Topologie di caratteri per moduli su anelli Noetheriani

Riassunto Si determinano i rapporti sussistenti fra le topologie di caratteri e leE-compattificazioni dei moduli sopra un anello noetheriano; si considerano, in particolare, lel-compattificazioni (=E-compattificazioni linearmente compatte) e le compatti-ficazioni lineari. Si stabiliscono delle condizioni necessarie e sufficienti affinchè la topologia Ω-adica sia una topologia di caratteri.

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Summary We determine the relations between the topologies induced by modules of characters and theE-compactifications for modules over noetherian rings; we consider, in particular, thel-compactifications (=E-compactifications which are linearly compact) and the linear compactifications. We state some necessary and sufficient conditions so that the Ω-adic topology is a topology induced by a module of characters.

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Lavoro eseguito nell’ambito dell’attività dei gruppi di ricerca matematica del C.N.R.     

OnE-compact modules over SISI rings

Summary We extend to the case of SISI rings, studied by Vamos in [8], the duality for noetherian rings studied by Orsatti in [7]. We prove that some properties of this duality can be generalized, while others hold only in the noetherian case.

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Riassunto Si estende al caso dei SISI anelli, studiati da Vamos in [8], la dualità studiata da Orsatti in [7] per gli anelli noetheriani. Si dimostra che alcune proprietà di questa dualità si possono generalizzare, mentre altre sono caratteristiche del caso noetheriano.

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Lavoro eseguito nell’ambito dell’attività dei gruppi di ricerca matematici del C.N.R.     

Dirhenium paddlewheel compounds supported by N,N'-dialkylbenzamidinates: synthesis, structures, and photophysical properties

Dirhenium(III,III) compounds Re2(DMBA)4Cl2 (1, DMBA=N,N'-dimethylbenzamidinate) and Re2(DEBA)4Cl2 (2, DEBA=N,N'-diethylbenzamidinate) were synthesized via molten reactions between Re2(OAc)4Cl2 and the corresponding amidine. Re2(DMBA)4(NO3)2 (3) was obtained through reacting Re2(DMBA)4Cl2 with AgNO3. Single crystal X-ray diffraction studies revealed that the Re-Re distances in compounds 1-3 are 2.212(1), 2.217(1), and 2.173(1) A, respectively, which are consistent with the presence of a Re-Re quadruple bond. Voltammetric studies revealed that compound 2 exhibits two quasireversible couples, an oxidation and a reduction, and an irreversible reduction, while compound 1 displays irreversible couples at similar potentials. The three complexes exhibit 1deltadelta* absorption as a shoulder at approximately 440 nm (epsilon approximately 1500 M(-1) cm(-1)). Upon excitation of solid samples or CH2Cl2 solutions of 2 with visible light, emission is observed at 824 nm (77 K) and 833 nm (298 K), respectively. The luminescence is assigned as arising from the 3deltadelta* excited state.     

The footprint sorting problem

Phylogenetic footprints are short pieces of noncoding DNA sequence in the vicinity of a gene that are conserved between evolutionary distant species. A seemingly simple problem is to sort footprints in their order along the genomes. It is complicated by the fact that not all footprints are collinear: they may cross each other. The problem thus becomes the identification of the crossing footprints, the sorting of the remaining collinear cliques, and finally the insertion of the noncollinear ones at "reasonable" positions. We show that solving the footprint sorting problem requires the solution of the "Minimum Weight Vertex Feedback Set Problem", which is known to be NP-complete and APX-hard. Nevertheless good approximations can be obtained for data sets of interest. The remaining steps of the sorting process are straightforward: computation of the transitive closure of an acyclic graph, linear extension of the resulting partial order, and finally sorting w.r.t. the linear extension. Alternatively, the footprint sorting problem can be rephrased as a combinatorial optimization problem for which approximate solutions can be obtained by means of general purpose heuristics. Footprint sortings obtained with different methods can be compared using a version of multiple sequence alignment that allows the identification of unambiguously ordered sublists. As an application we show that the rat has a slightly increased insertion/deletion rate in comparison to the mouse genome.     

An Inorganic Double Helix Sheathing Alkali Metal Cations: ANb2P2S12 (A=K,Rb, Cs), A Series of Thiophosphates Close to the Metal–Nonmetal Boundary—Chalcogenide Analogues of Transition‐Metal Phosphate Bronzes?

The new quaternary niobium thiophosphates ANb(2)P(2)S(12) (A=K, Rb, Cs) have been prepared and characterized. The title compounds were synthesized by reacting Nb metal, A(2)S, P(2)S(5), and S at 600-700 degrees C in evacuated silica tubes. They crystallize as "stuffed" variants of the tetragonal TaPS(6) structure type in the tetragonal space group I$\bar 4$2d with eight formula units per unit cell and lattice constants a=15.923(2) and c=13.238(3) A for CsNb(2)P(2)S(12), a=15.887(3) and c=13.132(3) A for RbNb(2)P(2)S(12), and a=15.850(2) and c=13.119(3) A for KNb(2)P(2)S(12). Their structures are based on double helices formed from interpenetrating, noninteracting spiral chains of binuclear [Nb(2)S(12)] cluster units and [PS(4)] thiophosphate groups. The cavities and tunnels, which are formed by the helical chains, are filled with A(+) ions. Temperature-dependent conductivity studies reveal thermally activated electrical transport behavior. This result is consistent with the observation of a temperature-dependent contribution to the (31)P MAS-NMR shift, suggesting that the delocalized s-electron spin density increases with increasing temperature. These findings are supported by the results of tight-binding band structure calculations which reveal that the unusual electrical transport behavior of ANb(2)P(2)S(12) is a consequence of the structure symmetry. Therefore, CsNb(2)P(2)S(12) may be considered a chalcogenide analogue of metal phosphate bronzes.