In this paper we present a topological duality for a certain subclass of the Fω-structures defined by M. M. Fidel, which conform to a non-standard semantics for the paraconsistent N. C. A. da Costa logic Cω. Actually, the duality introduced here is focused on Fω-structures whose supports are chains. For our purposes, we characterize every Fω-chain by means of a new structure that we will call down-covered chain (DCC) here. This characterization will allow us to prove the dual equivalence between the category of Fω-chains and a new category, whose objects are certain special topological spaces (together with a distinguished family of open sets) and whose morphisms are particular continuous functions.
Lattices of submodules of modules and the operators we can define on these lattices are useful tools in the study of rings and modules and their properties. Here we shall consider some submodule operators defined by sets of left ideals. First we focus our attention on the relationship between properties of a set of ideals and properties of a submodule operator it defines. Our second goal will be to apply these results to the study of the structure of certain classes of rings and modules. In particular some applications to the study and the structure theory of torsion modules are provided.
The oxidizing side of photosystem 2 (PS2) contains a set of unique redox components including two tyrosine radicals, Tyr2 and Tyrp, and a cluster of 4 Mn atoms that are involved in the oxidation of water to molecular oxygen. The structural environment of these components is unknown; we ušed computer-assisted modelling to create a three-dimensional model for the structure around Tyr^ and Tyrj). The tyrosines are predicted to be located in hydrophobic cavities in the Dl and D2 reaction centre proteins, respectively. The cavities are situated close to the lumenal surface of the thylakoid membrane and are surrounded mainly by highly conserved amino acid residues. Both tyrosines are proposed to be hydrogen-bonded to the nearby histidine residues Hisl90 on respective protein. We tested the model by electron paramagnetic resonance (EPR) spectroscopy of Tyr^ and site-directed mutagenesis of the D2 protein in the cyanobacterium Synechocystis 6803. In two mutants, where the corresponding histidine is changed to a tyrosine or a leucine, the normál EPR spectra from Tyr^ were drastically altered to narrow structureless radical signals with g-values similar to that of Tyrp (g » 2.0050). The new spectra were assigned to Tyrp from functional experiments and the spectral modification indicated that the introduced point-mutation of His 190 (D2-Hisl89 in Synechocystis 6803) modified the environment around Tyr^ supporting the structural model. In a third mutant where Glnl65 (D2-Glnl64 in Synechocystis 6803) was exchanged to a leucine we also observed a modified EPR spectrum consistent with the predictions firom the model. AU the experimental data obtained strengthen the Computer derived model in essential aspects. We also predicted a possible location for the Mn-cluster to the loop that connects the membrane spanning helices A and B on the Dl protein. In addition the structural model suggests the presence of a metal-site, possibly a Mn site, close to Tyrz on the Dl protein. The site is proposed to be constituted of three residues on the Dl protein, Glnl65, Aspl70 and Glul89.