Randomized greedy matching

We consider a randomized version of the greedy algorithm for finding a large matching in a graph. We assume that the next edge is always randomly chosen from those remaining. We analyze the performance of this algorithm when the input graph is fixed. We show that there are graphs for which this Randomized Greedy Algorithm (RGA) usually only obtains a matching close in size to that guaranteed by worst-case analysis (i.e., half the size of the maximum). For some classes of sparse graphs (e.g., planar graphs and forests) we show that the RGA performs significantly better than the worst-case. Our main theorem concerns forests. We prove that the ratio to maximum here is at least 0.7690…, and that this bound is tight.     

On isomorphic factorizations of circulant graphs

We investigate the conjecture that every circulant graph X admits a k‐isofactorization for every k dividing |E(X)|. We obtain partial results with an emphasis on small values of k. © 2006 Wiley Periodicals, Inc. J Combin Designs 14: 406–414, 2006     

Corrigendum: The complexity of counting graph homomorphisms

We close a gap in the proof of Theorem 4.1 in our paper “The complexity of counting graph homomorphisms” [Random Structures Algorithms 17 (2000), 260–289]. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

Treatment of zinc-contaminated water using a multistage ferrihydrite sorption system

Previous studies demonstrated the environmental and economic benefits of treating lead(II)-contaminated water streams with ferrihydrite in multiple equilibrium sorption stages. In this work, multistage ferrihydrite sorption systems were evaluated for their effectiveness in reducing single-solute zinc(II) (Zn(II)) concentrations in contaminated water streams to very low levels. As for lead(II) (Pb(II)), experimental data and modeling results indicate that a multistage sorption system can significantly reduce Zn(II) effluent concentrations for the same total amount of sorbent or, alternatively, dramatically lower total sorbent consumption for the same effluent Zn(II) concentration. Compared to Pb(II), however, Zn(II) removal requires on the order of 10 times more sorbent to achieve the same target effluent concentration for the same pH and number of stages. Model predictions were made using a steady-state, multistage, equilibrium adsorber model that was previously developed for and integrated into OLI Systems' Environmental Simulation Program (ESP). The modified triple-layer model was used to simulate Zn(II) surface-liquid equilibria within the adsorber model. Engineering screening evaluations again indicate that a 2- to 3-stage sorption process can provide significant economic savings when compared to a 1-stage process operating with the same target effluent Zn(II) concentration. Additional equilibrium stages beyond 2 or 3 provide diminishing economic returns. The major economic driver for multiple contacting stages is reduced capital investment and operating costs for sludge handling, dewatering, and disposal.     

A repetitively pulsed sealed-TE CO2 laser using an oxygen tolerant discharge scheme

A repetitively pulsed (40 Hz) TE CO₂ laser using an oxygen tolerant discharge scheme is described. Long lived (>10⁵ shots) stable discharges at high pump energy density (200 J.l^–1 atm^–1) have been achieved both with and without the use of additive gases.     

SENSITIVITY OF Porphyromonas AND Prevotella SPECIES IN LIQUID MEDIA TO ARGON LASER

Abstract— The phototoxicity of argon laser irradiation was studied in aqueous suspensions of Porphyromonas endodontalis (American Type Culture Collection [ATCC] 35406), Porphyromonas gingivalis (ATCC 33277), Prevotella denticola (ATCC 33184) and two strains of Prevotella intermedia (ATCC 15033 and 49046), all "black-pigmented bacteria," BPB, that accumulate cellular porphyrins. Several of these species have been implicated in the etiology of Periodontol disease. Non-black-pigmented bacteria were also studied to test the specificity of irradiation as a potential photodynamic treatment for Periodontol infections. Cell suspensions were irradiated with an argon laser at fluences of 20–200 J/cm². When cultured in hemin-supplemented media, ATCC 15033 was the most sensitive to irradiation. However, a second strain of the same species (ATCC 49046) was resistant. The photosensitivity of other species ranked ATCC 33277 > 35406 = 33184 = 35496. When hemin was replaced in media by hemoglobin, ATCC 33277 became resistant to irradiation. Protoporphyrin IX content in BPB cells was shown not to be a major factor determining photosensitivity. Oxygen was required during irradiation for BPB species to be affected. Non-black-pigmented bacteria were much less sensitive to irradiation than BPB.     

Influence of weak reflections from anti-reflection coated surfaces on CO2 laser optics design

The influence of interference due to weak reflections from anti-reflection coated surfaces in CO₂ laser optics is discussed and analysed. In certain cases quite low reflection levels (1%) are shown to lead to uncertainties in the mirror transmission coefficient or produce a non-uniform power loading on the mirror surface, resulting in damage.     

A Convenient One-Step Gingerol Synthesis

Racemic 6-gingerol can be obtained in a one-pot reaction by hexanal addition to the dianion of zingerone at low temperature. Similarly, addition of octanal or decanal to the dianion provides 8-gingerol or 10-gingerol, respectively. Acid treatment of the gingerols allows for formation of the corresponding shogaols.