{"id":"https://openalex.org/W47969230","doi":"https://doi.org/10.1007/978-1-4613-9647-5_31","title":"Using MACSyma to Calculate the Extrinsic Geometry of a Tube in a Riemannian Manifold","display_name":"Using MACSyma to Calculate the Extrinsic Geometry of a Tube in a Riemannian Manifold","publication_year":1989,"publication_date":"1989-01-01","ids":{"openalex":"https://openalex.org/W47969230","doi":"https://doi.org/10.1007/978-1-4613-9647-5_31","mag":"47969230"},"language":"en","primary_location":{"id":"doi:10.1007/978-1-4613-9647-5_31","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-1-4613-9647-5_31","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers and Mathematics","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000553752","display_name":"Harry S. D. Mills","orcid":null},"institutions":[{"id":"https://openalex.org/I155093810","display_name":"University of Idaho","ror":"https://ror.org/03hbp5t65","country_code":"US","type":"education","lineage":["https://openalex.org/I155093810"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Harry S. D. Mills","raw_affiliation_strings":["Department of Mathematics, University of Idaho, USA","University of Idaho"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Idaho, USA","institution_ids":["https://openalex.org/I155093810"]},{"raw_affiliation_string":"University of Idaho","institution_ids":["https://openalex.org/I155093810"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065022926","display_name":"Micheal H. Vernon","orcid":null},"institutions":[{"id":"https://openalex.org/I157609188","display_name":"Lewis Clark State College","ror":"https://ror.org/038x7ta12","country_code":"US","type":"education","lineage":["https://openalex.org/I157609188"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Micheal H. Vernon","raw_affiliation_strings":["Division of Natural Sciences, Lewis Clark State College, USA","Lewis Clark State College"],"affiliations":[{"raw_affiliation_string":"Division of Natural Sciences, Lewis Clark State College, USA","institution_ids":["https://openalex.org/I157609188"]},{"raw_affiliation_string":"Lewis Clark State College","institution_ids":["https://openalex.org/I157609188"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5000553752"],"corresponding_institution_ids":["https://openalex.org/I155093810"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03131991,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"269","last_page":"278"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13267","display_name":"Advanced Theoretical and Applied Studies in Material Sciences and Geometry","score":0.21060000360012054,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13267","display_name":"Advanced Theoretical and Applied Studies in Material Sciences and Geometry","score":0.21060000360012054,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/hypersurface","display_name":"Hypersurface","score":0.8974754810333252},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.6515607833862305},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.646865963935852},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5205912590026855},{"id":"https://openalex.org/keywords/tube","display_name":"Tube (container)","score":0.5151249766349792},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.47548139095306396},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.45987457036972046},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3420352339744568},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32927799224853516},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2389504313468933},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.08679261803627014},{"id":"https://openalex.org/keywords/mechanical-engineering","display_name":"Mechanical engineering","score":0.07369890809059143}],"concepts":[{"id":"https://openalex.org/C114410712","wikidata":"https://www.wikidata.org/wiki/Q973321","display_name":"Hypersurface","level":2,"score":0.8974754810333252},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.6515607833862305},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.646865963935852},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5205912590026855},{"id":"https://openalex.org/C2777551473","wikidata":"https://www.wikidata.org/wiki/Q2093072","display_name":"Tube (container)","level":2,"score":0.5151249766349792},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.47548139095306396},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.45987457036972046},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3420352339744568},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32927799224853516},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2389504313468933},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.08679261803627014},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.07369890809059143},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-1-4613-9647-5_31","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-1-4613-9647-5_31","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers and Mathematics","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W135690750","https://openalex.org/W1975289811","https://openalex.org/W2011078074","https://openalex.org/W2032237871","https://openalex.org/W2045864953","https://openalex.org/W2089465567","https://openalex.org/W2104068117","https://openalex.org/W2107480556","https://openalex.org/W2574702429","https://openalex.org/W2971268466","https://openalex.org/W3040192017"],"related_works":["https://openalex.org/W834447687","https://openalex.org/W4239786835","https://openalex.org/W2952832090","https://openalex.org/W2040382607","https://openalex.org/W2121611394","https://openalex.org/W2120845638","https://openalex.org/W1616296999","https://openalex.org/W2546668543","https://openalex.org/W4302389195","https://openalex.org/W2952208990"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}