,给出了算术平均亚式期权的近似定价公式.最后分析了近似结论的误差估计,并通过数值算例验证了所得近似结论的合理性.     

误差合成空间固定系数模型的多阶段广义最小二乘估计

本文对时变系数的空间面板数据模型进行了研究,所研究的模型利用扰动项中的空间个体成分将不同时期的方程联系起来,同时,自变量系数和空间自回归系数是时变的,但不会随着观测个体的变动而变动。本文利用基于可行的广义最小二乘估计的多阶段方法对模型参数进行了估计,研究了估计量的大样本性质,并利用Monte Carlo方法模拟了其小样本性质。模拟结果表明,估计量的渐近性质随着样本容量的增加而改善。对中国省级地区间财税策略互动行为的实证案例也体现了本文理论模型的应用价值。