图腾艺术在现代设计中的应用略论

图腾艺术所体现的深刻历史文化内涵在现代社会有了新的延伸,并被现代设计师们以全新的方式进行表达,最终成为一种新形式。设计师通过取其＂形＂、延其＂意＂、传其＂神＂的运用,展现了远古图腾再现的艺术魅力,赋予了图腾新的时代特色,也使得图腾文化与现代设计紧密的结合在一起。     

Using intersection matrices to identify graphical structure

Intersection matrices help identify the common graphical structure of two or more objects. They arise naturally in a variety of settings. Several examples of their use in a computer algebra environment are given. These include: simplifying an expression involving array products, automating cumulant calculations, determining the behaviour of an expected value operator and identifying model hierarchy in a factorial experiment. The emphasis is placed on the graphical structure, and the symmetry of arrays help reduce the complexity of the graphical problem.     

Construction of repeated measurements designs strongly balanced for residual effects

Abstract

Repeated Measurements Designs have been widely used in agriculture, animal husbandry, education, biology, botany and engineering. Balanced or strongly balanced repeated measurements designs are useful to balance out the residual effects. In this article, some new generators and construction procedures are proposed to obtain circular strongly balanced repeated measurements designs in periods of (a) equal sizes, (b) two different sizes, and (c) three different sizes.     

Incomplete block designs for symmetrical parallel line assays

New series of incomplete block designs for symmetrical parallel lines are proposed. From these designs important contrasts like L_p, L₁ and L′₁ are estimated free from block effects. In addition to these, other odd order contrasts are also estimated orthogonal to block effects. The designs are shown to have simple analysis.     

Approximate theory of multiway block designs

Optimality properties of multiway block designs are deduced from the general results of J. Kiefer's approximate-design theory. In the model with additive effects these optimality properties solely depend on the two-dimensional marginals of the designs. Uniform designs, and designs whose two-dimensional marginals are products of the one-dimensional marginals, are shown to be optimal. Approximate Youden designs are introduced for the case when the support sets of the two-dimensional marginals are prescribed in advance. They are optimal in a relatively small class of competing designs only.     

E-optimal designs for regression models with quantitative factors— a reasonable choice?

For regression models with quantitative factors it is illustrated that the E-optimal design can be extremely inefficient in the sense that it degenerates to a design which takes all observations at only one point. This phenomenon is caused by the different size of the elements in the covariance matrix of the least-squares estimator for the unknown parameters. For these reasons we propose to replace the E-criterion by a corresponding standardized version. The advantage of this approach is demonstrated for the polynomial regression on a nonnegative interval, where the classical and standardized E-optimal designs can be found explicitly. The described phenomena are not restricted to the E-criterion but appear for nearly all optimality criteria proposed in the literature. Therefore standardization is recommended for optimal experimental design in regression models with quantitative factors. The optimal designs with respect to the new standardized criteria satisfy a similar invariance property as the famous D-optimal designs, which allows an easy calculation of standardized optimal designs on many linearly transformed design spaces.     

计算机辅助正交试验设计

因素(析因)试验是一种常见的试验。当部分因素间交互作用可以忽略时,正交试验设计是一种快速、有效的方法。本文分析了L_tu(t~q)型正交表的特性,探索应用计算机编制正交表及其交互作用列表的方法,并在此基础上,设计了功能齐全的通用软件。计算机辅助试验将帮助那些不熟悉试验设计理论的工程技术人员合理地安排试验。     

COMPUTER-AIDED CONSTRUCTION OF SMALL (M, S)-OPTIMAL INCOMPLETE BLOCK DESIGNS

A new exchange algorithm for the construction of (M, S)-optimal incomplete block designs (IBDS) is developed. This exchange algorithm is used to construct 973 (M, S)-optimal IBDs (v, k, b) for v= 4,…,12 (varieties) with arbitrary v, k (block size) and b (number of blocks). The efficiencies of the “best” (M, S)-optimal IBDs constructed by this algorithm are compared with the efficiencies of the corresponding nearly balanced incomplete block designs (NBIBDs) of Cheng(1979), Cheng & Wu (1981) and Mitchell & John(1976).     

Some new construction of circular weakly balanced repeated measurements designs in periods of two different sizes

Abstract

Balanced repeated measurements designs (RMDs) balance out the residual effects. Williams Latin square designs work as minimal combinatorial balanced as well as variance balanced for RMDs for p (period sizes) = v (number of treatments). If minimal balanced RMDs cannot be constructed for the situations where p must be less than v then weakly balanced RMDs should be preferred. In this article, some generators are developed to generate circular weakly balanced RMDs in periods of two different sizes. To obtain the proposed designs, some construction procedures are also described for some of the cases where we could not develop generators.     

Asympitic approach to families of desigh problems

Examples are given that demonstrate the usefulness, for obtaining near-optimum designs in analytically intractable settings, of embedding such settings in a regular family of designs whose limit is easier to treat.