The author constructed a linear schemes type Region-Project-Join-Normal-Form based on lossless join decomposition, and gave the form of RPJNF through the presentation of equivalence between semantic variable independence and syntax variable independence under finite precision domain. Some other new constraint data dependencies including partitioned multi-region existence dependency and single region existence dependency were also presented. A result of variables set under linear transformation was discussed.
文中给出并证明了多区域存在依赖满足的几条推理规则；提出并证明了线性序约束关系进行模式无损连接分解的充要条件是变量集满足变量独立和多区域存在依赖；设计了一种基于模式无损连接分解的区域投影连接范式；通过证明有限精度域上语义变量独立和语法变量独立的等价性，给出有限精度域上RPJ范式的表达形式。
In addition, This chapter also explains how to analyze edge finite element by the traditional vector presentation.
第4章应用微分形式对Whitney型六面体单元和三棱柱单元进行详细的分析，这里给出的分析方法同样适合Mur型棱边有限元各种单元的分析。
Introduction of multivariate Variational principles for the formulation of finite element methods for solid mechanics, presentation of the progress made in advancing the method for constructing hybrid stress finite elements, and description of special applications of the hybrid stress finite element methods.
介绍了建立固体力学有限元法的多变量变分原理，和推导杂交应力有限元方法的演变.并指出杂交应力有限元法的许多特殊应用。