An automata theoretic decision procedure for the propositional mu-calculus

The propositional mu-calculus is a propositional logic of programs which incorporates a least fixpoint operator and subsumes the propositional dynamic logic of Fischer and Ladner, the infinite looping construct of Streett, and the game logic of Parikh. We give an elementary time decision procedure, using a reduction to the emptiness problem for automata on infinite trees. A small model theorem is obtained as a corollary.

Formalin fixation affects equilibrium partitioning of an ionic contrast agent-microcomputed tomography (EPIC-[mu]CT) imaging of osteochondral samples

Equilibrium Partitioning of an Ionic Contrast agent with microcomputed tomography (EPIC-[mu]CT) is a non-invasive technique to quantify and visualize the three-dimensional distribution of glycosaminoglycans (GAGs) in fresh cartilage tissue. However, it is unclear whether this technique is applicable to already fixed tissues. Therefore, this study aimed at investigating whether formalin fixation of bovine cartilage affects X-ray attenuation, and thus the interpretation of EPIC-[mu]CT data.Design Osteochondral samples (n = 24) were incubated with ioxaglate, an ionic contrast agent, for 22 h prior to [mu]CT scanning. The samples were scanned in both formalin-fixed and fresh conditions. GAG content was measured using a biochemical assay and normalized to wet weight, dry weight, and water content to determine potential reasons for differences in X-ray attenuation.Results The expected zonal distribution of contrast agent/GAGs was observed for both fixed and fresh cartilage specimens. However, despite no significant differences in GAG concentrations or physical properties between fixed and fresh samples, the average attenuation levels of formalin-fixed cartilage were 14.3% lower than in fresh samples.Conclusions EPIC-[mu]CT is useful for three-dimensional visualization of GAGs in formalin-fixed cartilage. However, a significant reduction in X-ray attenuation for fixed (compared to fresh) cartilage must be taken into account and adjusted for accordingly when quantifying GAG concentrations using EPIC-[mu]CT.

catena-Poly[[[diaquacobalt(II)]-mu-(3,5-dinitro-2-oxidobenzoato)-kappa3O1,O2:O1'-[tetraaquacobalt(II)]-mu-(3,5-dinitro-2-oxidobenzoato)-kappa3-O1:O1',O2] dihydrate]

In the structure of polymeric title compound, {[Co2(C7H2N2O7)2(H2O)6] . 2H2O}n from the reaction of 3,5-dinitrosalicylic acid with cobalt(II) acetate, both slightly distorted octahedral Co(II) centres have crystallographic inversion symmetry. The coordination sphere about one Co centre comprises four O donors from two bidentate chelate O(phenolate), O(carboxyl) and bridging dianionic ligands and two water molecules [Co-O range, 2.0249(11)-2.1386(14)A] while that about the second Co centre has four water molecules and two bridging carboxyl O donor atoms [Co-O range, 2.0690(14)-2.1364(11)A]. The coordinated water molecules as well as the water molecules of solvation give water-water and water-carboxyl hydrogen-bonding interactions in the three-dimensional framework structure.

Poly[di-mu-aqua-bis(mu-2-amino-4-nitrobenzoato)dicaesium]

In the structure of title compound [Cs2(C7H5N2O4)2(H2O)2]n the asymmetric unit comprises two independent and different Cs centres, one nine-coordinate, the other seven coordinate, with both having irregular stereochemistry. The CsO9 coordination comprises oxygen donors from three bridging water molecules, one of which is doubly bridging, three from carboxylate groups, and three from nitro groups, of which two are bidentate chelate bridging. The CsO6N coordination comprises the two bridging water molecules, one amine N donor, one carboxyl O donor and four O donors from nitro groups (two from the chelate bridges). The extension of the dimeric unit gives a two-dimensional polymeric structure which is stabilized by both intra- and intermolecular amine N-H...O and water O-H...O hydrogen bonds to carboxyl O acceptors, as well as inter-ring pi-pi interactions [minimum ring centroid separation, 3.4172(15)A].

Poly[aqua([mu]3-2-hydroxy-5-nitrobenzoato-[kappa]3O1:O1':O2)rubidium]

In the structure of title compound [Rb2(C7H4NO2)2(H2O)2]n the centrosymmetric cyclic dimeric repeating unit comprises two irregular RbO4 complex centres bridged by the carboxylate groups of the 5-nitrosalicylate ligands. The coordination about each Rb is completed by a monodentate water molecule and a phenolic O donor which gives a bridging extension [Rb-O range 3.116(7)-3.135(5)A]. The two-dimensional polymeric structure is stabilized by intermolecular water O-H...O(carboxyl) hydrogen bonds and weak inter-ring pi--pi interactions [minimum ring centroid separation, 3.620(4)A].

Poly[tetra-mu-aqua-diaquatetrakis[mu-(E)-2-nitrocinnamato]tetrarubidium]

In the structure of the title compound [Rb4(C9H6NO4)4(H~2~O)6]n, the asymmetric unit comprises four rubidium complex cations, two of which have an RbO7 coordination polyhedron with a monocapped distorted octahedral stereochemistry and two of which have a distorted RbO6 octahedral coordination. The bonding about both the seven-coordinate centres is similar, comprising one monodentate water molecule together with three bridging water molecules and three carboxylate O-atom donors, two of which are bridging. The environments about the six-coordinate cations are also similar, comprising a monodentate nitro O-atom donor, a bridging water molecule and four bridging carboxylate O-atom donors [overall Rb-O range, 2.849(2)-3.190(2)A]. The coordination leads to a two-dimensional polymeric structure extending parallel to (001), which is stabilized by interlayer water O-H...O hydrogen-bonding associations to water, carboxyl and nitro O-atom acceptors, together with weak inter-ring pi--pi interactions [minimum ring centroid separation = 3.5319(19)A].