Equivalencies, Identities, Symmetric Differences, and Congruencies in Orthomodular Lattices

It is shown that operations of equivalence cannot serve for building algebras which would induce orthomodular lattices as the operations of implication can. Several properties of equivalence operations have been investigated. Distributivity of equivalence terms and several other 3-variable expressions involving equivalence terms have been proved to hold in any orthomodular lattice. Symmetric differences have been shown to reduce to complements of equivalence terms. Some congruence relations related to equivalence operations and symmetric differences have been considered.     

Enantiomers and barriers to racemization of sterically hindered N-aryl- and N-heteroarylpyrroles

The N-aryl- and N-heteroaryl-2,5-dimethylpyrrole-3-carbaldehydes 2–8 have been synthesized by condensation of hexane-2,5-dione with the appropriate amine and subsequent Vilsmeier-Haack formylation of the pyrrole ring. Diastereomeric association complexes of the racemic pyrrole 8 were studied by pmr chemical shifts and the splittings induced by (+)-1-(9-anthryl)-2,2,2-trifluoroethanol. Enrichment of the enantiomers M and P of 2 and 6 was achieved by liquid chromatography on triacethylcellulose. The barrier to partial rotation about the C-N bond in 6 was determined by thermal racemization and its lower limits in 2 and 8 were estimated.     

Morse theory and finiteness properties of groups

. We examine the finiteness properties of certain subgroups of “right angled” Artin groups. In particular, we find an example of a group that is of type FP(Z) but is not finitely presented. Oblatum X-1995 & 7-X-1996     

Interactions of 10.6 GeV/nucleon gold nuclei in nuclear emulsion

Stacks of nuclear emulsion were exposed at the Brookhaven AGS to a 10.6 GeV/n beam of gold nuclei in the BNL 868 experiment. A preliminary analysis of the main features of the interactions of these nuclei is reported here and compared with those observed previously at lower energies,E<1 GeV/n. The multiplicity and pseudo-rapidity distributions of the singly charged particles emitted both in central and in minimum bias samples of interactions have been analyzed in order to look for any non random effects indicative of the nuclear state during the interactions. The fragmentation characteristics of the gold projectiles appear to be different at 10.6 GeV/n from those at ≦1 GeV/n incident energy. Fission of the gold projectiles, which was relatively frequent at low energy, is almost entirely suppressed. Some of alpha particles from the projectile are emitted with very large transverse momenta. In gold-emulsion interactions the residual target nuclei are significantly smaller than in oxygen and sulfur interactions in emulsion.

     

Equations, State, and Lattices of Infinite-Dimensional Hilbert Spaces

We provide several new result on quantum state space, on the lattice of subspacesof an infinite-dimensional Hilbert space, and on infinite-dimensional Hilbert spaceequations as well as on connections between them. In particular, we obtainan n-variable generalized orthoarguesian equation which holds in anyinfinite-dimensional Hilbert space. Then we strengthen Godowski's equationsas well ass the orthomodularity hold. We also prove that all six- and four-variableorthoarguesian equation presented in the literature can be reduced to newfour- and three-variable ones, respectively, and that Mayet's examples follow fromGodowski's equations. To make a breakthrough in testing these massive equations,we designed several novel algorithms for generating Greechie diagrams with anarbitrary number of blocks and atoms (currently testing with up to 50) and forautomated checking of equations on them. A way of obtaining complexinfinite-dimensional Hilbert space from the Hilbert lattice equipped with several additionalconditions and without invoking the notion of state is presented. Possiblerepercussions of the results on quantum computing problems are discussed.     

Structure and bonding of vanadium(V) complexes with hydroxyurea in aqueous solution: density functional theory investigations of isomers and intramolecular rearrangements

Extensive geometry optimizations have been performed at the BP86 level of density functional theory, in order to identify the most stable isomer of pentacoordinated [VO(OH)UH2O]+ and [VOU(H2O)2]2+ as well as of hexacoordinated [VO(OH)U(H2O)2]+ and [VOU(H2O)3]2+ complexes (U = hydroxyurea anion). Most of these are conformationally very flexible, with up to 12 isomers within an energy range of 5 kcal/mol. The most stable hexacoordinate forms are characterized by the oxo ligand in trans position to the carbonyl O atom of U. Bulk solvent effects on the relative stabilities, estimated from a polarizable continuum model, are indicated to be small and do not affect the energetic sequence of the isomers significantly. Details of the coordination sphere of the most stable isomers in aqueous solution (coordination number, protonation state) have been studied with Car-Parrinello molecular dynamics simulations. The preferred mechanisms of interconversion between selected [VO(OH)U(H2O)2]+ isomers, according to the DFT computations, involve proton transfers between H2O and OH or between O and OH ligands in the coordination sphere of the metal, assisted by a water molecule from the second hydration sphere.     

Synthesis of 2‐formyl‐1‐aza‐dibenzo[e,h]azulenes

Synthesis of a novel heterocyclic class of compounds, 1‐aza‐dibenzo[e,h]azulenes [1] ( 6a‐c and 7a‐c ), derived from dibenzo[b,f]oxepin, its 8‐chloro analogue and dibenzo[b,f]thiepin, respectively, is described. Aldol condensation of the starting ketones 4a‐c with (dimethyl‐hydrazono)‐acetaldehyde affords hydrazonoethylidene derivatives 5a‐c , which on reduction with sodium dithionite and subsequent cyclization provide the target tetracyclic 1‐aza‐dibenzo[e,h]azulenes 6a‐c . Regiospecific formylation of 6a‐c with Vilsmeier reagent leads to 2‐formyl derivatives 7a‐c . A series of derivatives 6a‐c and 7a‐c was tested for antiinflammatory activity as potential inhibitors of tumor necrosis factor alpha (TNF‐α) production in vitro.     

Hydrogen bonding topology influences gelating properties of malonamides

Preparation, structural characterisation and topology of hydrogen bonding networks of bis(phenylglycinol)malonamide, as well as its Cα mono- and dialkyl-substituted derivatives are described. Their hydrogen bonding motifs are described in view of their gelling properties. Topology of hydrogen bonding typical of malonamide gelators is compared with those of well-examined oxalamide gelators.     

Crystal and molecular structures of atropisomeric N‐aryl‐1,2,3,4‐tetrahydro‐3,3‐dimethyl‐2,4‐quinolinediones

The crystal structures of N‐aryl‐1,2,3,4‐tetrahydro‐3,3‐dimethyl‐2,4‐quinolinediones bearing methoxy‐ ( 1 ), methyl‐ ( 2 ), and chloro‐ ( 3 ) substituents in 2′‐position of the phenyl ring have been determined by X‐ray crystal structure analysis. The heterocyclic ring in 1–3 adopts an envelope conformation, with the smallest ring puckering in the ortho‐chloro derivative 3 . The N‐aryl ring is almost perpendicular with respect to the quinoline‐2,4‐dione ring. The corresponding dihedral angle values are 83.2(1)°, 80.0(9)°, and 83.4(2)° in 1, 2 and 3 , respectively. The hydrogen bond of C H⋅⋅⋅O type joins the molecules of the ortho‐methoxy derivative 1 into dimers. The supramolecular structure also contains two C H⋅⋅⋅π interactions that link the hydrogen‐bonded dimers into sheets. In ortho‐methyl derivative 2 , one C H⋅⋅⋅π interaction generates infinite chains, whereas two C H⋅⋅⋅O hydrogen bonds and three C H⋅⋅⋅π interactions in the ortho‐chloro derivative 3 form three‐dimensional framework. © 2008 Wiley Periodicals, Inc. Heteroatom Chem 19:325–331, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20436