{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:39Z","timestamp":1740134559184,"version":"3.37.3"},"reference-count":24,"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","award":["11201037","QC2010024"],"award-info":[{"award-number":["11201037","QC2010024"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005046","name":"Natural Science Foundation of Heilongjiang Province, China","doi-asserted-by":"crossref","award":["11201037","QC2010024"],"award-info":[{"award-number":["11201037","QC2010024"]}],"id":[{"id":"10.13039\/501100005046","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>A repairable computer system model which consists of hardware and software in series is established in this paper. This study is devoted to discussing the unique existence of the solution and the stability of the studied system. In view of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:msub><mml:mi>c<\/mml:mi><mml:mn>0<\/mml:mn><\/mml:msub><\/mml:mrow><\/mml:math>semigroup theory, we prove the existence of a unique nonnegative solution of the system. Then by analyzing the spectra distribution of the system operator, we deduce that the transient solution of the system strongly converges to the nonnegative steady-state solution which is the eigenvector corresponding to eigenvalue 0 of the system operator. Finally, some reliability indices of the system are provided at the end of the paper with a new method.<\/jats:p>","DOI":"10.1155\/2013\/131076","type":"journal-article","created":{"date-parts":[[2013,4,24]],"date-time":"2013-04-24T17:01:02Z","timestamp":1366822862000},"page":"1-9","source":"Crossref","is-referenced-by-count":5,"title":["The Well-Posedness and Stability Analysis of a Computer Series System"],"prefix":"10.1155","volume":"2013","author":[{"given":"Xing","family":"Qiao","sequence":"first","affiliation":[{"name":"School of Mathematical Science, Daqing Normal University, Daqing 163712, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dan","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Mathematical Science, Daqing Normal University, Daqing 163712, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fu","family":"Zheng","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Bohai University, Jinzhou 121013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guangtian","family":"Zhu","sequence":"additional","affiliation":[{"name":"Academy of Mathematics and System Sciences C.A.S., Beijing 100080, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","first-page":"251","volume":"38","year":"2009","journal-title":"Computers & Industrial Engineering"},{"doi-asserted-by":"publisher","key":"2","DOI":"10.1016\/S0167-6377(02)00106-2"},{"key":"3","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/S0307-904X(02)00133-6","volume":"27","year":"2003","journal-title":"Applied Mathematical Modelling"},{"key":"4","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1016\/j.ejor.2006.09.075","volume":"183","year":"2007","journal-title":"European Journal of Operational Research"},{"doi-asserted-by":"publisher","key":"5","DOI":"10.1016\/S0377-2217(01)00135-7"},{"year":"1975","key":"7"},{"key":"8","first-page":"187","volume":"34","year":"1985","journal-title":"IEEE Transactions on Reliability"},{"key":"10","doi-asserted-by":"crossref","first-page":"1997","DOI":"10.1016\/j.apm.2006.08.021","volume":"31","year":"2007","journal-title":"Applied Mathematical Modelling"},{"issue":"1","key":"11","first-page":"33","volume":"22","year":"1996","journal-title":"Acta Automation Sinica"},{"doi-asserted-by":"publisher","key":"12","DOI":"10.1007\/BF02007241"},{"issue":"11","key":"13","first-page":"1","volume":"20","year":"2000","journal-title":"Computer Applications"},{"issue":"1","key":"14","first-page":"33","volume":"17","year":"2006","journal-title":"Journal of Civil Aviation Flight University of China"},{"issue":"4","key":"15","first-page":"311","volume":"9","year":"2007","journal-title":"Acta Analysis Functionalis Applicata"},{"doi-asserted-by":"publisher","key":"16","DOI":"10.1007\/s11424-007-9039-9"},{"key":"17","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1007\/BF00250793","volume":"54","year":"1974","journal-title":"Archive for Rational Mechanics and Analysis"},{"year":"2006","key":"18"},{"year":"1986","series-title":"Lecture Notes in Mathematics","key":"19"},{"year":"2001","key":"20"},{"issue":"4","key":"22","first-page":"125","volume":"10","year":"2011","journal-title":"WSEAS Transactions on Mathematics"},{"year":"1958","key":"23"},{"doi-asserted-by":"publisher","key":"25","DOI":"10.1007\/978-1-4612-5561-1"},{"year":"1980","key":"26"},{"issue":"4","key":"27","first-page":"493","volume":"22","year":"2005","journal-title":"Journal of Natural Science of Heilongjiang University"},{"key":"28","first-page":"299","volume":"139","year":"2011","journal-title":"Advances in Electrical Engineering and Automation, AISC"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/131076.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/131076.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/131076.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,12]],"date-time":"2019-07-12T20:31:17Z","timestamp":1562963477000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/131076\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":24,"alternative-id":["131076","131076"],"URL":"https:\/\/doi.org\/10.1155\/2013\/131076","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2013]]}}}