{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,5]],"date-time":"2025-07-05T07:40:10Z","timestamp":1751701210581,"version":"3.41.0"},"publisher-location":"Cham","reference-count":15,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031970764","type":"print"},{"value":"9783031970771","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025]]},"DOI":"10.1007\/978-3-031-97077-1_4","type":"book-chapter","created":{"date-parts":[[2025,7,5]],"date-time":"2025-07-05T07:14:20Z","timestamp":1751699660000},"page":"50-61","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the\u00a0Study of\u00a0Some Sufficient Conditions for\u00a0the\u00a0Existence of\u00a0Regular Zeros of\u00a0Quadratic Mappings"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6579-4276","authenticated-orcid":false,"given":"Dmitry","family":"Karamzin","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,7,6]]},"reference":[{"key":"4_CR1","doi-asserted-by":"crossref","unstructured":"Arutyunov, A.V.: Optimality conditions: Abnormal and Degenerate Problems. Mathematics and its Application. Kluwer Academic Publisher, Amsterdam (2000)","DOI":"10.1007\/978-94-015-9438-7"},{"issue":"2","key":"4_CR2","first-page":"30","volume":"15","author":"AV Arutyunov","year":"1999","unstructured":"Arutyunov, A.V.: Some properties of quadratic mappings. Bull. Moscow State Univ. Ser. 15(2), 30\u201332 (1999)","journal-title":"Bull. Moscow State Univ. Ser."},{"issue":"6","key":"4_CR3","doi-asserted-by":"publisher","first-page":"635","DOI":"10.1016\/s0294-1449(16)30118-4","volume":"13","author":"AA Agrachev","year":"1996","unstructured":"Agrachev, A.A., Sarychev, A.V.: Abnormal sub-Riemannian geodesics: morse index and rigidity. Ann. Inst. H. Poincare Anal. Non Lineaire 13(6), 635\u2013690 (1996)","journal-title":"Ann. Inst. H. Poincare Anal. Non Lineaire"},{"issue":"5","key":"4_CR4","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1007\/BF01158081","volume":"47","author":"ER Avakov","year":"1990","unstructured":"Avakov, E.R.: Theorems on estimates in the neighborhood of a singular point of a mapping. Math. Notes 47(5), 425\u2013432 (1990)","journal-title":"Math. Notes"},{"issue":"2","key":"4_CR5","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1070\/SM1992v073n02ABEH002555","volume":"73","author":"ER Avakov","year":"1992","unstructured":"Avakov, E.R., Agrachev, A.A., Arutyunov, A.V.: The level set of a smooth mapping in a neighborhood of a singular point, and zeros of a quadratic mapping. Math. USSR-Sb. 73(2), 455\u2013466 (1992)","journal-title":"Math. USSR-Sb."},{"key":"4_CR6","doi-asserted-by":"crossref","unstructured":"Arutyunov, A.V.: Smooth abnormal problems in extremum theory and analysis. Uspekhi Mat. Nauk, 67(3), 405, 3\u201362 (2012). Russian Math. Surv. 67(3), 403\u2013457 (2012)","DOI":"10.1070\/RM2012v067n03ABEH004793"},{"key":"4_CR7","doi-asserted-by":"crossref","unstructured":"Izmailov, A.F.: Optimality conditions in extremal problems with nonregular inequality constraints. Mat. Zametki 66(1), 89-101 (1999). Math. Notes 66(1), 72\u201381 (1999)","DOI":"10.1007\/BF02674072"},{"key":"4_CR8","doi-asserted-by":"crossref","unstructured":"Agrachev, A.A., Gamkrelidze, R.V.: Quasi-extremality for controllable systems. Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 35, VINITI, Moscow, 109\u2013134 (1989). J. Soviet Math. 55(4), 1849\u20131864 (1991)","DOI":"10.1007\/BF01095137"},{"issue":"8","key":"4_CR9","doi-asserted-by":"publisher","first-page":"1293","DOI":"10.1134\/S0965542506080033","volume":"46","author":"AV Arutyunov","year":"2006","unstructured":"Arutyunov, A.V., Karamzin, D.Y.: Necessary optimality conditions in an abnormal optimization problem with equality constraints. Comput. Math. Math. Phys. 46(8), 1293\u20131298 (2006)","journal-title":"Comput. Math. Math. Phys."},{"key":"4_CR10","doi-asserted-by":"publisher","first-page":"1380","DOI":"10.1137\/20M1337697","volume":"31","author":"AV Arutyunov","year":"2021","unstructured":"Arutyunov, A.V., Karamzin, D.Y.: Square-root metric regularity and related stability theorems for smooth mappings. SIAM J. Optim. 31, 1380\u20131409 (2021)","journal-title":"SIAM J. Optim."},{"key":"4_CR11","doi-asserted-by":"crossref","unstructured":"Avakov, E.R., Arutyunov, A.V., Karamzin, D.Yu.: An investigation of smooth maps in a neighbourhood of an abnormal point. Izv. RAN. Ser. Mat. 78(2), 3\u201342 (2014). Izv. Math. 78(2), 213\u2013250 (2014)","DOI":"10.1070\/IM2014v078n02ABEH002686"},{"issue":"115","key":"4_CR12","first-page":"464","volume":"113","author":"AV Sarychev","year":"1980","unstructured":"Sarychev, A.V.: Index of second variation of a control system. Mat. Sb. 113(115), 464\u2013486 (1980)","journal-title":"Mat. Sb."},{"key":"4_CR13","volume-title":"Optimal Control","author":"VM Alekseev","year":"1979","unstructured":"Alekseev, V.M., Tikhomirov, V.M., Fomin, S.V.: Optimal Control. Nauka, Moscow (1979)"},{"issue":"1","key":"4_CR14","first-page":"34","volume":"15","author":"AV Arutyunov","year":"2000","unstructured":"Arutyunov, A.V., Yacimovic, V.: On the theory of extremum for abnormal problems. Bull. Moscow State Univ. Ser. 15(1), 34\u201340 (2000)","journal-title":"Bull. Moscow State Univ. Ser."},{"issue":"6","key":"4_CR15","doi-asserted-by":"publisher","first-page":"783","DOI":"10.1070\/SM2011v202n06ABEH004166","volume":"202","author":"AV Arutyunov","year":"2011","unstructured":"Arutyunov, A.V., Karamzin, D.Y.: Regular zeros of quadratic maps and their application. Mat. Sb. 202(6), 783\u2013806 (2011)","journal-title":"Mat. Sb."}],"container-title":["Lecture Notes in Computer Science","Mathematical Optimization Theory and Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-97077-1_4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,5]],"date-time":"2025-07-05T07:14:22Z","timestamp":1751699662000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-97077-1_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"ISBN":["9783031970764","9783031970771"],"references-count":15,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-97077-1_4","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025]]},"assertion":[{"value":"6 July 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"MOTOR","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Mathematical Optimization Theory and Operations Research","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Novosibirsk","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Russia","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"7 July 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"11 July 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"24","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"motor2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/old.math.nsc.ru\/conference\/motor\/2025\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}