 NSFPAR ID:
 10317810
 Date Published:
 Journal Name:
 Atoms
 Volume:
 9
 Issue:
 3
 ISSN:
 22182004
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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We consider the maximum matching problem in the semistreaming model formalized by Feigenbaum, Kannan, McGregor, Suri, and Zhang that is inspired by giant graphs of today. As our main result, we give a twopass (1/2 + 1/16)approximation algorithm for trianglefree graphs and a twopass (1/2 + 1/32)approximation algorithm for general graphs; these improve the approximation ratios of 1/2 + 1/52 for bipartite graphs and 1/2 + 1/140 for general graphs by Konrad, Magniez, and Mathieu. In three passes, we are able to achieve approximation ratios of 1/2 + 1/10 for trianglefree graphs and 1/2 + 1/19.753 for general graphs. We also give a multipass algorithm where we bound the number of passes precisely—we give a (2/3 − ε) approximation algorithm that uses 2/(3ε) passes for trianglefree graphs and 4/(3ε) passes for general graphs. Our algorithms are simple and combinatorial, use O(n log n) space, and (can be implemented to) have O(1) update time per edge. For general graphs, our multipass algorithm improves the best known deterministic algorithms in terms of the number of passes: * Ahn and Guha give a (2/3−ε)approximation algorithm that uses O(log(1/ε)/ε2) passes, whereas our (2/3 − ε)approximation algorithm uses 4/(3ε) passes; * they also give a (1 − ε)approximation algorithm that uses O(log n · poly(1/ε)) passes, where n is the number of vertices of the input graph; although our algorithm is (2/3−ε)approximation, our number of passes do not depend on n. Earlier multipass algorithms either have a large constant inside bigO notation for the number of passes or the constant cannot be determined due to the involved analysis, so our multipass algorithm should use much fewer passes for approximation ratios bounded slightly below 2/3.more » « less

Abstract We measure the low J CO line ratios R 21 ≡ CO (2–1)/CO (1–0), R 32 ≡ CO (3–2)/CO (2–1), and R 31 ≡CO (3–2)/CO (1–0) using wholedisk CO maps of nearby galaxies. We draw CO (2–1) from PHANGSALMA, HERACLES, and followup IRAM surveys; CO (1–0) from COMING and the Nobeyama CO Atlas of Nearby Spiral Galaxies; and CO (3–2) from the James Clerk Maxwell Telescope Nearby Galaxy Legacy Survey and Atacama Pathfinder Experiment Large APEX SubMillimetre Array mapping. All together, this yields 76, 47, and 29 maps of R 21 , R 32 , and R 31 at 20″ ∼ 1.3 kpc resolution, covering 43, 34, and 20 galaxies. Disk galaxies with high stellar mass, log ( M ⋆ / M ⊙ ) = 10.25 – 11 , and star formation rate (SFR) = 1–5 M ⊙ yr −1 , dominate the sample. We find galaxyintegrated mean values and a 16%–84% range of R 21 = 0.65 (0.50–0.83), R 32 = 0.50 (0.23–0.59), and R 31 = 0.31 (0.20–0.42). We identify weak trends relating galaxyintegrated line ratios to properties expected to correlate with excitation, including SFR/ M ⋆ and SFR/ L CO . Within galaxies, we measure central enhancements with respect to the galaxyaveraged value of ∼ 0.18 − 0.14 + 0.09 dex for R 21 , 0.27 − 0.15 + 0.13 dex for R 31 , and 0.08 − 0.09 + 0.11 dex for R 32 . All three line ratios anticorrelate with galactocentric radius and positively correlate with the local SFR surface density and specific SFR, and we provide approximate fits to these relations. The observed ratios can be reasonably reproduced by models with low temperature, moderate opacity, and moderate densities, in good agreement with expectations for the cold interstellar medium. Because the line ratios are expected to anticorrelate with the CO (1–0)toH 2 conversion factor, α CO 1 − 0 , these results have general implications for the interpretation of CO emission from galaxies.more » « less

We unravel, for the very first time, the formation pathways of hydroxyacetone (CH 3 COCH 2 OH), methyl acetate (CH 3 COOCH 3 ), and 3hydroxypropanal (HCOCH 2 CH 2 OH), as well as their enol tautomers within mixed ices of methanol (CH 3 OH) and acetaldehyde (CH 3 CHO) analogous to interstellar ices in the ISM exposed to ionizing radiation at ultralow temperatures of 5 K. Exploiting photoionization reflectron timeofflight mass spectrometry (PIReToFMS) and isotopically labeled ices, the reaction products were selectively photoionized allowing for isomer discrimination during the temperatureprogrammed desorption phase. Based on the distinct masstocharge ratios and ionization energies of the identified species, we reveal the formation pathways of hydroxyacetone (CH 3 COCH 2 OH), methyl acetate (CH 3 COOCH 3 ), and 3hydroxypropanal (HCOCH 2 CH 2 OH) via radical–radical recombination reactions and of their enol tautomers (prop1ene1,2diol (CH 3 C(OH)CHOH), prop2ene1,2diol (CH 2 C(OH)CH 2 OH), 1methoxyethen1ol (CH 3 OC(OH)CH 2 ) and prop1ene1,3diol (HOCH 2 CHCHOH)) via ketoenol tautomerization. To the best of our knowledge, 1methoxyethen1ol (CH 3 OC(OH)CH 2 ) and prop1ene1,3diol (HOCH 2 CHCHOH) are experimentally identified for the first time. Our findings help to constrain the formation mechanism of hydroxyacetone and methyl acetate detected within starforming regions and suggest that the hitherto astronomically unobserved isomer 3hydroxypropanal and its enol tautomers represent promising candidates for future astronomical searches. These enol tautomers may contribute to the molecular synthesis of biologically relevant molecules in deep space due to their nucleophilic character and high reactivity.more » « less

The use of 18crown6 (18c6) in place of 2.2.2cryptand (crypt) in rare earth amide reduction reactions involving potassium has proven to be crucial in the synthesis of Ln( ii ) complexes and isolation of their CO reduction products. The faster speed of crystallization with 18c6 appears to be important. Previous studies have shown that reduction of the trivalent amide complexes Ln(NR 2 ) 3 (R = SiMe 3 ) with potassium in the presence of 2.2.2cryptand (crypt) forms the divalent [K(crypt)][Ln II (NR 2 ) 3 ] complexes for Ln = Gd, Tb, Dy, and Tm. However, for Ho and Er, the [Ln(NR 2 ) 3 ] 1− anions were only isolable with [Rb(crypt)] 1+ countercations and isolation of the [Y II (NR 2 ) 3 ] 1− anion was not possible under any of these conditions. We now report that by changing the potassium chelator from crypt to 18crown6 (18c6), the [Ln(NR 2 ) 3 ] 1− anions can be isolated not only for Ln = Gd, Tb, Dy, and Tm, but also for Ho, Er, and Y. Specifically, these anions are isolated as salts of a 1 : 2 potassium : crown sandwich cation, [K(18c6) 2 ] 1+ , i.e. [K(18c6) 2 ][Ln(NR 2 ) 3 ]. The [K(18c6) 2 ] 1+ countercation was superior not only in the synthesis, but it also allowed the isolation of crystallographicallycharacterizable products from reactions of CO with the [Ln(NR 2 ) 3 ] 1− anions that were not obtainable from the [K(crypt)] 1+ analogs. Reaction of CO with [K(18c6) 2 ][Ln(NR 2 ) 3 ], generated in situ , yielded crystals of the ynediolate products, {[(R 2 N) 3 Ln] 2 (μOCCO)} 2− , which crystallized with countercations possessing 2 : 3 potassium : crown ratios, i.e. {[K 2 (18c6) 3 ]} 2+ , for Gd, Dy, Ho. In contrast, reaction of CO with a solution of isolated [K(18c6) 2 ][Gd(NR 2 ) 3 ], produced crystals of an enediolate complex isolated with a countercation with a 2 : 2 potassium : crown ratio namely [K(18c6)] 2 2+ in the complex [K(18c6)] 2 {[(R 2 N) 2 Gd 2 (μOCHCHO) 2 ]}.more » « less

Abstract Phase One of the Transportation and Transformation of Ammonia (TRANS^{2}Am) field campaign took place in northeastern Colorado during the summer of 2021. One of the goals of TRANS^{2}Am was to measure ammonia (NH_{3}) emissions from cattle feedlots and dairies. Most of these animal husbandry facilities are co‐located within oil and gas development, an important source of methane (CH_{4}) and ethane (C_{2}H_{6}) in the region. Phase One of TRANS^{2}Am included 12 near‐source research flights. We present estimates of NH_{3}emissions ratios with respect to CH_{4}(NH_{3}EmR), with and without correction of CH_{4}from oil and gas, for 29 feedlots and dairies in the region. The data shows larger emissions ratios than previously reported in the literature with a large range of values (i.e., 0.1–2.6 ppbv ppbv^{−1}). Facilities housing cattle and dairy had a mean (std) of 1.20 (0.63) and 0.29 (0.08) ppbv ppbv^{−1}, respectively. We also found that only 15% of the total ammonia (NH_{x}) is in the particle phase (i.e., ) near major sources during the warm summertime months. We examined the evolution of NH_{3}in one plume that was sampled at different distances and altitudes up to 25 km downwind and estimated the NH_{3}lifetime against deposition and partitioning to the particle phase to be 87–120 min. Finally, we calculated estimates of NH_{3}emission rates from four optimally sampled facilities. These ranged from 4 to 29 g NH_{3} · h^{−1} · hd^{−1}.