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The existence, non-existence and uniqueness of solutions are investigated in terms of \u003Cjats:italic>a, b, p\u003C\u002Fjats:italic> and \u003Cjats:italic>q\u003C\u002Fjats:italic>.\u003C\u002Fjats:p>",{"EN":345},"A Lane–Emden system with singular data",{"VOID":347},"10.1017\u002Fs0308210510000302",[124],"https:\u002F\u002Fwww.cambridge.org\u002Fcore\u002Fproduct\u002Fidentifier\u002FS0308210510000302\u002Ftype\u002Fjournal_article",[351],{"id":352,"sortIndex":25,"researcher":24,"roles":353,"affiliations":354,"properties":365},"9ca9117d-7a95-40cc-9b2d-a3229ce12643",[],[355],{"id":356,"sortIndex":25,"affiliation":357,"properties":24},"b1fc23ca-ffcd-4d87-9547-fef825818e36",{"id":358,"createTime":359,"updateTime":359,"relativeEntities":360,"slug":361,"properties":362,"entityType":45,"verifyStatus":23,"verifyTime":24,"verifyNote":24,"syncStatus":23,"languages":24,"translateLanguages":24,"viewCount":25},"1734972b-cbd1-4813-afce-c9716c7c60b1","2024-09-24T23:18:23.887+00:00",[],"School-of-Mathematical-Sciences-University-College-Dublin-Belfield-Dublin-4-Ireland-marius-ghergu-ucd-ie",{"title":363},{"EN":364},"School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland (marius.ghergu@ucd.ie",{"openalex":366,"orcid":368,"title":370},{"VOID":367},"A5046418385",{"VOID":369},"https:\u002F\u002Forcid.org\u002F0000-0001-9104-5295",{"EN":371},"Marius Ghergu",{"url":24,"publisher":373,"properties":398},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":374,"slug":10,"properties":375,"entityType":22,"verifyStatus":23,"verifyTime":24,"verifyNote":24,"syncStatus":23,"languages":24,"translateLanguages":24,"viewCount":25,"subjectFields":381,"manageAffiliations":382,"indexDatabases":383,"url":98,"thumbnailPath":24,"statistic":24,"gsStatistic":24,"type":24,"analyzePriority":24},[],{"country":376,"issn":377,"introduce":378,"eissn":379,"title":380},{"VOID":13},{"VOID":15},{"EN":17},{"VOID":19},{"EN":21},[],[],[384,391],{"id":61,"indexDatabase":385,"url":76,"indexYears":24,"academicFieldIds":390,"indexDatabaseRanking":24},{"id":63,"createTime":64,"updateTime":65,"relativeEntities":386,"label":387,"description":388,"key":72,"publicationTags":389,"standard":24},[],{"EN":68,"VI":68},{"VI":70,"EN":71},[74,75],[78],{"id":80,"indexDatabase":392,"url":93,"indexYears":94,"academicFieldIds":397,"indexDatabaseRanking":97},{"id":82,"createTime":83,"updateTime":84,"relativeEntities":393,"label":394,"description":395,"key":90,"publicationTags":396,"standard":24},[],{"EN":87,"VI":87},{"EN":87,"VI":89},[92],[96],{"volume":399,"pages":401,"issue":403},{"VOID":400},"141",{"VOID":402},"1279-1294",{"VOID":404},"6",12,{"total":405,"publishYear":24,"statisticByYear":407},{"2015":57,"2016":170,"2017":46,"2018":46,"2019":170,"2020":46,"2023":170},"2011-12-01",2011,[],{"id":412,"createTime":413,"updateTime":413,"relativeEntities":414,"slug":415,"properties":416,"entityType":120,"verifyStatus":121,"verifyTime":428,"verifyNote":122,"syncStatus":23,"languages":429,"translateLanguages":24,"viewCount":25,"primaryUrl":430,"fullTextUrl":24,"authors":431,"publicationType":191,"publisherRelationship":469,"citationCount":502,"citationInfo":503,"publishDate":511,"publishYear":512,"citationAnalyzeStatus":23,"lastCitationAnalyze":24,"indexDatabases":24,"openAccess":24,"references":513,"isForceReanalyzing":231},"41aa1c64-f9c2-4fb4-94f0-a78c0d30c221","2024-09-12T22:57:33.453+00:00",[],"Local-existence-and-blow-up-criterion-for-the-Boussinesq-equations",{"mag":417,"keywords":419,"openalex":420,"abstract":422,"title":424,"doi":426},{"VOID":418},"2114304587",{},{"VOID":421},"W2114304587",{"EN":423},"\u003Cjats:title>Synopsis\u003C\u002Fjats:title>\u003Cjats:p>In this paper, we prove local existence and uniqueness of smooth solutions of the Boussinesq equations. We also obtain a blow-up criterion for these smooth solutions. This shows that the maximum norm of the gradient of the passive scalar controls the breakdown of smooth solutions of the Boussinesq equations. As an application of this criterion, we prove global existence of smooth solutions in the case of zero external force.\u003C\u002Fjats:p>",{"EN":425},"Local existence and blow-up criterion for the Boussinesq equations",{"VOID":427},"10.1017\u002Fs0308210500026810","2024-09-12T22:57:33.452+00:00",[124],"https:\u002F\u002Fwww.cambridge.org\u002Fcore\u002Fproduct\u002Fidentifier\u002FS0308210500026810\u002Ftype\u002Fjournal_article",[432,454],{"id":433,"sortIndex":25,"researcher":24,"roles":434,"affiliations":435,"properties":447},"1d3b7aee-5841-4127-88d9-236908aa6cff",[],[436],{"id":437,"sortIndex":25,"affiliation":438,"properties":24},"e683a589-8333-4dcc-b23b-19f76dd6d587",{"id":439,"createTime":440,"updateTime":441,"relativeEntities":442,"slug":443,"properties":444,"entityType":45,"verifyStatus":23,"verifyTime":24,"verifyNote":24,"syncStatus":23,"languages":24,"translateLanguages":24,"viewCount":25},"928a029b-1c88-4e55-9414-0e61a455d792","2023-12-06T07:11:53.627+00:00","2024-09-29T14:50:36.919+00:00",[],"Department-of-Mathematics-Seoul-National-University-Seoul-151-742-Korea",{"title":445},{"VI":446},"Department of Mathematics, Seoul National University, Seoul, 151–742, Korea",{"openalex":448,"orcid":450,"title":452},{"VOID":449},"A5041354678",{"VOID":451},"https:\u002F\u002Forcid.org\u002F0000-0001-7630-3479",{"EN":453},"Dongho Chae",{"id":455,"sortIndex":170,"researcher":24,"roles":456,"affiliations":457,"properties":464},"e5758a4b-66fa-4c2e-b1e4-1f2e37b89b39",[],[458],{"id":459,"sortIndex":25,"affiliation":460,"properties":24},"a9b2eb09-d3b3-4e03-b5c7-92b13ea14eca",{"id":439,"createTime":440,"updateTime":441,"relativeEntities":461,"slug":443,"properties":462,"entityType":45,"verifyStatus":23,"verifyTime":24,"verifyNote":24,"syncStatus":23,"languages":24,"translateLanguages":24,"viewCount":25},[],{"title":463},{"VI":446},{"openalex":465,"title":467},{"VOID":466},"A5102062317",{"EN":468},"Hee-Seok Nam",{"url":24,"publisher":470,"properties":495},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":471,"slug":10,"properties":472,"entityType":22,"verifyStatus":23,"verifyTime":24,"verifyNote":24,"syncStatus":23,"languages":24,"translateLanguages":24,"viewCount":25,"subjectFields":478,"manageAffiliations":479,"indexDatabases":480,"url":98,"thumbnailPath":24,"statistic":24,"gsStatistic":24,"type":24,"analyzePriority":24},[],{"country":473,"issn":474,"introduce":475,"eissn":476,"title":477},{"VOID":13},{"VOID":15},{"EN":17},{"VOID":19},{"EN":21},[],[],[481,488],{"id":61,"indexDatabase":482,"url":76,"indexYears":24,"academicFieldIds":487,"indexDatabaseRanking":24},{"id":63,"createTime":64,"updateTime":65,"relativeEntities":483,"label":484,"description":485,"key":72,"publicationTags":486,"standard":24},[],{"EN":68,"VI":68},{"VI":70,"EN":71},[74,75],[78],{"id":80,"indexDatabase":489,"url":93,"indexYears":94,"academicFieldIds":494,"indexDatabaseRanking":97},{"id":82,"createTime":83,"updateTime":84,"relativeEntities":490,"label":491,"description":492,"key":90,"publicationTags":493,"standard":24},[],{"EN":87,"VI":87},{"EN":87,"VI":89},[92],[96],{"volume":496,"pages":498,"issue":500},{"VOID":497},"127",{"VOID":499},"935-946",{"VOID":501},"5",182,{"total":502,"publishYear":24,"statisticByYear":504},{"2012":505,"2013":506,"2014":507,"2015":508,"2016":509,"2017":505,"2018":510,"2019":325,"2020":508,"2021":325,"2022":325,"2023":405,"2024":508},8,7,11,14,16,6,"1997-01-01",1997,[514,518,521,524,527],{"id":24,"text":515,"url":24,"identifiers":516},"Majda, 1986, Vorticity and the mathematical theory of incompressible fluid flow, 10.1002\u002Fcpa.3160390711",{"doi":517},"10.1002\u002Fcpa.3160390711",{"id":24,"text":519,"url":24,"identifiers":520},"Ohkitani, 1997, Some mathematical aspects of 2D vortex dynamics. Proc. Miniconference of Partial Differential Equations and Applications, RIM-GARC Lecture Note Ser., 38, 35",{},{"id":24,"text":522,"url":24,"identifiers":523},"10.1007\u002FBF01212349",{"doi":522},{"id":24,"text":525,"url":24,"identifiers":526},"10.1002\u002Fcpa.3160410704",{"doi":525},{"id":24,"text":528,"url":24,"identifiers":529},"Weinan, 1994, Small-scale structures in Boussinesq convection, Phys. Fluids, 6, 49, 10.1063\u002F1.868044",{"doi":530},"10.1063\u002F1.868044",{"id":532,"createTime":533,"updateTime":533,"relativeEntities":534,"slug":535,"properties":536,"entityType":120,"verifyStatus":121,"verifyTime":533,"verifyNote":122,"syncStatus":23,"languages":548,"translateLanguages":24,"viewCount":25,"primaryUrl":549,"fullTextUrl":24,"authors":550,"publicationType":191,"publisherRelationship":573,"citationCount":606,"citationInfo":607,"publishDate":611,"publishYear":612,"citationAnalyzeStatus":23,"lastCitationAnalyze":24,"indexDatabases":24,"openAccess":24,"references":613,"isForceReanalyzing":231},"10330b5c-cdbb-4d20-9bec-fb0876c0b247","2024-09-03T22:34:06.424+00:00",[],"Using-Melnikov-s-method-to-solve-Silnikov-s-problems",{"mag":537,"keywords":539,"openalex":540,"abstract":542,"title":544,"doi":546},{"VOID":538},"2040995216",{},{"VOID":541},"W2040995216",{"EN":543},"\u003Cjats:title>Synopsis\u003C\u002Fjats:title>\u003Cjats:p>A function space approach is employed to obtain bifurcation functions for which the zeros correspond to the occurrence of periodic or aperiodic solutions near heteroclinic or homoclinic cycles. The bifurcation function for the existence of homoclinic solutions is the limiting case where the period is infinite. Examples include generalisations of Silnikov's main theorems and a retreatment of a singularly perturbed delay differential equation.\u003C\u002Fjats:p>",{"EN":545},"Using Melnikov's method to solve Silnikov's problems",{"VOID":547},"10.1017\u002Fs0308210500031528",[124],"https:\u002F\u002Fwww.cambridge.org\u002Fcore\u002Fproduct\u002Fidentifier\u002FS0308210500031528\u002Ftype\u002Fjournal_article",[551],{"id":552,"sortIndex":25,"researcher":24,"roles":553,"affiliations":554,"properties":566},"373ae10a-e382-4bc0-be06-287612d2094a",[],[555],{"id":556,"sortIndex":25,"affiliation":557,"properties":24},"10eb720a-d0e8-454e-88a2-7e1331433ac3",{"id":558,"createTime":559,"updateTime":560,"relativeEntities":561,"slug":562,"properties":563,"entityType":45,"verifyStatus":23,"verifyTime":24,"verifyNote":24,"syncStatus":23,"languages":24,"translateLanguages":24,"viewCount":25},"979c468c-1fa6-4666-a011-a3de8d460892","2024-01-04T14:42:37.264+00:00","2024-09-03T22:34:06.437+00:00",[],"Department-of-Mathematics-North-Carolina-State-University-Raleigh-North-Carolina-27695-8205-U-S-A-",{"title":564},{"VI":565},"Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205 U.S.A.",{"openalex":567,"orcid":569,"title":571},{"VOID":568},"A5101764662",{"VOID":570},"https:\u002F\u002Forcid.org\u002F0000-0001-6572-5545",{"EN":572},"Xiao-Biao Lin",{"url":24,"publisher":574,"properties":599},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":575,"slug":10,"properties":576,"entityType":22,"verifyStatus":23,"verifyTime":24,"verifyNote":24,"syncStatus":23,"languages":24,"translateLanguages":24,"viewCount":25,"subjectFields":582,"manageAffiliations":583,"indexDatabases":584,"url":98,"thumbnailPath":24,"statistic":24,"gsStatistic":24,"type":24,"analyzePriority":24},[],{"country":577,"issn":578,"introduce":579,"eissn":580,"title":581},{"VOID":13},{"VOID":15},{"EN":17},{"VOID":19},{"EN":21},[],[],[585,592],{"id":61,"indexDatabase":586,"url":76,"indexYears":24,"academicFieldIds":591,"indexDatabaseRanking":24},{"id":63,"createTime":64,"updateTime":65,"relativeEntities":587,"label":588,"description":589,"key":72,"publicationTags":590,"standard":24},[],{"EN":68,"VI":68},{"VI":70,"EN":71},[74,75],[78],{"id":80,"indexDatabase":593,"url":93,"indexYears":94,"academicFieldIds":598,"indexDatabaseRanking":97},{"id":82,"createTime":83,"updateTime":84,"relativeEntities":594,"label":595,"description":596,"key":90,"publicationTags":597,"standard":24},[],{"EN":87,"VI":87},{"EN":87,"VI":89},[92],[96],{"volume":600,"pages":602,"issue":604},{"VOID":601},"116",{"VOID":603},"295-325",{"VOID":605},"3-4",157,{"total":606,"publishYear":24,"statisticByYear":608},{"2012":510,"2013":609,"2014":609,"2015":46,"2016":505,"2017":609,"2018":610,"2019":46,"2020":610,"2021":609,"2022":609,"2023":506,"2024":610},4,5,"1990-01-01",1990,[614,617,620,623,626,629,632,635,638,641,644,647,650,653,656,659,662,665,668,671,674,677,680,683,686,689,692,695,698],{"id":24,"text":615,"url":24,"identifiers":616},"10.1016\u002F0022-0396(84)90082-2",{"doi":615},{"id":24,"text":618,"url":24,"identifiers":619},"4 Chow S. N. , Deng B. and Fiedler B. . Homoclinic bifurcations at resonant eigenvalues (preprint).",{},{"id":24,"text":621,"url":24,"identifiers":622},"Hartman, 1964, Ordinary Differential Equations",{},{"id":24,"text":624,"url":24,"identifiers":625},"10.1007\u002F978-3-642-86458-2_37",{"doi":624},{"id":24,"text":627,"url":24,"identifiers":628},"10.1007\u002F978-1-4612-9892-2",{"doi":627},{"id":24,"text":630,"url":24,"identifiers":631},"Bohr, 1951, Almost Periodic Functions",{},{"id":24,"text":633,"url":24,"identifiers":634},"10.1007\u002FBF01048789",{"doi":633},{"id":24,"text":636,"url":24,"identifiers":637},"10.1090\u002Fpspum\u002F045.2\u002F843604",{"doi":636},{"id":24,"text":639,"url":24,"identifiers":640},"5 Chow S. N. , Deng B. and Terman D. . The bifurcation of a homoclinic orbit from two heteroclinic orbits—a topological approach (preprint).",{},{"id":24,"text":642,"url":24,"identifiers":643},"10.1016\u002FS0196-8858(82)80012-2",{"doi":642},{"id":24,"text":645,"url":24,"identifiers":646},"Silnikov, 1965, A case of the existence of a countable number of periodic motions, Soviet Math. Dokl., 6, 163",{},{"id":24,"text":648,"url":24,"identifiers":649},"6 Chow S. N. , Deng B. and Terman D. . The bifurcation of a homoclinic and a periodic orbit from two heteroclinic orbits—an analytic approach. SIAM J. App. Math. (to appear).",{},{"id":24,"text":651,"url":24,"identifiers":652},"10.1007\u002FBF01790539",{"doi":651},{"id":24,"text":654,"url":24,"identifiers":655},"10.1016\u002F0022-0396(87)90034-9",{"doi":654},{"id":24,"text":657,"url":24,"identifiers":658},"10.1017\u002FS0308210500018916",{"doi":657},{"id":24,"text":660,"url":24,"identifiers":661},"3 Chow S. N. and Deng B. . Homoclinic and heteroclinic bifurcation in Banach spaces (preprint).",{},{"id":24,"text":663,"url":24,"identifiers":664},"10.1016\u002F0022-0396(80)90104-7",{"doi":663},{"id":24,"text":666,"url":24,"identifiers":667},"Schwartz, 1969, Nonlinear Functional Analysis",{},{"id":24,"text":669,"url":24,"identifiers":670},"10.1016\u002F0022-0396(86)90032-X",{"doi":669},{"id":24,"text":672,"url":24,"identifiers":673},"Hartman, 1960, On local homeomorphisms of Euclidean spaces, Bol. Soc. Mat. Mexicana, 5, 220",{},{"id":24,"text":675,"url":24,"identifiers":676},"10.1016\u002F0022-0396(86)90048-3",{"doi":675},{"id":24,"text":678,"url":24,"identifiers":679},"Guckenheimer, 1983, Applied Mathematical Sciences, 42",{},{"id":24,"text":681,"url":24,"identifiers":682},"Schecter, 1971, Principles of functional analysis",{},{"id":24,"text":684,"url":24,"identifiers":685},"Silnikov, 1967, The existence of a denumerable set of periodic motions in four-dimensional space in an extended neighborhood of a saddle-focus, Soviet Math. Dokl., 8, 54",{},{"id":24,"text":687,"url":24,"identifiers":688},"10.1070\u002FSM1968v006n03ABEH001069",{"doi":687},{"id":24,"text":690,"url":24,"identifiers":691},"10.1070\u002FSM1970v010n01ABEH001588",{"doi":690},{"id":24,"text":693,"url":24,"identifiers":694},"10.1007\u002FBFb0103264",{"doi":693},{"id":24,"text":696,"url":24,"identifiers":697},"10.1007\u002FBF03167912",{"doi":696},{"id":24,"text":699,"url":24,"identifiers":700},"10.1016\u002F0022-0396(86)90043-4",{"doi":699},{"id":702,"createTime":703,"updateTime":703,"relativeEntities":704,"slug":705,"properties":706,"entityType":120,"verifyStatus":121,"verifyTime":703,"verifyNote":122,"syncStatus":23,"languages":718,"translateLanguages":24,"viewCount":25,"primaryUrl":719,"fullTextUrl":24,"authors":720,"publicationType":191,"publisherRelationship":761,"citationCount":793,"citationInfo":794,"publishDate":796,"publishYear":797,"citationAnalyzeStatus":23,"lastCitationAnalyze":24,"indexDatabases":24,"openAccess":24,"references":798,"isForceReanalyzing":231},"cb01abca-0fcc-448a-9603-59bf18b278b0","2024-10-06T22:20:11.401+00:00",[],"Symmetry-for-elliptic-equations-in-a-half-space-without-strong-maximum-principle",{"mag":707,"keywords":709,"openalex":710,"abstract":712,"title":714,"doi":716},{"VOID":708},"1966586731",{},{"VOID":711},"W1966586731",{"EN":713},"\u003Cjats:p>For a wide class of nonlinearities \u003Cjats:italic>f\u003C\u002Fjats:italic>(\u003Cjats:italic>u\u003C\u002Fjats:italic>) satisfying\n\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=\"S0308210500003218disp001\" \u002F>\u003C\u002Fjats:disp-formula>\nbut not necessarily Lipschitz continuous, we study the quasi-linear equation\n\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=\"S0308210500003218disp002\" \u002F>\u003C\u002Fjats:disp-formula>\nwhere \u003Cjats:italic>T\u003C\u002Fjats:italic> = {\u003Cjats:italic>x\u003C\u002Fjats:italic> = (\u003Cjats:italic>x\u003C\u002Fjats:italic>\u003Cjats:sub>1\u003C\u002Fjats:sub>, \u003Cjats:italic>x\u003C\u002Fjats:italic>\u003Cjats:sub>2\u003C\u002Fjats:sub>, …, \u003Cjats:italic>x\u003Cjats:sub>N\u003C\u002Fjats:sub>\u003C\u002Fjats:italic>) ∈ R\u003Cjats:sup>\u003Cjats:italic>N\u003C\u002Fjats:italic>\u003C\u002Fjats:sup>: \u003Cjats:italic>x\u003C\u002Fjats:italic>\u003Cjats:sub>1\u003C\u002Fjats:sub> > 0} with \u003Cjats:italic>N\u003C\u002Fjats:italic> ≥ 2. By using a new approach based on the weak maximum principle, we show that any positive solution on \u003Cjats:italic>T\u003C\u002Fjats:italic> must be a function of \u003Cjats:italic>x\u003C\u002Fjats:italic>\u003Cjats:sub>1\u003C\u002Fjats:sub> only. Under our assumptions, the strong maximum principle does not hold in general and the solution may develop a flat core; our symmetry result allows an easy and precise determination of the flat core.\u003C\u002Fjats:p>",{"EN":715},"Symmetry for elliptic equations in a half-space without strong maximum principle",{"VOID":717},"10.1017\u002Fs0308210500003218",[124],"https:\u002F\u002Fwww.cambridge.org\u002Fcore\u002Fproduct\u002Fidentifier\u002FS0308210500003218\u002Ftype\u002Fjournal_article",[721,740],{"id":722,"sortIndex":170,"researcher":24,"roles":723,"affiliations":724,"properties":735},"592893c3-0123-4e5a-8236-ae109fa21c33",[],[725],{"id":726,"sortIndex":25,"affiliation":727,"properties":24},"e0421641-1215-4713-9186-0adc7baf596d",{"id":728,"createTime":729,"updateTime":729,"relativeEntities":730,"slug":731,"properties":732,"entityType":45,"verifyStatus":23,"verifyTime":24,"verifyNote":24,"syncStatus":23,"languages":24,"translateLanguages":24,"viewCount":25},"a8ccfe7e-229e-4e06-98b6-b6605e0ecdd2","2024-10-06T22:20:11.432+00:00",[],"Department-of-Mathematics-Dong-Hua-University-Shanghai-200051-People-s-Republic-of-China-guozm-public-xxptt-ha-cn",{"title":733},{"EN":734},"Department of Mathematics, Dong Hua University, Shanghai 200051, People's Republic of China (guozm@public.xxptt.ha.cn",{"openalex":736,"title":738},{"VOID":737},"A5103530644",{"EN":739},"Zongming Guo",{"id":741,"sortIndex":25,"researcher":24,"roles":742,"affiliations":743,"properties":754},"f85eaedc-8a71-453c-8f3c-13d6f83be1f9",[],[744],{"id":745,"sortIndex":25,"affiliation":746,"properties":24},"9e9870c6-e175-4d7e-871f-808596eb00e3",{"id":747,"createTime":748,"updateTime":748,"relativeEntities":749,"slug":750,"properties":751,"entityType":45,"verifyStatus":23,"verifyTime":24,"verifyNote":24,"syncStatus":23,"languages":24,"translateLanguages":24,"viewCount":25},"fd054fd5-03ef-402f-b940-1ea5c1494a7d","2024-10-06T22:20:11.421+00:00",[],"School-of-Mathematics-Statistics-and-Computer-Science-University-of-New-England-Armidale-NSW-2351-Australia-ydu-turing-une-edu-au",{"title":752},{"EN":753},"School of Mathematics, Statistics and Computer Science, University of New England, Armidale, NSW 2351, Australia (ydu@turing.une.edu.au",{"openalex":755,"orcid":757,"title":759},{"VOID":756},"A5087725227",{"VOID":758},"https:\u002F\u002Forcid.org\u002F0000-0002-1235-0636",{"EN":760},"Yihong Du",{"url":24,"publisher":762,"properties":787},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":763,"slug":10,"properties":764,"entityType":22,"verifyStatus":23,"verifyTime":24,"verifyNote":24,"syncStatus":23,"languages":24,"translateLanguages":24,"viewCount":25,"subjectFields":770,"manageAffiliations":771,"indexDatabases":772,"url":98,"thumbnailPath":24,"statistic":24,"gsStatistic":24,"type":24,"analyzePriority":24},[],{"country":765,"issn":766,"introduce":767,"eissn":768,"title":769},{"VOID":13},{"VOID":15},{"EN":17},{"VOID":19},{"EN":21},[],[],[773,780],{"id":61,"indexDatabase":774,"url":76,"indexYears":24,"academicFieldIds":779,"indexDatabaseRanking":24},{"id":63,"createTime":64,"updateTime":65,"relativeEntities":775,"label":776,"description":777,"key":72,"publicationTags":778,"standard":24},[],{"EN":68,"VI":68},{"VI":70,"EN":71},[74,75],[78],{"id":80,"indexDatabase":781,"url":93,"indexYears":94,"academicFieldIds":786,"indexDatabaseRanking":97},{"id":82,"createTime":83,"updateTime":84,"relativeEntities":782,"label":783,"description":784,"key":90,"publicationTags":785,"standard":24},[],{"EN":87,"VI":87},{"EN":87,"VI":89},[92],[96],{"volume":788,"pages":790,"issue":792},{"VOID":789},"134",{"VOID":791},"259-269",{"VOID":324},22,{"total":793,"publishYear":24,"statisticByYear":795},{"2012":170,"2013":609,"2014":170,"2015":57,"2018":46,"2019":170,"2021":170,"2022":46,"2023":46,"2024":170},"2004-04-01",2004,[],{"id":800,"createTime":801,"updateTime":801,"relativeEntities":802,"slug":803,"properties":804,"entityType":120,"verifyStatus":23,"verifyTime":801,"verifyNote":816,"syncStatus":23,"languages":817,"translateLanguages":24,"viewCount":25,"primaryUrl":818,"fullTextUrl":24,"authors":819,"publicationType":191,"publisherRelationship":831,"citationCount":864,"citationInfo":865,"publishDate":867,"publishYear":868,"citationAnalyzeStatus":23,"lastCitationAnalyze":24,"indexDatabases":24,"openAccess":24,"references":869,"isForceReanalyzing":231},"75c34b89-dffe-4f84-be37-68ae37f96d02","2024-10-03T19:18:33.377+00:00",[],"A-deletion-contraction-algorithm-for-the-characteristic-polynomial-of-a-multigraph",{"mag":805,"keywords":807,"openalex":808,"abstract":810,"title":812,"doi":814},{"VOID":806},"2325736576",{},{"VOID":809},"W2325736576",{"EN":811},"\u003Cjats:title>Synopsis\u003C\u002Fjats:title>\u003Cjats:p>The characteristic polynomial of a finite multigraph \u003Cjats:italic>G\u003C\u002Fjats:italic> is expressed in terms of characteristic polynomials oflocal modifications of \u003Cjats:italic>G\u003C\u002Fjats:italic>. The resulting formula is used to investigate the largest eigenvalues of certain theta graphs.\u003C\u002Fjats:p>",{"EN":813},"A deletion-contraction algorithm for the characteristic polynomial of a multigraph",{"VOID":815},"10.1017\u002Fs0308210500021983","Author affiliation is blank",[124],"https:\u002F\u002Fwww.cambridge.org\u002Fcore\u002Fproduct\u002Fidentifier\u002FS0308210500021983\u002Ftype\u002Fjournal_article",[820],{"id":821,"sortIndex":25,"researcher":24,"roles":822,"affiliations":823,"properties":824},"cf94037a-3cec-4696-a4e6-81a981832cf9",[],[],{"openalex":825,"orcid":827,"title":829},{"VOID":826},"A5084840125",{"VOID":828},"https:\u002F\u002Forcid.org\u002F0000-0003-4878-3203",{"EN":830},"Peter Rowlinson",{"url":24,"publisher":832,"properties":857},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":833,"slug":10,"properties":834,"entityType":22,"verifyStatus":23,"verifyTime":24,"verifyNote":24,"syncStatus":23,"languages":24,"translateLanguages":24,"viewCount":25,"subjectFields":840,"manageAffiliations":841,"indexDatabases":842,"url":98,"thumbnailPath":24,"statistic":24,"gsStatistic":24,"type":24,"analyzePriority":24},[],{"country":835,"issn":836,"introduce":837,"eissn":838,"title":839},{"VOID":13},{"VOID":15},{"EN":17},{"VOID":19},{"EN":21},[],[],[843,850],{"id":61,"indexDatabase":844,"url":76,"indexYears":24,"academicFieldIds":849,"indexDatabaseRanking":24},{"id":63,"createTime":64,"updateTime":65,"relativeEntities":845,"label":846,"description":847,"key":72,"publicationTags":848,"standard":24},[],{"EN":68,"VI":68},{"VI":70,"EN":71},[74,75],[78],{"id":80,"indexDatabase":851,"url":93,"indexYears":94,"academicFieldIds":856,"indexDatabaseRanking":97},{"id":82,"createTime":83,"updateTime":84,"relativeEntities":852,"label":853,"description":854,"key":90,"publicationTags":855,"standard":24},[],{"EN":87,"VI":87},{"EN":87,"VI":89},[92],[96],{"volume":858,"pages":860,"issue":862},{"VOID":859},"105",{"VOID":861},"153-160",{"VOID":863},"1",18,{"total":864,"publishYear":24,"statisticByYear":866},{"2012":170,"2015":170,"2016":170,"2017":170,"2018":170,"2021":170},"1987-01-01",1987,[870,873,876,879,882,885,888,891],{"id":24,"text":871,"url":24,"identifiers":872},"Cvetković, 1986, Recent Results in the Theory of Graph Spectra",{},{"id":24,"text":874,"url":24,"identifiers":875},"Sachs, 1985, Graphs, Hypergraphs and Applications, 73",{},{"id":24,"text":877,"url":24,"identifiers":878},"Cvetković, 1979, Spectra of Graphs",{},{"id":24,"text":880,"url":24,"identifiers":881},"Woodall, 1977, Combinatorial Surveys, 199",{},{"id":24,"text":883,"url":24,"identifiers":884},"Wilson, 1979, Applications of Graph Theory",{},{"id":24,"text":886,"url":24,"identifiers":887},"10.1090\u002FS0002-9947-1946-0018401-4",{"doi":886},{"id":24,"text":889,"url":24,"identifiers":890},"10.1002\u002Fhlca.19530360125",{"doi":889},{"id":24,"text":892,"url":24,"identifiers":893},"Schwenk, 1974, Lecture Notes in Mathematics, 406, 153",{},{"id":895,"createTime":896,"updateTime":896,"relativeEntities":897,"slug":898,"properties":899,"entityType":120,"verifyStatus":121,"verifyTime":896,"verifyNote":122,"syncStatus":23,"languages":911,"translateLanguages":24,"viewCount":25,"primaryUrl":912,"fullTextUrl":24,"authors":913,"publicationType":191,"publisherRelationship":953,"citationCount":985,"citationInfo":986,"publishDate":990,"publishYear":991,"citationAnalyzeStatus":23,"lastCitationAnalyze":24,"indexDatabases":24,"openAccess":24,"references":992,"isForceReanalyzing":231},"3a8ed155-232b-4c35-a62a-ce52b0fc983d","2024-10-03T16:21:42.340+00:00",[],"The-bond-based-peridynamic-system-with-Dirichlet-type-volume-constraint",{"mag":900,"keywords":902,"openalex":903,"abstract":905,"title":907,"doi":909},{"VOID":901},"2063253250",{},{"VOID":904},"W2063253250",{"EN":906},"\u003Cjats:p>In this paper, the bond-based peridynamic system is analysed as a non-local boundary-value problem with volume constraint. The study extends earlier works in the literature on non-local diffusion and non-local peridynamic models, to include non-positive definite kernels. We prove the well-posedness of both linear and nonlinear variational problems with volume constraints. The analysis is based on some non-local Poincaré-type inequalities and the compactness of the associated non-local operators. It also offers careful characterizations of the associated solution spaces, such as compact embedding, separability and completeness. 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The ratio between the coefficients of the elasticity tensor of the two materials is assumed to be 1\u002F\u003Cjats:italic>ε\u003C\u002Fjats:italic>\u003Cjats:sup>4\u003C\u002Fjats:sup>. 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This relationship may be useful in explaining the difference between the nonresonance of singular and nonsingular differential equations. 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