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Some new general theorems are proved, in particular the existence of a work-equivalent function of the tensor strain-rate over any yield surface. The status of the classical theory of plastic anisotropy is re-appraised in the light of recent experiments, which are themselves critically reviewed. A new type of yield function is proposed to account for the so-called anomalous behaviour of some materials.\u003C\u002Fjats:p>",{"EN":112},"Theoretical plasticity of textured aggregates",{"VOID":114},"10.1017\u002Fs0305004100055596","PUBLICATION","VERIFIED","Auto Verify",[119],"EN","https:\u002F\u002Fwww.cambridge.org\u002Fcore\u002Fproduct\u002Fidentifier\u002FS0305004100055596\u002Ftype\u002Fjournal_article",[122],{"id":123,"sortIndex":25,"researcher":24,"roles":124,"affiliations":125,"properties":134,"displayName":138,"givenName":24,"familyName":24},"faf54119-8a5c-44b1-aac6-e1a4eb698758",[],[126],{"id":127,"sortIndex":25,"affiliation":128,"properties":24},"89b02b1f-3ff8-464b-aea5-f827503d8e8b",{"id":127,"createTime":24,"updateTime":24,"relativeEntities":129,"slug":24,"properties":130,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":133,"statistic":24},[],{"title":131},{"EN":132}," Department 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Metal Forming",{},false,{"id":272,"createTime":273,"updateTime":274,"relativeEntities":275,"slug":276,"properties":277,"entityType":115,"verifyStatus":116,"verifyTime":273,"verifyNote":117,"languages":292,"translateLanguages":293,"viewCount":25,"primaryUrl":295,"fullTextUrl":24,"authors":296,"publicationType":141,"publisherRelationship":314,"citationCount":364,"citationInfo":365,"publishDate":381,"publishYear":366,"citationAnalyzeStatus":23,"lastCitationAnalyze":24,"indexDatabases":382,"openAccess":24,"references":383,"isForceReanalyzing":270},"258274ad-be59-4ab6-af4b-0cce3193ef05","2024-11-25T13:49:32.083+00:00","2025-02-08T18:02:53.955+00:00",[],"A-generalized-inverse-for-matrices",{"openalex":278,"mag":280,"abstract":282,"title":285,"keywords":288,"doi":290},{"VOID":279},"W1974511160",{"VOID":281},"1974511160",{"EN":283,"VI":284},"\u003Cjats:p>This paper describes a generalization of the inverse of a non-singular matrix, as the unique solution of a certain set of equations. This generalized inverse exists for any (possibly rectangular) matrix whatsoever with complex elements. It is used here for solving linear matrix equations, and among other applications for finding an expression for the principal idempotent elements of a matrix. Also a new type of spectral decomposition is given.\u003C\u002Fjats:p>","\u003Cjats:p>Bài báo này mô tả một phép nghịch đảo tổng quát của một ma trận không suy biến, dưới dạng nghiệm duy nhất của một tập hợp phương trình nhất định. Phép nghịch đảo tổng quát này tồn tại cho bất kỳ ma trận nào (có thể là hình chữ nhật) với các phần tử phức. Nó được sử dụng ở đây để giải các phương trình ma trận tuyến tính, và trong số những ứng dụng khác là để tìm biểu thức cho các phần tử idempotent chính của một ma trận. Cũng một loại phân rã phổ mới được đưa ra.\u003C\u002Fjats:p>",{"EN":286,"VI":287},"A generalized inverse for matrices","Một phép nghịch đảo tổng quát cho ma trận",{"VI":289},"",{"VOID":291},"10.1017\u002Fs0305004100030401",[119],[294],"VI","https:\u002F\u002Fwww.cambridge.org\u002Fcore\u002Fproduct\u002Fidentifier\u002FS0305004100030401\u002Ftype\u002Fjournal_article",[297],{"id":298,"sortIndex":25,"researcher":24,"roles":299,"affiliations":300,"properties":309,"displayName":311,"givenName":24,"familyName":24},"fe2c3c3a-5a23-41ca-b74f-baaf296ee418",[],[301],{"id":302,"sortIndex":25,"affiliation":303,"properties":24},"1fda75cc-0fb2-4f5a-84d0-9b17c5fde9bc",{"id":302,"createTime":24,"updateTime":24,"relativeEntities":304,"slug":24,"properties":305,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":308,"statistic":24},[],{"title":306},{"VI":307},"St John's College, Cambridge",[],{"title":310,"openalex":312},{"EN":311},"Roger Penrose",{"VOID":313},"A5014894861",{"url":24,"publisher":315,"properties":358},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":316,"slug":10,"properties":317,"entityType":22,"verifyStatus":23,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":25,"subjectFields":322,"manageAffiliations":327,"indexDatabases":338,"url":83,"thumbnailPath":24,"statistic":353,"gsStatistic":24,"type":24,"analyzePriority":24},[],{"country":318,"eissn":319,"issn":320,"title":321},{"VOID":13},{"VOID":15},{"VOID":17},{"EN":19},[323],{"id":28,"createTime":24,"updateTime":24,"relativeEntities":324,"label":325,"description":326,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":31},{},[328,333],{"id":35,"createTime":24,"updateTime":24,"relativeEntities":329,"slug":24,"properties":330,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":332,"statistic":24},[],{"title":331},{"EN":39},[],{"id":42,"createTime":24,"updateTime":24,"relativeEntities":334,"slug":24,"properties":335,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":337,"statistic":24},[],{"title":336},{"EN":46},[],[339,346],{"id":50,"indexDatabase":340,"url":61,"indexYears":62,"academicFieldIds":345,"indexDatabaseRanking":65},{"id":52,"createTime":24,"updateTime":24,"relativeEntities":341,"label":342,"description":343,"key":58,"publicationTags":344,"standard":24},[],{"EN":55,"VI":55},{"EN":55,"VI":57},[60],[64],{"id":67,"indexDatabase":347,"url":80,"indexYears":24,"academicFieldIds":352,"indexDatabaseRanking":24},{"id":69,"createTime":24,"updateTime":24,"relativeEntities":348,"label":349,"description":350,"key":76,"publicationTags":351,"standard":24},[],{"EN":72,"VI":72},{"EN":74,"VI":75},[78,79],[82],{"impactFactor":25,"impactFactorByYear":354,"i10Index":86,"i10IndexLast5Year":25,"totalPublication":86,"totalPublicationByYear":355,"totalCitation":89,"totalCitationByYear":356,"totalCitationPerPublication":93,"totalCitationPerPublicationByYear":357,"hindexLast5Year":86,"hindex":86},{},{"1938":88,"1948":88},{"1938":91,"1948":92},{"1938":91,"1948":92},{"issue":359,"pages":361,"volume":363},{"VOID":360},"3",{"VOID":362},"406-413",{"VOID":97},4167,{"total":364,"publishYear":366,"statisticByYear":367},1955,{"2012":368,"2013":369,"2014":370,"2015":371,"2016":372,"2017":373,"2018":374,"2019":375,"2020":376,"2021":377,"2022":378,"2023":379,"2024":380},118,155,162,148,152,167,175,246,184,228,185,229,153,"1955-07-01",[78,65],[384,387,390,393,396,399,403],{"id":24,"text":385,"url":24,"identifiers":386},"10.1007\u002FBF02526278",{"doi":385},{"id":24,"text":388,"url":24,"identifiers":389},"Halmos, 1942, Finite dimensional vector spaces",{},{"id":24,"text":391,"url":24,"identifiers":392},"Cecioni, 1910, Sopra operazioni algebriche, Ann. 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Lyon, 38, 1",{},{"id":407,"createTime":408,"updateTime":409,"relativeEntities":410,"slug":411,"properties":412,"entityType":115,"verifyStatus":116,"verifyTime":426,"verifyNote":117,"languages":427,"translateLanguages":428,"viewCount":25,"primaryUrl":429,"fullTextUrl":24,"authors":430,"publicationType":141,"publisherRelationship":469,"citationCount":519,"citationInfo":520,"publishDate":523,"publishYear":521,"citationAnalyzeStatus":23,"lastCitationAnalyze":24,"indexDatabases":524,"openAccess":24,"references":525,"isForceReanalyzing":270},"fe69b936-16de-4e38-b0b4-e691980ef463","2024-11-26T21:13:45.555+00:00","2025-02-08T18:01:59.137+00:00",[],"Some-combinatorial-series-identities",{"openalex":413,"mag":415,"abstract":417,"title":420,"keywords":423,"doi":424},{"VOID":414},"W2003324906",{"VOID":416},"2003324906",{"EN":418,"VI":419},"\u003Cjats:title>Abstract\u003C\u002Fjats:title>\u003Cjats:p>While expanding upon the work of H. M. Srivastava [6] on generalizations of an interesting identity of Carlson, R. G. Buschman and H. M. Srivastava [2] proved a number of double-series identities and listed various cases of reducibility of certain hypergeometric series in two variables (cf. [1], p. 150, equation (29)). The object of the present paper is to derive three new classes of combinatorial series identities (contained in Theorems 1, 2 and 3 below) which unify and extend the results of these earlier papers ([2], [6]). A multiple-series analogue of one of the combinatorial series identities presented here is also recorded.\u003C\u002Fjats:p>","\u003Cjats:title>Tóm tắt\u003C\u002Fjats:title>\u003Cjats:p>Khi mở rộng công trình của H. M. Srivastava [6] về các tổng quát của một định danh thú vị của Carlson, R. G. Buschman và H. M. Srivastava [2] đã chứng minh một số định danh chuỗi đôi và liệt kê các trường hợp khác nhau về khả năng rút gọn của một số chuỗi siêu hình học trong hai biến (xem [1], trang 150, phương trình (29)). Mục tiêu của bài viết này là để suy ra ba lớp định danh chuỗi tổ hợp mới (chứa trong Định lý 1, 2 và 3 dưới đây) mà hợp nhất và mở rộng các kết quả của những bài viết trước đó ([2], [6]). Một tương đương chuỗi nhiều chiều của một trong các định danh chuỗi tổ hợp được trình bày ở đây cũng được ghi nhận.\u003C\u002Fjats:p>",{"EN":421,"VI":422},"Some combinatorial series identities","Một số định danh chuỗi tổ hợp",{"VI":289},{"VOID":425},"10.1017\u002Fs0305004100061880","2024-11-26T21:13:45.554+00:00",[119],[294],"https:\u002F\u002Fwww.cambridge.org\u002Fcore\u002Fproduct\u002Fidentifier\u002FS0305004100061880\u002Ftype\u002Fjournal_article",[431,450],{"id":432,"sortIndex":25,"researcher":24,"roles":433,"affiliations":434,"properties":443,"displayName":447,"givenName":24,"familyName":24},"3c4bcdf2-4ef8-4776-8254-84ae8c0efd0f",[],[435],{"id":436,"sortIndex":25,"affiliation":437,"properties":24},"c6e1a8f7-26df-4968-815b-b28f5c0d3094",{"id":436,"createTime":24,"updateTime":24,"relativeEntities":438,"slug":24,"properties":439,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":442,"statistic":24},[],{"title":440},{"VI":441},"Department of Mathematics, University of Victoria, Victoria, British Columbia V8W 2Y2, Canada",[],{"orcid":444,"title":446,"openalex":448},{"VOID":445},"https:\u002F\u002Forcid.org\u002F0000-0002-9277-8092",{"EN":447},"H. M. Srivástava",{"VOID":449},"A5079512627",{"id":451,"sortIndex":88,"researcher":24,"roles":452,"affiliations":453,"properties":462,"displayName":466,"givenName":24,"familyName":24},"ff1e141e-e808-46df-b089-95a4c5536679",[],[454],{"id":455,"sortIndex":25,"affiliation":456,"properties":24},"483ecc1e-3e02-4855-8b9e-31306e130b99",{"id":455,"createTime":24,"updateTime":24,"relativeEntities":457,"slug":24,"properties":458,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":461,"statistic":24},[],{"title":459},{"EN":460},"Department of Mathematics, S.K.N. Agriculture College, University of Udaipur, Jobmer-303329, Rajasthan, India",[],{"orcid":463,"title":465,"openalex":467},{"VOID":464},"https:\u002F\u002Forcid.org\u002F0000-0003-0423-4122",{"EN":466},"R. K. Raina",{"VOID":468},"A5055809132",{"url":24,"publisher":470,"properties":513},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":471,"slug":10,"properties":472,"entityType":22,"verifyStatus":23,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":25,"subjectFields":477,"manageAffiliations":482,"indexDatabases":493,"url":83,"thumbnailPath":24,"statistic":508,"gsStatistic":24,"type":24,"analyzePriority":24},[],{"country":473,"eissn":474,"issn":475,"title":476},{"VOID":13},{"VOID":15},{"VOID":17},{"EN":19},[478],{"id":28,"createTime":24,"updateTime":24,"relativeEntities":479,"label":480,"description":481,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":31},{},[483,488],{"id":35,"createTime":24,"updateTime":24,"relativeEntities":484,"slug":24,"properties":485,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":487,"statistic":24},[],{"title":486},{"EN":39},[],{"id":42,"createTime":24,"updateTime":24,"relativeEntities":489,"slug":24,"properties":490,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":492,"statistic":24},[],{"title":491},{"EN":46},[],[494,501],{"id":50,"indexDatabase":495,"url":61,"indexYears":62,"academicFieldIds":500,"indexDatabaseRanking":65},{"id":52,"createTime":24,"updateTime":24,"relativeEntities":496,"label":497,"description":498,"key":58,"publicationTags":499,"standard":24},[],{"EN":55,"VI":55},{"EN":55,"VI":57},[60],[64],{"id":67,"indexDatabase":502,"url":80,"indexYears":24,"academicFieldIds":507,"indexDatabaseRanking":24},{"id":69,"createTime":24,"updateTime":24,"relativeEntities":503,"label":504,"description":505,"key":76,"publicationTags":506,"standard":24},[],{"EN":72,"VI":72},{"EN":74,"VI":75},[78,79],[82],{"impactFactor":25,"impactFactorByYear":509,"i10Index":86,"i10IndexLast5Year":25,"totalPublication":86,"totalPublicationByYear":510,"totalCitation":89,"totalCitationByYear":511,"totalCitationPerPublication":93,"totalCitationPerPublicationByYear":512,"hindexLast5Year":86,"hindex":86},{},{"1938":88,"1948":88},{"1938":91,"1948":92},{"1938":91,"1948":92},{"issue":514,"pages":515,"volume":517},{"VOID":188},{"VOID":516},"9-13",{"VOID":518},"96",13,{"total":519,"publishYear":521,"statisticByYear":522},1984,{"2013":88,"2016":88,"2021":86,"2023":88,"2024":88},"1984-07-01",[78,65],[526,529,532,535,538,541],{"id":24,"text":527,"url":24,"identifiers":528},"Erdélyi, 1953, Higher Transcendental Functions, I",{},{"id":24,"text":530,"url":24,"identifiers":531},"Srivastava, 1981, Some generalizations of Carlson's identity, Boll. Un. Mat. Ital, 18, 138",{},{"id":24,"text":533,"url":24,"identifiers":534},"Riordan, 1968, Combinatorial Identities",{},{"id":24,"text":536,"url":24,"identifiers":537},"Appell, 1926, Fonctions hypergéométriques et hypersphériques; poly-nômes d'Hermite",{},{"id":24,"text":539,"url":24,"identifiers":540},"Gould, 1972, Combinatorial Identities",{},{"id":24,"text":542,"url":24,"identifiers":543},"10.1017\u002FS0305004100059478",{"doi":542},{"id":545,"createTime":546,"updateTime":547,"relativeEntities":548,"slug":549,"properties":550,"entityType":115,"verifyStatus":116,"verifyTime":546,"verifyNote":117,"languages":564,"translateLanguages":565,"viewCount":25,"primaryUrl":566,"fullTextUrl":24,"authors":567,"publicationType":141,"publisherRelationship":585,"citationCount":635,"citationInfo":636,"publishDate":648,"publishYear":637,"citationAnalyzeStatus":23,"lastCitationAnalyze":24,"indexDatabases":649,"openAccess":24,"references":650,"isForceReanalyzing":270},"c1ff116d-17d1-4c7f-8899-85fc51fa7e74","2024-11-29T08:43:42.281+00:00","2025-02-08T18:01:04.153+00:00",[],"The-flow-due-to-a-rotating-disc",{"openalex":551,"mag":553,"abstract":555,"title":558,"keywords":561,"doi":562},{"VOID":552},"W2125692555",{"VOID":554},"2125692555",{"EN":556,"VI":557},"\u003Cjats:p>1. The steady motion of an incompressible viscous fluid, due to an infinite rotating plane lamina, has been considered by Kármán. If \u003Cjats:italic>r\u003C\u002Fjats:italic>, θ, \u003Cjats:italic>z\u003C\u002Fjats:italic> are cylindrical polar coordinates, the plane lamina is taken to be \u003Cjats:italic>z\u003C\u002Fjats:italic> = 0; it is rotating with constant angular velocity ω about the axis \u003Cjats:italic>r\u003C\u002Fjats:italic> = 0. We consider the motion of the fluid on the side of the plane for which \u003Cjats:italic>z\u003C\u002Fjats:italic> is positive; the fluid is infinite in extent and \u003Cjats:italic>z\u003C\u002Fjats:italic> = 0 is the only boundary. If \u003Cjats:italic>u, v, w\u003C\u002Fjats:italic> are the components of the velocity of the fluid in the directions of \u003Cjats:italic>r\u003C\u002Fjats:italic>, θ and \u003Cjats:italic>z\u003C\u002Fjats:italic> increasing, respectively, and \u003Cjats:italic>p\u003C\u002Fjats:italic> is the pressure, then Kármán shows that the equations of motion and continuity are satisfied by taking\u003C\u002Fjats:p>\u003Cjats:p>\u003Cjats:disp-formula>\u003Cjats:graphic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0305004100012561eqn1\" \u002F>\u003C\u002Fjats:disp-formula>\u003C\u002Fjats:p>","\u003Cjats:p>1. Chuyển động ổn định của một chất lỏng nhớt không nén, do một tấm phẳng quay vô hạn gây ra, được Kármán xem xét. Nếu \u003Cjats:italic>r\u003C\u002Fjats:italic>, θ, \u003Cjats:italic>z\u003C\u002Fjats:italic> là các tọa độ cực trụ, tấm phẳng được coi là \u003Cjats:italic>z\u003C\u002Fjats:italic> = 0; nó quay với vận tốc góc không đổi ω quanh trục \u003Cjats:italic>r\u003C\u002Fjats:italic> = 0. Chúng tôi xem xét chuyển động của chất lỏng ở phía của tấm mà tại đó \u003Cjats:italic>z\u003C\u002Fjats:italic> là dương; chất lỏng là vô hạn và \u003Cjats:italic>z\u003C\u002Fjats:italic> = 0 là ranh giới duy nhất. Nếu \u003Cjats:italic>u, v, w\u003C\u002Fjats:italic> là các thành phần vận tốc của chất lỏng theo các hướng \u003Cjats:italic>r\u003C\u002Fjats:italic>, θ và \u003Cjats:italic>z\u003C\u002Fjats:italic> tăng lên, tương ứng, và \u003Cjats:italic>p\u003C\u002Fjats:italic> là áp suất, thì Kármán chỉ ra rằng các phương trình chuyển động và liên tục được thỏa mãn bằng cách lấy\u003C\u002Fjats:p>\u003Cjats:p>\u003Cjats:disp-formula>\u003Cjats:graphic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0305004100012561eqn1\" \u002F>\u003C\u002Fjats:disp-formula>\u003C\u002Fjats:p>",{"EN":559,"VI":560},"The flow due to a rotating disc","Dòng chảy do một đĩa quay",{"VI":289},{"VOID":563},"10.1017\u002Fs0305004100012561",[119],[294],"https:\u002F\u002Fwww.cambridge.org\u002Fcore\u002Fproduct\u002Fidentifier\u002FS0305004100012561\u002Ftype\u002Fjournal_article",[568],{"id":569,"sortIndex":25,"researcher":24,"roles":570,"affiliations":571,"properties":580,"displayName":582,"givenName":24,"familyName":24},"9a912c34-f5de-4904-852e-909d49cdb199",[],[572],{"id":573,"sortIndex":25,"affiliation":574,"properties":24},"fbbd1df4-0fd8-4c97-8edd-77904f7d7637",{"id":573,"createTime":24,"updateTime":24,"relativeEntities":575,"slug":24,"properties":576,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":579,"statistic":24},[],{"title":577},{"EN":578},"St-John's College",[],{"title":581,"openalex":583},{"EN":582},"W. G. Cochran",{"VOID":584},"A5109201460",{"url":24,"publisher":586,"properties":629},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":587,"slug":10,"properties":588,"entityType":22,"verifyStatus":23,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":25,"subjectFields":593,"manageAffiliations":598,"indexDatabases":609,"url":83,"thumbnailPath":24,"statistic":624,"gsStatistic":24,"type":24,"analyzePriority":24},[],{"country":589,"eissn":590,"issn":591,"title":592},{"VOID":13},{"VOID":15},{"VOID":17},{"EN":19},[594],{"id":28,"createTime":24,"updateTime":24,"relativeEntities":595,"label":596,"description":597,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":31},{},[599,604],{"id":35,"createTime":24,"updateTime":24,"relativeEntities":600,"slug":24,"properties":601,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":603,"statistic":24},[],{"title":602},{"EN":39},[],{"id":42,"createTime":24,"updateTime":24,"relativeEntities":605,"slug":24,"properties":606,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":608,"statistic":24},[],{"title":607},{"EN":46},[],[610,617],{"id":50,"indexDatabase":611,"url":61,"indexYears":62,"academicFieldIds":616,"indexDatabaseRanking":65},{"id":52,"createTime":24,"updateTime":24,"relativeEntities":612,"label":613,"description":614,"key":58,"publicationTags":615,"standard":24},[],{"EN":55,"VI":55},{"EN":55,"VI":57},[60],[64],{"id":67,"indexDatabase":618,"url":80,"indexYears":24,"academicFieldIds":623,"indexDatabaseRanking":24},{"id":69,"createTime":24,"updateTime":24,"relativeEntities":619,"label":620,"description":621,"key":76,"publicationTags":622,"standard":24},[],{"EN":72,"VI":72},{"EN":74,"VI":75},[78,79],[82],{"impactFactor":25,"impactFactorByYear":625,"i10Index":86,"i10IndexLast5Year":25,"totalPublication":86,"totalPublicationByYear":626,"totalCitation":89,"totalCitationByYear":627,"totalCitationPerPublication":93,"totalCitationPerPublicationByYear":628,"hindexLast5Year":86,"hindex":86},{},{"1938":88,"1948":88},{"1938":91,"1948":92},{"1938":91,"1948":92},{"issue":630,"pages":631,"volume":633},{"VOID":360},{"VOID":632},"365-375",{"VOID":634},"30",1004,{"total":635,"publishYear":637,"statisticByYear":638},1934,{"2012":639,"2013":640,"2014":641,"2015":201,"2016":642,"2017":643,"2018":642,"2019":644,"2020":645,"2021":643,"2022":646,"2023":640,"2024":647},37,36,32,30,39,41,44,42,31,"1934-07-01",[78,65],[651,654,657,660,663,666,669,673],{"id":24,"text":652,"url":24,"identifiers":653},"Kármán and Levi-Civitá (1924), 168–70",{},{"id":24,"text":655,"url":24,"identifiers":656},"Kempf, 1922, Vorträge aus dem Gebiete der Hydro- und Aerodynamik",{},{"id":24,"text":658,"url":24,"identifiers":659},"Lamb , Hydrodynamics (1932), 280–2",{},{"id":24,"text":661,"url":24,"identifiers":662},"Kármán, 1927, Handbuch der Physik, 7, 158",{},{"id":24,"text":664,"url":24,"identifiers":665},"Whittaker, Calculus of Observations, 363",{},{"id":24,"text":667,"url":24,"identifiers":668},"Handbuch der Experimental-Physik, 4 (1931), Part I, 255–7",{},{"id":24,"text":670,"url":24,"identifiers":671},"Zeitschrift für angewandte Mathematik u. Mechanik, 1 (1921), 244–7.",{"doi":672},"10.1002\u002Fzamm.19210010209",{"id":24,"text":674,"url":24,"identifiers":675},"Müller , Einführung in die Theorie der zähen Flüssigkeiten (1932), 226–9",{},{"id":677,"createTime":678,"updateTime":679,"relativeEntities":680,"slug":681,"properties":682,"entityType":115,"verifyStatus":116,"verifyTime":678,"verifyNote":117,"languages":697,"translateLanguages":698,"viewCount":25,"primaryUrl":699,"fullTextUrl":24,"authors":700,"publicationType":141,"publisherRelationship":718,"citationCount":769,"citationInfo":770,"publishDate":774,"publishYear":771,"citationAnalyzeStatus":23,"lastCitationAnalyze":24,"indexDatabases":775,"openAccess":24,"references":776,"isForceReanalyzing":270},"bab28a0e-f781-4610-94b9-013bcc79c9d8","2024-12-04T03:10:13.055+00:00","2025-02-08T18:00:05.901+00:00",[],"Generalizations-to-several-variables-of-Lagrange-s-expansion-with-applications-to-stochastic-processes",{"openalex":683,"mag":685,"abstract":687,"title":690,"keywords":693,"doi":695},{"VOID":684},"W2054775758",{"VOID":686},"2054775758",{"EN":688,"VI":689},"\u003Cjats:title>ABSTRACT\u003C\u002Fjats:title>\u003Cjats:p>A generalization to two independent variables of Lagrange's expansion of an inverse function was given by Stieltjes and proved rigorously by Poincaré. A new method of proof is given here that also provides a new and sometimes more convenient form of the generalization. The results are given for an arbitrary number of independent variables. Applications are pointed out to random branching processes, to queues with various types of customers, and to some enumeration problems.\u003C\u002Fjats:p>","\u003Cjats:title>TÓM TẮT\u003C\u002Fjats:title>\u003Cjats:p>Một sự tổng quát cho hai biến độc lập của khai triển Lagrange cho một hàm nghịch đảo đã được Stieltjes đề xuất và được Poincaré chứng minh một cách chặt chẽ. Một phương pháp chứng minh mới được đưa ra ở đây cũng cung cấp một dạng mới và đôi khi thuận tiện hơn của sự tổng quát này. Các kết quả được trình bày cho một số lượng biến độc lập tùy ý. Các ứng dụng được chỉ ra đối với các quá trình phân nhánh ngẫu nhiên, các hàng đợi với nhiều loại khách hàng khác nhau, và một số vấn đề đếm.\u003C\u002Fjats:p>",{"EN":691,"VI":692},"Generalizations to several variables of Lagrange's expansion, with applications to stochastic processes","Các sự tổng quát cho nhiều biến của khai triển Lagrange, với các ứng dụng cho các quá trình ngẫu nhiên",{"VI":694},"Khai triển Lagrange, hàm nghịch đảo, biến độc lập, quá trình ngẫu nhiên, hàng đợi, vấn đề đếm",{"VOID":696},"10.1017\u002Fs0305004100034666",[119],[294],"https:\u002F\u002Fwww.cambridge.org\u002Fcore\u002Fproduct\u002Fidentifier\u002FS0305004100034666\u002Ftype\u002Fjournal_article",[701],{"id":702,"sortIndex":25,"researcher":24,"roles":703,"affiliations":704,"properties":713,"displayName":715,"givenName":24,"familyName":24},"d2d89dce-cc91-4786-bc0c-5b37ef4b29b8",[],[705],{"id":706,"sortIndex":25,"affiliation":707,"properties":24},"ad6c816f-96ab-483a-b5db-c5ab669342fa",{"id":706,"createTime":24,"updateTime":24,"relativeEntities":708,"slug":24,"properties":709,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":712,"statistic":24},[],{"title":710},{"EN":711},"Admiralty Research Laboratory, Teddington, Middlesex.",[],{"title":714,"openalex":716},{"EN":715},"I. J. Good",{"VOID":717},"A5028584551",{"url":24,"publisher":719,"properties":762},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":720,"slug":10,"properties":721,"entityType":22,"verifyStatus":23,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":25,"subjectFields":726,"manageAffiliations":731,"indexDatabases":742,"url":83,"thumbnailPath":24,"statistic":757,"gsStatistic":24,"type":24,"analyzePriority":24},[],{"country":722,"eissn":723,"issn":724,"title":725},{"VOID":13},{"VOID":15},{"VOID":17},{"EN":19},[727],{"id":28,"createTime":24,"updateTime":24,"relativeEntities":728,"label":729,"description":730,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":31},{},[732,737],{"id":35,"createTime":24,"updateTime":24,"relativeEntities":733,"slug":24,"properties":734,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":736,"statistic":24},[],{"title":735},{"EN":39},[],{"id":42,"createTime":24,"updateTime":24,"relativeEntities":738,"slug":24,"properties":739,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":741,"statistic":24},[],{"title":740},{"EN":46},[],[743,750],{"id":50,"indexDatabase":744,"url":61,"indexYears":62,"academicFieldIds":749,"indexDatabaseRanking":65},{"id":52,"createTime":24,"updateTime":24,"relativeEntities":745,"label":746,"description":747,"key":58,"publicationTags":748,"standard":24},[],{"EN":55,"VI":55},{"EN":55,"VI":57},[60],[64],{"id":67,"indexDatabase":751,"url":80,"indexYears":24,"academicFieldIds":756,"indexDatabaseRanking":24},{"id":69,"createTime":24,"updateTime":24,"relativeEntities":752,"label":753,"description":754,"key":76,"publicationTags":755,"standard":24},[],{"EN":72,"VI":72},{"EN":74,"VI":75},[78,79],[82],{"impactFactor":25,"impactFactorByYear":758,"i10Index":86,"i10IndexLast5Year":25,"totalPublication":86,"totalPublicationByYear":759,"totalCitation":89,"totalCitationByYear":760,"totalCitationPerPublication":93,"totalCitationPerPublicationByYear":761,"hindexLast5Year":86,"hindex":86},{},{"1938":88,"1948":88},{"1938":91,"1948":92},{"1938":91,"1948":92},{"issue":763,"pages":765,"volume":767},{"VOID":764},"4",{"VOID":766},"367-380",{"VOID":768},"56",186,{"total":769,"publishYear":771,"statisticByYear":772},1960,{"2012":206,"2013":206,"2014":773,"2015":773,"2016":206,"2017":773,"2018":86,"2019":88,"2021":773,"2022":86,"2023":773,"2024":86},4,"1960-10-01",[78,65],[777,780,783,786,789,792,795,798,801,804,807,810,813,816,820,822,825,828,831,834,836,839,842,845,847,850,853,856,859,862,865,868,871,874,877,880],{"id":24,"text":778,"url":24,"identifiers":779},"10.2307\u002F1969046",{"doi":778},{"id":24,"text":781,"url":24,"identifiers":782},"10.1007\u002FBF02546665",{"doi":781},{"id":24,"text":784,"url":24,"identifiers":785},"Jacobson, 1951, Lectures in abstract algebra, I",{},{"id":24,"text":787,"url":24,"identifiers":788},"10.1214\u002Faoms\u002F1177730031",{"doi":787},{"id":24,"text":790,"url":24,"identifiers":791},"Behnke, 1933, Theorie der Funktionen mehrerer komplexen Veränderlichen",{},{"id":24,"text":793,"url":24,"identifiers":794},"10.1090\u002FS0002-9947-1952-0052057-2",{"doi":793},{"id":24,"text":796,"url":24,"identifiers":797},"Whittle, 1955, Some distribution and moment formulae for the Markov chain, J. R. Statist. Soc., 17, 235",{},{"id":24,"text":799,"url":24,"identifiers":800},"10.1080\u002F14786445708642275",{"doi":799},{"id":24,"text":802,"url":24,"identifiers":803},"10.1093\u002Fqmath\u002F7.1.316",{"doi":802},{"id":24,"text":805,"url":24,"identifiers":806},"Kendall, 1951, The theory of queues, J. R. Statist. Soc., 13, 151",{},{"id":24,"text":808,"url":24,"identifiers":809},"Sevasty'astov, 1951, The theory of branching random processes, Usp. Matem. Nauk, 6, 47",{},{"id":24,"text":811,"url":24,"identifiers":812},"10.1007\u002FBF02406742",{"doi":811},{"id":24,"text":814,"url":24,"identifiers":815},"(25) Stieltjes T. J. An unpublished manuscript sent to C. Hermite.",{},{"id":24,"text":817,"url":24,"identifiers":818},"Blair, 1931, J. Amer. Chem. Soc., 53, 3042, 10.1021\u002Fja01359a027",{"doi":819},"10.1021\u002Fja01359a027",{"id":24,"text":799,"url":24,"identifiers":821},{"doi":799},{"id":24,"text":823,"url":24,"identifiers":824},"Bochner, 1948, Several complex variables",{},{"id":24,"text":826,"url":24,"identifiers":827},"Jeffreys, 1946, Methods of mathematical physics",{},{"id":24,"text":829,"url":24,"identifiers":830},"Lagrange, Mém. Acad., 24, 25",{},{"id":24,"text":832,"url":24,"identifiers":833},"1889, Collected mathematical papers, 9, 202",{},{"id":24,"text":799,"url":24,"identifiers":835},{"doi":799},{"id":24,"text":837,"url":24,"identifiers":838},"1889, Collected mathematical papers, 13, 26",{},{"id":24,"text":840,"url":24,"identifiers":841},"1889, Collected mathematical papers, 11, 365",{},{"id":24,"text":843,"url":24,"identifiers":844},"Good, 1951, Contribution to the discussion on D. G. Kendall's paper (16), J. R. Statist. Soc., 13, 182",{},{"id":24,"text":799,"url":24,"identifiers":846},{"doi":799},{"id":24,"text":848,"url":24,"identifiers":849},"Everett, 1948, Multiplicative systems in several variables, Los Alamos Scientific Laboratory, II, 23",{},{"id":24,"text":851,"url":24,"identifiers":852},"10.1214\u002Faoms\u002F1177706795",{"doi":851},{"id":24,"text":854,"url":24,"identifiers":855},"10.1017\u002FS0305004100030115",{"doi":854},{"id":24,"text":857,"url":24,"identifiers":858},"10.1017\u002FS030500410002497X",{"doi":857},{"id":24,"text":860,"url":24,"identifiers":861},"10.1214\u002Faoms\u002F1177706623",{"doi":860},{"id":24,"text":863,"url":24,"identifiers":864},"Goursat, 1904, A course in mathematical analysis",{},{"id":24,"text":866,"url":24,"identifiers":867},"Forsyth, 1914, Lectures introductory to the theory of functions of two complex variables",{},{"id":24,"text":869,"url":24,"identifiers":870},"Mirsky, 1955, An introduction to linear algebra",{},{"id":24,"text":872,"url":24,"identifiers":873},"1889, Collected mathematical papers, 3, 242",{},{"id":24,"text":875,"url":24,"identifiers":876},"Whittaker, 1935, A course of modern analysis",{},{"id":24,"text":878,"url":24,"identifiers":879},"Price, 1947, Review of a paper by C. Massonnet, Math. Rev., 8, 499",{},{"id":24,"text":881,"url":24,"identifiers":882},"Whittaker, 1949, From Euclid to Eddington",{},{"id":884,"createTime":885,"updateTime":886,"relativeEntities":887,"slug":888,"properties":889,"entityType":115,"verifyStatus":116,"verifyTime":903,"verifyNote":117,"languages":904,"translateLanguages":905,"viewCount":25,"primaryUrl":906,"fullTextUrl":24,"authors":907,"publicationType":141,"publisherRelationship":927,"citationCount":978,"citationInfo":979,"publishDate":987,"publishYear":980,"citationAnalyzeStatus":23,"lastCitationAnalyze":24,"indexDatabases":988,"openAccess":24,"references":989,"isForceReanalyzing":270},"7b0355e6-73ff-48c1-a7a7-f2765a3f7f55","2024-12-10T15:48:58.358+00:00","2025-02-08T17:59:10.193+00:00",[],"Certain-fractional-i-q-i-integrals-and-i-q-i-derivatives",{"openalex":890,"mag":892,"abstract":894,"title":897,"keywords":900,"doi":901},{"VOID":891},"W2119573410",{"VOID":893},"2119573410",{"EN":895,"VI":896},"\u003Cjats:p>In a recent paper Al-Salam(1) has denned a fractional \u003Cjats:italic>q\u003C\u002Fjats:italic>-integral operator by the basic integral\u003C\u002Fjats:p>\u003Cjats:p>\u003Cjats:disp-formula>\u003Cjats:graphic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0305004100045060_eqn001\" \u002F>\u003C\u002Fjats:disp-formula>\u003C\u002Fjats:p>\u003Cjats:p>(1) Where α ≠ 0, −1, −2, …. Using the series definition of the basic integrals, (1·1) is written as\u003C\u002Fjats:p>\u003Cjats:p>\u003Cjats:disp-formula>\u003Cjats:graphic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0305004100045060_eqn002\" \u002F>\u003C\u002Fjats:disp-formula>\u003C\u002Fjats:p>\u003Cjats:p>valid for all α\u003C\u002Fjats:p>","\u003Cjats:p>Trong một bài báo gần đây, Al-Salam(1) đã định nghĩa một toán tử tích phân phân thức \u003Cjats:italic>q\u003C\u002Fjats:italic> bằng tích phân cơ bản\u003C\u002Fjats:p>\u003Cjats:p>\u003Cjats:disp-formula>\u003Cjats:graphic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0305004100045060_eqn001\" \u002F>\u003C\u002Fjats:disp-formula>\u003C\u002Fjats:p>\u003Cjats:p>(1) Trong đó α ≠ 0, −1, −2, …. Sử dụng định nghĩa dãy của các tích phân cơ bản, (1·1) được viết lại thành\u003C\u002Fjats:p>\u003Cjats:p>\u003Cjats:disp-formula>\u003Cjats:graphic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0305004100045060_eqn002\" \u002F>\u003C\u002Fjats:disp-formula>\u003C\u002Fjats:p>\u003Cjats:p>có giá trị cho mọi α\u003C\u002Fjats:p>",{"EN":898,"VI":899},"Certain fractional \u003Ci>q\u003C\u002Fi>-integrals and \u003Ci>q\u003C\u002Fi>-derivatives","Một số tích phân phân thức \u003Ci>q\u003C\u002Fi> và đạo hàm \u003Ci>q\u003C\u002Fi> nhất định",{"VI":289},{"VOID":902},"10.1017\u002Fs0305004100045060","2024-12-10T15:48:58.357+00:00",[119],[294],"https:\u002F\u002Fwww.cambridge.org\u002Fcore\u002Fproduct\u002Fidentifier\u002FS0305004100045060\u002Ftype\u002Fjournal_article",[908],{"id":909,"sortIndex":25,"researcher":24,"roles":910,"affiliations":911,"properties":920,"displayName":924,"givenName":24,"familyName":24},"ee613225-caef-468d-b83a-a90e953c226f",[],[912],{"id":913,"sortIndex":25,"affiliation":914,"properties":24},"62165ecc-947b-4dd4-9529-cd4cf5c4326b",{"id":913,"createTime":24,"updateTime":24,"relativeEntities":915,"slug":24,"properties":916,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":919,"statistic":24},[],{"title":917},{"EN":918},"WEST VIRGINIA UNIVERSITY",[],{"orcid":921,"title":923,"openalex":925},{"VOID":922},"https:\u002F\u002Forcid.org\u002F0000-0003-0075-1704",{"EN":924},"Ravi P. Agarwal",{"VOID":926},"A5064952177",{"url":24,"publisher":928,"properties":971},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":929,"slug":10,"properties":930,"entityType":22,"verifyStatus":23,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":25,"subjectFields":935,"manageAffiliations":940,"indexDatabases":951,"url":83,"thumbnailPath":24,"statistic":966,"gsStatistic":24,"type":24,"analyzePriority":24},[],{"country":931,"eissn":932,"issn":933,"title":934},{"VOID":13},{"VOID":15},{"VOID":17},{"EN":19},[936],{"id":28,"createTime":24,"updateTime":24,"relativeEntities":937,"label":938,"description":939,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":31},{},[941,946],{"id":35,"createTime":24,"updateTime":24,"relativeEntities":942,"slug":24,"properties":943,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":945,"statistic":24},[],{"title":944},{"EN":39},[],{"id":42,"createTime":24,"updateTime":24,"relativeEntities":947,"slug":24,"properties":948,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":950,"statistic":24},[],{"title":949},{"EN":46},[],[952,959],{"id":50,"indexDatabase":953,"url":61,"indexYears":62,"academicFieldIds":958,"indexDatabaseRanking":65},{"id":52,"createTime":24,"updateTime":24,"relativeEntities":954,"label":955,"description":956,"key":58,"publicationTags":957,"standard":24},[],{"EN":55,"VI":55},{"EN":55,"VI":57},[60],[64],{"id":67,"indexDatabase":960,"url":80,"indexYears":24,"academicFieldIds":965,"indexDatabaseRanking":24},{"id":69,"createTime":24,"updateTime":24,"relativeEntities":961,"label":962,"description":963,"key":76,"publicationTags":964,"standard":24},[],{"EN":72,"VI":72},{"EN":74,"VI":75},[78,79],[82],{"impactFactor":25,"impactFactorByYear":967,"i10Index":86,"i10IndexLast5Year":25,"totalPublication":86,"totalPublicationByYear":968,"totalCitation":89,"totalCitationByYear":969,"totalCitationPerPublication":93,"totalCitationPerPublicationByYear":970,"hindexLast5Year":86,"hindex":86},{},{"1938":88,"1948":88},{"1938":91,"1948":92},{"1938":91,"1948":92},{"issue":972,"pages":974,"volume":976},{"VOID":973},"2",{"VOID":975},"365-370",{"VOID":977},"66",373,{"total":978,"publishYear":980,"statisticByYear":981},1969,{"2012":982,"2013":983,"2014":984,"2015":199,"2016":200,"2017":985,"2018":986,"2019":201,"2020":202,"2021":983,"2022":641,"2023":639,"2024":639},18,27,29,12,15,"1969-09-01",[78,65],[990,993,996,999,1002,1005],{"id":24,"text":991,"url":24,"identifiers":992},"10.1002\u002Fmana.19490030502",{"doi":991},{"id":24,"text":994,"url":24,"identifiers":995},"Erdelyi, 1951, On some functional transformations, Univ. e Politecnico Torino Rend. Sem. Mat., 10, 217",{},{"id":24,"text":997,"url":24,"identifiers":998},"10.1002\u002Fmana.19490020604",{"doi":997},{"id":24,"text":1000,"url":24,"identifiers":1001},"10.1093\u002Fqmath\u002Fos-11.1.193",{"doi":1000},{"id":24,"text":1003,"url":24,"identifiers":1004},"10.1017\u002FS0013091500011469",{"doi":1003},{"id":24,"text":1006,"url":24,"identifiers":1007},"Slater, 1966, J. Generalized Hypergeometric Functions",{},{"id":1009,"createTime":1010,"updateTime":1011,"relativeEntities":1012,"slug":1013,"properties":1014,"entityType":115,"verifyStatus":116,"verifyTime":1029,"verifyNote":117,"languages":1030,"translateLanguages":1031,"viewCount":25,"primaryUrl":1032,"fullTextUrl":24,"authors":1033,"publicationType":141,"publisherRelationship":1053,"citationCount":1103,"citationInfo":1104,"publishDate":1109,"publishYear":1105,"citationAnalyzeStatus":23,"lastCitationAnalyze":24,"indexDatabases":1110,"openAccess":24,"references":1111,"isForceReanalyzing":270},"2b9e4c77-2516-4bf1-abd5-0593e6cd662d","2024-12-21T10:39:12.661+00:00","2025-02-08T17:58:13.720+00:00",[],"Double-bosonization-of-braided-groups-and-the-construction-of-i-U-i-sub-i-q-i-sub-i-g-i-",{"openalex":1015,"mag":1017,"abstract":1019,"title":1022,"keywords":1025,"doi":1027},{"VOID":1016},"W2138968575",{"VOID":1018},"2138968575",{"EN":1020,"VI":1021},"\u003Cjats:p>We introduce a quasitriangular Hopf algebra or ‘quantum group’\n \u003Cjats:italic>U\u003C\u002Fjats:italic>(\u003Cjats:italic>B\u003C\u002Fjats:italic>), \nthe \u003Cjats:italic>double-bosonization\u003C\u002Fjats:italic>, associated to every braided group \n\u003Cjats:italic>B\u003C\u002Fjats:italic> in the category of \u003Cjats:italic>H\u003C\u002Fjats:italic>-modules over \na quasitriangular Hopf algebra \u003Cjats:italic>H\u003C\u002Fjats:italic>, such that \u003Cjats:italic>B\u003C\u002Fjats:italic> appears\n as the ‘positive root space’, \n\u003Cjats:italic>H\u003C\u002Fjats:italic> as the ‘Cartan subalgebra’ and the dual \nbraided group \u003Cjats:italic>B\u003C\u002Fjats:italic>* as the ‘negative root \nspace’ of \u003Cjats:italic>U\u003C\u002Fjats:italic>(\u003Cjats:italic>B\u003C\u002Fjats:italic>). The choice \n\u003Cjats:italic>B\u003C\u002Fjats:italic>=\u003Cjats:italic>U\u003C\u002Fjats:italic>\u003Cjats:sub>\u003Cjats:italic>q\u003C\u002Fjats:italic>\u003C\u002Fjats:sub>(\u003Cjats:italic>n\u003C\u002Fjats:italic>\u003Cjats:sub>+\u003C\u002Fjats:sub>) recovers\n Lusztig's \nconstruction of \u003Cjats:italic>U\u003C\u002Fjats:italic>\u003Cjats:sub>\u003Cjats:italic>q\u003C\u002Fjats:italic>\u003C\u002Fjats:sub>(\u003Cjats:italic>g\u003C\u002Fjats:italic>); other \nchoices give more novel quantum groups. As an application, our construction\n \nprovides a canonical way of building up quantum groups from smaller ones\n by \nrepeatedly extending their positive and negative root spaces by linear\n braided \ngroups; we explicitly construct \u003Cjats:italic>U\u003C\u002Fjats:italic>\u003Cjats:sub>\u003Cjats:italic>q\u003C\u002Fjats:italic>\u003C\u002Fjats:sub>(\u003Cjats:italic>sl\u003C\u002Fjats:italic>\u003Cjats:sub>3\u003C\u002Fjats:sub>)\n from \n\u003Cjats:italic>U\u003C\u002Fjats:italic>\u003Cjats:sub>\u003Cjats:italic>q\u003C\u002Fjats:italic>\u003C\u002Fjats:sub>(\u003Cjats:italic>sl\u003C\u002Fjats:italic>\u003Cjats:sub>2\u003C\u002Fjats:sub>) by this method,\n extending it by \nthe quantum-braided plane. We provide a fundamental representation \nof \u003Cjats:italic>U\u003C\u002Fjats:italic>(\u003Cjats:italic>B\u003C\u002Fjats:italic>) in \u003Cjats:italic>B\u003C\u002Fjats:italic>. \nA projection from the quantum double, a theory of double biproducts and\n a \nTannaka–Krein reconstruction point of view are also provided.\u003C\u002Fjats:p>","\u003Cjats:p>Chúng tôi giới thiệu một đại số Hopf quasi tam giác hoặc ‘nhóm lượng tử’ \u003Cjats:italic>U\u003C\u002Fjats:italic>(\u003Cjats:italic>B\u003C\u002Fjats:italic>), phép \u003Cjats:italic>double-bosonization\u003C\u002Fjats:italic>, gắn liền với mỗi nhóm tết \u003Cjats:italic>B\u003C\u002Fjats:italic> trong danh mục các mô-đun \u003Cjats:italic>H\u003C\u002Fjats:italic> trên một đại số Hopf quasi tam giác \u003Cjats:italic>H\u003C\u002Fjats:italic>, sao cho \u003Cjats:italic>B\u003C\u002Fjats:italic> xuất hiện như ‘không gian gốc dương’, \u003Cjats:italic>H\u003C\u002Fjats:italic> như ‘đại số Cartan’ và nhóm tết đối ngẫu \u003Cjats:italic>B\u003C\u002Fjats:italic>* là ‘không gian gốc âm’ của \u003Cjats:italic>U\u003C\u002Fjats:italic>(\u003Cjats:italic>B\u003C\u002Fjats:italic>). Sự lựa chọn \u003Cjats:italic>B\u003C\u002Fjats:italic>=\u003Cjats:italic>U\u003C\u002Fjats:italic>\u003Cjats:sub>\u003Cjats:italic>q\u003C\u002Fjats:italic>\u003C\u002Fjats:sub>(\u003Cjats:italic>n\u003C\u002Fjats:italic>\u003Cjats:sub>+\u003C\u002Fjats:sub>) phục hồi cấu trúc của Lusztig cho \u003Cjats:italic>U\u003C\u002Fjats:italic>\u003Cjats:sub>\u003Cjats:italic>q\u003C\u002Fjats:italic>\u003C\u002Fjats:sub>(\u003Cjats:italic>g\u003C\u002Fjats:italic>); các lựa chọn khác mang lại nhiều nhóm lượng tử mới mẻ hơn. Như một ứng dụng, cấu trúc của chúng tôi cung cấp một cách chính quy để xây dựng các nhóm lượng tử từ những nhóm nhỏ hơn bằng cách liên tục mở rộng không gian gốc dương và âm của chúng bằng các nhóm tết tuyến tính; chúng tôi rõ ràng xây dựng \u003Cjats:italic>U\u003C\u002Fjats:italic>\u003Cjats:sub>\u003Cjats:italic>q\u003C\u002Fjats:italic>\u003C\u002Fjats:sub>(\u003Cjats:italic>sl\u003C\u002Fjats:italic>\u003Cjats:sub>3\u003C\u002Fjats:sub>) từ \u003Cjats:italic>U\u003C\u002Fjats:italic>\u003Cjats:sub>\u003Cjats:italic>q\u003C\u002Fjats:italic>\u003C\u002Fjats:sub>(\u003Cjats:italic>sl\u003C\u002Fjats:italic>\u003Cjats:sub>2\u003C\u002Fjats:sub>) bằng phương pháp này, mở rộng nó bằng mặt phẳng lượng tử-tết. Chúng tôi cung cấp một đại diện cơ bản của \u003Cjats:italic>U\u003C\u002Fjats:italic>(\u003Cjats:italic>B\u003C\u002Fjats:italic>) trong \u003Cjats:italic>B\u003C\u002Fjats:italic>. Một phép chiếu từ đối lượng tử, một lý thuyết về các sản phẩm hai lần và một quan điểm xây dựng Tannaka–Krein cũng được cung cấp.",{"EN":1023,"VI":1024},"Double-bosonization of braided groups and the \nconstruction of \u003Ci>U\u003C\u002Fi>\u003Csub>\u003Ci>q\u003C\u002Fi>\u003C\u002Fsub>\u003Ci>(g)\u003C\u002Fi>","Phép hai-boson hóa của các nhóm tết và sự xây dựng \u003Ci>U\u003C\u002Fi>\u003Csub>\u003Ci>q\u003C\u002Fi>\u003C\u002Fsub>\u003Ci>(g)\u003C\u002Fi>",{"VI":1026},"nhóm lượng tử, đại số Hopf quasi tam giác, không gian gốc dương, không gian gốc âm, nhóm tết, cấu trúc Lusztig",{"VOID":1028},"10.1017\u002Fs0305004198002576","2024-12-21T10:39:12.660+00:00",[119],[294],"https:\u002F\u002Fwww.cambridge.org\u002Fcore\u002Fproduct\u002Fidentifier\u002FS0305004198002576\u002Ftype\u002Fjournal_article",[1034],{"id":1035,"sortIndex":25,"researcher":24,"roles":1036,"affiliations":1037,"properties":1046,"displayName":1050,"givenName":24,"familyName":24},"8b13aade-69ac-4f26-a93b-cb1cf0107ce8",[],[1038],{"id":1039,"sortIndex":25,"affiliation":1040,"properties":24},"943ceb21-17ed-445b-8191-5aec92fb9e36",{"id":1039,"createTime":24,"updateTime":24,"relativeEntities":1041,"slug":24,"properties":1042,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1045,"statistic":24},[],{"title":1043},{"VI":1044},"Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 9EW, UK",[],{"orcid":1047,"title":1049,"openalex":1051},{"VOID":1048},"https:\u002F\u002Forcid.org\u002F0000-0003-1657-5434",{"EN":1050},"Shahn Majid",{"VOID":1052},"A5074290225",{"url":24,"publisher":1054,"properties":1097},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":1055,"slug":10,"properties":1056,"entityType":22,"verifyStatus":23,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":25,"subjectFields":1061,"manageAffiliations":1066,"indexDatabases":1077,"url":83,"thumbnailPath":24,"statistic":1092,"gsStatistic":24,"type":24,"analyzePriority":24},[],{"country":1057,"eissn":1058,"issn":1059,"title":1060},{"VOID":13},{"VOID":15},{"VOID":17},{"EN":19},[1062],{"id":28,"createTime":24,"updateTime":24,"relativeEntities":1063,"label":1064,"description":1065,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":31},{},[1067,1072],{"id":35,"createTime":24,"updateTime":24,"relativeEntities":1068,"slug":24,"properties":1069,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1071,"statistic":24},[],{"title":1070},{"EN":39},[],{"id":42,"createTime":24,"updateTime":24,"relativeEntities":1073,"slug":24,"properties":1074,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1076,"statistic":24},[],{"title":1075},{"EN":46},[],[1078,1085],{"id":50,"indexDatabase":1079,"url":61,"indexYears":62,"academicFieldIds":1084,"indexDatabaseRanking":65},{"id":52,"createTime":24,"updateTime":24,"relativeEntities":1080,"label":1081,"description":1082,"key":58,"publicationTags":1083,"standard":24},[],{"EN":55,"VI":55},{"EN":55,"VI":57},[60],[64],{"id":67,"indexDatabase":1086,"url":80,"indexYears":24,"academicFieldIds":1091,"indexDatabaseRanking":24},{"id":69,"createTime":24,"updateTime":24,"relativeEntities":1087,"label":1088,"description":1089,"key":76,"publicationTags":1090,"standard":24},[],{"EN":72,"VI":72},{"EN":74,"VI":75},[78,79],[82],{"impactFactor":25,"impactFactorByYear":1093,"i10Index":86,"i10IndexLast5Year":25,"totalPublication":86,"totalPublicationByYear":1094,"totalCitation":89,"totalCitationByYear":1095,"totalCitationPerPublication":93,"totalCitationPerPublicationByYear":1096,"hindexLast5Year":86,"hindex":86},{},{"1938":88,"1948":88},{"1938":91,"1948":92},{"1938":91,"1948":92},{"issue":1098,"pages":1099,"volume":1101},{"VOID":188},{"VOID":1100},"151-192",{"VOID":1102},"125",75,{"total":1103,"publishYear":1105,"statisticByYear":1106},1999,{"2012":86,"2013":86,"2014":86,"2015":1107,"2016":1108,"2017":773,"2018":773,"2019":773,"2020":985,"2021":206,"2022":773,"2023":86,"2024":88},6,9,"1999-01-01",[78,65],[],{"id":1113,"createTime":1114,"updateTime":1115,"relativeEntities":1116,"slug":1117,"properties":1118,"entityType":115,"verifyStatus":116,"verifyTime":1133,"verifyNote":117,"languages":1134,"translateLanguages":1135,"viewCount":25,"primaryUrl":1136,"fullTextUrl":24,"authors":1137,"publicationType":141,"publisherRelationship":1155,"citationCount":1205,"citationInfo":1206,"publishDate":1210,"publishYear":1207,"citationAnalyzeStatus":23,"lastCitationAnalyze":24,"indexDatabases":1211,"openAccess":24,"references":1212,"isForceReanalyzing":270},"40eeed8b-8ce6-4b34-a7d6-c1338d009dad","2024-12-21T10:39:13.704+00:00","2025-02-08T17:57:16.364+00:00",[],"Quantum-groups-and-representations-of-monoidal-categories",{"openalex":1119,"mag":1121,"abstract":1123,"title":1126,"keywords":1129,"doi":1131},{"VOID":1120},"W2140764430",{"VOID":1122},"2140764430",{"EN":1124,"VI":1125},"\u003Cjats:p>This paper is intended to make explicit some aspects of the interactions which have recently come to light between the theory of classical knots and links, the theory of monoidal categories, Hopf-algebra theory, quantum integrable systems, the theory of exactly solvable models in statistical mechanics, and quantum field theories. The main results herein show an intimate relation between representations of certain monoidal categories arising from the study of new knot invariants or from physical considerations and quantum groups (that is, Hopf algebras). In particular categories of modules and comodules over Hopf algebras would seem to be much more fundamental examples of monoidal categories than might at first be apparent. This fundamental role of Hopf algebras in monoidal categories theory is also manifest in the Tannaka duality theory of Deligne and Mime [\u003Cjats:bold>8a\u003C\u002Fjats:bold>], although the relationship of that result and the present work is less clear than might be hoped.\u003C\u002Fjats:p>","\u003Cjats:p>Bài báo này nhằm mục đích làm rõ một số khía cạnh của các tương tác vừa được phát hiện giữa lý thuyết các nút và liên kết cổ điển, lý thuyết các danh mục monoidal, lý thuyết đại số Hopf, hệ thống tích phân lượng tử, lý thuyết các mô hình có thể giải được chính xác trong cơ học thống kê, và lý thuyết trường lượng tử. Các kết quả chính ở đây cho thấy một mối quan hệ mật thiết giữa các phép biểu diễn của một số danh mục monoidal xuất phát từ việc nghiên cứu các bất biến nút mới hoặc từ các cân nhắc vật lý với các nhóm lượng tử (tức là, các đại số Hopf). Đặc biệt, các danh mục của các mô-đun và co-mô-đun trên đại số Hopf dường như là những ví dụ cơ bản hơn về các danh mục monoidal so với những gì có thể nhận thấy ban đầu. Vai trò cơ bản của đại số Hopf trong lý thuyết danh mục monoidal cũng được thể hiện trong lý thuyết đối ngẫu Tannaka của Deligne và Mime [\u003Cjats:bold>8a\u003C\u002Fjats:bold>], mặc dù mối quan hệ giữa kết quả đó và công việc hiện tại không rõ ràng như mong đợi.",{"EN":1127,"VI":1128},"Quantum groups and representations of monoidal categories","Nhóm lượng tử và các phép biểu diễn của các danh mục monoidal",{"VI":1130},"Nhóm lượng tử, đại số Hopf, danh mục monoidal, lý thuyết nút và liên kết",{"VOID":1132},"10.1017\u002Fs0305004100069139","2024-12-21T10:39:13.703+00:00",[119],[294],"https:\u002F\u002Fwww.cambridge.org\u002Fcore\u002Fproduct\u002Fidentifier\u002FS0305004100069139\u002Ftype\u002Fjournal_article",[1138],{"id":1139,"sortIndex":25,"researcher":24,"roles":1140,"affiliations":1141,"properties":1150,"displayName":1152,"givenName":24,"familyName":24},"a2d758a6-deb1-4a01-a4cc-94e8adf1e176",[],[1142],{"id":1143,"sortIndex":25,"affiliation":1144,"properties":24},"0fc661eb-ad2d-40c9-a2b5-89299034a260",{"id":1143,"createTime":24,"updateTime":24,"relativeEntities":1145,"slug":24,"properties":1146,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1149,"statistic":24},[],{"title":1147},{"VI":1148},"Ohio State University",[],{"title":1151,"openalex":1153},{"EN":1152},"David N. Yettera",{"VOID":1154},"A5076218975",{"url":24,"publisher":1156,"properties":1199},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":1157,"slug":10,"properties":1158,"entityType":22,"verifyStatus":23,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":25,"subjectFields":1163,"manageAffiliations":1168,"indexDatabases":1179,"url":83,"thumbnailPath":24,"statistic":1194,"gsStatistic":24,"type":24,"analyzePriority":24},[],{"country":1159,"eissn":1160,"issn":1161,"title":1162},{"VOID":13},{"VOID":15},{"VOID":17},{"EN":19},[1164],{"id":28,"createTime":24,"updateTime":24,"relativeEntities":1165,"label":1166,"description":1167,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":31},{},[1169,1174],{"id":35,"createTime":24,"updateTime":24,"relativeEntities":1170,"slug":24,"properties":1171,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1173,"statistic":24},[],{"title":1172},{"EN":39},[],{"id":42,"createTime":24,"updateTime":24,"relativeEntities":1175,"slug":24,"properties":1176,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1178,"statistic":24},[],{"title":1177},{"EN":46},[],[1180,1187],{"id":50,"indexDatabase":1181,"url":61,"indexYears":62,"academicFieldIds":1186,"indexDatabaseRanking":65},{"id":52,"createTime":24,"updateTime":24,"relativeEntities":1182,"label":1183,"description":1184,"key":58,"publicationTags":1185,"standard":24},[],{"EN":55,"VI":55},{"EN":55,"VI":57},[60],[64],{"id":67,"indexDatabase":1188,"url":80,"indexYears":24,"academicFieldIds":1193,"indexDatabaseRanking":24},{"id":69,"createTime":24,"updateTime":24,"relativeEntities":1189,"label":1190,"description":1191,"key":76,"publicationTags":1192,"standard":24},[],{"EN":72,"VI":72},{"EN":74,"VI":75},[78,79],[82],{"impactFactor":25,"impactFactorByYear":1195,"i10Index":86,"i10IndexLast5Year":25,"totalPublication":86,"totalPublicationByYear":1196,"totalCitation":89,"totalCitationByYear":1197,"totalCitationPerPublication":93,"totalCitationPerPublicationByYear":1198,"hindexLast5Year":86,"hindex":86},{},{"1938":88,"1948":88},{"1938":91,"1948":92},{"1938":91,"1948":92},{"issue":1200,"pages":1201,"volume":1203},{"VOID":973},{"VOID":1202},"261-290",{"VOID":1204},"108",309,{"total":1205,"publishYear":1207,"statisticByYear":1208},1990,{"2012":206,"2013":206,"2014":1107,"2015":1108,"2016":773,"2017":206,"2018":1108,"2019":985,"2020":985,"2021":773,"2022":773,"2023":1209,"2024":88},10,"1990-09-01",[78,65],[1213,1216,1219,1222,1225,1228,1231,1234,1237,1240,1243,1246,1249,1252,1255,1258,1261,1263,1266,1269,1272,1275,1278,1282,1285,1288,1291,1294,1297,1300,1303,1306,1309,1312,1315,1318,1321,1324],{"id":24,"text":1214,"url":24,"identifiers":1215},"Penrose, 1971, Combinatorial Mathematics and its Applications, 221",{},{"id":24,"text":1217,"url":24,"identifiers":1218},"10.1007\u002FBF01247086",{"doi":1217},{"id":24,"text":1220,"url":24,"identifiers":1221},"10.1143\u002FJPSJ.56.3039",{"doi":1220},{"id":24,"text":1223,"url":24,"identifiers":1224},"10.1016\u002F0001-8708(89)90018-2",{"doi":1223},{"id":24,"text":1226,"url":24,"identifiers":1227},"10.1070\u002FRM1986v041n05ABEH003441",{"doi":1226},{"id":24,"text":1229,"url":24,"identifiers":1230},"[21a] Majid S. . Doubles of quasitriangular Hopf algebras. (Preprint.)",{},{"id":24,"text":1232,"url":24,"identifiers":1233},"Abe, 1977, Hopf Algebras",{},{"id":24,"text":1235,"url":24,"identifiers":1236},"[23] Moore G. and Seiberg N. . Classical and quantum conformal field theory. (Preprint.)",{},{"id":24,"text":1238,"url":24,"identifiers":1239},"Sweedler, 1969, Hopf Algebras",{},{"id":24,"text":1241,"url":24,"identifiers":1242},"10.1103\u002FPhysRevLett.19.1312",{"doi":1241},{"id":24,"text":1244,"url":24,"identifiers":1245},"[28] Street R. S. (Private communication.)",{},{"id":24,"text":1247,"url":24,"identifiers":1248},"10.1143\u002FJPSJ.57.1173",{"doi":1247},{"id":24,"text":1250,"url":24,"identifiers":1251},"[26] Segal G. . The definition of conformal theory. (Preprint.)",{},{"id":24,"text":1253,"url":24,"identifiers":1254},"[12] Joyal A. and Street R. . Braided tensor categories. (Preprint.)",{},{"id":24,"text":1256,"url":24,"identifiers":1257},"[6] Brustein R. , Ne'eman V. and Sternberg S. . Duality, crossing and Mac Lane's coherence. (Preprint.)",{},{"id":24,"text":1259,"url":24,"identifiers":1260},"10.1143\u002FJPSJ.56.3464",{"doi":1259},{"id":24,"text":1247,"url":24,"identifiers":1262},{"doi":1247},{"id":24,"text":1264,"url":24,"identifiers":1265},"Atiyah, 1988, Notes on the Oxford seminar on Jones–Witten theory",{},{"id":24,"text":1267,"url":24,"identifiers":1268},"10.1016\u002F0003-4916(72)90335-1",{"doi":1267},{"id":24,"text":1270,"url":24,"identifiers":1271},"10.1090\u002Fconm\u002F078\u002F975085",{"doi":1270},{"id":24,"text":1273,"url":24,"identifiers":1274},"[7] Carboni A. . Matrices, relations and group representations. (Preprint, 1988.)",{},{"id":24,"text":1276,"url":24,"identifiers":1277},"[8] Deligne P. . (Private communication.)",{},{"id":24,"text":1279,"url":24,"identifiers":1280},"Deligne, 1982, Hodge Cycles, Motives and Shimura Varieties, 900, 10.1007\u002F978-3-540-38955-2",{"doi":1281},"10.1007\u002F978-3-540-38955-2",{"id":24,"text":1283,"url":24,"identifiers":1284},"[27] Shum M.-C. . Tortile Tensor Categories. Ph.D. thesis, Macquarie University (1989).",{},{"id":24,"text":1286,"url":24,"identifiers":1287},"Kauffman, An invariant of regular isotopy, Trans. Amer. Math. Soc.",{},{"id":24,"text":1289,"url":24,"identifiers":1290},"[11] Joyal A. . Lecture at McGill University (Autumn, 1987).",{},{"id":24,"text":1292,"url":24,"identifiers":1293},"[13] Joyal A. and Street R. . Planar diagrams and tensor algebra. (Preprint.)",{},{"id":24,"text":1295,"url":24,"identifiers":1296},"10.1016\u002F0022-4049(80)90101-2",{"doi":1295},{"id":24,"text":1298,"url":24,"identifiers":1299},"10.1007\u002FBF01406222",{"doi":1298},{"id":24,"text":1301,"url":24,"identifiers":1302},"Kulish, 1980, Solutions of the Yang–Baxter equation, Zap. Nauchn. Sem. Leningrad Otdel. Mat. Inst. Steklov, 95, 129",{},{"id":24,"text":1304,"url":24,"identifiers":1305},"10.1007\u002F978-1-4612-9839-7",{"doi":1304},{"id":24,"text":1307,"url":24,"identifiers":1308},"10.1070\u002FRM1979v034n05ABEH003909",{"doi":1307},{"id":24,"text":1310,"url":24,"identifiers":1311},"Mac Lane, 1963, Natural associativity and commutativity, Rice Univ. Stud., 49, 28",{},{"id":24,"text":1313,"url":24,"identifiers":1314},"Reidemeister, 1983, Knot Theory",{},{"id":24,"text":1316,"url":24,"identifiers":1317},"Reidemeister, 1932, Knotentheorie",{},{"id":24,"text":1319,"url":24,"identifiers":1320},"[31] Witten E. . Quantum field theory and the Jones polynomial. (Preprint.)",{},{"id":24,"text":1322,"url":24,"identifiers":1323},"Freyd, Coherence theorems via knot theory, J. Pure Appl. Algebra",{},{"id":24,"text":1325,"url":24,"identifiers":1326},"Manin, 1988, Quantum groups and non-commutative geometry",{},{"id":1328,"createTime":1329,"updateTime":1330,"relativeEntities":1331,"slug":1332,"properties":1333,"entityType":115,"verifyStatus":116,"verifyTime":1329,"verifyNote":117,"languages":1347,"translateLanguages":1348,"viewCount":25,"primaryUrl":1349,"fullTextUrl":24,"authors":1350,"publicationType":141,"publisherRelationship":1368,"citationCount":1418,"citationInfo":1419,"publishDate":1422,"publishYear":1420,"citationAnalyzeStatus":23,"lastCitationAnalyze":24,"indexDatabases":1423,"openAccess":24,"references":1424,"isForceReanalyzing":270},"d75fe878-cb1c-41b2-b141-cf9d7b391dd4","2024-12-26T16:16:29.338+00:00","2025-02-08T17:56:19.495+00:00",[],"On-hearing-the-shape-of-a-drum-an-extension-to-higher-dimensions",{"openalex":1334,"mag":1336,"abstract":1338,"title":1341,"keywords":1344,"doi":1345},{"VOID":1335},"W2131050155",{"VOID":1337},"2131050155",{"EN":1339,"VI":1340},"\u003Cjats:p>The inverse eigenvalue problem for vibrating membranes (4), may also be examined in three or more dimensions. Let us suppose that λ\u003Cjats:sub>\u003Cjats:italic>n\u003C\u002Fjats:italic>\u003C\u002Fjats:sub> are the eigen values of the problem\u003C\u002Fjats:p>\u003Cjats:p>\u003Cjats:disp-formula>\u003Cjats:graphic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0305004100047277_eqn001\" \u002F>\u003C\u002Fjats:disp-formula>\u003C\u002Fjats:p>\u003Cjats:p>where Ω is a closed convex region or body in \u003Cjats:italic>E\u003Cjats:sub>n\u003C\u002Fjats:sub>\u003C\u002Fjats:italic> and \u003Cjats:italic>S\u003C\u002Fjats:italic> is the bounding surface of Ω. The basic problem is to determine the precise shape of Ω on being given the spectrum of eigenvalues λ\u003Cjats:sub>\u003Cjats:italic>n\u003C\u002Fjats:italic>\u003C\u002Fjats:sub>. In analogy with the membrane problem, it is clear that the trace function \u003Cjats:inline-graphic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0305004100047277_inline001\" \u002F> may be constructed in identical fashion; thus\u003C\u002Fjats:p>\u003Cjats:p>\u003Cjats:disp-formula>\u003Cjats:graphic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0305004100047277_eqn002\" \u002F>\u003C\u002Fjats:disp-formula>\u003C\u002Fjats:p>\u003Cjats:p>where \u003Cjats:italic>G\u003C\u002Fjats:italic>(r, r', \u003Cjats:italic>t\u003C\u002Fjats:italic>) is the Green's function of the diffusion equation\u003C\u002Fjats:p>\u003Cjats:p>\u003Cjats:disp-formula>\u003Cjats:graphic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0305004100047277_eqn003\" \u002F>\u003C\u002Fjats:disp-formula>\u003C\u002Fjats:p>\u003Cjats:p>and satisfies the Dirichiet condition \u003Cjats:italic>G\u003C\u002Fjats:italic>(r, r', \u003Cjats:italic>t\u003C\u002Fjats:italic>) = 0, r∈\u003Cjats:italic>S\u003C\u002Fjats:italic>, and the initial condition \u003Cjats:italic>G\u003C\u002Fjats:italic>(r, r', \u003Cjats:italic>t\u003C\u002Fjats:italic>) → δ(r–r') as \u003Cjats:italic>t\u003C\u002Fjats:italic> → 0.\u003C\u002Fjats:p>","\u003Cjats:p>Vấn đề giá trị riêng nghịch đảo cho các màng dao động (4), cũng có thể được xem xét trong ba chiều hoặc nhiều hơn. Giả sử rằng λ\u003Cjats:sub>\u003Cjats:italic>n\u003C\u002Fjats:italic>\u003C\u002Fjats:sub> là các giá trị riêng của vấn đề\u003C\u002Fjats:p>\u003Cjats:p>\u003Cjats:disp-formula>\u003Cjats:graphic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0305004100047277_eqn001\" \u002F>\u003C\u002Fjats:disp-formula>\u003C\u002Fjats:p>\u003Cjats:p>trong đó Ω là một vùng hoặc thể đóng lồi trong \u003Cjats:italic>E\u003Cjats:sub>n\u003C\u002Fjats:sub>\u003C\u002Fjats:italic> và \u003Cjats:italic>S\u003C\u002Fjats:italic> là bề mặt biên của Ω. Vấn đề cơ bản là xác định hình dạng chính xác của Ω khi được cung cấp phổ các giá trị riêng λ\u003Cjats:sub>\u003Cjats:italic>n\u003C\u002Fjats:italic>\u003C\u002Fjats:sub>. Theo sự tương đồng với vấn đề màng, rõ ràng rằng hàm dấu vết \u003Cjats:inline-graphic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0305004100047277_inline001\" \u002F> có thể được xây dựng theo cách tương tự; do đó\u003C\u002Fjats:p>\u003Cjats:p>\u003Cjats:disp-formula>\u003Cjats:graphic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0305004100047277_eqn002\" \u002F>\u003C\u002Fjats:disp-formula>\u003C\u002Fjats:p>\u003Cjats:p>trong đó \u003Cjats:italic>G\u003C\u002Fjats:italic>(r, r', \u003Cjats:italic>t\u003C\u002Fjats:italic>) là hàm Green của phương trình khuếch tán\u003C\u002Fjats:p>\u003Cjats:p>\u003Cjats:disp-formula>\u003Cjats:graphic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0305004100047277_eqn003\" \u002F>\u003C\u002Fjats:disp-formula>\u003C\u002Fjats:p>\u003Cjats:p>và thỏa mãn điều kiện Dirichlet \u003Cjats:italic>G\u003C\u002Fjats:italic>(r, r', \u003Cjats:italic>t\u003C\u002Fjats:italic>) = 0, r∈\u003Cjats:italic>S\u003C\u002Fjats:italic>, và điều kiện ban đầu \u003Cjats:italic>G\u003C\u002Fjats:italic>(r, r', \u003Cjats:italic>t\u003C\u002Fjats:italic>) → δ(r–r') khi \u003Cjats:italic>t\u003C\u002Fjats:italic> → 0.\u003C\u002Fjats:p>",{"EN":1342,"VI":1343},"On hearing the shape of a drum: an extension to higher dimensions","Về việc nghe hình dạng của một cái trống: một mở rộng tới các chiều cao hơn",{"VI":289},{"VOID":1346},"10.1017\u002Fs0305004100047277",[119],[294],"https:\u002F\u002Fwww.cambridge.org\u002Fcore\u002Fproduct\u002Fidentifier\u002FS0305004100047277\u002Ftype\u002Fjournal_article",[1351],{"id":1352,"sortIndex":25,"researcher":24,"roles":1353,"affiliations":1354,"properties":1363,"displayName":1365,"givenName":24,"familyName":24},"51221aab-fa3c-4aee-bbe8-b4613669a227",[],[1355],{"id":1356,"sortIndex":25,"affiliation":1357,"properties":24},"4a00dd84-c85c-4508-a03e-164ac6447669",{"id":1356,"createTime":24,"updateTime":24,"relativeEntities":1358,"slug":24,"properties":1359,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1362,"statistic":24},[],{"title":1360},{"EN":1361},"Department of Mathematics, University College London, Gower Street, London, W.C.1",[],{"title":1364,"openalex":1366},{"EN":1365},"R. T. Waechter",{"VOID":1367},"A5073499832",{"url":24,"publisher":1369,"properties":1412},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":1370,"slug":10,"properties":1371,"entityType":22,"verifyStatus":23,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":25,"subjectFields":1376,"manageAffiliations":1381,"indexDatabases":1392,"url":83,"thumbnailPath":24,"statistic":1407,"gsStatistic":24,"type":24,"analyzePriority":24},[],{"country":1372,"eissn":1373,"issn":1374,"title":1375},{"VOID":13},{"VOID":15},{"VOID":17},{"EN":19},[1377],{"id":28,"createTime":24,"updateTime":24,"relativeEntities":1378,"label":1379,"description":1380,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":31},{},[1382,1387],{"id":35,"createTime":24,"updateTime":24,"relativeEntities":1383,"slug":24,"properties":1384,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1386,"statistic":24},[],{"title":1385},{"EN":39},[],{"id":42,"createTime":24,"updateTime":24,"relativeEntities":1388,"slug":24,"properties":1389,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1391,"statistic":24},[],{"title":1390},{"EN":46},[],[1393,1400],{"id":50,"indexDatabase":1394,"url":61,"indexYears":62,"academicFieldIds":1399,"indexDatabaseRanking":65},{"id":52,"createTime":24,"updateTime":24,"relativeEntities":1395,"label":1396,"description":1397,"key":58,"publicationTags":1398,"standard":24},[],{"EN":55,"VI":55},{"EN":55,"VI":57},[60],[64],{"id":67,"indexDatabase":1401,"url":80,"indexYears":24,"academicFieldIds":1406,"indexDatabaseRanking":24},{"id":69,"createTime":24,"updateTime":24,"relativeEntities":1402,"label":1403,"description":1404,"key":76,"publicationTags":1405,"standard":24},[],{"EN":72,"VI":72},{"EN":74,"VI":75},[78,79],[82],{"impactFactor":25,"impactFactorByYear":1408,"i10Index":86,"i10IndexLast5Year":25,"totalPublication":86,"totalPublicationByYear":1409,"totalCitation":89,"totalCitationByYear":1410,"totalCitationPerPublication":93,"totalCitationPerPublicationByYear":1411,"hindexLast5Year":86,"hindex":86},{},{"1938":88,"1948":88},{"1938":91,"1948":92},{"1938":91,"1948":92},{"issue":1413,"pages":1414,"volume":1416},{"VOID":360},{"VOID":1415},"439-447",{"VOID":1417},"72",73,{"total":1418,"publishYear":1420,"statisticByYear":1421},1972,{"2013":88,"2015":88,"2018":88,"2020":88,"2022":88,"2023":88,"2024":88},"1972-11-01",[78,65],[1425,1428,1431,1434],{"id":24,"text":1426,"url":24,"identifiers":1427},"10.1017\u002FS0305004100046764",{"doi":1426},{"id":24,"text":1429,"url":24,"identifiers":1430},"10.1007\u002F978-3-642-47404-0",{"doi":1429},{"id":24,"text":1432,"url":24,"identifiers":1433},"10.1007\u002F978-3-0348-6953-9",{"doi":1432},{"id":24,"text":1435,"url":24,"identifiers":1436},"10.4310\u002Fjdg\u002F1214427880",{"doi":1435},{"id":1438,"createTime":1439,"updateTime":1440,"relativeEntities":1441,"slug":1442,"properties":1443,"entityType":115,"verifyStatus":116,"verifyTime":1439,"verifyNote":117,"languages":1457,"translateLanguages":1458,"viewCount":25,"primaryUrl":1459,"fullTextUrl":24,"authors":1460,"publicationType":141,"publisherRelationship":1495,"citationCount":1545,"citationInfo":1546,"publishDate":1562,"publishYear":1547,"citationAnalyzeStatus":23,"lastCitationAnalyze":24,"indexDatabases":1563,"openAccess":24,"references":1564,"isForceReanalyzing":270},"852b9f1c-d902-4149-9f3d-0612599055aa","2024-12-28T17:29:02.319+00:00","2025-02-08T17:55:19.838+00:00",[],"A-practical-method-for-numerical-evaluation-of-solutions-of-partial-differential-equations-of-the-heat-conduction-type",{"openalex":1444,"mag":1446,"abstract":1448,"title":1451,"keywords":1454,"doi":1455},{"VOID":1445},"W2167657634",{"VOID":1447},"2167657634",{"EN":1449,"VI":1450},"\u003Cjats:p>This paper is concerned with methods of evaluating numerical solutions of the non-linear partial differential equation\u003C\u002Fjats:p>\u003Cjats:p>\u003Cjats:disp-formula>\u003Cjats:graphic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0305004100023197_eqn001\" \u002F>\u003C\u002Fjats:disp-formula>\u003C\u002Fjats:p>\u003Cjats:p>where\u003C\u002Fjats:p>\u003Cjats:p>\u003Cjats:disp-formula>\u003Cjats:graphic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0305004100023197_eqn002\" \u002F>\u003C\u002Fjats:disp-formula>\u003C\u002Fjats:p>\u003Cjats:p>subject to the boundary conditions\u003C\u002Fjats:p>\u003Cjats:p>\u003Cjats:disp-formula>\u003Cjats:graphic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0305004100023197_eqn003\" \u002F>\u003C\u002Fjats:disp-formula>\u003C\u002Fjats:p>\u003Cjats:p>\u003Cjats:italic>A, k, q\u003C\u002Fjats:italic> are known constants.\u003C\u002Fjats:p>\u003Cjats:p>Equation (1) is of the type which arises in problems of heat flow when there is an internal generation of heat within the medium; if the heat is due to a chemical reaction proceeding at each point at a rate depending upon the local temperature, the rate of heat generation is often defined by an equation such as (2).\u003C\u002Fjats:p>","\u003Cjats:p>Bài báo này đề cập đến các phương pháp đánh giá các nghiệm số của phương trình vi phân riêng không tuyến tính\u003C\u002Fjats:p>\u003Cjats:p>\u003Cjats:disp-formula>\u003Cjats:graphic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0305004100023197_eqn001\" \u002F>\u003C\u002Fjats:disp-formula>\u003C\u002Fjats:p>\u003Cjats:p>trong đó\u003C\u002Fjats:p>\u003Cjats:p>\u003Cjats:disp-formula>\u003Cjats:graphic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0305004100023197_eqn002\" \u002F>\u003C\u002Fjats:disp-formula>\u003C\u002Fjats:p>\u003Cjats:p>tuân theo các điều kiện biên\u003C\u002Fjats:p>\u003Cjats:p>\u003Cjats:disp-formula>\u003Cjats:graphic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0305004100023197_eqn003\" \u002F>\u003C\u002Fjats:disp-formula>\u003C\u002Fjats:p>\u003Cjats:p>\u003Cjats:italic>A, k, q\u003C\u002Fjats:italic> là các hằng số đã biết.\u003C\u002Fjats:p>\u003Cjats:p>Phương trình (1) thuộc loại phát sinh trong các vấn đề dòng nhiệt khi có sự phát sinh nhiệt bên trong môi trường; nếu nhiệt do một phản ứng hóa học diễn ra tại từng điểm với tốc độ phụ thuộc vào nhiệt độ tại chỗ, thì tốc độ phát sinh nhiệt thường được định nghĩa bởi một phương trình như (2).\u003C\u002Fjats:p>",{"EN":1452,"VI":1453},"A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type","Một phương pháp thực tiễn để đánh giá số liệu của các phương trình vi phân riêng loại dẫn nhiệt",{"VI":289},{"VOID":1456},"10.1017\u002Fs0305004100023197",[119],[294],"https:\u002F\u002Fwww.cambridge.org\u002Fcore\u002Fproduct\u002Fidentifier\u002FS0305004100023197\u002Ftype\u002Fjournal_article",[1461,1478],{"id":1462,"sortIndex":25,"researcher":24,"roles":1463,"affiliations":1464,"properties":1473,"displayName":1475,"givenName":24,"familyName":24},"3e1d3634-eb34-4b4b-9d8c-1b86497b1cd2",[],[1465],{"id":1466,"sortIndex":25,"affiliation":1467,"properties":24},"145d1644-4330-43e5-9e34-09265644d6cf",{"id":1466,"createTime":24,"updateTime":24,"relativeEntities":1468,"slug":24,"properties":1469,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1472,"statistic":24},[],{"title":1470},{"EN":1471},"The Mathematical LaboratoryCambridge",[],{"title":1474,"openalex":1476},{"EN":1475},"J 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