New double integral inequality with application to stability analysis for linear retarded systems Article Swipe
Rupak Datta
,
Rajeeb Dey
,
Baby Bhattacharya
,
R. Saravanakumar
,
Choon Ki Ahn
·
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.1049/iet-cta.2018.5732
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.1049/iet-cta.2018.5732
This paper presents the development of a new double integral inequality (II) with the motivation of yielding quadratic approximation. It is well known that approximating integral quadratic terms with quadratic terms involves a certain degree of conservatism. In this paper, a sufficient gap has been identified in the approximation of two recent IIs reported in the literature, thereby leading to the new double II. The developed inequality has been applied to access the stability of a linear retarded system to estimate a maximum delay upper‐bound. Furthermore, a mathematical relationship of the new double II with existing inequalities is discussed to show that the developed inequality is more general, effective and bears less computational burden. Four numerical examples are given to validate the authors' claim with regard to the effective estimate of delay bound results for a linear retarded system.
Related Topics
Concepts
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1049/iet-cta.2018.5732
- https://ietresearch.onlinelibrary.wiley.com/doi/pdfdirect/10.1049/iet-cta.2018.5732
- OA Status
- bronze
- Cited By
- 14
- References
- 62
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2936233507
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W2936233507Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1049/iet-cta.2018.5732Digital Object Identifier
- Title
-
New double integral inequality with application to stability analysis for linear retarded systemsWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2019Year of publication
- Publication date
-
2019-04-17Full publication date if available
- Authors
-
Rupak Datta, Rajeeb Dey, Baby Bhattacharya, R. Saravanakumar, Choon Ki AhnList of authors in order
- Landing page
-
https://doi.org/10.1049/iet-cta.2018.5732Publisher landing page
- PDF URL
-
https://ietresearch.onlinelibrary.wiley.com/doi/pdfdirect/10.1049/iet-cta.2018.5732Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
bronzeOpen access status per OpenAlex
- OA URL
-
https://ietresearch.onlinelibrary.wiley.com/doi/pdfdirect/10.1049/iet-cta.2018.5732Direct OA link when available
- Concepts
-
Quadratic equation, Mathematics, Inequality, Linear inequality, Stability (learning theory), Conservatism, Upper and lower bounds, Multiple integral, Applied mathematics, Mathematical analysis, Computer science, Law, Machine learning, Geometry, Politics, Political scienceTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
14Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 1, 2022: 2, 2021: 4, 2020: 7Per-year citation counts (last 5 years)
- References (count)
-
62Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W2936233507 |
|---|---|
| doi | https://doi.org/10.1049/iet-cta.2018.5732 |
| ids.doi | https://doi.org/10.1049/iet-cta.2018.5732 |
| ids.mag | 2936233507 |
| ids.openalex | https://openalex.org/W2936233507 |
| fwci | 2.39961722 |
| type | article |
| title | New double integral inequality with application to stability analysis for linear retarded systems |
| biblio.issue | 10 |
| biblio.volume | 13 |
| biblio.last_page | 1524 |
| biblio.first_page | 1514 |
| topics[0].id | https://openalex.org/T10928 |
| topics[0].field.id | https://openalex.org/fields/18 |
| topics[0].field.display_name | Decision Sciences |
| topics[0].score | 0.9990000128746033 |
| topics[0].domain.id | https://openalex.org/domains/2 |
| topics[0].domain.display_name | Social Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/1804 |
| topics[0].subfield.display_name | Statistics, Probability and Uncertainty |
| topics[0].display_name | Probabilistic and Robust Engineering Design |
| topics[1].id | https://openalex.org/T10046 |
| topics[1].field.id | https://openalex.org/fields/22 |
| topics[1].field.display_name | Engineering |
| topics[1].score | 0.998199999332428 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/2207 |
| topics[1].subfield.display_name | Control and Systems Engineering |
| topics[1].display_name | Stability and Control of Uncertain Systems |
| topics[2].id | https://openalex.org/T10792 |
| topics[2].field.id | https://openalex.org/fields/17 |
| topics[2].field.display_name | Computer Science |
| topics[2].score | 0.996999979019165 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/1703 |
| topics[2].subfield.display_name | Computational Theory and Mathematics |
| topics[2].display_name | Matrix Theory and Algorithms |
| is_xpac | False |
| apc_list.value | 3200 |
| apc_list.currency | USD |
| apc_list.value_usd | 3200 |
| apc_paid | |
| concepts[0].id | https://openalex.org/C129844170 |
| concepts[0].level | 2 |
| concepts[0].score | 0.7357927560806274 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q41299 |
| concepts[0].display_name | Quadratic equation |
| concepts[1].id | https://openalex.org/C33923547 |
| concepts[1].level | 0 |
| concepts[1].score | 0.7210257053375244 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[1].display_name | Mathematics |
| concepts[2].id | https://openalex.org/C45555294 |
| concepts[2].level | 2 |
| concepts[2].score | 0.6406586766242981 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q28113351 |
| concepts[2].display_name | Inequality |
| concepts[3].id | https://openalex.org/C84135550 |
| concepts[3].level | 3 |
| concepts[3].score | 0.5595725774765015 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q3154022 |
| concepts[3].display_name | Linear inequality |
| concepts[4].id | https://openalex.org/C112972136 |
| concepts[4].level | 2 |
| concepts[4].score | 0.5359386205673218 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q7595718 |
| concepts[4].display_name | Stability (learning theory) |
| concepts[5].id | https://openalex.org/C96640997 |
| concepts[5].level | 3 |
| concepts[5].score | 0.5241394639015198 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q5163004 |
| concepts[5].display_name | Conservatism |
| concepts[6].id | https://openalex.org/C77553402 |
| concepts[6].level | 2 |
| concepts[6].score | 0.5133904218673706 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q13222579 |
| concepts[6].display_name | Upper and lower bounds |
| concepts[7].id | https://openalex.org/C54865166 |
| concepts[7].level | 2 |
| concepts[7].score | 0.42697712779045105 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q844937 |
| concepts[7].display_name | Multiple integral |
| concepts[8].id | https://openalex.org/C28826006 |
| concepts[8].level | 1 |
| concepts[8].score | 0.412389874458313 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q33521 |
| concepts[8].display_name | Applied mathematics |
| concepts[9].id | https://openalex.org/C134306372 |
| concepts[9].level | 1 |
| concepts[9].score | 0.2635009288787842 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q7754 |
| concepts[9].display_name | Mathematical analysis |
| concepts[10].id | https://openalex.org/C41008148 |
| concepts[10].level | 0 |
| concepts[10].score | 0.17286014556884766 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q21198 |
| concepts[10].display_name | Computer science |
| concepts[11].id | https://openalex.org/C199539241 |
| concepts[11].level | 1 |
| concepts[11].score | 0.047654807567596436 |
| concepts[11].wikidata | https://www.wikidata.org/wiki/Q7748 |
| concepts[11].display_name | Law |
| concepts[12].id | https://openalex.org/C119857082 |
| concepts[12].level | 1 |
| concepts[12].score | 0.0 |
| concepts[12].wikidata | https://www.wikidata.org/wiki/Q2539 |
| concepts[12].display_name | Machine learning |
| concepts[13].id | https://openalex.org/C2524010 |
| concepts[13].level | 1 |
| concepts[13].score | 0.0 |
| concepts[13].wikidata | https://www.wikidata.org/wiki/Q8087 |
| concepts[13].display_name | Geometry |
| concepts[14].id | https://openalex.org/C94625758 |
| concepts[14].level | 2 |
| concepts[14].score | 0.0 |
| concepts[14].wikidata | https://www.wikidata.org/wiki/Q7163 |
| concepts[14].display_name | Politics |
| concepts[15].id | https://openalex.org/C17744445 |
| concepts[15].level | 0 |
| concepts[15].score | 0.0 |
| concepts[15].wikidata | https://www.wikidata.org/wiki/Q36442 |
| concepts[15].display_name | Political science |
| keywords[0].id | https://openalex.org/keywords/quadratic-equation |
| keywords[0].score | 0.7357927560806274 |
| keywords[0].display_name | Quadratic equation |
| keywords[1].id | https://openalex.org/keywords/mathematics |
| keywords[1].score | 0.7210257053375244 |
| keywords[1].display_name | Mathematics |
| keywords[2].id | https://openalex.org/keywords/inequality |
| keywords[2].score | 0.6406586766242981 |
| keywords[2].display_name | Inequality |
| keywords[3].id | https://openalex.org/keywords/linear-inequality |
| keywords[3].score | 0.5595725774765015 |
| keywords[3].display_name | Linear inequality |
| keywords[4].id | https://openalex.org/keywords/stability |
| keywords[4].score | 0.5359386205673218 |
| keywords[4].display_name | Stability (learning theory) |
| keywords[5].id | https://openalex.org/keywords/conservatism |
| keywords[5].score | 0.5241394639015198 |
| keywords[5].display_name | Conservatism |
| keywords[6].id | https://openalex.org/keywords/upper-and-lower-bounds |
| keywords[6].score | 0.5133904218673706 |
| keywords[6].display_name | Upper and lower bounds |
| keywords[7].id | https://openalex.org/keywords/multiple-integral |
| keywords[7].score | 0.42697712779045105 |
| keywords[7].display_name | Multiple integral |
| keywords[8].id | https://openalex.org/keywords/applied-mathematics |
| keywords[8].score | 0.412389874458313 |
| keywords[8].display_name | Applied mathematics |
| keywords[9].id | https://openalex.org/keywords/mathematical-analysis |
| keywords[9].score | 0.2635009288787842 |
| keywords[9].display_name | Mathematical analysis |
| keywords[10].id | https://openalex.org/keywords/computer-science |
| keywords[10].score | 0.17286014556884766 |
| keywords[10].display_name | Computer science |
| keywords[11].id | https://openalex.org/keywords/law |
| keywords[11].score | 0.047654807567596436 |
| keywords[11].display_name | Law |
| language | en |
| locations[0].id | doi:10.1049/iet-cta.2018.5732 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S46640599 |
| locations[0].source.issn | 1751-8644, 1751-8652 |
| locations[0].source.type | journal |
| locations[0].source.is_oa | False |
| locations[0].source.issn_l | 1751-8644 |
| locations[0].source.is_core | True |
| locations[0].source.is_in_doaj | True |
| locations[0].source.display_name | IET Control Theory and Applications |
| locations[0].source.host_organization | https://openalex.org/P4310311714 |
| locations[0].source.host_organization_name | Institution of Engineering and Technology |
| locations[0].source.host_organization_lineage | https://openalex.org/P4310311714 |
| locations[0].source.host_organization_lineage_names | Institution of Engineering and Technology |
| locations[0].license | |
| locations[0].pdf_url | https://ietresearch.onlinelibrary.wiley.com/doi/pdfdirect/10.1049/iet-cta.2018.5732 |
| locations[0].version | publishedVersion |
| locations[0].raw_type | journal-article |
| locations[0].license_id | |
| locations[0].is_accepted | True |
| locations[0].is_published | True |
| locations[0].raw_source_name | IET Control Theory & Applications |
| locations[0].landing_page_url | https://doi.org/10.1049/iet-cta.2018.5732 |
| indexed_in | crossref, doaj |
| authorships[0].author.id | https://openalex.org/A5064198189 |
| authorships[0].author.orcid | https://orcid.org/0000-0002-2469-6925 |
| authorships[0].author.display_name | Rupak Datta |
| authorships[0].countries | IN |
| authorships[0].affiliations[0].institution_ids | https://openalex.org/I196486160 |
| authorships[0].affiliations[0].raw_affiliation_string | Department of Mathematics, National Institute of Technology Agartala, Agartala, 799046 India |
| authorships[0].institutions[0].id | https://openalex.org/I196486160 |
| authorships[0].institutions[0].ror | https://ror.org/03swyrn62 |
| authorships[0].institutions[0].type | education |
| authorships[0].institutions[0].lineage | https://openalex.org/I196486160 |
| authorships[0].institutions[0].country_code | IN |
| authorships[0].institutions[0].display_name | National Institute of Technology Agartala |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Rupak Datta |
| authorships[0].is_corresponding | False |
| authorships[0].raw_affiliation_strings | Department of Mathematics, National Institute of Technology Agartala, Agartala, 799046 India |
| authorships[1].author.id | https://openalex.org/A5102829470 |
| authorships[1].author.orcid | https://orcid.org/0000-0002-6573-0114 |
| authorships[1].author.display_name | Rajeeb Dey |
| authorships[1].countries | IN |
| authorships[1].affiliations[0].institution_ids | https://openalex.org/I151903974 |
| authorships[1].affiliations[0].raw_affiliation_string | Department of Electrical Engineering, National Institute of Technology Silchar, Silchar, 788010 India |
| authorships[1].institutions[0].id | https://openalex.org/I151903974 |
| authorships[1].institutions[0].ror | https://ror.org/001ws2a36 |
| authorships[1].institutions[0].type | education |
| authorships[1].institutions[0].lineage | https://openalex.org/I151903974 |
| authorships[1].institutions[0].country_code | IN |
| authorships[1].institutions[0].display_name | National Institute Of Technology Silchar |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | Rajeeb Dey |
| authorships[1].is_corresponding | False |
| authorships[1].raw_affiliation_strings | Department of Electrical Engineering, National Institute of Technology Silchar, Silchar, 788010 India |
| authorships[2].author.id | https://openalex.org/A5111785213 |
| authorships[2].author.orcid | https://orcid.org/0000-0001-6053-6067 |
| authorships[2].author.display_name | Baby Bhattacharya |
| authorships[2].countries | IN |
| authorships[2].affiliations[0].institution_ids | https://openalex.org/I196486160 |
| authorships[2].affiliations[0].raw_affiliation_string | Department of Mathematics, National Institute of Technology Agartala, Agartala, 799046 India |
| authorships[2].institutions[0].id | https://openalex.org/I196486160 |
| authorships[2].institutions[0].ror | https://ror.org/03swyrn62 |
| authorships[2].institutions[0].type | education |
| authorships[2].institutions[0].lineage | https://openalex.org/I196486160 |
| authorships[2].institutions[0].country_code | IN |
| authorships[2].institutions[0].display_name | National Institute of Technology Agartala |
| authorships[2].author_position | middle |
| authorships[2].raw_author_name | Baby Bhattacharya |
| authorships[2].is_corresponding | False |
| authorships[2].raw_affiliation_strings | Department of Mathematics, National Institute of Technology Agartala, Agartala, 799046 India |
| authorships[3].author.id | https://openalex.org/A5012694572 |
| authorships[3].author.orcid | https://orcid.org/0000-0002-4772-1732 |
| authorships[3].author.display_name | R. Saravanakumar |
| authorships[3].countries | JP |
| authorships[3].affiliations[0].institution_ids | https://openalex.org/I113306721 |
| authorships[3].affiliations[0].raw_affiliation_string | Graduate School of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima, 739-8527 Japan |
| authorships[3].institutions[0].id | https://openalex.org/I113306721 |
| authorships[3].institutions[0].ror | https://ror.org/03t78wx29 |
| authorships[3].institutions[0].type | education |
| authorships[3].institutions[0].lineage | https://openalex.org/I113306721 |
| authorships[3].institutions[0].country_code | JP |
| authorships[3].institutions[0].display_name | Hiroshima University |
| authorships[3].author_position | middle |
| authorships[3].raw_author_name | Ramasamy Saravanakumar |
| authorships[3].is_corresponding | False |
| authorships[3].raw_affiliation_strings | Graduate School of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima, 739-8527 Japan |
| authorships[4].author.id | https://openalex.org/A5084993350 |
| authorships[4].author.orcid | https://orcid.org/0000-0003-0993-9658 |
| authorships[4].author.display_name | Choon Ki Ahn |
| authorships[4].countries | KR |
| authorships[4].affiliations[0].institution_ids | https://openalex.org/I197347611 |
| authorships[4].affiliations[0].raw_affiliation_string | School of Electrical Engineering, Korea University, Anam-Dong 5-Ga, Sungbuk-Gu, Seoul, 136-701 Republic of Korea |
| authorships[4].institutions[0].id | https://openalex.org/I197347611 |
| authorships[4].institutions[0].ror | https://ror.org/047dqcg40 |
| authorships[4].institutions[0].type | education |
| authorships[4].institutions[0].lineage | https://openalex.org/I197347611 |
| authorships[4].institutions[0].country_code | KR |
| authorships[4].institutions[0].display_name | Korea University |
| authorships[4].author_position | last |
| authorships[4].raw_author_name | Choon Ki Ahn |
| authorships[4].is_corresponding | True |
| authorships[4].raw_affiliation_strings | School of Electrical Engineering, Korea University, Anam-Dong 5-Ga, Sungbuk-Gu, Seoul, 136-701 Republic of Korea |
| has_content.pdf | True |
| has_content.grobid_xml | True |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://ietresearch.onlinelibrary.wiley.com/doi/pdfdirect/10.1049/iet-cta.2018.5732 |
| open_access.oa_status | bronze |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | New double integral inequality with application to stability analysis for linear retarded systems |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-06T03:46:38.306776 |
| primary_topic.id | https://openalex.org/T10928 |
| primary_topic.field.id | https://openalex.org/fields/18 |
| primary_topic.field.display_name | Decision Sciences |
| primary_topic.score | 0.9990000128746033 |
| primary_topic.domain.id | https://openalex.org/domains/2 |
| primary_topic.domain.display_name | Social Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/1804 |
| primary_topic.subfield.display_name | Statistics, Probability and Uncertainty |
| primary_topic.display_name | Probabilistic and Robust Engineering Design |
| related_works | https://openalex.org/W2381997239, https://openalex.org/W1592764918, https://openalex.org/W1975687574, https://openalex.org/W2347774719, https://openalex.org/W4385983104, https://openalex.org/W4246523182, https://openalex.org/W2376556533, https://openalex.org/W2808367679, https://openalex.org/W4245885004, https://openalex.org/W3206779990 |
| cited_by_count | 14 |
| counts_by_year[0].year | 2025 |
| counts_by_year[0].cited_by_count | 1 |
| counts_by_year[1].year | 2022 |
| counts_by_year[1].cited_by_count | 2 |
| counts_by_year[2].year | 2021 |
| counts_by_year[2].cited_by_count | 4 |
| counts_by_year[3].year | 2020 |
| counts_by_year[3].cited_by_count | 7 |
| locations_count | 1 |
| best_oa_location.id | doi:10.1049/iet-cta.2018.5732 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S46640599 |
| best_oa_location.source.issn | 1751-8644, 1751-8652 |
| best_oa_location.source.type | journal |
| best_oa_location.source.is_oa | False |
| best_oa_location.source.issn_l | 1751-8644 |
| best_oa_location.source.is_core | True |
| best_oa_location.source.is_in_doaj | True |
| best_oa_location.source.display_name | IET Control Theory and Applications |
| best_oa_location.source.host_organization | https://openalex.org/P4310311714 |
| best_oa_location.source.host_organization_name | Institution of Engineering and Technology |
| best_oa_location.source.host_organization_lineage | https://openalex.org/P4310311714 |
| best_oa_location.source.host_organization_lineage_names | Institution of Engineering and Technology |
| best_oa_location.license | |
| best_oa_location.pdf_url | https://ietresearch.onlinelibrary.wiley.com/doi/pdfdirect/10.1049/iet-cta.2018.5732 |
| best_oa_location.version | publishedVersion |
| best_oa_location.raw_type | journal-article |
| best_oa_location.license_id | |
| best_oa_location.is_accepted | True |
| best_oa_location.is_published | True |
| best_oa_location.raw_source_name | IET Control Theory & Applications |
| best_oa_location.landing_page_url | https://doi.org/10.1049/iet-cta.2018.5732 |
| primary_location.id | doi:10.1049/iet-cta.2018.5732 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S46640599 |
| primary_location.source.issn | 1751-8644, 1751-8652 |
| primary_location.source.type | journal |
| primary_location.source.is_oa | False |
| primary_location.source.issn_l | 1751-8644 |
| primary_location.source.is_core | True |
| primary_location.source.is_in_doaj | True |
| primary_location.source.display_name | IET Control Theory and Applications |
| primary_location.source.host_organization | https://openalex.org/P4310311714 |
| primary_location.source.host_organization_name | Institution of Engineering and Technology |
| primary_location.source.host_organization_lineage | https://openalex.org/P4310311714 |
| primary_location.source.host_organization_lineage_names | Institution of Engineering and Technology |
| primary_location.license | |
| primary_location.pdf_url | https://ietresearch.onlinelibrary.wiley.com/doi/pdfdirect/10.1049/iet-cta.2018.5732 |
| primary_location.version | publishedVersion |
| primary_location.raw_type | journal-article |
| primary_location.license_id | |
| primary_location.is_accepted | True |
| primary_location.is_published | True |
| primary_location.raw_source_name | IET Control Theory & Applications |
| primary_location.landing_page_url | https://doi.org/10.1049/iet-cta.2018.5732 |
| publication_date | 2019-04-17 |
| publication_year | 2019 |
| referenced_works | https://openalex.org/W1506119886, https://openalex.org/W2054534795, https://openalex.org/W2051591980, https://openalex.org/W2037378252, https://openalex.org/W2123369396, https://openalex.org/W2086850342, https://openalex.org/W2077154900, https://openalex.org/W1842434514, https://openalex.org/W2103242076, https://openalex.org/W2061996363, https://openalex.org/W2077320235, https://openalex.org/W2016562720, https://openalex.org/W2382669442, https://openalex.org/W2626984388, https://openalex.org/W2619229533, https://openalex.org/W2806372745, https://openalex.org/W2037686415, https://openalex.org/W1990022107, https://openalex.org/W1986582332, https://openalex.org/W2601868485, https://openalex.org/W1963839355, https://openalex.org/W2773679848, https://openalex.org/W1195653569, https://openalex.org/W2568015519, https://openalex.org/W2068176649, https://openalex.org/W2049252140, https://openalex.org/W2016565902, https://openalex.org/W325253995, https://openalex.org/W2297555855, https://openalex.org/W2194523473, https://openalex.org/W2040313521, https://openalex.org/W1965587013, https://openalex.org/W2008421196, https://openalex.org/W2345130507, https://openalex.org/W2557896077, https://openalex.org/W2796186786, https://openalex.org/W2546546403, https://openalex.org/W2085052679, https://openalex.org/W2600488854, https://openalex.org/W1864738275, https://openalex.org/W2017008592, https://openalex.org/W2900879533, https://openalex.org/W2755913107, https://openalex.org/W1417252082, https://openalex.org/W1969471037, https://openalex.org/W2744010868, https://openalex.org/W847970389, https://openalex.org/W2087483936, https://openalex.org/W2575553522, https://openalex.org/W2487750779, https://openalex.org/W2791418764, https://openalex.org/W2072494890, https://openalex.org/W2560401208, https://openalex.org/W2888775341, https://openalex.org/W2895318622, https://openalex.org/W2082026451, https://openalex.org/W2734450298, https://openalex.org/W2059494740, https://openalex.org/W2896122684, https://openalex.org/W3210839039, https://openalex.org/W2803627327, https://openalex.org/W2249728259 |
| referenced_works_count | 62 |
| abstract_inverted_index.a | 6, 32, 40, 75, 81, 86, 135 |
| abstract_inverted_index.II | 93 |
| abstract_inverted_index.In | 37 |
| abstract_inverted_index.It | 19 |
| abstract_inverted_index.in | 46, 54 |
| abstract_inverted_index.is | 20, 97, 105 |
| abstract_inverted_index.of | 5, 15, 35, 49, 74, 89, 130 |
| abstract_inverted_index.to | 59, 70, 79, 99, 119, 126 |
| abstract_inverted_index.II. | 63 |
| abstract_inverted_index.IIs | 52 |
| abstract_inverted_index.The | 64 |
| abstract_inverted_index.and | 109 |
| abstract_inverted_index.are | 117 |
| abstract_inverted_index.for | 134 |
| abstract_inverted_index.gap | 42 |
| abstract_inverted_index.has | 43, 67 |
| abstract_inverted_index.new | 7, 61, 91 |
| abstract_inverted_index.the | 3, 13, 47, 55, 60, 72, 90, 102, 121, 127 |
| abstract_inverted_index.two | 50 |
| abstract_inverted_index.(II) | 11 |
| abstract_inverted_index.Four | 114 |
| abstract_inverted_index.This | 0 |
| abstract_inverted_index.been | 44, 68 |
| abstract_inverted_index.less | 111 |
| abstract_inverted_index.more | 106 |
| abstract_inverted_index.show | 100 |
| abstract_inverted_index.that | 23, 101 |
| abstract_inverted_index.this | 38 |
| abstract_inverted_index.well | 21 |
| abstract_inverted_index.with | 12, 28, 94, 124 |
| abstract_inverted_index.bears | 110 |
| abstract_inverted_index.bound | 132 |
| abstract_inverted_index.claim | 123 |
| abstract_inverted_index.delay | 83, 131 |
| abstract_inverted_index.given | 118 |
| abstract_inverted_index.known | 22 |
| abstract_inverted_index.paper | 1 |
| abstract_inverted_index.terms | 27, 30 |
| abstract_inverted_index.access | 71 |
| abstract_inverted_index.degree | 34 |
| abstract_inverted_index.double | 8, 62, 92 |
| abstract_inverted_index.linear | 76, 136 |
| abstract_inverted_index.paper, | 39 |
| abstract_inverted_index.recent | 51 |
| abstract_inverted_index.regard | 125 |
| abstract_inverted_index.system | 78 |
| abstract_inverted_index.applied | 69 |
| abstract_inverted_index.burden. | 113 |
| abstract_inverted_index.certain | 33 |
| abstract_inverted_index.leading | 58 |
| abstract_inverted_index.maximum | 82 |
| abstract_inverted_index.results | 133 |
| abstract_inverted_index.system. | 138 |
| abstract_inverted_index.thereby | 57 |
| abstract_inverted_index.authors' | 122 |
| abstract_inverted_index.estimate | 80, 129 |
| abstract_inverted_index.examples | 116 |
| abstract_inverted_index.existing | 95 |
| abstract_inverted_index.general, | 107 |
| abstract_inverted_index.integral | 9, 25 |
| abstract_inverted_index.involves | 31 |
| abstract_inverted_index.presents | 2 |
| abstract_inverted_index.reported | 53 |
| abstract_inverted_index.retarded | 77, 137 |
| abstract_inverted_index.validate | 120 |
| abstract_inverted_index.yielding | 16 |
| abstract_inverted_index.developed | 65, 103 |
| abstract_inverted_index.discussed | 98 |
| abstract_inverted_index.effective | 108, 128 |
| abstract_inverted_index.numerical | 115 |
| abstract_inverted_index.quadratic | 17, 26, 29 |
| abstract_inverted_index.stability | 73 |
| abstract_inverted_index.identified | 45 |
| abstract_inverted_index.inequality | 10, 66, 104 |
| abstract_inverted_index.motivation | 14 |
| abstract_inverted_index.sufficient | 41 |
| abstract_inverted_index.development | 4 |
| abstract_inverted_index.literature, | 56 |
| abstract_inverted_index.Furthermore, | 85 |
| abstract_inverted_index.inequalities | 96 |
| abstract_inverted_index.mathematical | 87 |
| abstract_inverted_index.relationship | 88 |
| abstract_inverted_index.approximating | 24 |
| abstract_inverted_index.approximation | 48 |
| abstract_inverted_index.computational | 112 |
| abstract_inverted_index.conservatism. | 36 |
| abstract_inverted_index.approximation. | 18 |
| abstract_inverted_index.upper‐bound. | 84 |
| cited_by_percentile_year.max | 99 |
| cited_by_percentile_year.min | 91 |
| corresponding_author_ids | https://openalex.org/A5084993350 |
| countries_distinct_count | 3 |
| institutions_distinct_count | 5 |
| corresponding_institution_ids | https://openalex.org/I197347611 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/10 |
| sustainable_development_goals[0].score | 0.5600000023841858 |
| sustainable_development_goals[0].display_name | Reduced inequalities |
| citation_normalized_percentile.value | 0.89902808 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |