A finite horizon model for repairable systems with repair restrictions

In this paper, we will present a new finite horizon repair/replacement decision model and derive the structure of the optimal policy for components that have a failure intensity that is a non-decreasing function of the number of times the component has been repaired, and independent of the component's age. Furthermore, the component has physical restrictions on the number of times it can be repaired, after which the only feasible decision is to replace the component. The fundamentals of this new decision model are based on the outcomes of several case studies done by the authors. Besides presenting the model and showing the structure of the optimal policy, the model will be applied to a real industry data set, and its results discussed.     

Precise mass measurement of a double-stranded 500 base-pair (309 kDa) polymerase chain reaction product by negative ion electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry

Electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry (ESI-FTICRMS) has been used to determine the mass of a double-stranded 500 base-pair (bp) polymerase chain reaction (PCR) product with an average theoretical mass of the blunt-ended (i.e. unadenylated) species of 308 859.35 Da. The PCR product was generated from the linearized bacteriophage Lambda genome which is a double-stranded template. Utilization of ethanol precipitation in tandem with a rapid microdialysis step to purify and desalt the PCR product was crucial to obtain a precise mass measurement. The PCR product (0.8 pmol/μL) was electrosprayed from a solution containing 75% acetonitrile, 25 mM piperidine, and 25 mM imidazole and was infused at a rate of 200 nL/min. The average molecular mass and the corresponding precision were determined using the charge-states ranging from 172 to 235 net negative charges. The experimental mass and corresponding precision (reported as the 95% confidence interval of the mean) was 309 406 +/- 27 Da (87 ppm). The mass accuracy was compromised due to the fact that the PCR generates multiple products when using Taq polymerase due to the non-template directed 3'-adenylation. This results in a mixture of three PCR products with nearly identical mass (i.e. blunt-ended, mono-adenylated and di-adenylated) with unknown relative abundances that were not resolved in the spectrum. Thus, the experimental mass will be a weighted average of the three species which, under our experimental conditions, reflects a nearly equal concentration of the mono- and di-adenylated species. This report demonstrates that precise mass measurements of PCR products up to 309 kDa (500 bp) can be routinely obtained by ESI-FTICR requiring low femtomole amounts. Copyright 1999 John Wiley & Sons, Ltd.     

Hydroformylation of 1-octene using low-generation Rh(i) metallodendritic catalysts based on a tris-2-(2-pyridyliminoethyl)amine scaffold

The synthesis and characterization of low-generation pyridylimine Rh(i) metallodendrimers is described. These metallodendrimers were obtained via a Schiff base condensation of tris-2-(aminoethyl)amine with 2-pyridinecarboxaldehyde to afford the tris-2-(2-pyridylimine ethyl) amine ligand (1). Subsequent complexation reactions with [RhCl(CO)(2)](2) and [RhCl(COD)](2) yielded the corresponding metal-containing dendrimers containing -RhCl(CO) and -Rh(COD) moieties on the periphery. These new rhodium metallodendrimers (2 and 3) and their precursor ligand (1) are thermally stable and have been characterized using (1)H NMR, (13)C NMR, (31)P NMR, FT-IR spectroscopy, elemental analysis as well as mass spectrometry. The Rh(i) metallodendrimers are highly active and chemo- and regioselective in the hydroformylation of 1-octene. Aldehydes were favoured at moderate to high temperatures (95 °C and 75 °C) and pressure (30 bars), while more iso-octenes were formed at low temperature (55 °C) and pressures (5 and 10 bars). The mononuclear analogues (5 and 6) also produced more aldehydes (albeit showing catalyst decomposition at 95 °C and 75 °C, 30 bars) and these aldehydes were mostly branched.     

Diagrams and torsors

Suppose that A is a presheaf of categories enriched in simplicial sets on a small Grothendieck site. It is shown that the homotopy theory of enriched A-diagrams of equivalences taking values in simplicial sets can be identified with the homotopy theory of simplicial presheaves fibred over the diagonalized nerve dBA of A. The set [*,dBA] of morphisms in the simplicial presheaf homotopy category is identified with the set of path components of a category of A-torsors, for a suitable definition of A-torsor. These statements are special cases of localized results which hold when the corresponding localized model structures are proper. Examples of the latter include the motivic homotopy category, and so these results lead to a theory of motivic A-torsors which is classifiable up to equivalence by a family of morphisms in the motivic homotopy category. This research was supported by NSERC. Received: March 2006     

Quasi-elastic lineshapes for atoms and simple molecules undergoing jump rotation on surfaces

We apply an analytic model for discrete jump rotation of a species moving around a circle, to quasi-elastic scattering from single crystal surfaces. Results for several molecule-like geometries are presented and the subsequent form of the intermediate scattering function is identified. These functions give clear signatures, enabling different forms of jump rotation to be distinguished. A simple data reduction is discussed and we show how the true ISF will appear within this simplification.     

Lineshapes in quasi-elastic scattering from species hopping between non-equivalent surface sites

We present an analytic model applied to quasi-elastic scattering from an adsorbed surface species undergoing jump diffusion between adsorption sites described by a Bravais lattice combined with a basis of multiple points. The model allows for hops between adsorption sites which are both symmetrically and energetically inequivalent. We give results for 1-D hopping, which are applicable to a species jumping between the top and bridge sites along the [11?0] direction on an fcc-(110) surface or for jumps along a step edge. In 2-D, results for hopping between fcc and hcp hollow sites and between the bridge sites of an fcc-(111) surface are presented. These examples give characteristic signatures which will allow these forms of motion to be recognized in experimental data and will enable the underlying physical parameters to be extracted by comparison with the analytical forms derived here.     

Tetraalkoxyphenanthrene: a new precursor for luminescent conjugated polymers

[reaction: see text] We have developed a convenient synthesis of tetraalkoxyphenanthrene derivatives and demonstrated their use to form luminescent conjugated oligomers and polymers. Palladium-catalyzed cross-coupling reactions of 2,7-diiodo-3,6-dimethoxy-9,10-di(2-ethylhexyloxy)phenanthrene produced high molecular weight poly(p-phenylene ethynylene)s and low molecular weight poly(p-phenylene vinylene)s. These new polymers, which are luminescent in the solid state and in solution, may be useful for developing LED or solar cell devices, or in chemical sensors.