A new model named DPE net is advanced for describing the WS-BPEL process under the dead-path-elimination semantics. Color sets CTRL and STAT are introduced to represent the states of activities and status of links within activity flow. This can reduce the scale of the model, thus a more intuitive model can be got. DPE net models for various control structures of WS-BPEL are given, which describe not only basic control flow, including basic activities and structured activities, but also dead path elimination semantics and relatively complete link semantics, including join conditions and transition conditions. Finally, a case study shows that modeling WS-BPEL process with DPE net will help get more accurate analysis results.

The two-value weak model for first order logic with generalized quantifier Q is generalized to be valued in complete weak complemented lattices. For finite linearly-ordered weak complemented lattice, some properties on elementary extension of models for L(Q), such as strong downward L-S-T Theorem and the preservation of the elementary diagram under elementary extensions, are discussed.

The two-valued weak model of the first order logic with generalized quantifier Q is generalized to be valued in complete weak complemented lattices. For finite linearly-ordered weak complemented lattice, the omitting type theorem is proved.

Viewing modules M_S^-1R over a fractional ring S^-1R of a ring R as modules M_R over R, It is proved that some model-theoretic properties of modules, such as purity, pure embedding, elementary equivalence, elementary embedding, are preserved. The relations of such properties between M_R and (S^-1M)_S^-1R are also considered.

Let R be an ideal of a ring with unity, M_R be a R-module. Then M also can be viewed as a I-module. It is proved that some elementary properties of the theory of modules, such as purity, pure-injectivity, elementary equivalent, elementary embedding etc. are reserved between M_R and M_I.