A term rewriting system is called complete if it is both confluent and strongly normalising. Barendregt and Klop showed that the disjoint union of complete term rewriting systems does not need to be complete. In other words, completeness is not a modular property of term rewriting systems. Toyama, Klop and Barendregt showed that completeness is a modular property of left-linear term rewriting s...

If (un)n∈IN is a sequence in L2(E; m) converging m-almost everywhere to u, then Fatou’s lemma says that (u, u)L2 ≤ lim infn(un, un)L2 , where we set (u, u)L2 = ∞ if u 6∈ L2(E; m). The corresponding result, where a Dirichlet form replaces the inner product, was used by Silverstein [5; Lemma 1.7] and by Fukushima, Oshima, and Takeda [2; Theorem 1.5.2] to define extended Dirichlet space and study ...

the objective of this research is to identify arabidopsis thaliana genes encoding acid phosphatases induced by phosphate starvation. multiple alignments of eukaryotic acid phosphatase amino acid sequences led to the classification of these proteins into four groups including purple acid phosphatases (paps). specific primers were degenerated and designed based on conserved sequences of paps isol...