Generalized Multiresolution Analyses with Given Multiplicity Functions

Generalized multiresolution analyses are increasing sequences of subspaces of a Hilbert space ℋ that fail to be multiresolution analyses in the sense of wavelet theory because the core subspace does not have an orthonormal basis generated by a fixed scaling function. Previous authors have studied a multiplicity function m which, loosely speaking, measures the failure of the GMRA to be an MRA. When the Hilbert space ℋ is L ²(ℝ ⁿ ), the possible multiplicity functions have been characterized by Baggett and Merrill. Here we start with a function m satisfying a consistency condition, which is known to be necessary, and build a GMRA in an abstract Hilbert space with multiplicity function m.     

Protein‐free ligand screening: simplification of chiral chromatographic development via novel adaptation of NMR screening methodologies

We demonstrate here a promising NMR method that provides evidence for chiral compound selector interaction as a first‐pass screening method. A novel adaptation of commonly used protein‐based screening technologies, this approach relies upon ligand‐to‐stationary phase interaction wherein the stationary phase is tethered to sepharose beads. At only minutes per experiment, this methodology significantly reduces the time required for chiral separation methodology development and complements currently available chromatographic purity technologies.Copyright © 2009 John Wiley & Sons, Ltd.     

Star-linear equational theories of groupoids

We prove that there are precisely six equational theories E of groupoids with the property that every term is E-equivalent to a unique linear term. Presented by J. Berman. Received November 11, 2004; accepted in final form March 12, 2006. The first and third authors were supported by the Ministry of Science and Environment of Serbia, grant no. 144011; the second and fifth authors were supported by MŠMT, research project MSM 0021620839, and by the Grant Agency of the Czech Republic, grant #201/02/0594; the fourth author was supported by the NSF grant #DMS-0245622.     

Synthesis of tetracyclic indole-containing ring systems by intramolecular cycloadditions of azomethine ylides

Dipolar cycloaddition of azomethine ylides derived from addition of amines to a 2-butenylindole-3-carboxaldehyde provides a stereoselective synthesis of tetracyclic products present in a variety of indole alkaloids. The chemistry was applied to a formal synthesis of the iboga alkaloid deethylibophyllidine.     

A hybrid particle approach for continuum and rarefied flow simulation

A hybrid particle scheme is presented for the simulation of compressible gas flows involving both continuum regions and rarefied regions with strong translational nonequilibrium. The direct simulation Monte Carlo (DSMC) method is applied in rarefied regions, while remaining portions of the flowfield are simulated using a DSMC-based low diffusion particle method for inviscid flow simulation. The hybrid scheme is suitable for either steady state or unsteady flow problems, and can simulate gas mixtures comprising an arbitrary number of species. Numerical procedures are described for strongly coupled two-way information transfer between continuum and rarefied regions, and additional procedures are outlined for the determination of continuum breakdown. The hybrid scheme is evaluated through a comparison with DSMC simulation results for a Mach 6 flow of N₂ over a cylinder, and good overall agreement is observed. Large potential efficiency gains (over three orders of magnitude) are estimated for the hybrid algorithm relative to DSMC in a simple example involving a rarefied expansion flow through a small nozzle into a vacuum chamber.     

Finite element modelling of dielectric elastomer minimum energy structures

This paper presents an experimentally validated finite element model suitable for simulating the quasi-static behaviour of Dielectric Elastomer Minimum Energy Structure(s) (DEMES). A DEMES consists of a pre-stretched Dielectric Elastomer Actuator (DEA) adhered to a thin, flexible frame. The tension in the stretched membrane causes the frame to curl up, and when a voltage is applied, the frame returns to its initial planar state thus forming a useful bending actuator. The simulation method presented here incorporates a novel strain energy function suitable for simulating general DEA actuator elements. When compared against blocked force data from our previous work, the new model provides a good fit with an order of magnitude reduction in computational time. Furthermore, the model accurately matched experimental data on the free displacement of DEMES formed with non-equibiaxially pre-stretched VHB4905 membranes driven by 2500 V. Non-equibiaxially pre-stretching the membranes allowed control of effective frame stiffness and bending moment, this was exploited by using the model to optimise stroke at 2500 V in a hypothetical case study. Dielectric constant measurements for non-equibiaxially stretched VHB4905 are also presented.     

Complementary closed relational clones are not always Krasner clones

In ZFC, it is shown that every relational clone on a set A closed under complementation is a Krasner clone if and only if A is at most countable. This is achieved by solving an equivalent problem on locally invertible monoids: A partially ordered set is constructed whose endomorphism monoid is not contained in the local closure of its automorphism group. Received September 5, 1998; accepted in final form December 10, 1998.     

Next‐Generation D2‐Symmetric Chiral Porphyrins for Cobalt(II)‐Based Metalloradical Catalysis: Catalyst Engineering by Distal Bridging

Novel D₂‐symmetric chiral amidoporphyrins with alkyl bridges across two chiral amide units on both sides of the porphyrin plane (designated “HuPhyrin”) have been effectively constructed in a modular fashion to permit variation of the bridge length. The Co^II complexes of HuPhyrin, [Co(HuPhyrin)], represent new‐generation metalloradical catalysts where the metal‐centered d‐radical is situated inside a cavity‐like ligand with a more rigid chiral environment and enhanced hydrogen‐bonding capability. As demonstrated with cyclopropanation and aziridination as model reactions, the bridged [Co(HuPhyrin)] functions notably different from the open catalysts, exhibiting significant enhancement in both reactivity and stereoselectivity. Furthermore, the length of the distal alkyl bridge can have a remarkable influence on the catalytic properties.     

Room Temperature Ferromagnetism in Ga1-xHoxN (x=0.0 and 0.05) Diluted Magnetic Semiconductor Thin Films

Holmium doped GaN diluted magnetic semiconductor thin films have been prepared by thermal evaporation technique and subsequent ammonia annealing. X-ray diffraction mea-surements reveal all peaks belong to the purely hexagonal wurtzite structure. Surface mor-phology and composition analysis were carried out by scanning electron microscopy and energy dispersive spectroscopy respectively. The room temperature ferromagnetic proper-ties of Ga_1-xHo_xN(x=0.0, 0.05) films were analyzed using vibrating sample magnetometer at room temperature. Magnetic measurements showed that the undoped films (i.e. GaN) exhibited diamagnetic behavior, while the Ho-doped (Ga_0.95Ho_0.05N) film exhibited a ferro-magnetic behavior.