The Crystal Structure of Pb8FeIIFeF24: an ordered Fluorite-like Compound

Pb₈Fe^IIFeF₂₄ is triclinic: a = 20.118(3) Å, b = 5.597(1) Å, c = 9.440(2) Å, α = 89.75(2)°, β = 105.79(2)°, α = 89.38(2)°, Z = 2. The structure is solved in the unconventional space group C1 , from X-ray single crystal data using 1 641 independent reflections (R = 0.048, R_w = 0.051). It is built up from the stacking of two subnetworks along the a axis: fluorite-like [Pb₈F₁₀]_n⁶ⁿ⁺ layers and infinite dimetallic [Fe^IIFeF₁₄]_n^6n? double-chains of corner-sharing octahedra running along the b axis.     

Generating M-Indeterminate Probability Densities by Way of Quantum Mechanics

Probability densities that are not uniquely determined by their moments are said to be “moment-indeterminate,” or “M-indeterminate.” Determining whether or not a density is M-indeterminate, or how to generate an M-indeterminate density, is a challenging problem with a long history. Quantum mechanics is inherently probabilistic, yet the way in which probability densities are obtained is dramatically different in comparison with standard probability theory, involving complex wave functions and operators, among other aspects. Nevertheless, the end results are standard probabilistic quantities, such as expectation values, moments and probability density functions. We show that the quantum mechanics procedure to obtain densities leads to a simple method to generate an infinite number of M-indeterminate densities. Different self-adjoint operators can lead to new classes of M-indeterminate densities. Depending on the operator, the method can produce densities that are of the Stieltjes class or new formulations that are not of the Stieltjes class. As such, the method complements and extends existing approaches and opens up new avenues for further development. The method applies to continuous and discrete probability densities. A number of examples are given.

     

Toward a formal specification of multimedia synchronization scenarios

This paper introduces time stream Pétri nets (Ts treamPn), a model for the formal specification of multimedia synchronization scenarios. This new model extends time Pétri nets to formally describe the timed behaviour of multimedia objects and streams in asynchronous distributed systems. The proposed approach uses time intervals to label the arcs exiting from the places of the net, and typed transitions to define different firing rules. This model allows a complete and accurate specification of synchronization constraints between multimedia streams and can be used at different levels of granularity.     

The finite element approximation of a coupled reaction-diffusion problem with non-Lipschitz nonlinearities

Summary. A coupled semilinear elliptic problem modelling an irreversible, isothermal chemical reaction is introduced, and discretised using the usual piecewise linear Galerkin finite element approximation. An interesting feature of the problem is that a reaction order of less than one gives rise to a "dead core" region. Initially, one reactant is assumed to be acting as a catalyst and is kept constant. It is shown that error bounds previously obtained for a scheme involving numerical integration can be improved upon by considering a quadratic regularisation of the nonlinear term. This technique is then applied to the full coupled problem, and optimal and error bounds are proved in the absence of quadrature. For a scheme involving numerical integration, bounds similar to those obtained for the catalyst problem are shown to hold. Received May 25, 1993 / Revised version received July 5, 1994     

Hardware Implementation of a Fixed-Point Decoder for Low-Density Lattice Codes

Journal of Signal Processing Systems - This paper describes a field-programmable gate array (FPGA) implementation of a fixed-point low-density lattice code (LDLC) decoder where the Gaussian mixture...     

Development of Molecular Mechanics Torsion Parameters for alpha,beta-Cyclopropyl Ketones and Conformational Analysis of Bicyclo[m.1.0]alkan-2-ones

Conformations of cyclopropyl methyl ketone have been studied using ab initio methods in an effort to quantify the effects of conjugative overlap between the cyclopropane ring and an adjacent ketone carbonyl. Results were comparable with previous experimental and theoretical studies. Cyclopropyl methyl ketone exhibits a global energy minimum in the s-cis conformer and a local energy minimum near the s-trans conformer. The potential energy curve obtained was used to derive torsion parameters which were employed in molecular mechanics studies of the conformations of the set of bicyclo[m.1.0]alkan-2-ones having larger ring sizes from five- to 16-membered. Similar conformations for the cyclopropyl ketone substructure are observed for all the medium and large ring systems examined. Possible synthetic ramifications of local conformational anchoring by this functional group array are discussed.     

Shape-tunable polymer nodules grown from liposomes via ring-opening metathesis polymerization

A new inisurf (acting as surfactant and initiator) molecule for ring-opening metathesis polymerization (ROMP) was synthesized and used in aqueous solution in order to control the size and shape of polymer nodules grown from liposomes. Nodules were observed to grow in size with conversion of monomer, and depending on the monomer used, they adopted either a spherical or comet-like shape. Here, we investigate polymer production from a liposome surface. We use a hydrophobic derivative of the Grubbs catalyst positioned at the liposome surface to allow for ROMP of monomers dissolved in the aqueous outer phase. We obtain nodules of polymer that can grow up to tens of micrometers, unveiling new efficient possibilities of polymerization from a membrane in an aqueous solution.     

Matrix-assisted laser desorption/ionisation mass spectrometry for the direct analysis of enzymatically digested kappa- iota- and hybrid iota/nu-carrageenans

Enzymatically digested oligosaccharides of kappa-, iota- and hybrid iota/nu-carrageenans were analysed using matrix-assisted laser desorption/ionisation time-of-flight mass spectrometry in the negative-ion mode. nor-Harmane was used as matrix. Depending on the stock concentration and the laser intensity applied, the oligosaccharides exhibited losses of sulphate units (neutralised by the Na+ ion, and thus non-stable), leaving the primary backbone structure in most cases with only the deprotonated sulphate groups (carrying the negative charge, stable). This meant that kappa- and iota-oligosaccharides could not be easily distinguished from one another since they share the same primary backbone structure. However, for the hybrid iota/nu-oligosaccharides the primary backbone structure could be identified since the nu-carrageenan repeating unit differs from that of the kappa/iota-carrageenan unit. For all types of oligosaccharides, the results indicated cleavage of an anhydrogalactose unit from the non-reducing end. Specifically, for the hybrid oligosaccharides of iota/nu-carrageenans, this type of fragmentation means that the nu-carrageenan unit is not positioned on the non-reducing end of the hybrid oligosaccharides. Dehydration reactions, and exchange reactions of Na+ with K+ and Ca2+, were also observed.     

Interdependence of redox state,hydrogen bonding,anion recognition and charge partition in crystals of (EDT-TTF-CONHMe)6 [Re6Se8(CN)6] (CH3CN)2(CH2Cl2)2

Neutral pi-conjugated molecules and their radical cations co-exist in [(EDT-TTF-CONHMe+*)4(EDT-TTF-CONHMe0)2] [Re6Se8(CN)6]4- (CH3CN)2(CH2Cl2)2 whose crystal structure reveals that, upon one-electron oxidation, an activation of the N-H and C-H hydrogen bond donor ability is coupled to a deactivation of the hydrogen bond acceptor character of the carbonyl oxygen atom: this is expressed in the supramolecular hydrogen bond pattern and, ultimately, into charge localisation and partition in the solid state.