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R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2019,12,19]]},"reference":[{"key":"2023033119370865500_j_gmj-2019-2073_ref_001_w2aab3b7e1160b1b6b1ab2ab1Aa","doi-asserted-by":"crossref","unstructured":"J.-F.  Chen,\nUniqueness of meromorphic functions sharing two finite sets,\nOpen Math. 15 (2017), no. 1, 1244\u20131250.","DOI":"10.1515\/math-2017-0102"},{"key":"2023033119370865500_j_gmj-2019-2073_ref_002_w2aab3b7e1160b1b6b1ab2ab2Aa","doi-asserted-by":"crossref","unstructured":"J. B.  Conway,\nFunctions of one Complex Variable,\nGrad. Texts in Math. 11,\nSpringer, New York, 1973.","DOI":"10.1007\/978-1-4615-9972-2_2"},{"key":"2023033119370865500_j_gmj-2019-2073_ref_003_w2aab3b7e1160b1b6b1ab2ab3Aa","doi-asserted-by":"crossref","unstructured":"W.  Doeringer,\nExceptional values of differential polynomials,\nPacific J. Math. 98 (1982), no. 1, 55\u201362.","DOI":"10.2140\/pjm.1982.98.55"},{"key":"2023033119370865500_j_gmj-2019-2073_ref_004_w2aab3b7e1160b1b6b1ab2ab4Aa","unstructured":"M.  Fang and W.  Xu,\nOn the uniqueness of entire functions,\nBull. Malaysian Math. Soc. (2) 19 (1996), no. 1, 29\u201337."},{"key":"2023033119370865500_j_gmj-2019-2073_ref_005_w2aab3b7e1160b1b6b1ab2ab5Aa","doi-asserted-by":"crossref","unstructured":"M.-L.  Fang and H.  Guo,\nOn meromorphic functions sharing two values,\nAnalysis 17 (1997), no. 4, 355\u2013366.","DOI":"10.1524\/anly.1997.17.4.355"},{"key":"2023033119370865500_j_gmj-2019-2073_ref_006_w2aab3b7e1160b1b6b1ab2ab6Aa","doi-asserted-by":"crossref","unstructured":"G.  Frank and M.  Reinders,\nA unique range set for meromorphic functions with 11 elements,\nComplex Variables Theory Appl. 37 (1998), no. 1\u20134, 185\u2013193.","DOI":"10.1080\/17476939808815132"},{"key":"2023033119370865500_j_gmj-2019-2073_ref_007_w2aab3b7e1160b1b6b1ab2ab7Aa","doi-asserted-by":"crossref","unstructured":"H.  Fujimoto,\nOn uniqueness of meromorphic functions sharing finite sets,\nAmer. J. Math. 122 (2000), no. 6, 1175\u20131203.","DOI":"10.1353\/ajm.2000.0045"},{"key":"2023033119370865500_j_gmj-2019-2073_ref_008_w2aab3b7e1160b1b6b1ab2ab8Aa","doi-asserted-by":"crossref","unstructured":"F.  Gross,\nFactorization of meromorphic functions and some open problems,\nComplex Analysis (Lexington 1976),\nLecture Notes in Math. 599,\nSpringer, Berlin (1977), 51\u201367.","DOI":"10.1007\/BFb0096825"},{"key":"2023033119370865500_j_gmj-2019-2073_ref_009_w2aab3b7e1160b1b6b1ab2ab9Aa","unstructured":"W. K.  Hayman,\nMeromorphic Functions,\nOxford Math. Monogr.,\nClarendon Press, Oxford, 1964."},{"key":"2023033119370865500_j_gmj-2019-2073_ref_010_w2aab3b7e1160b1b6b1ab2ac10Aa","doi-asserted-by":"crossref","unstructured":"P.  Li and C.-C.  Yang,\nSome further results on the unique range sets of meromorphic functions,\nKodai Math. J. 18 (1995), no. 3, 437\u2013450.","DOI":"10.2996\/kmj\/1138043482"},{"key":"2023033119370865500_j_gmj-2019-2073_ref_011_w2aab3b7e1160b1b6b1ab2ac11Aa","doi-asserted-by":"crossref","unstructured":"P.  Li and C.-C.  Yang,\nOn the unique range set of meromorphic functions,\nProc. Amer. Math. Soc. 124 (1996), no. 1, 177\u2013185.","DOI":"10.1090\/S0002-9939-96-03045-6"},{"key":"2023033119370865500_j_gmj-2019-2073_ref_012_w2aab3b7e1160b1b6b1ab2ac12Aa","doi-asserted-by":"crossref","unstructured":"E.  Mues and M.  Reinders,\nMeromorphic functions sharing one value and unique range sets,\nKodai Math. J. 18 (1995), no. 3, 515\u2013522.","DOI":"10.2996\/kmj\/1138043489"},{"key":"2023033119370865500_j_gmj-2019-2073_ref_013_w2aab3b7e1160b1b6b1ab2ac13Aa","doi-asserted-by":"crossref","unstructured":"C.-C.  Yang and H.-X.  Yi,\nUniqueness Theory of Meromorphic Functions,\nMath. Appl. 557,\nKluwer Academicp, Dordrecht, 2003.","DOI":"10.1007\/978-94-017-3626-8"},{"key":"2023033119370865500_j_gmj-2019-2073_ref_014_w2aab3b7e1160b1b6b1ab2ac14Aa","doi-asserted-by":"crossref","unstructured":"L.-Z.  Yang,\nMeromorphic functions that share two values,\nJ. Math. Anal. Appl. 209 (1997), no. 2, 542\u2013550.","DOI":"10.1006\/jmaa.1997.5329"},{"key":"2023033119370865500_j_gmj-2019-2073_ref_015_w2aab3b7e1160b1b6b1ab2ac15Aa","unstructured":"B.  Yi and Y. H.  Li,\nUniqueness of meromorphic functions that share two sets with CM,\nActa Math. Sinica (Chin. Ser.) 55 (2012), no. 2, 363\u2013368."},{"key":"2023033119370865500_j_gmj-2019-2073_ref_016_w2aab3b7e1160b1b6b1ab2ac16Aa","unstructured":"H. X.  Yi,\nUniqueness of meromorphic functions and question of Gross,\nSci. China Ser. A 37 (1994), no. 7, 802\u2013813."},{"key":"2023033119370865500_j_gmj-2019-2073_ref_017_w2aab3b7e1160b1b6b1ab2ac17Aa","doi-asserted-by":"crossref","unstructured":"H. X.  Yi,\nUnicity theorems for meromorphic or entire functions. II,\nBull. Aust. Math. Soc. 52 (1995), no. 2, 215\u2013224.","DOI":"10.1017\/S0004972700014635"},{"key":"2023033119370865500_j_gmj-2019-2073_ref_018_w2aab3b7e1160b1b6b1ab2ac18Aa","doi-asserted-by":"crossref","unstructured":"H.-X.  Yi,\nOn a question of Gross concerning uniqueness of entire functions,\nBull. Aust. Math. Soc. 57 (1998), no. 2, 343\u2013349.","DOI":"10.1017\/S0004972700031701"},{"key":"2023033119370865500_j_gmj-2019-2073_ref_019_w2aab3b7e1160b1b6b1ab2ac19Aa","unstructured":"H. X.  Yi,\nMeromorphic functions that share two sets,\nActa Math. Sinica (Chin. Ser.) 45 (2002), no. 1, 75\u201382."}],"container-title":["Georgian Mathematical Journal"],"language":"en","link":[{"URL":"http:\/\/www.degruyter.com\/view\/j\/gmj.ahead-of-print\/gmj-2019-2073\/gmj-2019-2073.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/gmj-2019-2073\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/gmj-2019-2073\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T07:22:02Z","timestamp":1680333722000},"score":0.0,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/gmj-2019-2073\/html"}},"issued":{"date-parts":[[2019,12,19]]},"references-count":19,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,11,7]]},"published-print":{"date-parts":[[2021,6,1]]}},"alternative-id":["10.1515\/gmj-2019-2073"],"URL":"https:\/\/doi.org\/10.1515\/gmj-2019-2073","ISSN":["1572-9176","1072-947X"],"issn-type":[{"value":"1572-9176","type":"electronic"},{"value":"1072-947X","type":"print"}],"published":{"date-parts":[[2019,12,19]]}},{"indexed":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T08:40:51Z","timestamp":1680338451022},"reference-count":5,"publisher":"Walter de Gruyter GmbH","issue":"2","funder":[{"DOI":"10.13039\/501100004801","name":"Shota Rustaveli National Science Foundation","doi-asserted-by":"publisher","award":["217-614"],"award-info":[{"award-number":["217-614"]}],"id":[{"id":"10.13039\/501100004801","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"published-print":{"date-parts":[[2019,6,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Let <jats:inline-formula id=\"j_gmj-2019-2016_ineq_9999_w2aab3b7b6b1b6b1aab1c16b1b1Aa\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mi>Y<\/m:mi>\n                              <m:mo>=<\/m:mo>\n                              <m:mrow>\n                                 <m:mo>|<\/m:mo>\n                                 <m:mi>X<\/m:mi>\n                                 <m:mo>|<\/m:mo>\n                              <\/m:mrow>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_gmj-2019-2016_eq_0104.png\" \/>\n                        <jats:tex-math>{Y=\\lvert X\\rvert}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> be the geometric realization of a path-connected simplicial set <jats:italic>X<\/jats:italic>, and let <jats:inline-formula id=\"j_gmj-2019-2016_ineq_9998_w2aab3b7b6b1b6b1aab1c16b1b5Aa\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mi>G<\/m:mi>\n                              <m:mo>=<\/m:mo>\n                              <m:mrow>\n                                 <m:msub>\n                                    <m:mi>\u03c0<\/m:mi>\n                                    <m:mn>1<\/m:mn>\n                                 <\/m:msub>\n                                 <m:mo>\u2062<\/m:mo>\n                                 <m:mrow>\n                                    <m:mo>(<\/m:mo>\n                                    <m:mi>X<\/m:mi>\n                                    <m:mo>)<\/m:mo>\n                                 <\/m:mrow>\n                              <\/m:mrow>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_gmj-2019-2016_eq_0079.png\" \/>\n                        <jats:tex-math>{G=\\pi_{1}(X)}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> be the fundamental group.\nGiven a subgroup <jats:inline-formula id=\"j_gmj-2019-2016_ineq_9997_w2aab3b7b6b1b6b1aab1c16b1b7Aa\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mi>H<\/m:mi>\n                              <m:mo>\u2282<\/m:mo>\n                              <m:mi>G<\/m:mi>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_gmj-2019-2016_eq_0084.png\" \/>\n                        <jats:tex-math>{H\\subset G}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>, let <jats:inline-formula id=\"j_gmj-2019-2016_ineq_9996_w2aab3b7b6b1b6b1aab1c16b1b9Aa\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mi>G<\/m:mi>\n                              <m:mo>\/<\/m:mo>\n                              <m:mi>H<\/m:mi>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_gmj-2019-2016_eq_0078.png\" \/>\n                        <jats:tex-math>{G\/H}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> be the set of cosets.\nUsing the combinatorial model <jats:inline-formula id=\"j_gmj-2019-2016_ineq_9995_w2aab3b7b6b1b6b1aab1c16b1c11Aa\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mrow>\n                                 <m:mi>\ud835\udec0<\/m:mi>\n                                 <m:mo>\u2062<\/m:mo>\n                                 <m:mi>X<\/m:mi>\n                              <\/m:mrow>\n                              <m:mo>\u2192<\/m:mo>\n                              <m:mrow>\n                                 <m:mi>\ud835\udc0f<\/m:mi>\n                                 <m:mo>\u2062<\/m:mo>\n                                 <m:mi>X<\/m:mi>\n                              <\/m:mrow>\n                              <m:mo>\u2192<\/m:mo>\n                              <m:mi>X<\/m:mi>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_gmj-2019-2016_eq_0124.png\" \/>\n                        <jats:tex-math>{\\boldsymbol{\\Omega}X\\to\\mathbf{P}X\\to X}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> of the path fibration <jats:inline-formula id=\"j_gmj-2019-2016_ineq_9994_w2aab3b7b6b1b6b1aab1c16b1c13Aa\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mrow>\n                                 <m:mi>\u03a9<\/m:mi>\n                                 <m:mo>\u2062<\/m:mo>\n                                 <m:mi>Y<\/m:mi>\n                              <\/m:mrow>\n                              <m:mo>\u2192<\/m:mo>\n                              <m:mrow>\n                                 <m:mi>P<\/m:mi>\n                                 <m:mo>\u2062<\/m:mo>\n                                 <m:mi>Y<\/m:mi>\n                              <\/m:mrow>\n                              <m:mo>\u2192<\/m:mo>\n                              <m:mi>Y<\/m:mi>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_gmj-2019-2016_eq_0234.png\" \/>\n                        <jats:tex-math>{{\\Omega}Y\\to{P}Y\\to Y}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> and a canonical action <jats:inline-formula id=\"j_gmj-2019-2016_ineq_9993_w2aab3b7b6b1b6b1aab1c16b1c15Aa\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mi>\u03bc<\/m:mi>\n                              <m:mo>:<\/m:mo>\n                              <m:mrow>\n                                 <m:mrow>\n                                    <m:mrow>\n                                       <m:mrow>\n                                          <m:mi>\ud835\udec0<\/m:mi>\n                                          <m:mo>\u2062<\/m:mo>\n                                          <m:mi>X<\/m:mi>\n                                       <\/m:mrow>\n                                       <m:mo>\u00d7<\/m:mo>\n                                       <m:mi>G<\/m:mi>\n                                    <\/m:mrow>\n                                    <m:mo>\/<\/m:mo>\n                                    <m:mi>H<\/m:mi>\n                                 <\/m:mrow>\n                                 <m:mo>\u2192<\/m:mo>\n                                 <m:mrow>\n                                    <m:mi>G<\/m:mi>\n                                    <m:mo>\/<\/m:mo>\n                                    <m:mi>H<\/m:mi>\n                                 <\/m:mrow>\n                              <\/m:mrow>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_gmj-2019-2016_eq_0140.png\" \/>\n                        <jats:tex-math>{\\mu\\colon\\boldsymbol{\\Omega}X\\times G\/H\\to G\/H}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>, we construct a covering map <jats:inline-formula id=\"j_gmj-2019-2016_ineq_9992_w2aab3b7b6b1b6b1aab1c16b1c17Aa\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mrow>\n                                 <m:mi>G<\/m:mi>\n                                 <m:mo>\/<\/m:mo>\n                                 <m:mi>H<\/m:mi>\n                              <\/m:mrow>\n                              <m:mo>\u2192<\/m:mo>\n                              <m:msub>\n                                 <m:mi>Y<\/m:mi>\n                                 <m:mi>H<\/m:mi>\n                              <\/m:msub>\n                              <m:mo>\u2192<\/m:mo>\n                              <m:mi>Y<\/m:mi>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_gmj-2019-2016_eq_0075.png\" \/>\n                        <jats:tex-math>{G\/H\\to Y_{H}\\to Y}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> as the geometric realization of the associated short sequence <jats:inline-formula id=\"j_gmj-2019-2016_ineq_9991_w2aab3b7b6b1b6b1aab1c16b1c19Aa\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mrow>\n                                 <m:mi>G<\/m:mi>\n                                 <m:mo>\/<\/m:mo>\n                                 <m:mi>H<\/m:mi>\n                              <\/m:mrow>\n                              <m:mo>\u2192<\/m:mo>\n                              <m:mrow>\n                                 <m:mrow>\n                                    <m:mrow>\n                                       <m:mi>\ud835\udc0f<\/m:mi>\n                                       <m:mo>\u2062<\/m:mo>\n                                       <m:mi>X<\/m:mi>\n                                    <\/m:mrow>\n                                    <m:msub>\n                                       <m:mo>\u00d7<\/m:mo>\n                                       <m:mi>\u03bc<\/m:mi>\n                                    <\/m:msub>\n                                    <m:mi>G<\/m:mi>\n                                 <\/m:mrow>\n                                 <m:mo>\/<\/m:mo>\n                                 <m:mi>H<\/m:mi>\n                              <\/m:mrow>\n                              <m:mo>\u2192<\/m:mo>\n                              <m:mi>X<\/m:mi>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_gmj-2019-2016_eq_0076.png\" \/>\n                        <jats:tex-math>{G\/H\\to\\mathbf{P}X\\times_{\\mu}G\/H\\to X}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>.\nThis construction, in particular, does not use the existence of a maximal tree in <jats:italic>X<\/jats:italic>.\nFor a 2-dimensional <jats:italic>X<\/jats:italic> and <jats:inline-formula id=\"j_gmj-2019-2016_ineq_9990_w2aab3b7b6b1b6b1aab1c16b1c25Aa\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mi>H<\/m:mi>\n                              <m:mo>=<\/m:mo>\n                              <m:mrow>\n                                 <m:mo>{<\/m:mo>\n                                 <m:mn>1<\/m:mn>\n                                 <m:mo>}<\/m:mo>\n                              <\/m:mrow>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_gmj-2019-2016_eq_0083.png\" \/>\n                        <jats:tex-math>{H=\\{1\\}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>, it can also be viewed as a simplicial approximation of a Cayley 2-complex of <jats:italic>G<\/jats:italic>.<\/jats:p>","DOI":"10.1515\/gmj-2019-2016","type":"journal-article","created":{"date-parts":[[2019,4,7]],"date-time":"2019-04-07T02:48:35Z","timestamp":1554605315000},"page":"303-309","source":"Crossref","is-referenced-by-count":0,"title":["On the construction of a covering map"],"prefix":"10.1515","volume":"26","author":[{"given":"Samson","family":"Saneblidze","sequence":"first","affiliation":[{"name":"A. Razmadze Mathematical Institute , I. Javakhishvili Tbilisi State University , 6 Tamarashvili Str. , Tbilisi 0177 , Georgia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2019,4,6]]},"reference":[{"key":"2023033120034825975_j_gmj-2019-2016_ref_001_w2aab3b7b6b1b6b1ab1b4b1Aa","doi-asserted-by":"crossref","unstructured":"M.  Gromov,\nHomotopical effects of dilatation,\nJ. Differential Geom. 13 (1978), no. 3, 303\u2013310.\n10.4310\/jdg\/1214434601","DOI":"10.4310\/jdg\/1214434601"},{"key":"2023033120034825975_j_gmj-2019-2016_ref_002_w2aab3b7b6b1b6b1ab1b4b2Aa","doi-asserted-by":"crossref","unstructured":"T.  Kadeishvili and S.  Saneblidze,\nA cubical model for a fibration,\nJ. Pure Appl. Algebra 196 (2005), no. 2\u20133, 203\u2013228.\n10.1016\/j.jpaa.2004.08.017","DOI":"10.1016\/j.jpaa.2004.08.017"},{"key":"2023033120034825975_j_gmj-2019-2016_ref_003_w2aab3b7b6b1b6b1ab1b4b3Aa","doi-asserted-by":"crossref","unstructured":"R. C.  Lyndon and P. E.  Schupp,\nCombinatorial Group Theory,\nClassics Math.,\nSpringer, Berlin, 2001.","DOI":"10.1007\/978-3-642-61896-3"},{"key":"2023033120034825975_j_gmj-2019-2016_ref_004_w2aab3b7b6b1b6b1ab1b4b4Aa","doi-asserted-by":"crossref","unstructured":"J.  Milnor,\nConstruction of universal bundles. I,\nAnn. of Math. (2) 63 (1956), 272\u2013284.\n10.2307\/1969609","DOI":"10.2307\/1969609"},{"key":"2023033120034825975_j_gmj-2019-2016_ref_005_w2aab3b7b6b1b6b1ab1b4b5Aa","doi-asserted-by":"crossref","unstructured":"M.  Rivera and S.  Saneblidze,\nA combinatorial model for the path fibration,\nJ. Homotopy Relat. Struct. (2018), 10.1007\/s40062-018-0216-4.","DOI":"10.1007\/s40062-018-0216-4"}],"container-title":["Georgian Mathematical Journal"],"language":"en","link":[{"URL":"http:\/\/www.degruyter.com\/view\/j\/gmj.2019.26.issue-2\/gmj-2019-2016\/gmj-2019-2016.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/gmj-2019-2016\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/gmj-2019-2016\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T08:08:07Z","timestamp":1680336487000},"score":0.0,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/gmj-2019-2016\/html"}},"issued":{"date-parts":[[2019,4,6]]},"references-count":5,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,5,16]]},"published-print":{"date-parts":[[2019,6,1]]}},"alternative-id":["10.1515\/gmj-2019-2016"],"URL":"https:\/\/doi.org\/10.1515\/gmj-2019-2016","ISSN":["1572-9176","1072-947X"],"issn-type":[{"value":"1572-9176","type":"electronic"},{"value":"1072-947X","type":"print"}],"published":{"date-parts":[[2019,4,6]]}},{"indexed":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T14:11:18Z","timestamp":1680358278477},"reference-count":34,"publisher":"Walter de Gruyter GmbH","issue":"5","funder":[{"DOI":"10.13039\/501100002261","name":"Russian Foundation for Basic Research","doi-asserted-by":"publisher","award":["17-01-00525"],"award-info":[{"award-number":["17-01-00525"]}],"id":[{"id":"10.13039\/501100002261","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"published-print":{"date-parts":[[2018,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We consider the inverse scattering problem in a layer-homogeneous elastic structure filling a half-plane. Scattering data is the seismic wave field registered on the boundary with a surface point source. We prove that velocities of longitudinal and transverse waves, and a density of the medium are recovered by a unique way. The algorithm of the inverse problem solution is based on the \u03c4-<jats:italic>p<\/jats:italic> Radon transform. Also, we present some results of numerical modeling for waves propagation and solving of the inverse problem.<\/jats:p>","DOI":"10.1515\/jiip-2017-0083","type":"journal-article","created":{"date-parts":[[2018,4,12]],"date-time":"2018-04-12T08:36:51Z","timestamp":1523522211000},"page":"607-622","source":"Crossref","is-referenced-by-count":0,"title":["Solution of the inverse seismic problem in a layered elastic medium by means of the \u03c4-<i>p<\/i> Radon transform"],"prefix":"10.1515","volume":"26","author":[{"given":"Andrey V.","family":"Baev","sequence":"first","affiliation":[{"name":"Lomonosov Moscow State University , Moscow , Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2018,3,13]]},"reference":[{"key":"2023040100065751525_j_jiip-2017-0083_ref_001_w2aab3b7b5b1b6b1ab1b6b1Aa","unstructured":"A. S.  Alekseev and A. G.  Megrabov,\nDirect and inverse scattering problems of plane waves in inhomogeneous layers (in Russian),\nMat. Problemy Geofiz. (1972), no. 3, 8\u201336."},{"key":"2023040100065751525_j_jiip-2017-0083_ref_002_w2aab3b7b5b1b6b1ab1b6b2Aa","doi-asserted-by":"crossref","unstructured":"A. V.  Baev,\nA method of solving the inverse scattering problem for the wave equation,\nComp. Math. Math. Phys. 28 (1988), no. 1, 15\u201321.\n10.1016\/0041-5553(88)90211-X","DOI":"10.1016\/0041-5553(88)90211-X"},{"key":"2023040100065751525_j_jiip-2017-0083_ref_003_w2aab3b7b5b1b6b1ab1b6b3Aa","unstructured":"A. V.  Baev,\nOn the solution of the inverse problem of scattering of a plane wave by a layered-inhomogeneous medium,\nSov. Phys. Dokl. 32 (1988), no. 1, 26\u201328."},{"key":"2023040100065751525_j_jiip-2017-0083_ref_004_w2aab3b7b5b1b6b1ab1b6b4Aa","doi-asserted-by":"crossref","unstructured":"A. V.  Baev,\nOn the solution of the inverse boundary value problem for the wave equation with a discontinuous coefficient,\nComp. Math. Math. Phys. 28 (1988), no. 6, 11\u201321.\n10.1016\/0041-5553(88)90037-7","DOI":"10.1016\/0041-5553(88)90037-7"},{"key":"2023040100065751525_j_jiip-2017-0083_ref_005_w2aab3b7b5b1b6b1ab1b6b5Aa","doi-asserted-by":"crossref","unstructured":"A. V.  Baev,\nOn t-local solvability of inverse scattering problems in two dimensional layered media,\nComp. Math. Math. Phys. 55 (2015), no. 6, 1033\u20131050.\n10.1134\/S0965542515060032","DOI":"10.1134\/S0965542515060032"},{"key":"2023040100065751525_j_jiip-2017-0083_ref_006_w2aab3b7b5b1b6b1ab1b6b6Aa","doi-asserted-by":"crossref","unstructured":"A. V.  Baev,\nSolution of an inverse scattering problem for the acoustic wave equation in three-dimensional media,\nComp. Math. Math. Phys. 56 (2016), no. 12, 15\u201321.","DOI":"10.1134\/S0965542516120034"},{"key":"2023040100065751525_j_jiip-2017-0083_ref_007_w2aab3b7b5b1b6b1ab1b6b7Aa","doi-asserted-by":"crossref","unstructured":"A. V.  Baev and N. V.  Kutsenko,\nSolving the inverse generalized problem of vertical seismic profiling,\nComput. Math. Model. 15 (2004), no. 1, 1\u201318.\n10.1023\/B:COMI.0000011680.61982.4f","DOI":"10.1023\/B:COMI.0000011680.61982.4f"},{"key":"2023040100065751525_j_jiip-2017-0083_ref_008_w2aab3b7b5b1b6b1ab1b6b8Aa","doi-asserted-by":"crossref","unstructured":"A. V.  Baev and N. V.  Kutsenko,\nIdentification of a dissipation coefficient by a variational method,\nComp. Math. Math. Phys. 46 (2006), no. 1, 1796\u20131807.\n10.1134\/S0965542506100150","DOI":"10.1134\/S0965542506100150"},{"key":"2023040100065751525_j_jiip-2017-0083_ref_009_w2aab3b7b5b1b6b1ab1b6b9Aa","doi-asserted-by":"crossref","unstructured":"E. N.  Bessonova, V. M.  Fishman, V. Z.  Ryaboy and G. A.  Sitnikova,\nThe tau method for inversion of travel times 1. Deep seismic sounding data,\nGeophys. J. R. Astron. Soc. 36 (1974), 377\u2013398.\n10.1111\/j.1365-246X.1974.tb03646.x","DOI":"10.1111\/j.1365-246X.1974.tb03646.x"},{"key":"2023040100065751525_j_jiip-2017-0083_ref_010_w2aab3b7b5b1b6b1ab1b6c10Aa","unstructured":"A. S.  Blagoveshchenskii,\nOn local method for solving of nonstationary inverse problem for inhomogeneous string (in Russian),\nTrudy MIAN V. A. Steklova 115 (1971), 28\u201338."},{"key":"2023040100065751525_j_jiip-2017-0083_ref_011_w2aab3b7b5b1b6b1ab1b6c11Aa","doi-asserted-by":"crossref","unstructured":"T. M.  Brocher and R. A.  Phinney,\nInversion of slant stacks using finite-length record sections,\nJ. Geophys. Res. 86 (1981), 7065\u20137072.\n10.1029\/JB086iB08p07065","DOI":"10.1029\/JB086iB08p07065"},{"key":"2023040100065751525_j_jiip-2017-0083_ref_012_w2aab3b7b5b1b6b1ab1b6c12Aa","doi-asserted-by":"crossref","unstructured":"C. H.  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Nowacki,\nTheory of Elasticity (in Polish),\nPWN, Warsawa, 1970."},{"key":"2023040100065751525_j_jiip-2017-0083_ref_026_w2aab3b7b5b1b6b1ab1b6c26Aa","doi-asserted-by":"crossref","unstructured":"I.  Psencik, V.  Cerveny and L.  Klimes,\nSeismic Waves in Laterally Inhomogeneous Media. Part I,\nBirkh\u00e4user, Berlin, 1996.","DOI":"10.1007\/978-3-0348-9213-1"},{"key":"2023040100065751525_j_jiip-2017-0083_ref_027_w2aab3b7b5b1b6b1ab1b6c27Aa","unstructured":"V. G.  Romanov,\nInverse Problems of Mathematical Physics,\nVSP, Netherlands, 1984."},{"key":"2023040100065751525_j_jiip-2017-0083_ref_028_w2aab3b7b5b1b6b1ab1b6c28Aa","doi-asserted-by":"crossref","unstructured":"V. G.  Romanov,\nDetermining the parameters of a stratified piecewise constant medium for the unknown shape of an impulse source,\nSib. Math. J. 48 (2007), no. 6, 1074\u20131084.\n10.1007\/s11202-007-0109-y","DOI":"10.1007\/s11202-007-0109-y"},{"key":"2023040100065751525_j_jiip-2017-0083_ref_029_w2aab3b7b5b1b6b1ab1b6c29Aa","doi-asserted-by":"crossref","unstructured":"V. G.  Romanov,\nOn the problem of determining the parameters of a layered elastic medium and an impulse source,\nSib. Math. J. 49 (2008), no. 5, 919\u2013943.\n10.1007\/s11202-008-0090-0","DOI":"10.1007\/s11202-008-0090-0"},{"key":"2023040100065751525_j_jiip-2017-0083_ref_030_w2aab3b7b5b1b6b1ab1b6c30Aa","doi-asserted-by":"crossref","unstructured":"P. S.  Schultz,\nVelocity estimation and downward continuation by wave front synthesis,\nGeophys. 43 (1978), 691\u2013714.\n10.1190\/1.1440847","DOI":"10.1190\/1.1440847"},{"key":"2023040100065751525_j_jiip-2017-0083_ref_031_w2aab3b7b5b1b6b1ab1b6c31Aa","unstructured":"A. N.  Tikhonov,\nOn uniqueness of solution of the electroprospecting problem (in Russian),\nDokl. Akad. Nauk SSSR 69 (1949), no. 6, 797\u2013800."},{"key":"2023040100065751525_j_jiip-2017-0083_ref_032_w2aab3b7b5b1b6b1ab1b6c32Aa","doi-asserted-by":"crossref","unstructured":"A. N.  Tikhonov,\nMathematical basis of the theory of electromagnetic soundings,\nComp. Math. Math. Phys. 5 (1965), no. 3, 207\u2013211.\n10.1016\/0041-5553(65)90157-6","DOI":"10.1016\/0041-5553(65)90157-6"},{"key":"2023040100065751525_j_jiip-2017-0083_ref_033_w2aab3b7b5b1b6b1ab1b6c33Aa","unstructured":"V. G.  Yakhno,\nInverse Problem for Differential Equations of Elasticity (in Russian),\nNauka, Novosibirsk, 1990."},{"key":"2023040100065751525_j_jiip-2017-0083_ref_034_w2aab3b7b5b1b6b1ab1b6c34Aa","doi-asserted-by":"crossref","unstructured":"B.  Zhou and S. A.  Greenhalgh,\nLinear and parabolic \u03c4-transforms revisited,\nGeophys. 59 (1994), no. 7, 1133\u20131149.\n10.1190\/1.1443669","DOI":"10.1190\/1.1443669"}],"container-title":["Journal of Inverse and Ill-posed Problems"],"language":"en","link":[{"URL":"http:\/\/www.degruyter.com\/view\/j\/jiip.2018.26.issue-5\/jiip-2017-0083\/jiip-2017-0083.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/jiip-2017-0083\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/jiip-2017-0083\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T13:56:18Z","timestamp":1680357378000},"score":0.0,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/jiip-2017-0083\/html"}},"issued":{"date-parts":[[2018,3,13]]},"references-count":34,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2018,4,11]]},"published-print":{"date-parts":[[2018,10,1]]}},"alternative-id":["10.1515\/jiip-2017-0083"],"URL":"https:\/\/doi.org\/10.1515\/jiip-2017-0083","ISSN":["1569-3945","0928-0219"],"issn-type":[{"value":"1569-3945","type":"electronic"},{"value":"0928-0219","type":"print"}],"published":{"date-parts":[[2018,3,13]]}},{"indexed":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T23:40:43Z","timestamp":1680306043111},"reference-count":25,"publisher":"Walter de Gruyter GmbH","issue":"5-6","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51277182"],"award-info":[{"award-number":["51277182"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"published-print":{"date-parts":[[2017,5,24]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>A practical new type direct lightning shielding rod is designed to reduce the electromagnetic radiation produced by lightning stroking to Franklin lightning rod in the paper. The Finite-Difference Time-Domain (FDTD) method is adopted for analyzing. It is the shielding layer that affects the electromagnetic fields and the insulating medium make no difference. All the electromagnetic fields amplitude obtained decrease for the shielding layer existing, regardless of any condition, but the extent is different. That is, the effect on the horizontal electric field is most noticeable, the vertical electric field comes second, minimum the azimuthal magnetic field. All the field components are affected by shielding layer height and the distance between shielding layer and lightning channel, but not significantly by the shielding layer grounding depth. The shielding effect is more obvious with lower ground conductivity, but the ground relative permittivity makes no difference.<\/jats:p>","DOI":"10.1515\/freq-2016-0016","type":"journal-article","created":{"date-parts":[[2016,10,21]],"date-time":"2016-10-21T10:00:51Z","timestamp":1477044051000},"page":"279-291","source":"Crossref","is-referenced-by-count":1,"title":["The Effect of Direct Lightning Shielding Rod on Lightning Electromagnetic Fields Aboveground"],"prefix":"10.1515","volume":"71","author":[{"given":"Ya-Peng","family":"Fu","sequence":"first","affiliation":[{"name":"National Key Laboratory on Electromagnetic Environmental Effects and Electro-optical Engineering, PLA University of Science & Technology , Nanjing 210007, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cheng","family":"Gao","sequence":"additional","affiliation":[{"name":"National Key Laboratory on Electromagnetic Environmental Effects and Electro-optical Engineering, PLA University of Science & Technology , Nanjing 210007, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo","family":"Yang","sequence":"additional","affiliation":[{"name":"National Key Laboratory on Electromagnetic Environmental Effects and Electro-optical Engineering, PLA University of Science & Technology , Nanjing 210007, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2016,10,20]]},"reference":[{"key":"2023033116451111581_j_freq-2016-0016_ref_001_w2aab2b8b1b1b7b1ab2ab1Aa","doi-asserted-by":"crossref","unstructured":"A. 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My deep expertise in electrochemistry perfectly matches the requirements of IBMs semiconductor interests and their integration technology. It is truly beneficial for both parties involved. 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By combination of measured kinetic energy dissipation rate in the bulk and wall shear stresses in the boundary layer, we will identify the advection patterns that generate the extreme dissipation events. The present experimental analysis will be complemented by existing training data records of high-resolution direct numerical simulations of the same flows. They serve to develop data-driven methods and algorithms, such as recurrent neural networks, to predict such extreme events in experimental analyses. The goal of this project is to advance our understanding of the dynamic evolution of such extreme events in a RBC flow and to develop reliable tools to predict the events. This research objective will be reached in a multidisciplinary way by a combination of high resolution optical flow measurements with the data-driven modeling and data analytics by machine learning.","language":"en"}],"award-amount":{"amount":162806.4,"currency":"EUR"},"award-start":{"date-parts":[[2021,6,1]]},"funding":[{"type":"grant","scheme":"MSCA-IF-2020","award-amount":{"amount":162806.4,"currency":"EUR","percentage":100},"funder":{"id":[{"id":"10.13039\/100010665","id-type":"DOI","asserted-by":"publisher"}],"name":"H2020 Marie Sk?odowska-Curie Actions"}}]}],"deposited":{"date-parts":[[2023,7,24]],"date-time":"2023-07-24T13:52:04Z","timestamp":1690206724000},"score":0.0,"resource":{"primary":{"URL":"https:\/\/cordis.europa.eu\/project\/id\/101024531"}},"issued":{"date-parts":[[2021,6,1]]},"URL":"https:\/\/doi.org\/10.3030\/101024531"},{"indexed":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T02:27:37Z","timestamp":1680316057340},"reference-count":27,"publisher":"Walter de Gruyter GmbH","issue":"3","license":[{"start":{"date-parts":[[2020,3,19]],"date-time":"2020-03-19T00:00:00Z","timestamp":1584576000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11771124"],"award-info":[{"award-number":["11771124"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"published-print":{"date-parts":[[2020,8,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this paper, we study properties of the lambda constants and the existence of ground states of Perelman\u2019s famous <jats:italic>W<\/jats:italic>-functional from a variational formulation. We have two kinds of results. One is about the estimation of the lambda constant of G. Perelman, and the other is about the existence of ground states of his <jats:italic>W<\/jats:italic>-functional, both on a complete non-compact Riemannian manifold <jats:inline-formula id=\"j_ans-2020-2077_ineq_9999\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mo stretchy=\"false\">(<\/m:mo>\n                              <m:mi>M<\/m:mi>\n                              <m:mo>,<\/m:mo>\n                              <m:mi>g<\/m:mi>\n                              <m:mo stretchy=\"false\">)<\/m:mo>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_ans-2020-2077_inl_001.png\" \/>\n                        <jats:tex-math>{(M,g)}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>. One consequence of our estimation is that, on an ALE (or asymptotic flat) manifold <jats:inline-formula id=\"j_ans-2020-2077_ineq_9998\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mo stretchy=\"false\">(<\/m:mo>\n                              <m:mi>M<\/m:mi>\n                              <m:mo>,<\/m:mo>\n                              <m:mi>g<\/m:mi>\n                              <m:mo stretchy=\"false\">)<\/m:mo>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_ans-2020-2077_inl_002.png\" \/>\n                        <jats:tex-math>{(M,g)}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>, if the scalar curvature <jats:italic>s<\/jats:italic> of <jats:inline-formula id=\"j_ans-2020-2077_ineq_9997\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mo stretchy=\"false\">(<\/m:mo>\n                              <m:mi>M<\/m:mi>\n                              <m:mo>,<\/m:mo>\n                              <m:mi>g<\/m:mi>\n                              <m:mo stretchy=\"false\">)<\/m:mo>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_ans-2020-2077_inl_003.png\" \/>\n                        <jats:tex-math>{(M,g)}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> is non-negative and has quadratical decay at infinity, then <jats:italic>M<\/jats:italic> is scalar flat, i.e., <jats:inline-formula id=\"j_ans-2020-2077_ineq_9996\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mi>s<\/m:mi>\n                              <m:mo>=<\/m:mo>\n                              <m:mn>0<\/m:mn>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_ans-2020-2077_inl_004.png\" \/>\n                        <jats:tex-math>{s=0}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> in <jats:italic>M<\/jats:italic>. We also introduce a new constant <jats:inline-formula id=\"j_ans-2020-2077_ineq_9995\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mi>d<\/m:mi>\n                              <m:mo>\u2062<\/m:mo>\n                              <m:mrow>\n                                 <m:mo stretchy=\"false\">(<\/m:mo>\n                                 <m:mi>M<\/m:mi>\n                                 <m:mo>,<\/m:mo>\n                                 <m:mi>g<\/m:mi>\n                                 <m:mo stretchy=\"false\">)<\/m:mo>\n                              <\/m:mrow>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_ans-2020-2077_inl_005.png\" \/>\n                        <jats:tex-math>{d(M,g)}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>. For the existence of the ground states, we use Lions\u2019 concentration-compactness method.<\/jats:p>","DOI":"10.1515\/ans-2020-2077","type":"journal-article","created":{"date-parts":[[2020,3,19]],"date-time":"2020-03-19T09:03:10Z","timestamp":1584608590000},"page":"651-661","source":"Crossref","is-referenced-by-count":2,"title":["New Results About the Lambda Constant and Ground States of the \ud835\udc4a-Functional"],"prefix":"10.1515","volume":"20","author":[{"given":"Li","family":"Ma","sequence":"first","affiliation":[{"name":"School of Mathematics and Physics , University of Science and Technology Beijing , 30 Xueyuan Road, Haidian District Beijing , 100083; and Department of Mathematics, Henan Normal University, Xinxiang, 453007 P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2020,3,19]]},"reference":[{"key":"2023033117073468884_j_ans-2020-2077_ref_001","doi-asserted-by":"crossref","unstructured":"A. S. Y. Chang, The Moser\u2013Onofri inequality and applications to some problems in conformal geometry, Nonlinear Partial Differential Equations in Differential Geometry, IAS\/Park city Math. Ser. 2, American Mathematical Society, Providence (1996), 65\u2013125.","DOI":"10.1090\/pcms\/002\/03"},{"key":"2023033117073468884_j_ans-2020-2077_ref_002","unstructured":"B. Chow, P. Lu and L. Ni, Hamilton\u2019s Ricci flow, Grad. Stud. in Math. 77, American Mathematical Society, Providence, 2006."},{"key":"2023033117073468884_j_ans-2020-2077_ref_003","doi-asserted-by":"crossref","unstructured":"B. Chow, S.-C. Chu, D. Glickenstein, C. Guenther, J. Isenberg, T. Ivey, D. Knopf, P. Lu, F. Luo and L. Ni, The Ricci flow: Techniques and Applications. Part I: Geometric Aspects, Math. Surveys Monogr. 135, American Mathematical Society, Providence, 2007.","DOI":"10.1090\/surv\/135"},{"key":"2023033117073468884_j_ans-2020-2077_ref_004","doi-asserted-by":"crossref","unstructured":"B. Chow, S.-C. Chu, D. Glickenstein, C. Guenther, J. Isenberg, T. Ivey, D. Knopf, P. Lu, F. Luo and L. Ni, The Ricci flow: Techniques and Applications. Part III: Geometric-analytica Aspects, Math. Surveys Monogr. 163, American Mathematical Society, Providence, 2010.","DOI":"10.1090\/surv\/163"},{"key":"2023033117073468884_j_ans-2020-2077_ref_005","doi-asserted-by":"crossref","unstructured":"S. Cheng and S. T. Yau, Differential equations on Riemannian manifolds and their geometric applications, Comm. Pure Appl. Math. 28 (1975), no. 3, 333\u2013354.","DOI":"10.1002\/cpa.3160280303"},{"key":"2023033117073468884_j_ans-2020-2077_ref_006","doi-asserted-by":"crossref","unstructured":"T. H. Colding, W. P. Minicozzi and II, Minimal Surfaces, Courant Lect. Notes Math. 4, New York University, New York, 1999.","DOI":"10.1155\/S1073792899000604"},{"key":"2023033117073468884_j_ans-2020-2077_ref_007","doi-asserted-by":"crossref","unstructured":"L. Gross, Logarithmic Sobolev inequalities, Amer. J. Math. 97 (1975), 1061\u20131083.","DOI":"10.2307\/2373688"},{"key":"2023033117073468884_j_ans-2020-2077_ref_008","doi-asserted-by":"crossref","unstructured":"R. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 2 (1982), 255\u2013306.","DOI":"10.4310\/jdg\/1214436922"},{"key":"2023033117073468884_j_ans-2020-2077_ref_009","doi-asserted-by":"crossref","unstructured":"B. Kleiner and J. Lott, Notes on Perelman\u2019s papers, Geom. Topol. 12 (2008), no. 5, 2587\u20132855.","DOI":"10.2140\/gt.2008.12.2587"},{"key":"2023033117073468884_j_ans-2020-2077_ref_010","doi-asserted-by":"crossref","unstructured":"P. Li and R. Schoen, Lp and mean value properties of subharmonic functions on Riemannian manifolds, Acta Math. 153 (1984), no. 3\u20134, 279\u2013301.","DOI":"10.1007\/BF02392380"},{"key":"2023033117073468884_j_ans-2020-2077_ref_011","doi-asserted-by":"crossref","unstructured":"P. L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case. I, Ann. Inst. H. Poincar\u00e9 Anal. Non Lin\u00e9aire 1 (1984), no. 2, 109\u2013145.","DOI":"10.1016\/s0294-1449(16)30428-0"},{"key":"2023033117073468884_j_ans-2020-2077_ref_012","doi-asserted-by":"crossref","unstructured":"P. L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case. II, Ann. Inst. H. Poincar\u00e9 Anal. Non Lin\u00e9aire 1 (1984), no. 4, 223\u2013283.","DOI":"10.1016\/s0294-1449(16)30422-x"},{"key":"2023033117073468884_j_ans-2020-2077_ref_013","doi-asserted-by":"crossref","unstructured":"L. Ma, Gradient estimates for a simple elliptic equation on complete non-compact Riemannian manifolds, J. Funct. Anal. 241 (2006), no. 1, 374\u2013382.","DOI":"10.1016\/j.jfa.2006.06.006"},{"key":"2023033117073468884_j_ans-2020-2077_ref_014","unstructured":"L. Ma, Lambda constant and ground states of Perelman\u2019s W-functionals, preprint (2015), https:\/\/arxiv.org\/abs\/1512.08405."},{"key":"2023033117073468884_j_ans-2020-2077_ref_015","doi-asserted-by":"crossref","unstructured":"L. Ma, Gradient estimates for a simple nonlinear heat equation on manifolds, Appl. Anal 96 (2017), no. 2, 225\u2013230.","DOI":"10.1080\/00036811.2015.1120290"},{"key":"2023033117073468884_j_ans-2020-2077_ref_016","doi-asserted-by":"crossref","unstructured":"L. Ma and Y. Liu, Harnack inequalities for simple heat equations on Riemannian manifolds, Math. Phys. Anal. Geom. 22 (2019), 10.1007\/s11040-019-9305-9.","DOI":"10.1007\/s11040-019-9305-9"},{"key":"2023033117073468884_j_ans-2020-2077_ref_017","doi-asserted-by":"crossref","unstructured":"L. Ma, L. Zhao and X. Song, Gradient estimate for the degenerate parabolic equation ut=\u0394\u2062F\u2062(u)+H\u2062(u){u_{t}=\\Delta F(u)+H(u)} on manifolds, J. Differential Equations 244 (2008), no. 5, 1157\u20131177.","DOI":"10.1016\/j.jde.2007.08.014"},{"key":"2023033117073468884_j_ans-2020-2077_ref_018","doi-asserted-by":"crossref","unstructured":"L. Ma and A. Zhu, Eigenvalues and lambda constants on Riemannian submersions, Geom. Dedicata 129 (2007), 73\u201382.","DOI":"10.1007\/s10711-007-9194-0"},{"key":"2023033117073468884_j_ans-2020-2077_ref_019","doi-asserted-by":"crossref","unstructured":"E. Hebey, Optimal Sobolev inequalities on complete Riemannian manifolds with Ricci curvature bounded below and positive injectivity radius, Amer. J. Math. 118 (1996), no. 2, 291\u2013300.","DOI":"10.1353\/ajm.1996.0014"},{"key":"2023033117073468884_j_ans-2020-2077_ref_020","doi-asserted-by":"crossref","unstructured":"N. Hirano, Existence of solutions for a nonlinear elliptic problem on a Riemannian manifold, J. Math. Anal. Appl. 368 (2010), 400\u2013412.","DOI":"10.1016\/j.jmaa.2010.03.067"},{"key":"2023033117073468884_j_ans-2020-2077_ref_021","unstructured":"G. Perelman, The entropy formula for the Ricci flow and its geometric applications, preprint (2002), https:\/\/arxiv.org\/abs\/math\/0211159."},{"key":"2023033117073468884_j_ans-2020-2077_ref_022","unstructured":"G. Perelman, Ricci flow with surgery on three-manifolds, preprint (2003), https:\/\/arxiv.org\/abs\/math\/0303109."},{"key":"2023033117073468884_j_ans-2020-2077_ref_023","doi-asserted-by":"crossref","unstructured":"O. S. Rothaus, Logarithmic Sobolev inequalities and the spectrum of Schrodinger operators, J.Funct. Anal. 42 (1981), 110\u2013120.","DOI":"10.1016\/0022-1236(81)90050-1"},{"key":"2023033117073468884_j_ans-2020-2077_ref_024","doi-asserted-by":"crossref","unstructured":"M. Struwe, Variational Methods, 2nd ed., Springer, Berlin, 1996.","DOI":"10.1007\/978-3-662-03212-1"},{"key":"2023033117073468884_j_ans-2020-2077_ref_025","unstructured":"T. Tao, Poincare\u2019s Legacies, Part 2: Pages from Year Two of a Mathematical Blog, American Mathematical Society, Providence, 2009."},{"key":"2023033117073468884_j_ans-2020-2077_ref_026","doi-asserted-by":"crossref","unstructured":"Q. S. Zhang, Extremal of log Sobolev inequality and W entropy on noncompact manifolds, J. Funct. Anal. 263 (2012), no. 7, 2051\u20132101.","DOI":"10.1016\/j.jfa.2012.07.005"},{"key":"2023033117073468884_j_ans-2020-2077_ref_027","doi-asserted-by":"crossref","unstructured":"Q. S. Zhang, A no breathers theorem for some noncompact Ricci flows, Asian J. 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It is proved that this class is a subgroup-closed formation of finite soluble groups which is not closed under taking Frattini extensions and whose members can be characterised by means of their Carter subgroups. This leads to new characterisations of finite soluble T-, PT- and PST-groups. Finite groups whose <jats:italic>p<\/jats:italic>-subgroups, <jats:italic>p<\/jats:italic> a prime, are self-normalising in their subnormal closure are also characterised.<\/jats:p>","DOI":"10.1515\/jgth-2018-0015","type":"journal-article","created":{"date-parts":[[2018,5,16]],"date-time":"2018-05-16T22:29:32Z","timestamp":1526509772000},"page":"839-846","source":"Crossref","is-referenced-by-count":1,"title":["On a class of finite soluble groups"],"prefix":"10.1515","volume":"21","author":[{"given":"Adolfo","family":"Ballester-Bolinches","sequence":"first","affiliation":[{"name":"Department of Mathematics , Guangdong University of Education , 510310 , Guangzhou , P. R. China ; and Departament de Matem\u00e0tiques, Universitat de Val\u00e8ncia, 46100 Burjassot, Val\u00e8ncia , Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"John","family":"Cossey","sequence":"additional","affiliation":[{"name":"Australian National University , Canberra , ACT 2601 , Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yangming","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Mathematics , Guangdong University of Education , 510310 , Guangzhou , P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2018,5,16]]},"reference":[{"key":"2023033122400910332_j_jgth-2018-0015_ref_001_w2aab3b7e2171b1b6b1ab2ab1Aa","doi-asserted-by":"crossref","unstructured":"A.  Ballester-Bolinches, R.  Esteban-Romero and M.  Asaad,\nProducts of Finite Groups,\nDe Gruyter Exp. Math. 53,\nWalter de Gruyter, Berlin, 2010.","DOI":"10.1515\/9783110220612"},{"key":"2023033122400910332_j_jgth-2018-0015_ref_002_w2aab3b7e2171b1b6b1ab2ab2Aa","doi-asserted-by":"crossref","unstructured":"A.  Ballester-Bolinches, R.  Esteban-Romero and Y.  Li,\nOn self-normalizing subgroups of finite groups,\nJ. Group Theory 13 (2010), 143\u2013149.","DOI":"10.1515\/jgt.2009.038"},{"key":"2023033122400910332_j_jgth-2018-0015_ref_003_w2aab3b7e2171b1b6b1ab2ab3Aa","doi-asserted-by":"crossref","unstructured":"K.  Doerk and T.  Hawkes,\nFinite Soluble Groups,\nDe Gruyter Exp. Math. 4,\nWalter de Gruyter, Berlin, 1992.","DOI":"10.1515\/9783110870138"},{"key":"2023033122400910332_j_jgth-2018-0015_ref_004_w2aab3b7e2171b1b6b1ab2ab4Aa","doi-asserted-by":"crossref","unstructured":"Y.  Li,\nFinite groups with NE-subgroups,\nJ. 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