{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:41:58Z","timestamp":1740134518752,"version":"3.37.3"},"reference-count":14,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11071079"],"award-info":[{"award-number":["11071079"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>Given<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>k<\/mml:mi><\/mml:mrow><\/mml:math>pairs of complex numbers and vectors (closed under conjugation), we consider the inverse quadratic eigenvalue problem of constructing<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mi>n<\/mml:mi><mml:mo>\u00d7<\/mml:mo><mml:mi>n<\/mml:mi><\/mml:math>real matrices<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mi>M<\/mml:mi><\/mml:mrow><\/mml:math>,<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mi>D<\/mml:mi><\/mml:mrow><\/mml:math>,<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:mi>G<\/mml:mi><\/mml:mrow><\/mml:math>, and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mrow><mml:mi>K<\/mml:mi><\/mml:mrow><\/mml:math>, where<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mi>M<\/mml:mi><mml:mo>&gt;<\/mml:mo><mml:mn>0<\/mml:mn><\/mml:math>,<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\"><mml:mrow><mml:mi>K<\/mml:mi><\/mml:mrow><\/mml:math>and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\"><mml:mrow><mml:mi>D<\/mml:mi><\/mml:mrow><\/mml:math>are symmetric, and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M10\"><mml:mrow><mml:mi>G<\/mml:mi><\/mml:mrow><\/mml:math>is skew-symmetric, so that the quadratic pencil<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M11\"><mml:mrow><mml:mi>Q<\/mml:mi><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>\u03bb<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><mml:mo>=<\/mml:mo><mml:msup><mml:mi>\u03bb<\/mml:mi><mml:mn>2<\/mml:mn><\/mml:msup><mml:mi>M<\/mml:mi><mml:mo>+<\/mml:mo><mml:mi>\u03bb<\/mml:mi><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow><mml:mi>D<\/mml:mi><mml:mo>+<\/mml:mo><mml:mi>G<\/mml:mi><\/mml:mrow><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><mml:mo>+<\/mml:mo><mml:mi>K<\/mml:mi><\/mml:mrow><\/mml:math>has the given<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M12\"><mml:mrow><mml:mi>k<\/mml:mi><\/mml:mrow><\/mml:math>pairs as eigenpairs. First, we construct a general solution to this problem with<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M13\"><mml:mi>k<\/mml:mi><mml:mo>\u2264<\/mml:mo><mml:mi>n<\/mml:mi><\/mml:math>. Then, with the special properties<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M14\"><mml:mi>D<\/mml:mi><mml:mo>=<\/mml:mo><mml:mn>0<\/mml:mn><\/mml:math>and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M15\"><mml:mi>K<\/mml:mi><mml:mo>&lt;<\/mml:mo><mml:mn>0<\/mml:mn><\/mml:math>, we construct a particular solution. Numerical results illustrate these solutions.<\/jats:p>","DOI":"10.1155\/2014\/703178","type":"journal-article","created":{"date-parts":[[2014,1,22]],"date-time":"2014-01-22T01:51:30Z","timestamp":1390355490000},"page":"1-9","source":"Crossref","is-referenced-by-count":0,"title":["Solutions of a Quadratic Inverse Eigenvalue Problem for Damped Gyroscopic Second-Order Systems"],"prefix":"10.1155","volume":"2014","author":[{"given":"Hong-Xiu","family":"Zhong","sequence":"first","affiliation":[{"name":"Department of Mathematics, East China Normal University, Shanghai 200241, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guo-Liang","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Mathematics, East China Normal University, Shanghai 200241, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiang-Yun","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, East China Normal University, Shanghai 200241, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"2","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1982.1102953"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479803438523"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2003.12.010"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1137\/07069273X"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsv.2007.05.009"},{"issue":"2","key":"13","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1137\/S0036144500381988","volume":"43","year":"2001","journal-title":"SIAM Review"},{"key":"15","first-page":"429","volume":"67","year":"2010","journal-title":"World Academy of Science, Engineering and Technology"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1007\/BF01682679"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-08-02128-5"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1137\/100792020"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1137\/05064134X"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2008.04.015"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1155\/2009\/725616"},{"issue":"2","key":"3","first-page":"295","volume":"20","year":"1999","journal-title":"Journal on Matrix Analysis and Applications"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/703178.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/703178.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/703178.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,22]],"date-time":"2017-06-22T02:26:01Z","timestamp":1498098361000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/703178\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":14,"alternative-id":["703178","703178"],"URL":"https:\/\/doi.org\/10.1155\/2014\/703178","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}