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In the online metric matching problem, there are servers on a given metric space and requests are given one-by-one. The task of an online algorithm is to match each request immediately and irrevocably with one of the unused servers. In this paper, we pursue competitive analysis for two variants of the online metric matching problem. The first variant is a restriction where each server is placed at one of two positions, which is denoted by OMM(2). We show that a simple greedy algorithm achieves the competitive ratio of 3 for OMM(2). We also show that this greedy algorithm is optimal by showing that the competitive ratio of any deterministic online algorithm for OMM(2) is at least 3. The second variant is the online facility assignment problem on a line. In this problem, the metric space is a line, the servers have capacities, and the distances between any two consecutive servers are the same. We denote this problem by OFAL(k), where k is the number of servers. We first observe that the upper and lower bounds for OMM(2) also hold for OFAL(2), so the competitive ratio for OFAL(2) is exactly 3. We then show lower bounds on the competitive ratio 1+6–√(>3.44948), 4+73√3(>4.18133) and 133(>4.33333) for OFAL(3), OFAL(4) and OFAL(5), respectively.

M. Satake et al., Journal of Vacuum Science & Technology B 33, 051810 (2015) https://doi.org/10.1116/1.4930242, Mechanisms of dry etching resistance of Ta masks, which are widely used for magnetic random access memory etching processes, have been investigated for a better understanding of their faceting characteristics. In magnetic-material etching processes by CO/NH3 or CH3OH plasmas, CO+ ion is considered as one of the most dominant ion species irradiating the substrate surface. An earlier study by Li et al. [J. Vac. Sci. Technol. A 33, 040602 (2015)] has shown that the Ta sputtering yield by CO+ ion irradiation depends strongly on the ion irradiation angle and the level of the surface oxidation. In this study, the primary focus is placed on the effects of surface oxidation and physical sputtering only (without possible chemical effects of carbon) on the etching rate of Ta, and the etching characteristics of Ta and Ta2O5 have been examined with Ar+ and/or oxygen ion beams. It has been found that there is a strong negative correlation between the etching rate of Ta and the oxidation states of the surface oxide layer formed during the etching process; the higher the oxidation states are, the lower the etching rate becomes. The results indicate that a strong propensity of a Ta mask to taper by irradiation of oxidizing ions (i.e., strong ion-irradiation-angle dependence of the Ta etching rate) arises from less efficient oxidation of a tapered surface by incident oxidizing ions, which enter the surface with an oblique angle.

The blood cells of ascidians accumulate extremely high levels of the transition metal vanadium. We previously isolated four vanadium-binding proteins (Vanabins 1–4) and a homologous protein (VanabinP) from the vanadium-rich ascidian Ascidia sydneiensis samea. In the present study, we identified cDNAs encoding five different Vanabin2-related proteins in A. sydneiensis samea blood cells. It was notable that the sequences of the encoded proteins vary from that of Vanabin2 at up to 14 specific positions, while both the polypeptide length and the 18 cysteine residues were completely conserved. The most divergent protein, named 14MT, differed from Vanabin2 at all 14 positions. Using immobilized metal-ion affinity chromatography, we found that Vanabin2 and 14MT have the same metal ion selectivity, but the overall affinity of 14MT for VO2+ is higher than that of Vanabin2. Binding number for VO2+ ions was same between Vanabin2 and 14MT as assessed by gel filtration. These results suggested that sequence variations were under strict evolutionary constraints and high affinity binding sites for VO2+ are conserved among Vanabin2 variants.