Uniqueness and nonuniqueness for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si38.svg"><mml:msup><mml:mi>L</mml:mi><mml:mn>1</mml:mn></mml:msup></mml:math> minimization source localization problem with three measurements

Kwon, Kiwoon

doi:10.1016/j.amc.2021.126649

Cited by 2 publications

(9 citation statements)

References 12 publications

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“…By Proposition 1 [2], there exists at least one solution X. If we notate |X| as the number of possible locations set X, then |X| ≥ 1.…”

Section: Introductionmentioning

confidence: 99%

“…Let S 1 , S 2 , and S 3 be the measurement circles, and further define [3], the present work [2] The objective function O(W ) = Table 1: Differences among the results in [2], [3], and the present work.…”

Section: Introductionmentioning

confidence: 99%

“…The number of possible source locations to (2) is already explained in [2]. But Theorem 2(a), 2(b), and 6(c) in [2] are misleading.…”

Section: Introductionmentioning

confidence: 99%

“…The number of possible source locations to (2) is already explained in [2]. But Theorem 2(a), 2(b), and 6(c) in [2] are misleading. Therefore, we correct the theorems in Theorem 1 and 2, where red phrases are the corrected ones to the thorems of [2].…”

Section: Introductionmentioning

confidence: 99%

“…But Theorem 2(a), 2(b), and 6(c) in [2] are misleading. Therefore, we correct the theorems in Theorem 1 and 2, where red phrases are the corrected ones to the thorems of [2]. Thus, Table 1 in [2] should be changed into Table 1 in the present paper.…”

Section: Introductionmentioning

confidence: 99%

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Greenhouse Gas Emissions from Incineration of Municipal Solid Waste in Seoul, South Korea

2023

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Greenhouse gas (GHG) emissions from the incineration of municipal solid waste (MSW) have become a concern in the solid waste community from the perspective of climate change mitigation and response. In this study, we aimed to estimate the GHG emissions from the incineration of MSW in Seoul, with a population of about 10 million, by using the IPCC (Intergovernmental Panel on Climate Change) 2006 guideline and scenario analysis for 2030 and 2040. In 2021, Seoul generated 2899 kt of MSW/yr. Approximately 40% (1163 kt/yr) of Seoul’s MSW was disposable (or non-recyclable) waste. Out of the disposable waste, about 741 kt/yr of combustible waste was treated by incineration, resulting in 545 kt CO2 eq emissions, which was about 7.5 times higher than the 74 kt CO2 eq in 2000. The dominant contributor to the GHG emissions was plastic waste, accounting for the largest fraction of 92% (501 kt CO2 eq/yr in 2021). Scenario analysis showed that if the current situation (BAU scenario) is considered, with the assumption of no reduction in MSW generation, the capacity of Seoul’s four incineration facilities will be exceeded in 2029. All other scenarios (S1, S2, and S3) showed reduced amounts of MSW incineration and GHG emissions compared to the BAU scenario. Especially, S3 (waste reduction and increased recycling rate) revealed a 53% reduction when compared to the BAU scenario. Based on the results of our scenario analysis, it is expected that in 2040, the GHG emissions from incineration will be in a range of from about 389 kt CO2 eq to 832 kt CO2 eq, depending on the waste minimization policy and recycling efforts in the future. Strengthened regulations on and efforts towards plastic waste reduction and the recycling of MSW will be crucial with the perspectives of GHG emissions by incineration and resource recovery.

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“…By Proposition 1 [2], there exists at least one solution X. If we notate |X| as the number of possible locations set X, then |X| ≥ 1.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The number of possible source locations to (2) is already explained in [2]. But Theorem 2(a), 2(b), and 6(c) in [2] are misleading.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Greenhouse Gas Emissions from Incineration of Municipal Solid Waste in Seoul, South Korea

2023

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The Number of Global Solutions for GPS Source Localization in Two‐Dimension

Kwon

2024

Journal of Mathematics

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Source localization is widely used in many areas including GPS, but the influence of possible noises cannot be overlooked. Many optimization methods have been attempted to mitigate different kinds of noises. However, the stability of the solution, even the number of global solutions, is not fully known. Only local convergence or stability for the optimization problem is known in simple L1 or L2 settings. In this paper, we prove that the number of possible two‐dimensional source locations with three measurements in L2 setting is at most 5. We also showed the sufficient and necessary condition for the number of the solutions being 1, 2, 3, 4, and 5, where the measurement triangle is isosceles and the measurement distance for the two isosceles triangles is the same.

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Uniqueness and nonuniqueness for the L1 minimization source localization problem with three measurements

Cited by 2 publications

References 12 publications

Greenhouse Gas Emissions from Incineration of Municipal Solid Waste in Seoul, South Korea

Greenhouse Gas Emissions from Incineration of Municipal Solid Waste in Seoul, South Korea

The Number of Global Solutions for GPS Source Localization in Two‐Dimension

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