Case studies in dynamic modelling of large-scale wastewater treatment plants

Several large-scale wastewater treatment plants have been modelled successfully using an extensive modelling library in the General Purpose Simulator, GPS-X. The mathematical models included all important processes on the selected wastewater treatment plants, i.e. primary sedimentation, activated sludge biokinetics and final clarification.The models have been used in different areas, such as: a)analysis of operational scenarios; b) determenation of sustained and peak capacity of plants(rated plant capacity) and c) investigation of plant expansion scenarios. Out of more than twenty documented cases four, involving simulation studies on large-scale wastewater plants are discussed.     

适用于二级与多级评分项目组成的混合测试的加权最大似然潜在特质估计（英文）

提出适用于二级与多级评分项目组成的混合测试的加权最大似然潜在特质估计.使用N-R算法获得WML估计,并给出相关方程的详细推导.为探讨WML的性能,进行了模拟研究,所得到的结果表明,WML的估计比最大似然估计（MLE）具有更好的性能.最后,基于一个实际例子对该方法进行了实证研究.     

FC模 型视角下基础设施建设与工业区位分布

最初的工业区位论过多从静态角度分析基础设施数量对工业区位分布影响,往往忽视基础设施效率的影响．基于此,本文在政府、消费者、企业三方博弈的基础上,探求扩展FC模型下短期及长期均衡条件,进而讨论基础设施数量及效率如何影响区域间产业分布格局．研究发现：基础设施效率影响着劳动力流动,从而影响着其他要素的区域分布．结果表明,不是基础设施数量而是基础设施交易效率影响了工业区位分布．也就是说,基础设施在落后地区的投入并非越多越好,而是效率越高越好．     

The Asymptotic Stability of x(n + k) + ax(n) + bx(n-l) = 0

We established necessary and sufficient conditions for the asymptotic stability of the difference equation where the coefficients a and b are real numbers and k and l are nonnegative integers.     

Approximate reduction of non-linear discrete models with two time scales

The aim of this work is to present a general class of nonlinear discrete time models with two time scales whose dynamics is susceptible of being approached by means of a reduced system. The reduction process is included in the so-called approximate aggregation of variables methods which consist of describing the dynamics of a complex system involving many coupled variables through the dynamics of a reduced system formulated in terms of a few global variables. For the time unit of the discrete system we use that of the slow dynamics and assume that fast dynamics acts a large number of times during it. After introducing a general two-time scales nonlinear discrete model we present its reduced accompanying model and the relationships between them. The main result proves that certain asymptotic behaviours, hyperbolic asymptotically stable (A.S.) periodic solutions, to the aggregated system entail that to the original system.     

半相依部分线性可加回归模型的统计推断

受实际问题研究的启发, 为减少模型偏差, 提出了一类半相依部分线性可加的半参数回归模型. 这类半相依模型中, 响应变量与 一部分解释变量之间的关系是线性的, 与另一部分解释变量之间的关系未知但具有可加结构, 各方程的误差之间是相关的. 将级 数逼近法、最小二乘法和同期相关的估计结合起来, 提出了用于估计模型参数分量的加权半参数最小二乘估计量(WSLSEs), 和用于估 计模型非参数分量的加权级数逼近估计量(WSEs). 证明了这些加权的估计量比相应的不加权的估计量渐近有效, 并导出了相应的渐近正态性. 另外, 还讨论了利用这些估计量的渐近性质来对模型的参数及非参数分量作统计推断. 用大量的模拟实验考察 了所提出的方法在有限样本情况下的表现, 并对美国的一个关于妇女工资问题的全国纵向调查(NLS)数据集进行了统计分析.     

皮肤毛孔照片诊断标准评价的潜在分类变量模型研究

本文在无金标准情况下探讨皮肤毛孔标准照片制定的合理性和可行性,对医师诊断正确性进行评价。按照毛孔粗大程度制定分类为5水平的毛孔标准照片。对128名女性志愿者制作鼻翼毛孔照片,5位年资相近的皮肤科医师按照诊断标准和标准照片对128例自愿者照片进行独立的等级评分。诊断结果数据采用潜在分类变量模型(Latent Class Model,LCM)进行分析,分别拟合5位医师诊断条件概率一致的模型和诊断条件概率不一致的模型。计算医师诊断的条件概率和后验概率。潜变量分析结果提示诊断标准过于细化且分类模糊,依据条件概率将原始分类重新划分为3类的模型较好地拟合了诊断数据。运用客观和准确的能够真实反应和区分个体情况的诊断标准是诊断试验评价的基础和前提。潜在分类模型能够有效地处理无金标准的诊断重复性或一致性研究数据。     

Two positivity preserving flux limited,second‐order numerical methods for a haptotaxis model

Two numerical methods for a one‐dimensional haptotaxis model, which exploit the use of van Leer flux limiter, are developed and analyzed. Sufficient conditions time step size and flux limiting are given for such formulation to ensure the non‐negativity of the discrete solution and second‐order accuracy in space. Another advantage is that we avoid solving large nonlinear systems of algebraic equations. The discrete preservation of total conservation of cell density, concentration, and logarithmic density is also verified for the numerical solution. Numerical results concerning accuracy, convergence rate, positivity, and conservation properties are presented and discussed. Similar approach could be applied efficiently in the corresponding two‐ and three‐dimensional problems. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013