{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,20]],"date-time":"2025-09-20T20:54:37Z","timestamp":1758401677747,"version":"3.41.2"},"reference-count":17,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,8,17]],"date-time":"2012-08-17T00:00:00Z","timestamp":1345161600000},"content-version":"vor","delay-in-days":229,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100008845","name":"Xinjiang University","doi-asserted-by":"crossref","award":["XY110101","2012211A023"],"award-info":[{"award-number":["XY110101","2012211A023"]}],"id":[{"id":"10.13039\/501100008845","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Natural Science Foundation of Xinjiang","award":["XY110101","2012211A023"],"award-info":[{"award-number":["XY110101","2012211A023"]}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>We study spectral properties of the operator which corresponds to the M\/G\/1 retrial queueing model with server breakdowns and obtain that all points on the imaginary axis except zero belong to the resolvent set of the operator and 0 is not an eigenvalue of the operator. 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