Construction of 2Ⅲ^[m-（m-k）] Designs with the Maximum Number of Clear Two-factor Interactions

It is useful to know the maximum number of clear two-factor interactions in a_Ⅲ~(m-(m-k))design.This paper provides a method to construct a 2_Ⅲ~(m-(m-k))design with the maximum number of clear two-factorinteractions.And it is proved that the resulting designs have more clear two-factor interactions than thoseconstructed by Tang et al.Moreover,the designs constructed are shown to have concise grid representations.     

Null Controllability in a Heat–Solid Structure Model

A model representing a coupling between a heat conducting medium and a solid structure is considered. We establish a Carleman inequality for this model. Next we deduce a null controllability result with an internal control in the conducting medium and there is no control in the solid part.     

Effect of nonlinear wave-current interaction on flow fields and hydrodynamic forces

A fifth-order theory for solving the problem of interaction between Stokes waves and exponential profile currents is proposed. The calculated flow fields are compared with measurements. Then the errors caused by the linear superposition method and approximate theory are discussed. It is found that the total wavccurrent field consists of pure wave, pure current and interaction components. The shear current not only directly changes the flow field, but also indirectly does so by changing the wave parameters due to wave-current interaction. The present theory can predict the wave kinematics on shear currents satisfactorily. The linear superposition method may give rise to more than 40% loading error in extreme conditions. When the apparent wave period is used and the Wheeler stretching method is adopted to extrapolate the current, application of the approximate theory is the best. Project supported by the Chinese Academy of Sciences.     

Hugoniót--Maslov Conditions for Vortex Singular Solutions of the Shallow Water Equations

For the phase of vortex singular solutions of the shallow water equations we justify the Hamilton--Jacobi equation corresponding to the hydrodynamical mode of perturbation propagation. We also obtain the next correction to the Cauchy--Riemann conditions describing how the singular part of the solution affects the smooth background.     

Coupled Amplitude-Streaming Flow Equations for Nearly Inviscid Faraday Waves in Small Aspect Ratio Containers

Summary. We derive a set of asymptotically exact coupled amplitude-streaming flow ({CASF}) equations governing the evolution of weakly nonlinear nearly inviscid multimode Faraday waves and the associated streaming flow in finite geometries. The streaming flow is found to play a particularly important role near mode interactions. Such interactions come about either through a suitable choice of parameters or through breaking of degeneracy among modes related by symmetry. An example of the first case is provided by the interaction of two nonaxisymmetric modes in a circular container with different azimuthal wavenumbers. The second case arises when the shape of the container is changed from square to slightly rectangular, or from circular to slightly noncircular but with a plane of symmetry. The generation of streaming flow in each of these cases is discussed in detail and the properties of the resulting CASF equations are described. A preliminary analysis suggests that these equations can resolve discrepancies between existing theory and experimental results in the first two of the above cases.     

Some results on 4<Superscript><Emphasis Type=Italic>m</Emphasis></Superscript>2<Superscript><Emphasis Type=Italic>n</Emphasis></Superscript> designs with clear two-factor interaction components

Clear effects criterion is one of the important rules for selecting optimal fractional factorial designs, and it has become an active research issue in recent years. Tang et al. derived upper and lower bounds on the maximum number of clear two-factor interactions (2fi’s) in 2 ^n−(n−k) fractional factorial designs of resolutions III and IV by constructing a 2 ^n−(n−k) design for given k, which are only restricted for the symmetrical case. This paper proposes and studies the clear effects problem for the asymmetrical case. It improves the construction method of Tang et al. for 2 ^n−(n−k) designs with resolution III and derives the upper and lower bounds on the maximum number of clear two-factor interaction components (2fic’s) in 4 ^m 2 ⁿ designs with resolutions III and IV. The lower bounds are achieved by constructing specific designs. Comparisons show that the number of clear 2fic’s in the resulting design attains its maximum number in many cases, which reveals that the construction methods are satisfactory when they are used to construct 4 ^m 2 ⁿ designs under the clear effects criterion. This work was supported by the National Natural Science Foundation of China (Grant Nos. 10571093, 10671099 and 10771123), the Research Foundation for Doctor Programme (Grant No. 20050055038) and the Natural Science Foundation of Shandong Province of China (Grant No. Q2007A05). Zhang’s research was also supported by the Visiting Scholar Program at Chern Institute of Mathematics.     

隐变量交互作用分析建模及其在SAS上的实现

探讨隐变量交互作用分析的建模方法及其在SA S软件上的实现;首先阐述隐变量交互作用分析建模的原理,通过拟合一个隐变量交互作用分析示例,对加入交互作用项的统计分析结果与无交互作用项的统计分析结果进行对比;示例中交互作用项引起的变异在结果变量的总变异中占到79.20%.在应用结构方程模型分析隐变量产生的效应时,有时候不进行隐变量交互作用的分析可能会产生偏倚.     

产品销售相关环境下的提成率研究

以往多产品销售的最优提成率研究多基于多产品销售相互独立的假设之上。本文将一种多产品销售的合同模型拓展到产品销售相互影响的环境中,对不同的销售相关性情况下销售提成率的设置进行了分析,推出了不同情况下各产品提成率之间的关系特点和指导性结论。最后研究了当厂商兼顾短期利润和长期利润时对主副产品销售提成率的影响,提出了根据产品所处生命周期的不同阶段,用价值权重向量来动态调整、优化负责销售主、副产品的销售人员薪酬合同参数设计的方法。