回归设计在增产菌、稀土、叶面宝混配试验中的应用

在农业科学实验中,经常会遇到确定最优农艺和最佳配方及制定自动控制中的数学模型等问题,在不完全了解生产过程中物理、化学和生物原理的情况下,用回归设计与分析的方法来解决是比较有效的.其优点是;试验处理组合少,计算方便,获得的信息多,其中一次回归的正交设计常被用来确定最优生产条件和因子筛选,二次回归的正交设计主要用于寻求最优配方和建立生产过程中的数学模型.本文介绍的是这两种设计方案在增产菌、稀土和叶面宝三     

一阶回归模型下Q和Q_B准则的几个结果

在试验设计中,一阶回归模型通常被作为合格拟合模型用来从众多因子中筛选出效应显著的特殊因子,而Q和Q_B准则能够比较简单地从大量的合格拟合模型中找出具有最优性质的设计.主要探讨了当拟合模型为一阶回归模型时,二水平的初始设计d与其Double设计(d d d -d)在Q和Q_B准则下的最优关系.给出了初始设计d的Q和Q_B值与其Double设计的Q和Q_B值之间的解析关系,从而得到在Q或Q_B准则下如果初始设计d是最优的,那么其Double设计也是最优的.此外,也分别给出了初始设计d及其Double设计的Q值和Q_B值的一个下界.     

装备系统的回归试验设计与分析优化算法

针对性能指标与影响因素间响应模型未知的试验设计与分析的优化问题进行理论研究和算例分析。利用装备系统的先验信息扩展回归基函数,构造二次回归模型来刻画系统的内在关系。基于模型驱动的最优设计,提出了相应的点交换迭代法以及梯度上升法选取最优试验点。为解决试验点数小于回归函数的维数时信息矩阵退化的问题,提出了基于成本和距离的"再筛选"方法,从已有的最优确切设计基础上"再筛选"试验点。将稀疏理论引入到回归试验设计中,把具有稀疏性的回归试验设计模型参数估计问题转换为稀疏重构问题。利用MP算法对回归模型进行参数估计,保证较高的参数估计精度。结合算例,对提出的试验设计优化方法和参数估计方法进行验证,表明最优确切设计比经典最大熵设计的精度更高。     

橡胶制品配方的二次回归正交优化设计

本文所介绍的二次回归正交设计方法,在杭州橡胶厂生产的内胎配方研究中得到了应用。该厂使用了优化后的配方不仅内胎的物理机械性能达到了世界先进水平,而且制品的成本也降低了。这种方法不仅适用于各类橡胶制品的最优配方的研究,也适用于各类化工产品最优工艺参数的研究。 橡胶制品配方的优化设计是一个多因素多指标的复杂课题。运用试验设计方法进行配方设计,将通过试验获得的数据进行回归分析,继而运用最优化方法,选出较优的配方,是目前世界上橡胶制品配方优化的先进方法,它已被世界先进国家所采用。     

利用回归设计模型寻求橡胶配方优化方案

一、前言橡胶配方是由天然胶、合成胶、硫化剂、促进剂、防老剂等组成的多因子体系.配方的评价又是涉及扯断强度、伸长率、硬度的一个多指标问题.本文首先运用回归设计的方法,建立了橡胶配方的数学模型.然后把多指标的优化问题归结为单指标的优化问题.最后,运用正交设计法寻优,获得了橡胶配方的最优配方.即在各项性能指标满足国家标准的前提下,设计出工艺性能良好、生产成本最低的配方。     

随机设计变量情形回归函数的非线性小波估计 *

在随机设计变量情形 ,构造了回归函数的非线性小波估计以及自适应非线性小波估计 .证明了非线性小波估计在Besov空间中可达到最优收敛速度 ,自适应非线性小波估计在一大类Besov空间中可达到次最优收敛速度 ,即和最优收敛速度只相差lnn .这样 ,在随机设计变量情形 ,所构造的回归函数的非线性小波估计和在固定设计点下对回归函数所构造的非线性小波估计几乎具有相同的优良性质 .进一步 ,只要求误差有有界三阶矩 ,而不要求误差服从正态分布 .     

基于工时优化的柔性生产人员配置模型及算法

为满足企业工时优化和提高运营效益的内在需求,针对柔性生产,以合理人工配置和最佳作业排序为目标建立了数学模型,并设计了递阶启发式搜索算法.根据组合并联作业结构特性,采用遗传算法优化子层作业的人工配置和作业工时,并将子层作业视为父层作业的相似阶段采用动态规划法决策父层的最优工时.在上述优化工作的基础上再利用改进蚁群算法,将其等效为具有m台处理机、目标函数为最优工时的流水车间作业排序问题,利用优先调度算法确定能见度因子并通过仿真和灵敏度分析优化了算法参数,最终生成最优作业排序计划.对实例问题的求解证明了研究模型和算法的有效性和鲁棒性.     

流态混凝土粗集料最佳级配的研究

本文通过D_n—最优三分量二次倒数项混料回归试验设计,综合考察了流态混凝土的工作性、离析行为以及28天强度等特性与粗集料级配之间的关系。建立的数学模型反映了流态混凝土的主要工程性质与粗集料级配之间的内在规律。通过计算机优化求解,找到了相应约束条件下的最佳级配。对丰富流态混凝土理论、试验研究,乃至指导现场工程质量管理与控制十分有益。     

政府补贴方式下排放许可交易生产优化

从学术上探讨了政府补贴方式下有排放许可交易的生产优化问题.分析了配额和补贴方式效果在管理上的差异,给出了补贴方式下的各经济核算关系及模型,给出了最低净化水平定理的证明;给出优化计算,求解了最优净化水平,并探讨了其与最优产量和企业最优收益间的关系;给出仿真计算,并对企业生产在这种支持方式下的优化管理进行了分析.研究表明:企业将对生产中产生的全部排放物进行相同净化水平α的处理时,所需要的处理费用最低;在线性反需求函数下,最优产量的变化量只与净化成本函数、排放交易价格、补助价格等几个量相关,最优收益与最优产量的平方成正比.     

最优分位水平及其衍生应用

分位数回归方法由于其具有稳健性,不仅能够全面刻画响应变量的条件分布,还能提供更有现实意义的回归参数,已经逐渐成为各个领域统计分析的强有力的工具.但在许多实际应用中,人们不仅想要探寻不同水平下(即不同分位数)响应变量与解释变量之间的关系,更希望找到一个最优水平,也即最优分位数,使其上的回归结果最真实可靠,最好地反映总体情况.文中提出一种新的回归方法一最优分位回归方法,给出此类问题一个完美的解决方案.该方法的灵感主要来源于稀疏函数的定义,可以证实与传统均值回归相比最优分位回归方法更具优势:(1)稳健性.不受误差分布的限制;(2)有效性.回归结果蕴含信息更丰富;(3)灵活性.对任意模型及数据均适用.文中的模拟结果也对以上三条性质给予极大的支持.最后食品消费数据的分析结果表明当考虑食品消费与人均收入的关系时,中下等收入人群的消费模式为社会的主流模式.     

Optimal yield in certain continuous chemical reactions

In this paper a consecutive chemical reaction of type A ? B ? C is considered where source A is turned to a product B in a catalytic reaction, and B is decomposed to C at the same time. Suppose that A can be supplied in a constant source concentration and B and C can be removed continuously. This continuous extraction process is modelled by means of partial differential equations and optimal yield of B is compared for different modelling assumptions. The complexity of the reaction models considered is increasing along the paper, starting from a simple flow model, to a percolation model and a transversal flow model describing the kinetics of a continuously operated flow reactor. It is shown that the efficiency of the reaction theoretically can be brought up arbitrary close to 1.     

Numerical simulation of line puff Via RNG ? - ? model

The time evolution of a line puff is studied using the renormalization group (RNG) κ - ? model. The predicted puff flow and mixing rate are substantially similar to those obtained from the standard k -? model, and are well-supported by experimental data. The computed scalar field reveals significant secondary concentration peaks trailing behind in the wake of the puff. The present results suggest that the overall mixing rate of a puff is primarily determined by the large scale motion, and that streamline curvature probably plays a minor role.     

A Shell Model for Optimal Mixing

What is the maximum mixing efficiency of an incompressible flow? To address this question we introduce a shell model—a reduced model mimicking the kinematics of advection and diffusion—to study the evolution of an initially inhomogeneous tracer concentration carried by a given incompressible fluid on a periodic spatial domain. We pose the mixing task as an optimization problem: Find the divergence-free velocity field (the control variable) that produces a well-mixed tracer concentration field (the state variable). We consider two alternative objectives: local-in-time optimization (maximize the instantaneous mixing rate) and global-in-time optimization (maximize mixing at a prescribed final time). Throughout, we use a shell-model analog of the \(H^{-1}\) mix-norm to measure mixing. In addition, lower bounds on the mix-norm are obtained and rule out perfect mixing in finite time in particular cases.     

Nonlinear reaction-diffusion models for interacting populations

This paper proves that several initial-boundary value problems for a wide class of nonlinear reaction-diffusion equations have solutions c_i(x, t), 1 ? i ? N (with c_i(x, t) representing the concentration of the ith species at position x in a set $\text{Ω}$ at time t ? 0), which exist for all t ? 0 and are unique, smooth, nonnegative, and strictly positive for t > 0. The Volterra-Lotka predator-prey model with diffusion (to which the results above are proved to apply) is then studied in more detail. It is proved that any bounded solution of this model loses its spatial dependence and behaves like a periodic function of time alone as t → ∞. It is proved that if the spatial dimension is one or if the diffusion coefficients of the two species are equal, then all solutions are bounded.     

Stability of solutions to a mathematical model for necrotic tumor growth with time delays in proliferation

In this paper, a mathematical model for a solid avascular tumor growth is studied. The model describes tumor growth with a necrotic core and a time delay in proliferation process. The model was proposed by Byrne and Chaplain, and was studied by M. Bodnar and U. Fory? (see [2]). Sufficient conditions which guarantee existence, uniqueness and stability of steady state are given. The results show that the dynamical behavior of the solutions of the model is similar to that of the solutions for the corresponding non-retarded problem under some assumptions. Our results partially improve the corresponding results given by M. Bodnar and U. Fory?. The results make the research for this model more perfect.     

Geometric measures in the dual Brunn–Minkowski theory and their associated Minkowski problems

A longstanding question in the dual Brunn–Minkowski theory is “What are the dual analogues of Federer’s curvature measures for convex bodies?” The answer to this is provided. This leads naturally to dual versions of Minkowski-type problems: What are necessary and sufficient conditions for a Borel measure to be a dual curvature measure of a convex body? Sufficient conditions, involving measure concentration, are established for the existence of solutions to these problems.     

Economic design of variable parameters <Emphasis Type="Italic">X̄</Emphasis> control charts for processes with fuzzy mean shifts

Modern studies have shown that the X? control charts with variable parameters (VPs) detect process shifts faster than the traditional X? control charts. This article developed the economic design of the VP X? control chart to determine the values of the design parameters of the chart. However, this study, different from previous studies, was focused on the process that is subject to a disturbing cause, and the occurrence of the cause can result in a fuzzy mean shift (ie the magnitude of the mean shift could not be recognized exactly). The issue of economically selecting the design parameters for the chart was firstly formulated as a mathematical programming model with a fuzzy objective function that could cope with fuzzy number type of mean shift. A fuzzy-simulation-based genetic algorithm was then employed to search for the optimal values of the design parameters from the model. An industrial example was provided to illustrate the solution procedure, and was used for comparison between the VP and the traditional X? chart. Effects of model parameters on the solution of the economic design were also discussed.     

一类新的污染环境下具有时滞增长反应及脉冲输入的Monod恒化器模型的定性分析

考虑了一类新的污染环境下具有时滞增长反应及脉冲输入的Monod恒化器模型．运用离散动力系统的频闪映射,获得了一个‘微生物灭绝’周期解,进一步获得了该周期解全局吸引的充分条件．运用脉冲时滞泛函微分方程新的计算技巧,证明了系统在适当的条件下是持久的,结论还表明该时滞是“有害”时滞．     

On the optimization of supply chain networking decisions

Companies strive to position themselves to maximize the value they add to the supply chains in which they are embedded. This raises strategic questions such as: Which durable resources should be developed to enhance current core competencies? Which activities should be externalized and to which potential partner should they be given? Which internal activities should be preserved and developed? How should the resources of the enterprise be allocated to activities? The aim of this paper is to propose a mathematical programming model of the extended enterprise which can be used to investigate this type of strategic networking issues. A number of general network modeling constructs are first proposed. A model to optimize the supply chain structure under specific assumptions on the nature of production, cost and value functions in typical production/distribution companies is then derived. A heuristic to obtain solutions from the model is also presented. Finally, an example based on a refrigerator company is used to illustrate the usefulness of the approach.     

Multistage reverse logistics of assembly systems in extended MRP Theory consisting of all material flows

In this paper we will address the issue of environmental problems in connection with extended MRP Theory. It is based on Grubbstr?m??s well developed MRP Theory (Grubbstr?m in Z für BetrWirthsch 77(3):297?C324, 2007). A major advantage of this theory is that timing and its impact on net present value can be easily calculated even for extended multilevel, multistage production-inventory systems and also for perturbed production systems consisting of many production cells. Theory has recently been extended by including reverse logistics of final and used products (Grubbstr?m et?al. in A compact representation of distribution and reverse logistics in the value chain. Faculty of Economics, Ljubljana, 2007). At each activity cell a certain percentage of scrapes is produced and sent for recycling after quality control. Here we present an input?Coutput model which includes all possible flows into a recycling sub-process with several stages of recycling. This model is presented in a generalized form of input and output matrices which has not been developed before. The model will be presented in two different ways which differ in the level of detailed information they contain. Contribution of recycling to the net present value of all activities in a supply chain is expressed and can be compared to environmental damage that could occur if reverse processes are not introduced. Using this approach, the losses and gains in both the economy and the environment could be evaluated more accurately considering all individual flows in the system. No other approaches besides input?Coutput analysis and Laplace transforms have been found so successful in compound supply systems.