{"id":"https://openalex.org/W2963171189","doi":"https://doi.org/10.1090/mcom/3462","title":"General superpositions of Gaussian beams and propagation errors","display_name":"General superpositions of Gaussian beams and propagation errors","publication_year":2019,"publication_date":"2019-07-24","ids":{"openalex":"https://openalex.org/W2963171189","doi":"https://doi.org/10.1090/mcom/3462","mag":"2963171189"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3462","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3462","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","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/A5100713577","display_name":"Hailiang Liu","orcid":"https://orcid.org/0000-0003-3948-2150"},"institutions":[{"id":"https://openalex.org/I173911158","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78","country_code":"US","type":"education","lineage":["https://openalex.org/I173911158"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Hailiang Liu","raw_affiliation_strings":["Department of Mathematics, Iowa State University, Ames, Iowa 50011"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Iowa State University, Ames, Iowa 50011","institution_ids":["https://openalex.org/I173911158"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031629681","display_name":"James Ralston","orcid":null},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James Ralston","raw_affiliation_strings":["Department of Mathematics, UCLA, Los Angeles, California 90095"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, UCLA, Los Angeles, California 90095","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010751299","display_name":"Peimeng Yin","orcid":"https://orcid.org/0000-0002-9188-8011"},"institutions":[{"id":"https://openalex.org/I173911158","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78","country_code":"US","type":"education","lineage":["https://openalex.org/I173911158"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Peimeng Yin","raw_affiliation_strings":["Departmetn of Mathematics, Iowa State University, Ames, Iowa 50011"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departmetn of Mathematics, Iowa State University, Ames, Iowa 50011","institution_ids":["https://openalex.org/I173911158"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100713577"],"corresponding_institution_ids":["https://openalex.org/I173911158"],"apc_list":null,"apc_paid":null,"fwci":0.1502,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.53410666,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"89","issue":"322","first_page":"675","last_page":"697"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9904000163078308,"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"}},"topics":[{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9904000163078308,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9900000095367432,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11061","display_name":"Ocean Waves and Remote Sensing","score":0.9883000254631042,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/superposition-principle","display_name":"Superposition principle","score":0.8203274011611938},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.7687735557556152},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.759254515171051},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6755986213684082},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6427310109138489},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.5169259905815125},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4963741898536682},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4839663803577423},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.46675539016723633},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.4487529993057251},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.44602668285369873},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2160491943359375},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1545332968235016},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1156148612499237},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07446649670600891}],"concepts":[{"id":"https://openalex.org/C27753989","wikidata":"https://www.wikidata.org/wiki/Q284885","display_name":"Superposition principle","level":2,"score":0.8203274011611938},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.7687735557556152},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.759254515171051},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6755986213684082},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6427310109138489},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.5169259905815125},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4963741898536682},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4839663803577423},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.46675539016723633},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.4487529993057251},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.44602668285369873},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2160491943359375},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1545332968235016},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1156148612499237},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07446649670600891},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/3462","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3462","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W756102934","https://openalex.org/W1978258427","https://openalex.org/W1992388197","https://openalex.org/W1996279390","https://openalex.org/W2034626996","https://openalex.org/W2045391874","https://openalex.org/W2054752286","https://openalex.org/W2119893484","https://openalex.org/W2134228643","https://openalex.org/W2266451974","https://openalex.org/W2318117809","https://openalex.org/W2734576260","https://openalex.org/W2963869816"],"related_works":["https://openalex.org/W4308749380","https://openalex.org/W1977264433","https://openalex.org/W2372481764","https://openalex.org/W2037841693","https://openalex.org/W2347371661","https://openalex.org/W4308448008","https://openalex.org/W2025961827","https://openalex.org/W1968349319","https://openalex.org/W2169866437","https://openalex.org/W1964286703"],"abstract_inverted_index":{"Gaussian":[0,20,40],"beams":[1,21,41,166],"are":[2],"asymptotically":[3],"valid":[4],"high":[5,30],"frequency":[6,31],"solutions":[7,32],"concentrated":[8],"on":[9],"a":[10,23,37],"single":[11],"curve":[12],"through":[13],"the":[14,67,83,163,181,187],"physical":[15],"domain,":[16],"and":[17,64,167],"superposition":[18,38],"of":[19,39,47,86,165,189],"provides":[22],"powerful":[24],"tool":[25],"to":[26,33,81],"generate":[27],"more":[28],"general":[29],"PDEs.":[34],"We":[35],"present":[36],"over":[42],"an":[43],"arbitrary":[44],"bounded":[45],"set":[46],"dimension":[48],"<inline-formula":[49,88,149,168],"content-type=\"math/mathml\">":[50,89,150,169],"<mml:math":[51,90,151,170],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[52,91,152,171],"alttext=\"m\">":[53],"<mml:semantics>":[54,110,155,173],"<mml:mi>m</mml:mi>":[55,132],"<mml:annotation":[56,138,157,175],"encoding=\"application/x-tex\">m</mml:annotation>":[57],"</mml:semantics>":[58,144,159,177],"</mml:math>":[59,145,160,178],"</inline-formula>":[60,146,161,179],"in":[61,71,192],"phase":[62],"space,":[63],"show":[65],"that":[66],"tools":[68],"recently":[69],"developed":[70],"[Math.":[72],"Comp.":[73],"82":[74],"(2013),":[75],"pp.":[76],"919\u2013952]":[77],"can":[78],"be":[79],"applied":[80],"obtain":[82],"propagation":[84],"error":[85],"order":[87,164],"alttext=\"k":[92],"Superscript":[93],"1":[94],"minus":[95,102,105],"StartFraction":[96,103],"upper":[97],"N":[98],"Over":[99,107],"2":[100],"EndFraction":[101],"d":[104],"m":[106],"4":[108],"EndFraction\">":[109],"<mml:msup>":[111],"<mml:mi>k</mml:mi>":[112],"<mml:mrow":[113],"class=\"MJX-TeXAtom-ORD\">":[114],"<mml:mn>1</mml:mn>":[115],"<mml:mo>":[116,123,129],"\u2212":[117,124,130],"</mml:mo>":[118,125,131],"<mml:mfrac>":[119,126],"<mml:mi>N</mml:mi>":[120,156],"<mml:mn>2</mml:mn>":[121],"</mml:mfrac>":[122,135],"<mml:mrow>":[127],"<mml:mi>d</mml:mi>":[128,174],"</mml:mrow>":[133,136],"<mml:mn>4</mml:mn>":[134],"</mml:msup>":[137],"encoding=\"application/x-tex\">k^{1-":[139],"\\frac":[140,142],"{N}{2}-":[141],"{d-m}{4}}</mml:annotation>":[143],",":[147],"where":[148],"alttext=\"upper":[153],"N\">":[154],"encoding=\"application/x-tex\">N</mml:annotation>":[158],"is":[162,180],"alttext=\"d\">":[172],"encoding=\"application/x-tex\">d</mml:annotation>":[176],"spatial":[182],"dimension.":[183],"Moreover,":[184],"we":[185],"study":[186],"sharpness":[188],"this":[190],"estimate":[191],"examples.":[193]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-23T06:14:38.165362","created_date":"2025-10-10T00:00:00"}
