Centrally orthocomplete effect algebras

Motivated by the theory of Loomis dimension lattices, we generalize the notion of a hull mapping to an arbitrary effect algebra (EA). Using hull mappings, we identify certain special types of elements in an EA, including generalizations of the invariant elements and of the simple elements in a dimension lattice. We introduce and study a new class of effect algebras, called centrally orthocomplete effect algebras (COEAs), satisfying the condition that every family of elements that is dominated by an orthogonal family of central elements has a supremum. We show that COEAs admit a central cover mapping and we develop the basic theory of direct decomposition of COEAs.     

Bogoliubov Spectrum of Interacting Bose Gases

We study the large‐N limit of a system of N bosons interacting with a potential of intensity 1/N. When the ground state energy is to the first order given by Hartree's theory, we study the next order, predicted by Bogoliubov's theory. We show the convergence of the lower eigenvalues and eigenfunctions towards that of the Bogoliubov Hamiltonian (up to a convenient unitary transform). We also prove the convergence of the free energy when the system is sufficiently trapped. Our results are valid in an abstract setting, our main assumptions being that the Hartree ground state is unique and nondegenerate, and that there is complete Bose‐Einstein condensation on this state. Using our method we then treat two applications: atoms with “bosonic” electrons on one hand, and trapped two‐dimensional and three‐dimensional Coulomb gases on the other hand. © 2015 Wiley Periodicals, Inc.     

New universal primers facilitate Pyrosequencing

A cost-driving factor in Pyrosequencing is the need for single-stranded PCR products that are usually obtained by biotin-labeling of one primer. We designed new universal primers that allow the introduction of biotin during the specific PCR at either the forward or the reverse primer in a single reaction. When converting five human single nucleotide polymorphism assays from the standard format into the universal format, we obtained pyrograms of similar good quality. Although the universal nonhuman sequences are unlikely to form loop structures, we mostly failed to establish assays without using the proprietary software from Biotage AB. Nevertheless, our universal primer pair adds flexibility to the process of assay design due to optional strand selection and contributes to the reduction of genotyping costs.     

Modular synthesis of tetrahydrofluorenones from 5-alkylidene Meldrum's acids

The one-pot synthesis of tetrahydrofluorenones, the core 6-5-6 tricyclic structural motif found in norditerpenoid natural products, from alkylidene Meldrum's acids via thermal Diels-Alder/BF3.OEt2-catalyzed Friedel-Crafts acylation reactions is described. A series of tetrahydrofluorenones was assembled in good yields, and the Diels-Alder/Friedel-Crafts acylation protocol allowed modification of the substitution within the rings.     

Intermolecular interactions of extended aromatic ligands: the synchrotron molecular structures of [Ru(bpy)2(N-HSB)].2PF6 and [Ru(bpy)2(N-(1/2)HSB)].2PF6

An off-set stack and a saddle-like distortion are revealed by the molecular structures of [Ru(bpy)2(N-HSB)].2PF6 and [Ru(bpy)2(N-(1/2)HSB)].2PF6.     

Structural diversity within analogous compounds: syntheses and studies of M(SCH2CH2NH2)Cl (M = Zn, Cd, Hg)

The novel complexes [Zn(L)Cl] (1), [Cd(L)Cl] (2), [Hg(L)Cl] (3), {[Hg(L)Cl].NaOH.2H2O} (3.NaOH.2H2O), and {[Hg3(HL)2Cl6].2H2O} (4) (L = -SCH2CH2NH2) were prepared and investigated by means of IR spectroscopy and single-crystal X-ray diffraction. The crystal structures of 1, 2, and 3.NaOH.2H2O show chelating N,S-coordination of the cysteaminate ligand, bridging S, and terminally coordinating Cl. Apart from these common features, the coordination geometries and modes of intermolecular association are different. 1 forms a cyclic tetramer with a Zn4S4 ring, and 3.NaOH.2H2O contains one-dimensional [Hg(L)Cl]n chains with S-bridged Hg atoms. Zn and Hg atoms in 1 and 3.NaOH.2H2O are tetracoordinate with a distorted tetrahedral M(ClNS2) geometry (M = Zn, Hg). Each Cd atom of 2 binds to three S atoms and vice versa, such that layers of distorted Cd3S3 hexagons are formed. 2 is the first example for a compound exhibiting a group 12-group 16 layer structure, which can be described as an analogue of a graphite layer. Additionally, each Cd atom binds to a chlorine atom and a nitrogen atom from a cysteaminate ligand resulting in pentacoordination with a distorted trigonal bipyramidal Cd(ClNS3) geometry. 4 contains two differently coordinate Hg atoms. One displays a distorted trans-octahedral Hg(Cl4S2) geometry, while the other is coordinated by four Cl atoms and one S atom and additionally forms a long Hg...Cl contact.