{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:59Z","timestamp":1740134579503,"version":"3.37.3"},"reference-count":7,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"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","id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Youth Fund of Mianyang Normal University"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>We study the configuration formed by two squares in two parallel layers separated by a distance. We picture the two layers horizontally with the<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>z<\/mml:mi><\/mml:mrow><\/mml:math>-axis passing through the centers of the two squares. The masses located on the vertices of each square are equal, but we do not assume that the masses of the top square are equal to the masses of the bottom square. We prove that the above configuration of two squares forms a central configuration if and only if the twist angle is equal to<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mi>k<\/mml:mi><mml:mi>\u03c0<\/mml:mi><mml:mo>\/<\/mml:mo><mml:mn mathvariant=\"normal\">2<\/mml:mn><\/mml:math>or (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mi>\u03c0<\/mml:mi><mml:mo>\/<\/mml:mo><mml:mn mathvariant=\"normal\">4<\/mml:mn><mml:mo>+<\/mml:mo><mml:mi>k<\/mml:mi><mml:mi>\u03c0<\/mml:mi><mml:mo>\/<\/mml:mo><mml:mn mathvariant=\"normal\">2<\/mml:mn><\/mml:math>)<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>k<\/mml:mi><mml:mo>=<\/mml:mo><mml:mn mathvariant=\"normal\">1,2<\/mml:mn><mml:mo>,<\/mml:mo><mml:mn mathvariant=\"normal\">3,4<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>.<\/jats:p>","DOI":"10.1155\/2013\/315976","type":"journal-article","created":{"date-parts":[[2013,11,3]],"date-time":"2013-11-03T16:00:53Z","timestamp":1383494453000},"page":"1-6","source":"Crossref","is-referenced-by-count":0,"title":["Spatial Central Configurations with Two Twisted Regular 4-Gons"],"prefix":"10.1155","volume":"2013","author":[{"given":"Sen","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Electronic Engineering, UEST Of China, Chengdu 610054, China"},{"name":"Department of Mathematics, Yibin University, Sichuan, 644007, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6154-7937","authenticated-orcid":true,"given":"Furong","family":"Zhao","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Mianyang Normal University, Mianyang, Sichuan 621000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"18","doi-asserted-by":"publisher","DOI":"10.1007\/BF02880037"},{"volume":"104","year":"2005","key":"11"},{"year":"1941","key":"14"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1137\/S0036141093248414"},{"key":"16"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/36\/45\/006"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.2307\/2045395"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/315976.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/315976.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/315976.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,30]],"date-time":"2016-07-30T07:47:56Z","timestamp":1469864876000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/315976\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":7,"alternative-id":["315976","315976"],"URL":"https:\/\/doi.org\/10.1155\/2013\/315976","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2013]]}}}