In this paper, our purpose is twofold. Firstly, the tensor andresiduum operations on $L-$nested systems are introduced under thecondition of complete residuated lattice. Then we show that$L-$nested systems form a complete residuated lattice, which isprecisely the classical isomorphic object of complete residuatedpower set lattice. Thus the new representation theorem of$L-$subsets on complete re...

in this paper, our purpose is twofold. firstly, the tensor andresiduum operations on $l-$nested systems are introduced under thecondition of complete residuated lattice. then we show that$l-$nested systems form a complete residuated lattice, which isprecisely the classical isomorphic object of complete residuatedpower set lattice. thus the new representation theorem of$l-$subsets on complete re...

The quantum integrable systems associated with the loop algebras $\mathrm U_q(\mathcal L(\mathfrak{sl}_{\, l + 1}))$ are considered. factorized form of transfer operators related to infinite dimensional evaluation representations is found and determinant finite obtained. master $TQ$- $TT$-relations derived. operatorial $T$- $Q$-systems found. nested Bethe equations

Abstract Justification theory is a general framework for the definition of semantics rule-based languages that has high explanatory potential. Nested justification systems, first introduced by Denecker et al. , allow composition systems. This notion nesting thus enables modular languages, and increases representational capacities theory. As we show in this paper, original characterization neste...

We prove a copying theorem for well-nested multiple contextfree languages: if L = {w#w | w ∈ L0 } has a well-nested m-MCFG, then L has a ‘non-branching’ well-nested m-MCFG. This can be used to give simple examples of multiple context-free languages that are not generated by any well-nested MCFGs.

Legionella pneumophila is involved in more than 95% cases of severe atypical pneumonia. Infection is mainly by inhalation the indoor aerosols through the water-coolant systems. Because some Legionella strains may be viable but not culturable, therefore, Taq polymerase, DNA amplification and semi-nested-PCR were carried out to detect Legionella-specific 16S-rDNA sequence. For this purpose, 1.5 l...