Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2034556120', 'doi': 'https://doi.org/10.1002/mana.200910045', 'title': 'Asymptotic treatment of perforated domains without homogenization', 'display_name': 'Asymptotic treatment of perforated domains without homogenization', 'publication_year': 2009, 'publication_date': '2009-12-23', 'ids': {'openalex': 'https://openalex.org/W2034556120', 'doi': 'https://doi.org/10.1002/mana.200910045', 'mag': '2034556120'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1002/mana.200910045', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S73458468', 'display_name': 'Mathematische Nachrichten', 'issn_l': '0025-584X', 'issn': ['0025-584X', '1522-2616'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320595', 'host_organization_name': 'Wiley', 'host_organization_lineage': ['https://openalex.org/P4310320595'], 'host_organization_lineage_names': ['Wiley'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': False, 'oa_status': 'closed', 'oa_url': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5036028881', 'display_name': 'Vladimir Maz’ya', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I102134673', 'display_name': 'Linköping University', 'ror': 'https://ror.org/05ynxx418', 'country_code': 'SE', 'type': 'education', 'lineage': ['https://openalex.org/I102134673']}, {'id': 'https://openalex.org/I146655781', 'display_name': 'University of Liverpool', 'ror': 'https://ror.org/04xs57h96', 'country_code': 'GB', 'type': 'education', 'lineage': ['https://openalex.org/I146655781']}], 'countries': ['GB', 'SE'], 'is_corresponding': False, 'raw_author_name': "Vladimir G. Maz'ya", 'raw_affiliation_strings': ['Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, U.K.', 'Department of Mathematics, Linköping University, SE–581 83 Linköping, Sweden'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics, Linköping University, SE–581 83 Linköping, Sweden', 'institution_ids': ['https://openalex.org/I102134673']}, {'raw_affiliation_string': 'Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, U.K.', 'institution_ids': ['https://openalex.org/I146655781']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5068777190', 'display_name': 'A. B. Movchan', 'orcid': 'https://orcid.org/0000-0001-8902-9923'}, 'institutions': [{'id': 'https://openalex.org/I102134673', 'display_name': 'Linköping University', 'ror': 'https://ror.org/05ynxx418', 'country_code': 'SE', 'type': 'education', 'lineage': ['https://openalex.org/I102134673']}], 'countries': ['SE'], 'is_corresponding': False, 'raw_author_name': 'A. Movchan', 'raw_affiliation_strings': ['Department of Mathematics, Linköping University, SE-581 83 Linköping, Sweden,'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics, Linköping University, SE-581 83 Linköping, Sweden,', 'institution_ids': ['https://openalex.org/I102134673']}]}], 'institution_assertions': [], 'countries_distinct_count': 2, 'institutions_distinct_count': 2, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': {'value': 3140, 'currency': 'USD', 'value_usd': 3140, 'provenance': 'doaj'}, 'apc_paid': None, 'fwci': 2.002, 'has_fulltext': True, 'fulltext_origin': 'ngrams', 'cited_by_count': 65, 'citation_normalized_percentile': {'value': 0.972054, 'is_in_top_1_percent': False, 'is_in_top_10_percent': True}, 'cited_by_percentile_year': {'min': 95, 'max': 96}, 'biblio': {'volume': '283', 'issue': '1', 'first_page': '104', 'last_page': '125'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T12100', 'display_name': 'Multiscale Methods for Heterogeneous Systems', 'score': 0.9994, 'subfield': {'id': 'https://openalex.org/subfields/1703', 'display_name': 'Computational Theory and Mathematics'}, 'field': {'id': 'https://openalex.org/fields/17', 'display_name': 'Computer Science'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, 'topics': [{'id': 'https://openalex.org/T12100', 'display_name': 'Multiscale Methods for Heterogeneous Systems', 'score': 0.9994, 'subfield': {'id': 'https://openalex.org/subfields/1703', 'display_name': 'Computational Theory and Mathematics'}, 'field': {'id': 'https://openalex.org/fields/17', 'display_name': 'Computer Science'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T10739', 'display_name': 'Electromagnetic Scattering with Integral Equations', 'score': 0.9987, 'subfield': {'id': 'https://openalex.org/subfields/3107', 'display_name': 'Atomic and Molecular Physics, and Optics'}, 'field': {'id': 'https://openalex.org/fields/31', 'display_name': 'Physics and Astronomy'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T11263', 'display_name': 'Finite-Difference Time-Domain Methods in Electromagnetics', 'score': 0.9965, 'subfield': {'id': 'https://openalex.org/subfields/2208', 'display_name': 'Electrical and Electronic Engineering'}, 'field': {'id': 'https://openalex.org/fields/22', 'display_name': 'Engineering'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/homogenization', 'display_name': 'Homogenization (climate)', 'score': 0.6657141}, {'id': 'https://openalex.org/keywords/asymptotic-expansion', 'display_name': 'Asymptotic expansion', 'score': 0.6493459}, {'id': 'https://openalex.org/keywords/domain-decomposition-method', 'display_name': 'Domain Decomposition Method', 'score': 0.530535}, {'id': 'https://openalex.org/keywords/multiscale-methods', 'display_name': 'Multiscale Methods', 'score': 0.520513}, {'id': 'https://openalex.org/keywords/time-domain-simulation', 'display_name': 'Time-Domain Simulation', 'score': 0.50854}, {'id': 'https://openalex.org/keywords/asymptotic-formula', 'display_name': 'Asymptotic formula', 'score': 0.43428838}], 'concepts': [{'id': 'https://openalex.org/C39613435', 'wikidata': 'https://www.wikidata.org/wiki/Q846677', 'display_name': 'Remainder', 'level': 2, 'score': 0.9054483}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.8878541}, {'id': 'https://openalex.org/C2778722038', 'wikidata': 'https://www.wikidata.org/wiki/Q17030643', 'display_name': 'Homogenization (climate)', 'level': 3, 'score': 0.6657141}, {'id': 'https://openalex.org/C11683690', 'wikidata': 'https://www.wikidata.org/wiki/Q752726', 'display_name': 'Asymptotic expansion', 'level': 2, 'score': 0.6493459}, {'id': 'https://openalex.org/C28826006', 'wikidata': 'https://www.wikidata.org/wiki/Q33521', 'display_name': 'Applied mathematics', 'level': 1, 'score': 0.49754837}, {'id': 'https://openalex.org/C9376300', 'wikidata': 'https://www.wikidata.org/wiki/Q168817', 'display_name': 'Algebraic number', 'level': 2, 'score': 0.4559702}, {'id': 'https://openalex.org/C182310444', 'wikidata': 'https://www.wikidata.org/wiki/Q1332643', 'display_name': 'Boundary value problem', 'level': 2, 'score': 0.4490618}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.4489653}, {'id': 'https://openalex.org/C24209939', 'wikidata': 'https://www.wikidata.org/wiki/Q752718', 'display_name': 'Asymptotic formula', 'level': 2, 'score': 0.43428838}, {'id': 'https://openalex.org/C130217890', 'wikidata': 'https://www.wikidata.org/wiki/Q47041', 'display_name': 'Biodiversity', 'level': 2, 'score': 0.0}, {'id': 'https://openalex.org/C18903297', 'wikidata': 'https://www.wikidata.org/wiki/Q7150', 'display_name': 'Ecology', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C94375191', 'wikidata': 'https://www.wikidata.org/wiki/Q11205', 'display_name': 'Arithmetic', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C86803240', 'wikidata': 'https://www.wikidata.org/wiki/Q420', 'display_name': 'Biology', 'level': 0, 'score': 0.0}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1002/mana.200910045', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S73458468', 'display_name': 'Mathematische Nachrichten', 'issn_l': '0025-584X', 'issn': ['0025-584X', '1522-2616'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320595', 'host_organization_name': 'Wiley', 'host_organization_lineage': ['https://openalex.org/P4310320595'], 'host_organization_lineage_names': ['Wiley'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}], 'best_oa_location': None, 'sustainable_development_goals': [], 'grants': [{'funder': 'https://openalex.org/F4320334627', 'funder_display_name': 'Engineering and Physical Sciences Research Council', 'award_id': 'EP/F005563/1'}], 'datasets': [], 'versions': [], 'referenced_works_count': 11, 'referenced_works': ['https://openalex.org/W1550621289', 'https://openalex.org/W1742698708', 'https://openalex.org/W1978581361', 'https://openalex.org/W2037229612', 'https://openalex.org/W2072628911', 'https://openalex.org/W2075877094', 'https://openalex.org/W2083206954', 'https://openalex.org/W2104917837', 'https://openalex.org/W2562800485', 'https://openalex.org/W3007766202', 'https://openalex.org/W593077420'], 'related_works': ['https://openalex.org/W3188679987', 'https://openalex.org/W3010683802', 'https://openalex.org/W2257007259', 'https://openalex.org/W2141283127', 'https://openalex.org/W2065042323', 'https://openalex.org/W2046748745', 'https://openalex.org/W2026561145', 'https://openalex.org/W1986261293', 'https://openalex.org/W1971270572', 'https://openalex.org/W1968145598'], 'abstract_inverted_index': {'Abstract': [0], 'As': [1], 'a': [2, 19, 46, 50, 71, 83], 'main': [3], 'result': [4], 'of': [5, 15, 37, 52, 58, 74, 89, 114, 126, 141], 'the': [6, 38, 42, 105, 111, 115, 117, 127, 131, 139, 142, 148], 'paper,': [7, 116], 'we': [8], 'construct': [9], 'and': [10, 98, 101], 'justify': [11], 'an': [12, 35, 123], 'asymptotic': [13, 54, 67, 124], 'approximation': [14], "Green's": [16, 128], 'function': [17, 129], 'in': [18, 44, 62, 130], 'domain': [20, 47], 'with': [21, 34, 145], 'many': [22], 'small': [23], 'inclusions.': [24], 'Periodicity': [25], 'ofthe': [26], 'array': [27], 'ofinclusions': [28], 'is': [29, 92, 119, 138], 'not': [30], 'required.': [31], 'We': [32], 'start': [33], 'analysis': [36], 'Dirichlet': [39], 'problem': [40], 'for': [41, 56, 104], 'Laplacian': [43], 'such': [45], 'to': [48, 76, 121, 147], 'illustrate': [49], 'method': [51, 118], 'mesoscale': [53], 'approximations': [55], 'solutions': [57, 75], 'boundary': [59], 'value': [60], 'problems': [61, 79], 'multiply': [63], 'perforated': [64, 133], 'domains.': [65], 'The': [66, 87, 135], 'formula': [68], 'obtained': [69], 'involves': [70], 'linear': [72, 84], 'combination': [73], 'certain': [77], 'model': [78], 'whose': [80], 'coefficients': [81], 'satisfy': [82], 'algebraic': [85], 'system.': [86], 'solvability': [88], 'this': [90], 'system': [91], 'proved': [93], 'under': [94], 'weak': [95], 'geometrical': [96], 'assumptions,': [97], 'both': [99], 'uniform': [100], 'energy': [102], 'estimates': [103], 'remainder': [106, 143], 'term': [107], 'are': [108], 'derived.': [109], 'In': [110], 'second': [112], 'part': [113], 'applied': [120], 'derive': [122], 'representation': [125], 'same': [132], 'domain.': [134], 'important': [136], 'feature': [137], 'uniformity': [140], 'estimate': [144], 'respect': [146], 'independent': [149], 'variables': [150], '(©': [151], '2010': [152], 'WILEY‐VCH': [153], 'Verlag': [154], 'GmbH': [155], '&': [156], 'Co.': [157], 'KGaA,': [158], 'Weinheim)': [159]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2034556120', 'counts_by_year': [{'year': 2023, 'cited_by_count': 2}, {'year': 2022, 'cited_by_count': 5}, {'year': 2021, 'cited_by_count': 2}, {'year': 2020, 'cited_by_count': 3}, {'year': 2019, 'cited_by_count': 3}, {'year': 2018, 'cited_by_count': 3}, {'year': 2017, 'cited_by_count': 6}, {'year': 2016, 'cited_by_count': 11}, {'year': 2015, 'cited_by_count': 7}, {'year': 2014, 'cited_by_count': 3}, {'year': 2013, 'cited_by_count': 13}, {'year': 2012, 'cited_by_count': 3}], 'updated_date': '2024-09-19T19:45:18.789727', 'created_date': '2016-06-24'}