[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"_public_publisher_byId_e1924783-9e02-43f3-8576-e947d13b701a":3,"_public_publication_all{\"sortAscending\":false,\"sortField\":\"updateTime\",\"page\":0,\"size\":10,\"facet\":true,\"searchKey\":\"publisherId:e1924783-9e02-43f3-8576-e947d13b701a,\"}":80},{"code":4,"data":5,"meta":20},"SUCCESS",{"id":6,"createTime":7,"updateTime":8,"relativeEntities":9,"slug":10,"properties":11,"entityType":18,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":21,"subjectFields":22,"manageAffiliations":35,"indexDatabases":44,"url":20,"thumbnailPath":20,"statistic":20,"gsStatistic":20,"type":20,"analyzePriority":20},"e1924783-9e02-43f3-8576-e947d13b701a","2023-12-05T07:06:53.083+00:00","2025-11-21T09:58:51.151+00:00",[],"Collectanea-Mathematica",{"issn":12,"title":14,"eissn":16},{"VOID":13},"20384815",{"EN":15},"Collectanea Mathematica",{"VOID":17},"00100757","PUBLISHER","PENDING",null,0,[23,29],{"id":24,"createTime":20,"updateTime":20,"relativeEntities":25,"label":26,"description":28,"parentId":20,"standard":20,"scholarHubFieldId":20},"ee33e266-088e-4829-aa2f-5ea59917dac0",[],{"EN":27},"Applied Mathematics",{},{"id":30,"createTime":20,"updateTime":20,"relativeEntities":31,"label":32,"description":34,"parentId":20,"standard":20,"scholarHubFieldId":20},"37634bef-3565-4ad6-b1ba-c43cf4d196be",[],{"EN":33},"Mathematics (miscellaneous)",{},[36],{"id":37,"createTime":20,"updateTime":20,"relativeEntities":38,"slug":20,"properties":39,"entityType":20,"verifyStatus":20,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":20,"url":20,"parentIds":42,"statistic":20},"2aacadb5-f013-42dd-b818-ddc2effcbf7e",[],{"title":40},{"EN":41},"Springer-Verlag Italia Srl",[43],"9a7c7208-b28a-42c2-a634-5a7f90eee3ab",[45,62],{"id":46,"indexDatabase":47,"url":59,"indexYears":20,"academicFieldIds":60,"indexDatabaseRanking":20},"f10f3457-da20-44dd-a8de-355cdd92ce20",{"id":48,"createTime":20,"updateTime":20,"relativeEntities":49,"label":50,"description":52,"key":55,"publicationTags":56,"standard":20},"a4921856-b128-4d9f-8f1f-e80813d3bbd4",[],{"EN":51,"VI":51},"ISI\u002FSCIE - Science Citation Index Expanded",{"EN":53,"VI":54},"SCIE database","Cơ sở dữ liệu SCIE","scie",[57,58],"SCIE","ISI","https:\u002F\u002Fmjl.clarivate.com\u002Fsearch-results?issn=0010-0757",[61],"a410dee4-fcd0-43bf-ac42-c2f733ee737f",{"id":63,"indexDatabase":64,"url":74,"indexYears":75,"academicFieldIds":76,"indexDatabaseRanking":79},"c508aab1-786a-4fb6-81c5-77d5e7dcc03b",{"id":65,"createTime":20,"updateTime":20,"relativeEntities":66,"label":67,"description":69,"key":71,"publicationTags":72,"standard":20},"3c7051d4-eb7d-4c57-a56b-36fc74c5d1e9",[],{"EN":68,"VI":68},"Scopus - Elsevier",{"EN":68,"VI":70},"Cơ sở dữ liệu Scopus thuộc Elsevier","scopus",[73],"SCOPUS","https:\u002F\u002Fwww.scopus.com\u002Fsourceid\u002F5600157643","2006-2025",[77,78],"825d41e1-f1f9-472e-aa11-78b85d501870","f58e9119-c14c-473f-8a7c-5a035e4ab69a","SCOPUS__Q2",{"meta":81,"data":83},{"total":82},"324",[84,173,288,432,526,640,784,891,1048,1140],{"id":85,"createTime":86,"updateTime":87,"relativeEntities":88,"slug":89,"properties":90,"entityType":101,"verifyStatus":102,"verifyTime":103,"verifyNote":104,"languages":20,"translateLanguages":20,"viewCount":21,"primaryUrl":105,"fullTextUrl":20,"authors":106,"publicationType":123,"publisherRelationship":124,"citationCount":21,"citationInfo":166,"publishDate":169,"publishYear":167,"citationAnalyzeStatus":170,"lastCitationAnalyze":87,"indexDatabases":171,"openAccess":20,"references":20,"isForceReanalyzing":172},"87b33b05-77d5-433e-813a-c7762a5111ea","2024-01-19T16:17:13.061+00:00","2026-07-28T04:41:07.347+00:00",[],"On-existence-of-solutions-of-a-neutral-differential-equation-with-deviating-argument",{"abstract":91,"title":93,"gsPaper":95,"references":97,"doi":99},{"EN":92},"We establish theorems on the existence and asymptotic characterization of solutions of a differential equation of neutral type with deviated argument on neutral type. The mentioned differential equation admits both delayed and advanced arguments. In our considerations we use technique linking measures of noncompactness with the Tikhonov fixed point principle in suitable Frechet space. This approach admits us to improve and extend some results.",{"EN":94},"On existence of solutions of a neutral differential equation with deviating argument",{"VOID":96},"[\"1288144829178334538\"]",{"VOID":98},"R.P. Agarwal, D. O’Regan, and P.J.Y. Wong,Positive Solutions of Differential, Difference and Integral Equations, Kluwer Academic Publishers, Dordrecht, 1999.\nO. Arino and M. Pituk, Convergence in asymptotically autonomous functional differential equations,J. Math. Anal. Appl. 237 (1999), 376–392.\nJ. Banaś,Applications of Measures of Noncompactness to Various Problems, Zeszyty Nauk. Politechn. Rzeszowskiej Mat. Fiz. 5, Rzesz∅w, 1987.\nJ. Banaś and I.J. Cabrero, On solutions of a neutral differential equation with deviating argument,Math. Comput. Modelling 44 (2006), 1080–1088.\nJ. Banaś and K. Goebel,Measures of Noncomapctness in Banach Spaces, Lecture Notes in Pure and Applied Mathematics60, Marcel Dekker, New York, 1980.\nJ. Banaś and U. Stopka, The existence and some properties of solutions of a differential equation with deviated argument,Comment. Math. Univ. Carolin. 22 (1981), 325–336.\nJ. Čermák, On the asymptotic behaviour of solutions of certain functionaldifferential equations,Math. Slovaca 48 (1998), 187–212.\nS. Czerwik, The existence of global solutions of a functionaldifferential equation,Colloq. Math. 36 (1976), 121–125.\nL.J. Grimm, Existence and uniqueness for nonlinear neutraldifferential equations,Bull. Amer. Math. Soc. 77 (1971), 374–376.\nL. Olszowy, On existence of solutions of a quadratic Urysohn integral equation on an unbounded interval,Comment. Math. Prace Mat. 48 (2008), 103–112.\nW.G. ElSayed, Solvability of a neutral differential equation with deviated argument,J. Math. Anal. Appl. 327 (2007), 342–350.\nB. Shi, M.J. Gai, D.C. Zhang, and J.C. Zhai, Global attractivity in nonlinear differential equations with delays,Nonlinear Anal. 47 (2001), 4071–4082.\nM. Zima,Positive Operators in Banach Spaces and Their Applications, Wyd. Uniw. Rzeszowskiego, Rzesz∅w, 2005.",{"VOID":100},"10.1007\u002FBF03191224","PUBLICATION","VERIFIED","2024-08-30T23:54:13.202+00:00","Auto Verify","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002FBF03191224",[107],{"id":108,"sortIndex":21,"researcher":20,"roles":109,"affiliations":111,"properties":120,"displayName":122,"givenName":20,"familyName":20},"f53997b6-6c78-414f-a31e-d9db1e1fb9ce",[110],"AUTHOR",[112],{"id":113,"sortIndex":21,"affiliation":114,"properties":20},"9e076b55-7596-4902-85d4-172940aaed1e",{"id":113,"createTime":20,"updateTime":20,"relativeEntities":115,"slug":20,"properties":116,"entityType":20,"verifyStatus":20,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":20,"url":20,"parentIds":119,"statistic":20},[],{"title":117},{"VI":118},"Department of Mathematics, Rzeszów University of Technology, Rzeszów, Poland",[],{"title":121},{"VI":122},"Leszek Olszowy","ARTICLE",{"url":105,"publisher":125,"properties":161},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":126,"slug":10,"properties":127,"entityType":18,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":21,"subjectFields":131,"manageAffiliations":140,"indexDatabases":146,"url":20,"thumbnailPath":20,"statistic":20,"gsStatistic":20,"type":20,"analyzePriority":20},[],{"issn":128,"title":129,"eissn":130},{"VOID":13},{"EN":15},{"VOID":17},[132,136],{"id":24,"createTime":20,"updateTime":20,"relativeEntities":133,"label":134,"description":135,"parentId":20,"standard":20,"scholarHubFieldId":20},[],{"EN":27},{},{"id":30,"createTime":20,"updateTime":20,"relativeEntities":137,"label":138,"description":139,"parentId":20,"standard":20,"scholarHubFieldId":20},[],{"EN":33},{},[141],{"id":37,"createTime":20,"updateTime":20,"relativeEntities":142,"slug":20,"properties":143,"entityType":20,"verifyStatus":20,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":20,"url":20,"parentIds":145,"statistic":20},[],{"title":144},{"EN":41},[43],[147,154],{"id":46,"indexDatabase":148,"url":59,"indexYears":20,"academicFieldIds":153,"indexDatabaseRanking":20},{"id":48,"createTime":20,"updateTime":20,"relativeEntities":149,"label":150,"description":151,"key":55,"publicationTags":152,"standard":20},[],{"EN":51,"VI":51},{"EN":53,"VI":54},[57,58],[61],{"id":63,"indexDatabase":155,"url":74,"indexYears":75,"academicFieldIds":160,"indexDatabaseRanking":79},{"id":65,"createTime":20,"updateTime":20,"relativeEntities":156,"label":157,"description":158,"key":71,"publicationTags":159,"standard":20},[],{"EN":68,"VI":68},{"EN":68,"VI":70},[73],[77,78],{"pages":162,"volume":164},{"VOID":163},"37-47",{"VOID":165},"61",{"total":21,"publishYear":167,"statisticByYear":168},2010,{},"2010-02-01","ERROR_IN_ANALYZE_CITATION",[79,57],false,{"id":174,"createTime":175,"updateTime":176,"relativeEntities":177,"slug":178,"properties":179,"entityType":101,"verifyStatus":102,"verifyTime":188,"verifyNote":104,"languages":20,"translateLanguages":20,"viewCount":21,"primaryUrl":189,"fullTextUrl":20,"authors":190,"publicationType":123,"publisherRelationship":206,"citationCount":248,"citationInfo":249,"publishDate":253,"publishYear":250,"citationAnalyzeStatus":19,"lastCitationAnalyze":254,"indexDatabases":255,"openAccess":20,"references":256,"isForceReanalyzing":172},"34e9f4e1-870f-4aaa-8080-ec522d9c8158","2024-01-12T18:49:22.476+00:00","2026-04-09T18:02:30.175+00:00",[],"Stone-Weierstrass-theorems-for-Riesz-ideals-of-continuous-functions",{"abstract":180,"title":182,"gsPaper":184,"doi":186},{"EN":181},"Notions of convergence and continuity specifically adapted to Riesz ideals \n                \n                  \n                \n                $$\\mathscr {I}$$\n                \n               of the space of continuous real-valued functions on a Lindelöf locally compact Hausdorff space are given, and used to prove Stone–Weierstrass-type theorems for \n                \n                  \n                \n                $$\\mathscr {I}$$\n                \n              . As applications, sufficient conditions are discussed that guarantee that various types of positive linear maps on \n                \n                  \n                \n                $$\\mathscr {I}$$\n                \n               are uniquely determined by their restriction to various point-separating subsets of \n                \n                  \n                \n                $$\\mathscr {I}$$\n                \n              . A very special case of this is the characterization of the strong determinacy of moment problems, which is rederived here in a rather general setting and without making use of spectral theory.\n",{"EN":183},"Stone–Weierstrass theorems for Riesz ideals of continuous functions",{"VOID":185},"[\"17087217028841840237\"]",{"VOID":187},"10.1007\u002Fs13348-020-00301-6","2024-05-04T05:48:02.506+00:00","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs13348-020-00301-6",[191],{"id":192,"sortIndex":21,"researcher":20,"roles":193,"affiliations":194,"properties":203,"displayName":205,"givenName":20,"familyName":20},"ab32c737-1c14-47f3-88c6-a505d4fac1e7",[110],[195],{"id":196,"sortIndex":21,"affiliation":197,"properties":20},"782d08c2-f1e4-4334-9b18-2931e81701b8",{"id":196,"createTime":20,"updateTime":20,"relativeEntities":198,"slug":20,"properties":199,"entityType":20,"verifyStatus":20,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":20,"url":20,"parentIds":202,"statistic":20},[],{"title":200},{"VI":201},"Département de Mathématiques, Université libre de Bruxelles, Bruxelles, Belgium",[],{"title":204},{"VI":205},"Matthias Schötz",{"url":189,"publisher":207,"properties":243},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":208,"slug":10,"properties":209,"entityType":18,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":21,"subjectFields":213,"manageAffiliations":222,"indexDatabases":228,"url":20,"thumbnailPath":20,"statistic":20,"gsStatistic":20,"type":20,"analyzePriority":20},[],{"issn":210,"title":211,"eissn":212},{"VOID":13},{"EN":15},{"VOID":17},[214,218],{"id":24,"createTime":20,"updateTime":20,"relativeEntities":215,"label":216,"description":217,"parentId":20,"standard":20,"scholarHubFieldId":20},[],{"EN":27},{},{"id":30,"createTime":20,"updateTime":20,"relativeEntities":219,"label":220,"description":221,"parentId":20,"standard":20,"scholarHubFieldId":20},[],{"EN":33},{},[223],{"id":37,"createTime":20,"updateTime":20,"relativeEntities":224,"slug":20,"properties":225,"entityType":20,"verifyStatus":20,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":20,"url":20,"parentIds":227,"statistic":20},[],{"title":226},{"EN":41},[43],[229,236],{"id":46,"indexDatabase":230,"url":59,"indexYears":20,"academicFieldIds":235,"indexDatabaseRanking":20},{"id":48,"createTime":20,"updateTime":20,"relativeEntities":231,"label":232,"description":233,"key":55,"publicationTags":234,"standard":20},[],{"EN":51,"VI":51},{"EN":53,"VI":54},[57,58],[61],{"id":63,"indexDatabase":237,"url":74,"indexYears":75,"academicFieldIds":242,"indexDatabaseRanking":79},{"id":65,"createTime":20,"updateTime":20,"relativeEntities":238,"label":239,"description":240,"key":71,"publicationTags":241,"standard":20},[],{"EN":68,"VI":68},{"EN":68,"VI":70},[73],[77,78],{"pages":244,"volume":246},{"VOID":245},"587-603",{"VOID":247},"72",2,{"total":248,"publishYear":250,"statisticByYear":251},2020,{"2023":252,"2025":252},1,"2020-10-31","2026-04-09T18:02:30.174+00:00",[79,57],[257,263,266,269,272,275,278,285],{"id":258,"text":259,"url":260,"identifiers":261},"4c68646b-0035-4279-8000-0006b275d4fa","Bishop, E.: A generalization of the Stone–Weierstrass theorem. Pac. J. Math. 11(3), 777–783 (1961)","https:\u002F\u002Flink.springer.com\u002F10.1007\u002Fs10440-022-00541-7",{"doi":262},"10.1007\u002Fs10440-022-00541-7",{"id":20,"text":264,"url":20,"identifiers":265},"Dugundji, J.: Topology. Allyn and Bacon, inc, Boston (1978)",{},{"id":258,"text":267,"url":260,"identifiers":268},"Jurzak, J.P.: Dominated convergence and Stone–Weierstrass theorem. J. Appl. Anal. 11(2), 207–223 (2010)",{"doi":262},{"id":20,"text":270,"url":20,"identifiers":271},"Kelley, J.L.: General Topology. D. van Nostrand Company Inc, New York (1955)",{},{"id":20,"text":273,"url":20,"identifiers":274},"Luxemburg, W.A.J., Zaanen, A.C.: Riesz Spaces I. North-Holland Publishing Company, Amsterdam (1971)",{},{"id":258,"text":276,"url":260,"identifiers":277},"Nachbin, L.: Weighted approximation for algebras and modules of continuous functions: real and self-adjoint complex cases. Ann. Math. 81(2), 289–302 (1965)",{"doi":262},{"id":20,"text":279,"url":280,"identifiers":281},"Sb, Ng, Warner, S.: Continuity of positive and multiplicative functionals. Duke Math. J. 39(2), 281–284 (1972). https:\u002F\u002Fdoi.org\u002F10.1215\u002FS0012-7094-72-03933-6","https:\u002F\u002Fdoi.org\u002F10.1215\u002Fs0012-7094-72-03933-6",{"mag":282,"openalex":283,"doi":284},"2061143439","W2061143439","10.1215\u002Fs0012-7094-72-03933-6",{"id":20,"text":286,"url":20,"identifiers":287},"Schmüdgen, K.: The Moment Problem. Springer, Berlin (2017)",{},{"id":289,"createTime":290,"updateTime":291,"relativeEntities":292,"slug":293,"properties":294,"entityType":101,"verifyStatus":102,"verifyTime":303,"verifyNote":104,"languages":20,"translateLanguages":20,"viewCount":21,"primaryUrl":304,"fullTextUrl":20,"authors":305,"publicationType":123,"publisherRelationship":323,"citationCount":252,"citationInfo":363,"publishDate":366,"publishYear":364,"citationAnalyzeStatus":19,"lastCitationAnalyze":291,"indexDatabases":367,"openAccess":20,"references":368,"isForceReanalyzing":172},"f3c2bea7-b99c-49fa-807c-a21c500a7183","2023-12-26T15:47:50.193+00:00","2026-03-18T23:16:26.952+00:00",[],"The-symmetrization-map-and-Gamma-contractions",{"abstract":295,"title":297,"gsPaper":299,"doi":301},{"EN":296},"The symmetrization map \n              \n                \n              \n              $$\\pi :{\\mathbb{C}}^2\\rightarrow {\\mathbb{C}}^2$$\n              \n             is defined by \n              \n                \n              \n              $$\\pi (z_1,z_2)=(z_1+z_2,z_1z_2).$$\n              \n             The closed symmetrized bidisc \n              \n                \n              \n              $$\\Gamma$$\n              \n             is the symmetrization of the closed unit bidisc \n              \n                \n              \n              $$\\overline{{\\mathbb{D}}^2}$$\n              \n            , that is, \n              \n                \n              \n              $$\\begin{aligned} \\Gamma = \\pi (\\overline{{\\mathbb{D}}^2})=\\{ (z_1+z_2,z_1z_2)\\,:\\, |z_i|\\le 1, i=1,2 \\}. \\end{aligned}$$\n              \n            A pair of commuting Hilbert space operators (S, P) for which \n              \n                \n              \n              $$\\Gamma$$\n              \n             is a spectral set is called a \n              \n                \n              \n              $$\\Gamma$$\n              \n            -contraction. Unlike the scalars in \n              \n                \n              \n              $$\\Gamma$$\n              \n            , a \n              \n                \n              \n              $$\\Gamma$$\n              \n            -contraction may not arise as a symmetrization of a pair of commuting contractions, even not as a symmetrization of a pair of commuting bounded operators. We characterize all \n              \n                \n              \n              $$\\Gamma$$\n              \n            -contractions which are symmetrization of pairs of commuting contractions. We show by constructing a family of examples that even if a \n              \n                \n              \n              $$\\Gamma$$\n              \n            -contraction \n              \n                \n              \n              $$(S,P)=(T_1+T_2,T_1T_2)$$\n              \n             for a pair of commuting bounded operators \n              \n                \n              \n              $$T_1,T_2$$\n              \n            , no real number less than 2 can be a bound for the set \n              \n                \n              \n              $$\\{ \\Vert T_1\\Vert ,\\Vert T_2\\Vert \\}$$\n              \n             in general. Then we prove that every \n              \n                \n              \n              $$\\Gamma$$\n              \n            -contraction (S, P) is the restriction of a \n              \n                \n              \n              $$\\Gamma$$\n              \n            -contraction \n              \n                \n              \n              $$({{\\widetilde{S}}}, {{\\widetilde{P}}})$$\n              \n             to a common reducing subspace of \n              \n                \n              \n              $${{\\widetilde{S}}}, {{\\widetilde{P}}}$$\n              \n             and that \n              \n                \n              \n              $$({{\\widetilde{S}}}, {{\\widetilde{P}}})=(A_1+A_2,A_1A_2)$$\n              \n             for a pair of commuting operators \n              \n                \n              \n              $$A_1,A_2$$\n              \n             with \n              \n                \n              \n              $$\\max \\{\\Vert A_1\\Vert , \\Vert A_2\\Vert \\} \\le 2$$\n              \n            . We find new characterizations for the \n              \n                \n              \n              $$\\Gamma$$\n              \n            -unitaries and describe the distinguished boundary of \n              \n                \n              \n              $$\\Gamma$$\n              \n             in a different way. We also show some interplay between the fundamental operators of two \n              \n                \n              \n              $$\\Gamma$$\n              \n            -contractions (S, P) and \n              \n                \n              \n              $$(S_1,P)$$\n              \n            .\n",{"EN":298},"The symmetrization map and $$\\Gamma$$ -contractions",{"VOID":300},"[\"536758806864355651\"]",{"VOID":302},"10.1007\u002Fs13348-022-00379-0","2024-05-03T11:26:39.929+00:00","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs13348-022-00379-0",[306],{"id":307,"sortIndex":21,"researcher":20,"roles":308,"affiliations":309,"properties":318,"displayName":320,"givenName":20,"familyName":20},"c403de03-32f9-4bd9-8fc9-e9b200b1135f",[110],[310],{"id":311,"sortIndex":21,"affiliation":312,"properties":20},"b8d87ae3-527a-4100-9c89-307a287d51c6",{"id":311,"createTime":20,"updateTime":20,"relativeEntities":313,"slug":20,"properties":314,"entityType":20,"verifyStatus":20,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":20,"url":20,"parentIds":317,"statistic":20},[],{"title":315},{"VI":316},"Mathematics Department, Indian Institute of Technology Bombay, Mumbai, India",[],{"title":319,"gsAuthor":321},{"VI":320},"Sourav Pal",{"VOID":322},"[\"TmdlTHYAAAAJ\"]",{"url":304,"publisher":324,"properties":360},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":325,"slug":10,"properties":326,"entityType":18,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":21,"subjectFields":330,"manageAffiliations":339,"indexDatabases":345,"url":20,"thumbnailPath":20,"statistic":20,"gsStatistic":20,"type":20,"analyzePriority":20},[],{"issn":327,"title":328,"eissn":329},{"VOID":13},{"EN":15},{"VOID":17},[331,335],{"id":24,"createTime":20,"updateTime":20,"relativeEntities":332,"label":333,"description":334,"parentId":20,"standard":20,"scholarHubFieldId":20},[],{"EN":27},{},{"id":30,"createTime":20,"updateTime":20,"relativeEntities":336,"label":337,"description":338,"parentId":20,"standard":20,"scholarHubFieldId":20},[],{"EN":33},{},[340],{"id":37,"createTime":20,"updateTime":20,"relativeEntities":341,"slug":20,"properties":342,"entityType":20,"verifyStatus":20,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":20,"url":20,"parentIds":344,"statistic":20},[],{"title":343},{"EN":41},[43],[346,353],{"id":46,"indexDatabase":347,"url":59,"indexYears":20,"academicFieldIds":352,"indexDatabaseRanking":20},{"id":48,"createTime":20,"updateTime":20,"relativeEntities":348,"label":349,"description":350,"key":55,"publicationTags":351,"standard":20},[],{"EN":51,"VI":51},{"EN":53,"VI":54},[57,58],[61],{"id":63,"indexDatabase":354,"url":74,"indexYears":75,"academicFieldIds":359,"indexDatabaseRanking":79},{"id":65,"createTime":20,"updateTime":20,"relativeEntities":355,"label":356,"description":357,"key":71,"publicationTags":358,"standard":20},[],{"EN":68,"VI":68},{"EN":68,"VI":70},[73],[77,78],{"pages":361},{"VOID":362},"1-19",{"total":252,"publishYear":364,"statisticByYear":365},2022,{"2017":252},"2022-10-25",[79,57],[369,372,375,378,384,387,390,393,396,402,405,408,414,417,420,423,426,429],{"id":20,"text":370,"url":20,"identifiers":371},"Agler, J., Young, N.J.: A commutant lifting theorem for a domain in \\({\\mathbb{C} }^2\\) and spectral interpolation. J. Funct. Anal. 161, 452–477 (1999)",{},{"id":258,"text":373,"url":260,"identifiers":374},"Agler, J., Young, N.J.: Operators having the symmetrized bidisc as a spectral set. Proc. Edinb. Math. Soc. (2) 43, 195–210 (2000)",{"doi":262},{"id":258,"text":376,"url":260,"identifiers":377},"Agler, J., Young, N.J.: A model theory for \\(\\Gamma\\)-contractions. J. Oper. Theory 49, 45–60 (2003)",{"doi":262},{"id":379,"text":380,"url":381,"identifiers":382},"da29abba-6040-4341-978f-b2da5ff2098a","Agler, J., Young, N.J.: The hyperbolic geometry of the symmetrized bidisc. J. Geom. Anal. 14, 375–403 (2004)","https:\u002F\u002Flink.springer.com\u002F10.1007\u002FBF02922097",{"doi":383},"10.1007\u002FBF02922097",{"id":258,"text":385,"url":260,"identifiers":386},"Agler, J., Lykova, Z., Young, N.J.: A geometric characterization of the symmetrized bidisc. J. Math. Anal. Appl. 473, 1377–1413 (2019)",{"doi":262},{"id":258,"text":388,"url":260,"identifiers":389},"Agler, J., Lykova, Z., Young, N.J.: Intrinsic directions, orthogonality, and distinguished geodesics in the symmetrized bidisc. J. Geom. Anal. 31, 8202–8237 (2021)",{"doi":262},{"id":258,"text":391,"url":260,"identifiers":392},"Bhattacharyya, T., Sau, H.: Interpolating sequences and the Toeplitz corona theorem on the symmetrized bidisk. J. Oper. Theory (to appear). arxiv:1909.03237",{"doi":262},{"id":258,"text":394,"url":260,"identifiers":395},"Bhattacharyya, T., Pal, S.: A functional model for pure \\(\\Gamma\\)-contractions. J. Oper. Thoery 71, 327–339 (2014)",{"doi":262},{"id":397,"text":398,"url":399,"identifiers":400},"39f40583-b7cf-4501-b267-189d5ede38c4","Bhattacharyya, T., Sau, H.: Holomorphic functions on the symmetrized bidisk-realization, interpolation and extension. J. Funct. Anal. 274, 504–524 (2018)","https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS0022123617303737",{"doi":401},"10.1016\u002Fj.jfa.2017.09.013",{"id":258,"text":403,"url":260,"identifiers":404},"Bhattacharyya, T., Pal, S., Roy, S.S.: Dilations of \\(\\Gamma\\)- contractions by solving operator equations. Adv. Math. 230, 577–606 (2012)",{"doi":262},{"id":258,"text":406,"url":260,"identifiers":407},"Bhattacharyya, T., Das, B.K., Sau, H.: Toeplitz operators on the symmetrized bidisc. Int. Math. Res. Not. IMRN 11, 8492–8520 (2021)",{"doi":262},{"id":409,"text":410,"url":411,"identifiers":412},"4efc3ada-015c-42b1-9596-eeb027da6b52","Bhattacharyys, T., Lata, S., Sau, H.: Admissible fundamental operators. J. Math. Anal. Appl. 425, 983–1003 (2015)","https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS0022247X15000128",{"doi":413},"10.1016\u002Fj.jmaa.2015.01.006",{"id":20,"text":415,"url":20,"identifiers":416},"Nikolov, N., Pflug, P., Thomas, P.J.: Spectral Nevanlinna–Pick and Caratheodory–Fejer problems for \\(n\\le 3\\). Indiana Univ. Math. J. 60, 883–893 (2011)",{},{"id":258,"text":418,"url":260,"identifiers":419},"Pal, S.: From Stinespring dilation to Sz.-Nagy dilation on the symmetrized bidisc and operator models. N. Y. J. Math. 20, 645–664 (2014)",{"doi":262},{"id":258,"text":421,"url":260,"identifiers":422},"Pal, S., Shalit, O.M.: Spectral sets and distinguished varieties in the symmetrized bidisc. J. Funct. Anal. 266, 5779–5800 (2014)",{"doi":262},{"id":258,"text":424,"url":260,"identifiers":425},"Pflug, P., Zwonek, W.: Exhausting domains of the symmetrized bidisc. Ark. Mat. 50, 397–402 (2012)",{"doi":262},{"id":20,"text":427,"url":20,"identifiers":428},"Sarkar, J.: Operator theory on symmetrized bidisc. Indiana Univer. Math. J. 64, 847–873 (2015)",{},{"id":20,"text":430,"url":20,"identifiers":431},"Sz.-Nagy, B., Foias, C., Kerchy, L., Bercovici, H.: Harmonic Analysis of Operators on Hilbert Space. Universitext, Springer, New York (2010)",{},{"id":433,"createTime":434,"updateTime":435,"relativeEntities":436,"slug":437,"properties":438,"entityType":101,"verifyStatus":102,"verifyTime":449,"verifyNote":104,"languages":20,"translateLanguages":20,"viewCount":21,"primaryUrl":450,"fullTextUrl":20,"authors":451,"publicationType":123,"publisherRelationship":479,"citationCount":20,"citationInfo":20,"publishDate":521,"publishYear":522,"citationAnalyzeStatus":523,"lastCitationAnalyze":524,"indexDatabases":525,"openAccess":20,"references":20,"isForceReanalyzing":172},"9dd4ebdc-9485-4e4f-80e9-1db6bd01e502","2023-12-11T00:22:55.099+00:00","2026-03-16T09:28:19.139+00:00",[],"A-model-theory-for-operators-associated-with-a-domain-related-to-mu-synthesis",{"abstract":439,"title":441,"gsPaper":443,"references":445,"doi":447},{"EN":440},"A commuting triple of Hilbert space operators (A, B, P) for which the closure of the tetrablock \n                \n                  \n                \n                $${\\mathbb {E}}$$\n                \n              , where \n                \n                  \n                \n                $$ \\begin{aligned} {\\mathbb {E}} = \\{ (x_1,x_2,x_3)\\in {\\mathbb {C}}^3 : \\; |x_3|\u003C1 \\;  \\&  \\; x_1=c_1+ x_3\\bar{c}_2\\,, x_2=c_2 +x_3\\bar{c}_1 \\,, \\; c_1,c_2 \\in {\\mathbb {C}} \\text { with } |c_1|+|c_2|\u003C1 \\}, \\end{aligned}$$\n                \n              is a spectral set is called a tetrablock contraction or an \n                \n                  \n                \n                $${\\mathbb {E}}$$\n                \n              -contraction. To every \n                \n                  \n                \n                $${\\mathbb {E}}$$\n                \n              -contraction (A, B, P), there are unique operators \n                \n                  \n                \n                $$F_1,F_2 \\in \\mathcal B(\\mathcal D_P)$$\n                \n              , which are called the fundamental operators of (A, B, P), satisfying \n                \n                  \n                \n                $$\\begin{aligned} A-B^*P=D_PF_1D_P\\;,\\; B-A^*P=D_PF_2D_P. \\end{aligned}$$\n                \n              An \n                \n                  \n                \n                $${\\mathbb {E}}$$\n                \n              -contraction (A, B, P) admits a canonical decomposition \n                \n                  \n                \n                $$(A_1\\oplus A_2, B_1 \\oplus B_2, P_1 \\oplus P_2)$$\n                \n               into an \n                \n                  \n                \n                $${\\mathbb {E}}$$\n                \n              -unitary \n                \n                  \n                \n                $$(A_1,B_1,P_1)$$\n                \n               and a completely non-unitary (c.n.u.) \n                \n                  \n                \n                $${\\mathbb {E}}$$\n                \n              -contraction \n                \n                  \n                \n                $$(A_2,B_2,P_2)$$\n                \n              . As there already exists an easily understood model for an \n                \n                  \n                \n                $${\\mathbb {E}}$$\n                \n              -unitary in the literature, it suffices to restrict attention to the c.n.u. \n                \n                  \n                \n                $${\\mathbb {E}}$$\n                \n              -contraction part. Here we construct an explicit minimal \n                \n                  \n                \n                $${\\mathbb {E}}$$\n                \n              -isometric dilation for a c.n.u. \n                \n                  \n                \n                $${\\mathbb {E}}$$\n                \n              -contraction whose fundamental operators satisfy (1.1) below (a class for which it is known that such dilation exists). As a consequence of this explicit dilation, we obtain a functional model for the same class of \n                \n                  \n                \n                $${\\mathbb {E}}$$\n                \n              -contractions. With the help of this functional model we express an \n                \n                  \n                \n                $${\\mathbb {E}}$$\n                \n              -contraction (A, B, P) as \n                \n                  \n                \n                $$\\begin{aligned} A=C_1+PC_2^*\\;,\\; B= C_2+PC_1^* \\end{aligned}$$\n                \n              for some operators \n                \n                  \n                \n                $$C_1,C_2$$\n                \n               and this representation is operator theoretic analogue of the representation of the points in \n                \n                  \n                \n                $${\\mathbb {E}}$$\n                \n              . We also construct a different functional model, which is not necessarily commutative, for a c.n.u. \n                \n                  \n                \n                $${\\mathbb {E}}$$\n                \n              -contraction (A, B, P) when A, B commute with \n                \n                  \n                \n                $$P^*$$\n                \n              . This functional model is obtained even without having an \n                \n                  \n                \n                $${\\mathbb {E}}$$\n                \n              -isometric dilation exhibited in the model. We show by an example that such a model may not be possessed by (A, B, P) if the condition that A, B commute with \n                \n                  \n                \n                $$P^*$$\n                \n              , is dropped from the hypothesis. A complete unitary invariant is achieved for a c.n.u. \n                \n                  \n                \n                $${\\mathbb {E}}$$\n                \n              -contraction (A, B, P) when A, B commute with \n                \n                  \n                \n                $$P^*$$\n                \n              . The fundamental operators play the central role in all these constructions. Also, we produce a new characterization for an \n                \n                  \n                \n                $${\\mathbb {E}}$$\n                \n              -unitary.",{"EN":442},"A model theory for operators associated with a domain related to $$\\mu $$ -synthesis",{"VOID":444},"[]",{"VOID":446},"Abouhajar, A.A., White, M.C., Young, N.J.: A Schwarz lemma for a domain related to \\(\\mu \\)-synthesis. J. Geom. Anal. 17, 717–750 (2007)\nAbouhajar, A.A., White, M.C., Young, N.J.: Corrections to ‘A Schwarz lemma for a domain related to \\(\\mu \\)-synthesis’, available online at http:\u002F\u002Fwww1.maths.leeds.ac.uk\u002F~nicholas\u002Fabstracts\u002Fcorrection.pdf\nBall, J.A., Sau, H.: Rational dilation of tetrablock contractions revisited. J. Funct. Anal. 278, 108275 (2020)\nBercovici, H., Foias, C., Kerchy, L., Sz.-Nagy, B.: Harmonic Analysis of Operators on Hilbert Space, Universitext. Springer, New York (2010)\nBharali, G.: A family of domains associated with Â-synthesis. Integr. Equ. Oper. Theory 82, 267–285 (2015)\nBhattacharyya, T.: The tetrablock as a spectral set. Indiana Univ. Math. J. 63, 1601–1629 (2014)\nBhattacharyya, T., Lata, S., Sau, H.: Admissible fundamental operators. J. Math. Anal. Appl. 425, 983–1003 (2015)\nBhattacharyya, T., Pal, S.: A functional model for pure \\(\\Gamma \\)-contractions. J. Oper. Theory 71, 327–339 (2014)\nBhattacharyya, T., Pal, S., ShyamRoy, S.: Dilations of \\(\\Gamma \\)- contractions by solving operator equations. Adv. Math. 230, 577–606 (2012)\nBisai, B., Pal, S.: Structure theorems for operators associated with two domains related to \\(\\mu \\)-synthesis. Bull. Sci. Math. 159, 102822 (2020)\nDoyle, J.: Analysis of feedback systems with structured uncertainties. IEE Proc. Control Theory Appl. 129, 242–250 (1982)\nDurszt, E.: Contractions as restricted shifts. Acta Sci. Math. (Szeged) 48, 129–134 (1985)\nEdigarian, A., Kosinski, L., Zwonek, W.: The Lempert theorem and the tetrablock. J. Geom. Anal. 23, 1818–1831 (2013)\nEdigarian, A., Zwonek, W.: Schwarz lemma for the tetrablock. Bull. Lond. Math. Soc. 41, 506–514 (2009)\nKosinski, L.: Geometry of quasi-circular domains and applications to tetrablock. Proc. Am. Math. Soc. 139, 559–569 (2011)\nKosinski, L., Zwonek, W.: Nevanlinna-Pick problem and uniqueness of left inverses in convex domains, symmetrized bidisc and tetrablock. J. Geom. Anal. 26, 1863–1890 (2016)\nKubrusly, C.S.: An Introduction to Models and Decompositions in Operator Theory. Birkhauser, Boston (1997)\nPal, S.: The failure of rational dilation on the tetrablock. J. Funct. Anal. 269(7), 1903–1924 (2015)\nPal, S.: Canonical decomposition of a tetrablock contraction and operator model. J. Math. Anal. Appl. 438, 274–284 (2016)\nPal, S.: Subvarieties of the tetrablock and von Neumann‘s inequality. Indiana Univ. Math. J. 65(6), 2051–2079 (2016)\nPal, S., Shalit, O.M.: Spectral sets and distinguished varieties in the symmetrized bidisc. J. Funct. Anal. 266, 5779–5800 (2014)\nPaulsen, V.: Completely Bounded Maps and Operator Algebras. Cambridge University Press (2002)\nSarkar, J.: Operator theory on symmetrized bidisc. Indiana Univ. Math. J. 64, 847–873 (2015)\nSau, H.: A note on tetrablock contractions. New York J. Math. 21, 1347–1369 (2015)\nTrybula, M.: Proper holomorphic mappings, Bell‘s formula, and the Lu Qi-Keng problem on the tetrablock. Arch. Math. (Basel) 101, 549–558 (2013)\nvon Neumann, J.: Eine Spektraltheorie für allgemeine Operatoren eines unitären Raumes. Math. Nachr. 4, 258–281 (1951)\nYoung, N.J.: The automorphism group of the tetrablock. J. Lond. Math. Soc. 77, 757–770 (2008)\nZwonek, W.: Geometric properties of the tetrablock. Arch. Math. 100, 159–165 (2013)",{"VOID":448},"10.1007\u002Fs13348-021-00341-6","2024-05-16T10:23:38.640+00:00","https:\u002F\u002Flink.springer.com\u002F10.1007\u002Fs13348-021-00341-6",[452,467],{"id":453,"sortIndex":21,"researcher":20,"roles":454,"affiliations":455,"properties":464,"displayName":466,"givenName":20,"familyName":20},"c8b2c32c-5429-4164-a4d0-7a6d1b40e7ea",[110],[456],{"id":457,"sortIndex":21,"affiliation":458,"properties":20},"c1ed3e2c-0374-4a11-bc1f-b5b9116aacb0",{"id":457,"createTime":20,"updateTime":20,"relativeEntities":459,"slug":20,"properties":460,"entityType":20,"verifyStatus":20,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":20,"url":20,"parentIds":463,"statistic":20},[],{"title":461},{"VI":462},"Mathematics Department, Indian Institute of Technology Bombay, Powai, Mumbai, India",[],{"title":465},{"VI":466},"Bappa Bisai",{"id":468,"sortIndex":252,"researcher":20,"roles":469,"affiliations":470,"properties":477,"displayName":320,"givenName":20,"familyName":20},"9f220cb0-9964-4bd0-b9f2-dcd7cf19e76a",[110],[471],{"id":457,"sortIndex":21,"affiliation":472,"properties":20},{"id":457,"createTime":20,"updateTime":20,"relativeEntities":473,"slug":20,"properties":474,"entityType":20,"verifyStatus":20,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":20,"url":20,"parentIds":476,"statistic":20},[],{"title":475},{"VI":462},[],{"title":478},{"VI":320},{"url":450,"publisher":480,"properties":516},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":481,"slug":10,"properties":482,"entityType":18,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":21,"subjectFields":486,"manageAffiliations":495,"indexDatabases":501,"url":20,"thumbnailPath":20,"statistic":20,"gsStatistic":20,"type":20,"analyzePriority":20},[],{"issn":483,"title":484,"eissn":485},{"VOID":13},{"EN":15},{"VOID":17},[487,491],{"id":24,"createTime":20,"updateTime":20,"relativeEntities":488,"label":489,"description":490,"parentId":20,"standard":20,"scholarHubFieldId":20},[],{"EN":27},{},{"id":30,"createTime":20,"updateTime":20,"relativeEntities":492,"label":493,"description":494,"parentId":20,"standard":20,"scholarHubFieldId":20},[],{"EN":33},{},[496],{"id":37,"createTime":20,"updateTime":20,"relativeEntities":497,"slug":20,"properties":498,"entityType":20,"verifyStatus":20,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":20,"url":20,"parentIds":500,"statistic":20},[],{"title":499},{"EN":41},[43],[502,509],{"id":46,"indexDatabase":503,"url":59,"indexYears":20,"academicFieldIds":508,"indexDatabaseRanking":20},{"id":48,"createTime":20,"updateTime":20,"relativeEntities":504,"label":505,"description":506,"key":55,"publicationTags":507,"standard":20},[],{"EN":51,"VI":51},{"EN":53,"VI":54},[57,58],[61],{"id":63,"indexDatabase":510,"url":74,"indexYears":75,"academicFieldIds":515,"indexDatabaseRanking":79},{"id":65,"createTime":20,"updateTime":20,"relativeEntities":511,"label":512,"description":513,"key":71,"publicationTags":514,"standard":20},[],{"EN":68,"VI":68},{"EN":68,"VI":70},[73],[77,78],{"pages":517,"volume":519},{"VOID":518},"173-198",{"VOID":520},"74","2021-11-02",2021,"ERROR_IN_GET_PLATFORM_ID","2026-03-16T09:28:19.138+00:00",[79,57],{"id":527,"createTime":528,"updateTime":529,"relativeEntities":530,"slug":531,"properties":532,"entityType":101,"verifyStatus":102,"verifyTime":541,"verifyNote":104,"languages":20,"translateLanguages":20,"viewCount":21,"primaryUrl":542,"fullTextUrl":20,"authors":543,"publicationType":123,"publisherRelationship":574,"citationCount":252,"citationInfo":616,"publishDate":619,"publishYear":617,"citationAnalyzeStatus":19,"lastCitationAnalyze":529,"indexDatabases":620,"openAccess":20,"references":621,"isForceReanalyzing":172},"6fa4dab4-e950-45c7-800a-69107c9e790b","2024-01-19T06:45:29.776+00:00","2025-08-05T15:32:37.615+00:00",[],"On-the-essential-bounded-variation-of-L-p-mathbb-R-X-functions",{"abstract":533,"title":535,"gsPaper":537,"doi":539},{"EN":534},"Let \n                  \n                    \n                  \n                  $$X$$\n                  \n                    \n                  \n                 be a Banach space. Nakamura and Hashimoto in (Proc Japan Acad Ser A 87:77–82, 2011), we showed that for every \n                  \n                    \n                  \n                  $$f\\in L_{1}(\\mathbb {R})$$\n                  \n                    \n                  \n                , \n                  \n                    \n                  \n                  $$\\begin{aligned} \\lim _{h\\rightarrow 0}\\int \\limits _{\\mathbb {R}}\\left| \\frac{f(t+h)-f(t)}{h}\\right| \\, dt=\\hbox {ess} V_{1}(f). \\end{aligned}$$\n                  \n                    \n                  \n                In this paper, we are concerned with the limit \n                  *\n                  \n                    \n                  \n                  $$\\begin{aligned} \\lim _{h\\rightarrow 0}\\int \\limits _{\\mathbb {R}}\\left\\| \\frac{f(t+h)-f(t)}{h}\\right\\| ^p\\, dt \\end{aligned}$$\n                  \n                    \n                  \n                for \n                  \n                    \n                  \n                  $$f\\in L_1^{\\hbox {loc}}(\\mathbb {R},X)$$\n                  \n                    \n                  \n                . We show that the limit \n                  \n                    \n                  \n                  $$(*)$$\n                  \n                    \n                  \n                 coincides with the essential \n                  \n                    \n                  \n                  $$p$$\n                  \n                    \n                  \n                -variation of \n                  \n                    \n                  \n                  $$f$$\n                  \n                    \n                  \n                 in the sense of F. Riesz, and we give characterizations of functions with bounded essential \n                  \n                    \n                  \n                  $$p$$\n                  \n                    \n                  \n                -variation, i.e, \n                  \n                    \n                  \n                  $$\\hbox {ess} V_p(f,X)\u003C\\infty $$\n                  \n                    \n                  \n                .",{"EN":536},"On the essential bounded variation of $$L_p(\\mathbb {R},X)$$ -functions",{"VOID":538},"[\"5509302085937242276\"]",{"VOID":540},"10.1007\u002Fs13348-013-0099-y","2024-04-29T14:03:00.408+00:00","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs13348-013-0099-y",[544,559],{"id":545,"sortIndex":21,"researcher":20,"roles":546,"affiliations":547,"properties":556,"displayName":558,"givenName":20,"familyName":20},"722808ab-303f-48ab-acd1-31ec9079b7a7",[110],[548],{"id":549,"sortIndex":21,"affiliation":550,"properties":20},"405b06bb-119b-49d2-9a25-a417972095a5",{"id":549,"createTime":20,"updateTime":20,"relativeEntities":551,"slug":20,"properties":552,"entityType":20,"verifyStatus":20,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":20,"url":20,"parentIds":555,"statistic":20},[],{"title":553},{"VI":554},"Matsue College of Technology, Matsue, Japan",[],{"title":557},{"VI":558},"Gen Nakamura",{"id":560,"sortIndex":252,"researcher":20,"roles":561,"affiliations":562,"properties":571,"displayName":573,"givenName":20,"familyName":20},"544048bd-eb98-4c79-8106-c8af6f3690c8",[110],[563],{"id":564,"sortIndex":21,"affiliation":565,"properties":20},"d39b0e49-e981-4b0c-bf78-645023c61d18",{"id":564,"createTime":20,"updateTime":20,"relativeEntities":566,"slug":20,"properties":567,"entityType":20,"verifyStatus":20,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":20,"url":20,"parentIds":570,"statistic":20},[],{"title":568},{"VI":569},"Hiroshima Jogakuin University, Faculty of Liberal Arts, Hiroshima, Japan",[],{"title":572},{"VI":573},"Kazuo Hashimoto",{"url":542,"publisher":575,"properties":611},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":576,"slug":10,"properties":577,"entityType":18,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":21,"subjectFields":581,"manageAffiliations":590,"indexDatabases":596,"url":20,"thumbnailPath":20,"statistic":20,"gsStatistic":20,"type":20,"analyzePriority":20},[],{"issn":578,"title":579,"eissn":580},{"VOID":13},{"EN":15},{"VOID":17},[582,586],{"id":24,"createTime":20,"updateTime":20,"relativeEntities":583,"label":584,"description":585,"parentId":20,"standard":20,"scholarHubFieldId":20},[],{"EN":27},{},{"id":30,"createTime":20,"updateTime":20,"relativeEntities":587,"label":588,"description":589,"parentId":20,"standard":20,"scholarHubFieldId":20},[],{"EN":33},{},[591],{"id":37,"createTime":20,"updateTime":20,"relativeEntities":592,"slug":20,"properties":593,"entityType":20,"verifyStatus":20,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":20,"url":20,"parentIds":595,"statistic":20},[],{"title":594},{"EN":41},[43],[597,604],{"id":46,"indexDatabase":598,"url":59,"indexYears":20,"academicFieldIds":603,"indexDatabaseRanking":20},{"id":48,"createTime":20,"updateTime":20,"relativeEntities":599,"label":600,"description":601,"key":55,"publicationTags":602,"standard":20},[],{"EN":51,"VI":51},{"EN":53,"VI":54},[57,58],[61],{"id":63,"indexDatabase":605,"url":74,"indexYears":75,"academicFieldIds":610,"indexDatabaseRanking":79},{"id":65,"createTime":20,"updateTime":20,"relativeEntities":606,"label":607,"description":608,"key":71,"publicationTags":609,"standard":20},[],{"EN":68,"VI":68},{"EN":68,"VI":70},[73],[77,78],{"pages":612,"volume":614},{"VOID":613},"407-416",{"VOID":615},"65",{"total":252,"publishYear":617,"statisticByYear":618},2013,{"2017":252},"2013-11-26",[79,57],[622,625,628,631,634],{"id":20,"text":623,"url":20,"identifiers":624},"Diestel, J., Uhl Jr J.: Vector Measures, Mathematical Surveys no. 15. Am. Math. Soc. Providence, RI (1977)",{},{"id":258,"text":626,"url":260,"identifiers":627},"Engel, K.-J., Nagel, R.: One-Parameter Semigroups for Linear Evolution Equations, GTM 194. Springer, New York (2000)",{"doi":262},{"id":258,"text":629,"url":260,"identifiers":630},"Leoni, G.: A first course in sobolev spaces. Graduate Studies in Mathematics, vol. 105. Am. Math. Soc. (2009)",{"doi":262},{"id":258,"text":632,"url":260,"identifiers":633},"Nakamura, G., Hashimoto, K.: On the linearity of some sets of sequences defined by \\(L_p\\)-functions and \\(L_1\\)-functions determining \\(\\ell _{1}\\)C. Proc. Japan Acad. Ser. A 87, 77–82 (2011)",{"doi":262},{"id":635,"text":636,"url":637,"identifiers":638},"2b8efcae-1510-4e9e-a512-6027f4381fc2","Riesz, F.: Untersuchungen über Systeme integrierbarer Funktionen. Math. Ann. 69(4), 449–497 (1910)","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002FBF01457637",{"doi":639},"10.1007\u002FBF01457637",{"id":641,"createTime":642,"updateTime":643,"relativeEntities":644,"slug":645,"properties":646,"entityType":101,"verifyStatus":102,"verifyTime":643,"verifyNote":104,"languages":653,"translateLanguages":20,"viewCount":21,"primaryUrl":655,"fullTextUrl":20,"authors":656,"publicationType":123,"publisherRelationship":676,"citationCount":21,"citationInfo":713,"publishDate":716,"publishYear":714,"citationAnalyzeStatus":19,"lastCitationAnalyze":20,"indexDatabases":717,"openAccess":20,"references":718,"isForceReanalyzing":172},"53318683-1b55-4dac-b4fd-c62982c3fee3","2024-04-11T16:46:02.407+00:00","2025-02-26T11:33:08.499+00:00",[],"Concerning-P-frames-and-the-Artin-Rees-property",{"title":647,"openalex":649,"doi":651},{"EN":648},"Concerning P-frames and the Artin–Rees property",{"VOID":650},"W4210443273",{"VOID":652},"10.1007\u002Fs13348-021-00346-1",[654],"EN","https:\u002F\u002Flink.springer.com\u002F10.1007\u002Fs13348-021-00346-1",[657],{"id":658,"sortIndex":21,"researcher":20,"roles":659,"affiliations":660,"properties":669,"displayName":673,"givenName":20,"familyName":20},"ed3311ff-8d12-47d8-b6c4-1743fe1f90cd",[],[661],{"id":662,"sortIndex":21,"affiliation":663,"properties":20},"9cc38e85-e0ec-4646-8bd9-d4f7a8e99ba7",{"id":662,"createTime":20,"updateTime":20,"relativeEntities":664,"slug":20,"properties":665,"entityType":20,"verifyStatus":20,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":20,"url":20,"parentIds":668,"statistic":20},[],{"title":666},{"VI":667},"Esfarayen University of Technology, Esfarayen, Iran",[],{"orcid":670,"title":672,"openalex":674},{"VOID":671},"https:\u002F\u002Forcid.org\u002F0000-0003-1508-7404",{"EN":673},"Mostafa Abedi",{"VOID":675},"A5052066312",{"url":20,"publisher":677,"properties":20},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":678,"slug":10,"properties":679,"entityType":18,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":21,"subjectFields":683,"manageAffiliations":692,"indexDatabases":698,"url":20,"thumbnailPath":20,"statistic":20,"gsStatistic":20,"type":20,"analyzePriority":20},[],{"issn":680,"title":681,"eissn":682},{"VOID":13},{"EN":15},{"VOID":17},[684,688],{"id":24,"createTime":20,"updateTime":20,"relativeEntities":685,"label":686,"description":687,"parentId":20,"standard":20,"scholarHubFieldId":20},[],{"EN":27},{},{"id":30,"createTime":20,"updateTime":20,"relativeEntities":689,"label":690,"description":691,"parentId":20,"standard":20,"scholarHubFieldId":20},[],{"EN":33},{},[693],{"id":37,"createTime":20,"updateTime":20,"relativeEntities":694,"slug":20,"properties":695,"entityType":20,"verifyStatus":20,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":20,"url":20,"parentIds":697,"statistic":20},[],{"title":696},{"EN":41},[43],[699,706],{"id":46,"indexDatabase":700,"url":59,"indexYears":20,"academicFieldIds":705,"indexDatabaseRanking":20},{"id":48,"createTime":20,"updateTime":20,"relativeEntities":701,"label":702,"description":703,"key":55,"publicationTags":704,"standard":20},[],{"EN":51,"VI":51},{"EN":53,"VI":54},[57,58],[61],{"id":63,"indexDatabase":707,"url":74,"indexYears":75,"academicFieldIds":712,"indexDatabaseRanking":79},{"id":65,"createTime":20,"updateTime":20,"relativeEntities":708,"label":709,"description":710,"key":71,"publicationTags":711,"standard":20},[],{"EN":68,"VI":68},{"EN":68,"VI":70},[73],[77,78],{"total":21,"publishYear":714,"statisticByYear":715},2023,{},"2023-01-01",[79,57],[719,723,727,730,734,737,740,743,746,750,754,758,762,765,769,772,776,780],{"id":20,"text":720,"url":20,"identifiers":721},"Abedi, M.: Concerning real-closed ideals in $${\\cal{R}}L$$ and SV-frames. Topol. Appl. 258, 402–414 (2019)",{"doi":722},"10.1016\u002Fj.topol.2019.03.013",{"id":20,"text":724,"url":20,"identifiers":725},"Abedi, M.: Some Notes on $$z$$-ideal and $$d$$-ideal in $${\\cal{R}}L$$. Bull. Iran. Math. Soc. 46, 593–611 (2020)",{"doi":726},"10.1007\u002Fs41980-019-00278-4",{"id":20,"text":728,"url":20,"identifiers":729},"Abedi, M.: Rings of quotients of the ring $${\\cal{R}}L$$. Houst. J. Math. (Accepted)",{},{"id":20,"text":731,"url":20,"identifiers":732},"Anderson, D.F., Badawi, A.: Divisibility conditions in commutative rings with zerodivisors. Commun. Algebra 3, 4031–4047 (2002)",{"doi":733},"10.1081\u002FAGB-120005834",{"id":20,"text":735,"url":20,"identifiers":736},"Azarpanah, F., Afrroz, S.: $$P$$-spaces and Artin–Rees property. Adv. Math. Model. 2, 61–76 (2012)",{},{"id":20,"text":738,"url":20,"identifiers":739},"Ball, R.N., Walters-Wayland, J.: $$C$$- and $$C^*$$-quotients in pointfree topology. Diss. Math. (Rozpr. Mat.) 412, 1–62 (2002)",{},{"id":20,"text":741,"url":20,"identifiers":742},"Banaschewski, B.: The real numbers in pointfree topology, Textos de Matemática, Série B, vol. 12. Departamento de Matemática da Universidade de Coimbra, Coimbra (1997)",{},{"id":20,"text":744,"url":20,"identifiers":745},"Banaschewski, B., Hong, S.S.: Completeness properties of function rings in pointfree topology. Comment. Math. Univ. Carol. 44, 245–259 (2003)",{},{"id":20,"text":747,"url":20,"identifiers":748},"Dube, T., Walters-Wayland, J.: Coz-onto frame maps and some applications. Appl. Categ. Struct. 15, 119–133 (2007)",{"doi":749},"10.1007\u002Fs10485-006-9022-y",{"id":20,"text":751,"url":20,"identifiers":752},"Dube, T.: Some ring-theoretic properties of almost $$\\text{ P }$$-frames. Algebra Universalis 60, 145–162 (2009)",{"doi":753},"10.1007\u002Fs00012-009-2093-5",{"id":20,"text":755,"url":20,"identifiers":756},"Dube, T.: Concerning P-frames, essential P-frames and strongly zero-dimensional frames. Algebra Universalis 69, 115–138 (2009)",{"doi":757},"10.1007\u002Fs00012-009-0006-2",{"id":20,"text":759,"url":20,"identifiers":760},"Dube, T.: Notes on point free disconnectivity with a ring-theoretic slant. Appl. Categ. Struct. 18, 55–72 (2010)",{"doi":761},"10.1007\u002Fs10485-008-9162-3",{"id":20,"text":763,"url":20,"identifiers":764},"Dube, T.: A note on the socle of certain types of $$f$$-rings. Bull. Iran. Math. Soc. 2, 517–528 (2012)",{},{"id":20,"text":766,"url":20,"identifiers":767},"Dube, T., Ighedo, O.: On lattices of $$z$$-ideals of function rings. Math. Slovaca 68, 271–284 (2018)",{"doi":768},"10.1515\u002Fms-2017-0099",{"id":20,"text":770,"url":20,"identifiers":771},"Gillman, L., Jerison, M.: Rings of Continuous Functions. Springer, Berlin (1976)",{},{"id":20,"text":773,"url":20,"identifiers":774},"Mason, G.: $$z$$-Ideals and prime ideals. J. Algebra 26, 280–297 (1973)",{"doi":775},"10.1016\u002F0021-8693(73)90024-0",{"id":20,"text":777,"url":20,"identifiers":778},"Picado, J., Pultr, A.: Frames and Locales: Topology without Points. Frontiers in Mathematics, Springer, Basel (2012)",{"doi":779},"10.1007\u002F978-3-0348-0154-6",{"id":20,"text":781,"url":20,"identifiers":782},"Rees, D.: Two classical theorems of ideal theory. Proc. Camb. Philos. Soc. 52, 155–157 (1956)",{"doi":783},"10.1017\u002FS0305004100031091",{"id":785,"createTime":786,"updateTime":787,"relativeEntities":788,"slug":789,"properties":790,"entityType":101,"verifyStatus":102,"verifyTime":787,"verifyNote":104,"languages":20,"translateLanguages":20,"viewCount":21,"primaryUrl":799,"fullTextUrl":20,"authors":800,"publicationType":123,"publisherRelationship":846,"citationCount":20,"citationInfo":20,"publishDate":888,"publishYear":889,"citationAnalyzeStatus":19,"lastCitationAnalyze":20,"indexDatabases":890,"openAccess":20,"references":20,"isForceReanalyzing":172},"8cb49459-6eb2-4d51-b480-b12ff5f3bcec","2023-12-28T05:33:38.965+00:00","2025-02-25T19:23:32.820+00:00",[],"Moduli-spaces-of-bundles-and-Hilbert-schemes-of-scrolls-over-nu-gonal-curves",{"abstract":791,"title":793,"references":795,"doi":797},{"EN":792},"The aim of this paper is twofold. We first strongly improve our previous main result Choi et al. (Proc Am Math Soc 146(8):3233–3248, 2018, Theorem 3.1), concerning classification of irreducible components of the Brill–Noether locus parametrizing rank 2 semistable vector bundles of suitable degrees d, with at least \n                  \n                    \n                  \n                  $$d-2g+4$$\n                  \n                    \n                  \n                 independent global sections, on a general \n                  \n                    \n                  \n                  $$\\nu $$\n                  \n                    \n                  \n                -gonal curve C of genus g. We then uses this classification to study several properties of the Hilbert scheme of suitable surface scrolls in projective space, which turn out to be special and stable.",{"EN":794},"Moduli spaces of bundles and Hilbert schemes of scrolls over $$\\nu $$ -gonal curves",{"VOID":796},"Arbarello, E., Cornalba, M.: Footnotes to a paper of Beniamino Segre. Math. Ann. 256, 341–362 (1981)\nArbarello, E., Cornalba, M., Griffiths, P., Harris, J.: Geometry of Algebraic Curves I. Springer, Berlin (1984)\nArbarello, E., Cornalba, M., Griffiths, P.: Geometry of Algebraic Curves II. Springer, Berlin (2011)\nChoi, Y., Flamini, F., Kim, S.: Brill–Noether loci of rank-two bundles on a general \\(\\nu \\)-gonal curve. Proc. Am. Math. Soc. 146(8), 3233–3248 (2018)\nCiliberto, C., Flamini, F.: Extensions of line bundles and Brill–Noether loci of rank-two vector bundles on a general curve. Revue Roumaine des Math. Pures et App. 60(3), 201–255 (2015)\nGriffiths, P., Harris, J.: Principles of Algebraic Geometry. Wyley Classics, New York (1994)\nHartshorne, R.: Algebraic geometry, Graduate Texts in Math. 52, Springer, New York (1977)\nLange, H., Narasimhan, M.S.: Maximal subbundles of rank two vector bundles on curves. Math. Ann. 266, 55–72 (1983)\nLange, H., Newstead, P., Strehl, V.: Non-emptiness of Brill–Noether loci in \\(M(2,L)\\). Int. J. Math. 26(13), 1550108 (2015). 26 pp\nLaumon, G.: Fibres vectoriels speciaux. Bull. Soc. Math. France 119, 97–119 (1990)\nMaruyama, M.: On automorphism group of ruled surfaces. J. Math. Kyoto Univ. 11, 89–112 (1971)\nKeem, C., Kim, S.: On the Clifford index of a general \\((e+2)\\)-gonal curve. Manuscipta Math. 63, 83–88 (1989)\nSernesi, E.: Deformations of Algebraic Schemes, Grundlehren der mathematischen Wissenschaften, 334. Springer, Berlin (2006)\nSundaram, N.: Special divisors and vector bundles. Tôhoku Math. J. 39, 175–213 (1987)\nTeixidor, M.: Brill–Noether theory for vector bundles of rank 2. Tôhoku Math. 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L.L., Conca, A., Iyengar, S.B.: Subadditivity of syzygies of Koszul algebras. Math. Ann. 361(1–2), 511–534 (2013)",{"doi":1014},"10.1007\u002Fs00208-014-1060-4",{"id":20,"text":1016,"url":20,"identifiers":1017},"Bayer, D., Mumford, D.: What can be computed in algebraic geometry? In: Computational algebraic geometry and commutative algebra, Sympos. Math., vol. XXXIV. Cambridge University Press, Cortona, pp. 1–48 (1993)",{},{"id":20,"text":1019,"url":20,"identifiers":1020},"Bayer, D., Stillman, M.: On the complexity of computing syzygies. J. Symb. Comput. 6(2), 135–147 (1988)",{"doi":1021},"10.1016\u002FS0747-7171(88)80039-7",{"id":20,"text":1023,"url":20,"identifiers":1024},"Davis, M.: The geometry and topology of Coxeter groups, vol. 32. Princeton University Press, Princeton, NJ (2008)",{},{"id":20,"text":1026,"url":20,"identifiers":1027},"Dao, H., Huneke, C., Schweig, J.: Bounds on the regularity and projective dimension of ideals associated to graphs. J. Algebr. Comb. 38(1), 37–55 (2013)",{"doi":1028},"10.1007\u002Fs10801-012-0391-z",{"id":20,"text":1030,"url":20,"identifiers":1031},"Eisenbud, D., Goto, S.: Linear free resolutions and minimal multiplicity. J. Algebr. 88(1), 89–133 (1984)",{"doi":1032},"10.1016\u002F0021-8693(84)90092-9",{"id":20,"text":1034,"url":20,"identifiers":1035},"Januszkiewicz, T., Świątkowski, J.: Hyperbolic Coxeter groups of large dimension. Comment. Math. Helvetici 78(3), 555–583 (2003)",{"doi":1036},"10.1007\u002Fs00014-003-0763-z",{"id":20,"text":1038,"url":20,"identifiers":1039},"Mayr, E.W., Meyer, A.R.: The complexity of the word problems for commutative semigroups and polynomial ideals. Adv. Math. 46(3), 305–329 (1982)",{"doi":1040},"10.1016\u002F0001-8708(82)90048-2",{"id":20,"text":1042,"url":20,"identifiers":1043},"Miller, E., Sturmfels, B.: Combinatorial commutative algebra, GTM, vol. 227. Springer, Berlin (2005)",{},{"id":20,"text":1045,"url":20,"identifiers":1046},"Stanley, R.P.: Cohen-Macaulay complexes. In: Higher Combinatorics, 31. pp. 51–62 (1977)",{"doi":1047},"10.1007\u002F978-94-010-1220-1_3",{"id":1049,"createTime":1050,"updateTime":1051,"relativeEntities":1052,"slug":1053,"properties":1054,"entityType":101,"verifyStatus":102,"verifyTime":1051,"verifyNote":104,"languages":20,"translateLanguages":20,"viewCount":21,"primaryUrl":1063,"fullTextUrl":20,"authors":1064,"publicationType":123,"publisherRelationship":1095,"citationCount":20,"citationInfo":20,"publishDate":1137,"publishYear":1138,"citationAnalyzeStatus":19,"lastCitationAnalyze":20,"indexDatabases":1139,"openAccess":20,"references":20,"isForceReanalyzing":172},"3c3bb362-439e-45dd-b3a4-42e07611f9f3","2024-01-25T06:20:33.676+00:00","2025-02-24T04:02:55.617+00:00",[],"A-remark-on-the-rational-cohomology-of-bar-S-1-n-",{"abstract":1055,"title":1057,"references":1059,"doi":1061},{"EN":1056},"We focus on the rational cohomology of Cornalba’s moduli space of spin curves of genus 1 withn marked points. In particular, we show that both its first and its third cohomology group vanish and the second cohomology group is generated by boundary classes.",{"EN":1058},"A remark on the rational cohomology of $$\\bar S_{1,n} $$",{"VOID":1060},"D. Abramovich and T.J. Jarvis, Moduli of twisted spin curves,Proc. Amer. Math. Soc. 131 (2003), 685–699.\nE. Arbarello and M. Cornalba, The Picard groups of the moduli spaces of curves,Topology 26 (1987), 153–171.\nE. Arbarello and M. Cornalba, Calculating cohomology groups of moduli spaces of curves via algebraic geometry,Inst. Hautes Études Sci. Publ. Math. 88 (1998), 97–127.\nG. Bini and C. Fontanari, Moduli of curves and spin structures via algebraic geometry,Trans. Amer. Math. Soc. 358 (2006), 3207–3217.\nG. Bini and C. Fontanari, On the geometry of\\(\\bar S_2 \\),Internat. J. Math., to appear.\nM. Cornalba, Moduli of curves and theta-characteristics,Lectures on Riemann surfaces (Trieste, 1987), 560–589, World Sci. Publ., Teaneck, NJ, 1989.\nM. Cornalba, A remark on the Picard group of spin moduli space,Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 2 (1991), 211–217.\nE. Getzler, The semiclassical approximation for modular operads,Comm. Math. Phys. 194 (1998), 481–492.\nR. Hartshorne,Algebraic Geometry, Graduate Texts in Mathematics52, SpringerVerlag, New York-Heidelberg, 1977.\nT.J. Jarvis, Geometry of the moduli of higher spin curves,Internat. J. Math. 11 (2000), 637–663.",{"VOID":1062},"10.1007\u002FBF03191369","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002FBF03191369",[1065,1080],{"id":1066,"sortIndex":21,"researcher":20,"roles":1067,"affiliations":1068,"properties":1077,"displayName":1079,"givenName":20,"familyName":20},"804bc856-aedc-46ec-81bd-0a63d4c9e368",[110],[1069],{"id":1070,"sortIndex":21,"affiliation":1071,"properties":20},"211259b8-115d-4319-8814-7cf365e52b9b",{"id":1070,"createTime":20,"updateTime":20,"relativeEntities":1072,"slug":20,"properties":1073,"entityType":20,"verifyStatus":20,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":20,"url":20,"parentIds":1076,"statistic":20},[],{"title":1074},{"VI":1075},"Dipartimento di Matematica, Università degli Studi di Milano, Milano, Italy",[],{"title":1078},{"VI":1079},"Gilberto Bini",{"id":1081,"sortIndex":252,"researcher":20,"roles":1082,"affiliations":1083,"properties":1092,"displayName":1094,"givenName":20,"familyName":20},"c5696b14-400f-4f31-b27d-e54a7d7d9dc0",[110],[1084],{"id":1085,"sortIndex":21,"affiliation":1086,"properties":20},"60654ffe-336f-4054-94c1-26c108424568",{"id":1085,"createTime":20,"updateTime":20,"relativeEntities":1087,"slug":20,"properties":1088,"entityType":20,"verifyStatus":20,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":20,"url":20,"parentIds":1091,"statistic":20},[],{"title":1089},{"VI":1090},"Dipartimento di Matematica, Politecnico di Torino, Torino, Italy",[],{"title":1093},{"VI":1094},"Claudio Fontanari",{"url":1063,"publisher":1096,"properties":1132},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":1097,"slug":10,"properties":1098,"entityType":18,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":21,"subjectFields":1102,"manageAffiliations":1111,"indexDatabases":1117,"url":20,"thumbnailPath":20,"statistic":20,"gsStatistic":20,"type":20,"analyzePriority":20},[],{"issn":1099,"title":1100,"eissn":1101},{"VOID":13},{"EN":15},{"VOID":17},[1103,1107],{"id":24,"createTime":20,"updateTime":20,"relativeEntities":1104,"label":1105,"description":1106,"parentId":20,"standard":20,"scholarHubFieldId":20},[],{"EN":27},{},{"id":30,"createTime":20,"updateTime":20,"relativeEntities":1108,"label":1109,"description":1110,"parentId":20,"standard":20,"scholarHubFieldId":20},[],{"EN":33},{},[1112],{"id":37,"createTime":20,"updateTime":20,"relativeEntities":1113,"slug":20,"properties":1114,"entityType":20,"verifyStatus":20,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":20,"url":20,"parentIds":1116,"statistic":20},[],{"title":1115},{"EN":41},[43],[1118,1125],{"id":46,"indexDatabase":1119,"url":59,"indexYears":20,"academicFieldIds":1124,"indexDatabaseRanking":20},{"id":48,"createTime":20,"updateTime":20,"relativeEntities":1120,"label":1121,"description":1122,"key":55,"publicationTags":1123,"standard":20},[],{"EN":51,"VI":51},{"EN":53,"VI":54},[57,58],[61],{"id":63,"indexDatabase":1126,"url":74,"indexYears":75,"academicFieldIds":1131,"indexDatabaseRanking":79},{"id":65,"createTime":20,"updateTime":20,"relativeEntities":1127,"label":1128,"description":1129,"key":71,"publicationTags":1130,"standard":20},[],{"EN":68,"VI":68},{"EN":68,"VI":70},[73],[77,78],{"pages":1133,"volume":1135},{"VOID":1134},"241-247",{"VOID":1136},"60","2009-10-01",2009,[79,57],{"id":1141,"createTime":1142,"updateTime":1143,"relativeEntities":1144,"slug":1145,"properties":1146,"entityType":101,"verifyStatus":102,"verifyTime":1143,"verifyNote":104,"languages":20,"translateLanguages":20,"viewCount":21,"primaryUrl":1155,"fullTextUrl":20,"authors":1156,"publicationType":123,"publisherRelationship":1187,"citationCount":20,"citationInfo":20,"publishDate":1229,"publishYear":1005,"citationAnalyzeStatus":19,"lastCitationAnalyze":20,"indexDatabases":1230,"openAccess":20,"references":20,"isForceReanalyzing":172},"5ff34f19-e394-446d-b342-72750f751449","2024-01-03T17:40:50.817+00:00","2025-02-23T14:27:46.331+00:00",[],"Some-extensions-of-Hilbert-Kunz-multiplicity",{"abstract":1147,"title":1149,"references":1151,"doi":1153},{"EN":1148},"Let R be an excellent Noetherian ring of prime characteristic. Consider an arbitrary nested pair of ideals (or more generally, a nested pair of submodules of a fixed finite module). We do not assume that their quotient has finite length. In this paper, we develop various sufficient numerical criteria for when the tight closures of these ideals (or submodules) match. For some of the criteria we only prove sufficiency, while some are shown to be equivalent to the tight closures matching. We compare the various numerical measures (in some cases demonstrating that the different measures give truly different numerical results) and explore special cases where equivalence with matching tight closure can be shown. All of our measures derive ultimately from Hilbert–Kunz multiplicity.",{"EN":1150},"Some extensions of Hilbert–Kunz multiplicity",{"VOID":1152},"Aberbach, I.M.: The existence of the F-signature for rings with large \\(\\mathbb{Q}\\)-Gorenstein locus. J. Algebra 319(7), 2994–3005 (2008)\nAchilles, R., Manaresi, M.: Multiplicity for ideals of maximal analytic spread and intersection theory. J. Math. Kyoto Univ. 33(4), 1029–1046 (1993)\nAchilles, R., Manaresi, M.: Multiplicities of a bigraded ring and intersection theory. Math. Ann. 309(4), 573–591 (1997)\nBrenner, H.: Irrational Hilbert-Kunz multiplicities. arXiv:1305.5873 (2013)\nBrenner, H., Monsky, P.: Tight closure does not commute with localization. Ann. of Math. (2) 171(1), 571–588 (2010)\nBuchsbaum, D.A., Eisenbud, D.: What makes a complex exact? J. Algebra 25, 259–268 (1973)\nDao, H., Smirnov, I.: On generalized Hilbert–Kunz function and multiplicity. arXiv:1305.1833 (2013)\nDao, H., Watanabe, K.: Some computations of generalized Hilbert–Kunz function and multiplicity. arXiv:1503.00894 (2015)\nEpstein, N.: Phantom depth and stable phantom exactness. Trans. Am. Math. Soc. 359(10), 4829–4864 (2007)\nEpstein, N., Yao, Y.: Criteria for flatness and injectivity. Math. Z. 271(3–4), 1193–1210 (2012)\nEpstein, N., Yao, Y.: A computation concerning relative Hilbert–Kunz multiplicities. arXiv:1605.01807 (2016)\nFlenner, H., Manaresi, M.: A numerical characterization of reduction ideals. Math. Z. 238(1), 205–214 (2001)\nHochster, M., Huneke, C.: Tight closure, invariant theory, and the Briançon-Skoda theorem. J. Am. Math. Soc. 3(1), 31–116 (1990)\nHochster, M., Huneke, C.: \\(F\\)-regularity, test elements, and smooth base change. Trans. Am. Math. Soc. 346(1), 1–62 (1994)\nHochster, M., Huneke, C.: Localization and test exponents for tight closure. Michigan Math. J. 48, 305–329 (2000)\nHuneke, C.: Tight Closure and its Applications. In: CBMS Reg. Conf. Ser. in Math., vol. 88, Amer. Math. Soc., Providence (1996)\nHuneke, C., Leuschke, G.J.: Two theorems about maximal Cohen–Macaulay modules. Math. Ann. 324(2), 391–404 (2002)\nKatzman, M., Sharp, R.Y.: Uniform behaviour of the Frobenius closures of ideals generated by regular sequences. J. Algebra 295(1), 231–246 (2006)\nKurano, K.: The singular Riemann–Roch theorem and Hilbert–Kunz functions. J. Algebra 304(1), 487–499 (2006)\nLam, T.Y.: A First Course in Noncommutative Rings. Graduate Texts in Mathematics. Springer, New York (1991)\nLyubeznik, G.: \\(F\\)-modules: applications to local cohomology and \\(D\\)-modules in characteristic \\(p>0\\). J. Reine Angew. Math. 491, 65–130 (1997)\nMonsky, P.: The Hilbert–Kunz function. Math. Ann. 263(1), 43–49 (1983)\nPeskine, C., Szpiro, L.: Dimension projective finie et cohomologie locale. applications à la démonstration de conjectures de M. Auslander, H. Bass et A. Grothendieck, Inst. Hautes Études Sci. Publ. Math. 42, 47–119 (1973)\nPolstra, T.: Uniform bounds in F-finite rings and lower semi-continuity of the F-signature. arXiv:1506.01073, (2015)\nSeibert, G.: Complexes with homology of finite length and Frobenius functors. J. 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Soc. 151(1), 95–102 (2011)\nVraciu, A.: An observation on generalized Hilbert-Kunz functions. arXiv:1510.00668, (2015)\nYao, Y.: Modules with finite \\(F\\)-representation type. J. Lond. Math. Soc. 2(72), 53–72 (2005)\nYoshino, Y.: Skew-polynomial rings of Frobenius type and the theory of tight closure. Comm. 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