{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T12:41:13Z","timestamp":1775047273998,"version":"3.50.1"},"publisher-location":"Cham","reference-count":32,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783030600259","type":"print"},{"value":"9783030600266","type":"electronic"}],"license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020]]},"DOI":"10.1007\/978-3-030-60026-6_12","type":"book-chapter","created":{"date-parts":[[2020,10,17]],"date-time":"2020-10-17T20:02:36Z","timestamp":1602964956000},"page":"206-227","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Symbolic-Numeric Algorithm for Computing Orthonormal Basis of $$\\text {O(5)}\\times \\text {SU(1,1)}$$ Group"],"prefix":"10.1007","author":[{"given":"Algirdas","family":"Deveikis","sequence":"first","affiliation":[]},{"given":"Alexander A.","family":"Gusev","sequence":"additional","affiliation":[]},{"given":"Vladimir P.","family":"Gerdt","sequence":"additional","affiliation":[]},{"given":"Sergue I.","family":"Vinitsky","sequence":"additional","affiliation":[]},{"given":"Andrzej","family":"G\u00f3\u017ad\u017a","sequence":"additional","affiliation":[]},{"given":"Aleksandra","family":"P\u0229drak","sequence":"additional","affiliation":[]},{"given":"\u010cestmir","family":"Burdik","sequence":"additional","affiliation":[]},{"given":"George S.","family":"Pogosyan","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,10,2]]},"reference":[{"key":"12_CR1","unstructured":"Bohr, A.: The coupling of nuclear surface oscillations to the motion of individual nucleons. Mat Fys. Medd. Dan. Vid. Selsk. 26 (14) (1952)"},{"key":"12_CR2","unstructured":"Bohr, A., Mottelson, B.: Collective and individual-particle aspects of nuclear structure. Mat. Fys. Medd. Dan. Vid. Selsk. 27 (16) (1953)"},{"key":"12_CR3","volume-title":"Nuclear Structure","author":"A Bohr","year":"1970","unstructured":"Bohr, A., Mottelson, B.R.: Nuclear Structure, vol. 2. W.A. Bejamin Inc., Amsterdam (1970)"},{"key":"12_CR4","unstructured":"Eisenberg, J.M., Greiner, W.: Nuclear Theory. Third edition, North-Holland, Vol. 1, (1987)"},{"key":"12_CR5","volume-title":"The Harmonic Oscillator in Modern Physics","author":"M Moshinsky","year":"1996","unstructured":"Moshinsky, M., Smirnov, Y.F.: The Harmonic Oscillator in Modern Physics. Harwood Academic Publishers GmbH, Netherlands (1996)"},{"key":"12_CR6","doi-asserted-by":"publisher","first-page":"668","DOI":"10.1063\/1.522961","volume":"17","author":"E Chac\u2019on","year":"1976","unstructured":"Chac\u2019on, E., Moshinsky, M., Sharp, R.T.: $$U(5)\\supset O(5)\\supset O(3)$$ and the exact solution for the problem of quadrupole vibrations of the nucleus. J. Math. Phys. 17, 668\u2013676 (1976)","journal-title":"J. Math. Phys."},{"key":"12_CR7","doi-asserted-by":"publisher","first-page":"870","DOI":"10.1063\/1.523352","volume":"18","author":"E Chac\u2019on","year":"1977","unstructured":"Chac\u2019on, E., Moshinsky, M.: Group theory of the collective model of the nucleus. J. Math. Phys. 18, 870\u2013880 (1977)","journal-title":"J. Math. Phys."},{"key":"12_CR8","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1016\/0375-9474(80)90323-1","volume":"340","author":"S Szpikowski","year":"1980","unstructured":"Szpikowski, S., G\u00f3\u017ad\u017a, A.: The orthonormal basis for symmetric irreducible representations of $$O(5)\\times SU(1, 1)$$ and its application to the interacting boson model. Nucl. Phys. A 340, 76\u201392 (1980)","journal-title":"Nucl. Phys. A"},{"key":"12_CR9","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1016\/0375-9474(80)90293-6","volume":"349","author":"A G\u00f3\u017ad\u017a","year":"1980","unstructured":"G\u00f3\u017ad\u017a, A., Szpikowski, S.: Complete and orthonormal solution of the five-dimensional spherical harmonic oscillator in Bohr-Mottelson collective internal coordinates. Nucl. Phys. A 349, 359\u2013364 (1980)","journal-title":"Nucl. Phys. A"},{"key":"12_CR10","first-page":"147","volume":"296","author":"PO Hess","year":"1980","unstructured":"Hess, P.O., Seiwert, M., Maruhn, J., Greiner, W.: General Collective Model and its Application to $$_{92}^{238}$$ UZ. Phys. A 296, 147\u2013163 (1980)","journal-title":"Phys. A"},{"key":"12_CR11","doi-asserted-by":"publisher","first-page":"116","DOI":"10.1007\/978-3-642-76356-4_6","volume-title":"Computational Nuclear Physics","author":"D Troltenier","year":"1991","unstructured":"Troltenier, D., Maruhn, J.A., Hess, P.O.: Numerical application of the geometric collective model. In: Langanke, K., Maruhn, J.A., Konin, S.E. (eds.) Computational Nuclear Physics, vol. 1, pp. 116\u2013139. Springer-Verlag, Berlin (1991). https:\/\/doi.org\/10.1007\/978-3-642-76356-4_6"},{"key":"12_CR12","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1016\/0010-4655(88)90175-0","volume":"52","author":"C Yannouleas","year":"1988","unstructured":"Yannouleas, C., Pacheco, J.M.: An algebraic program for the states associated with the $$ U(5) {\\supset } O(5){\\supset } O(3)$$ chain of groups. Comput. Phys. Commun. 52, 85\u201392 (1988)","journal-title":"Comput. Phys. Commun."},{"key":"12_CR13","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1016\/0010-4655(89)90094-5","volume":"54","author":"C Yannouleas","year":"1989","unstructured":"Yannouleas, C., Pacheco, J.M.: Algebraic manipulation of the states associated with the $$ U(5) {\\supset } O(5){\\supset } O(3)$$ chain of groups: orthonormalization and matrix elements. Comput. Phys. Commun. 54, 315\u2013328 (1989)","journal-title":"Comput. Phys. Commun."},{"key":"12_CR14","doi-asserted-by":"publisher","first-page":"220","DOI":"10.1016\/j.cpc.2015.10.017","volume":"200","author":"TA Welsh","year":"2016","unstructured":"Welsh, T.A., Rowe, D.J.: A computer code for calculations in the algebraic collective model of the atomic nucleus. Comput. Phys. Commun. 200, 220\u2013253 (2016)","journal-title":"Comput. Phys. Commun."},{"key":"12_CR15","doi-asserted-by":"crossref","unstructured":"Ferrari-Ruffino, F., Fortunato, L.: GCM Solver (Ver. 3.0): a mathematica notebook for diagonalization of the geometric collective model (Bohr Hamiltonian) with generalized gneuss-greiner potential. Computation 6, 48 (2018)","DOI":"10.3390\/computation6030048"},{"key":"12_CR16","doi-asserted-by":"publisher","first-page":"1347","DOI":"10.1088\/0305-4470\/16\/7\/012","volume":"16","author":"JQ Chen","year":"1983","unstructured":"Chen, J.Q., et al.: Intrinsic Lie group and nuclear collective rotation about intrinsic axes. J. Phys. A: Math. Gen. 16, 1347\u20131360 (1983)","journal-title":"J. Phys. A: Math. Gen."},{"key":"12_CR17","doi-asserted-by":"publisher","DOI":"10.1142\/5019","volume-title":"Group Representation Theory for Physicists","author":"JQ Chen","year":"2002","unstructured":"Chen, J.Q., Pingand, J., Wang, F.: Group Representation Theory for Physicists. World Sci, Singapore (2002)"},{"key":"12_CR18","first-page":"108","volume":"32","author":"A G\u00f3\u017ad\u017a","year":"2014","unstructured":"G\u00f3\u017ad\u017a, A., et al.: Structure of Bohr type collective spaces - a few symmetry related problems. Nuclear Theor. 32, 108\u2013122 (2014). Eds. A. Georgiewa, N. Minkov, Heron Press, Sofia (2014)","journal-title":"Nuclear Theor."},{"key":"12_CR19","doi-asserted-by":"publisher","first-page":"19","DOI":"10.5506\/APhysPolBSupp.11.19","volume":"11","author":"A G\u00f3\u017ad\u017a","year":"2018","unstructured":"G\u00f3\u017ad\u017a, A., P\u0229drak, A., Gusev, A.A., Vinitsky, S.I.: Point Symmetries in the Nuclear SU(3) Partner Groups Model. Acta Phys. Polonica B Proc. Suppl. 11, 19\u201328 (2018)","journal-title":"Acta Phys. Polonica B Proc. Suppl."},{"key":"12_CR20","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1016\/S0375-9474(99)00023-8","volume":"648","author":"L Pr\u2019ochniak","year":"1999","unstructured":"Pr\u2019ochniak, L., Zajac, K.K., Pomorski, K., et al.: Collective quadrupole excitations in the $$50 < Z$$, $$N < 82$$ nuclei with the general Bohr Hamiltonian. Nucl. Phys. A 648, 181\u2013202 (1999)","journal-title":"Nucl. Phys. A"},{"key":"12_CR21","doi-asserted-by":"publisher","first-page":"123101","DOI":"10.1088\/0954-3899\/36\/12\/123101","volume":"36","author":"L Pr\u2019ochniak","year":"2009","unstructured":"Pr\u2019ochniak, L., Rohozi\u2019nski, S.G.: Quadrupole collective states within the Bohr collective Hamiltonian. J. Phys. G: Nucl. Part. Phys. 36, 123101 (2009)","journal-title":"J. Phys. G: Nucl. Part. Phys."},{"key":"12_CR22","doi-asserted-by":"publisher","unstructured":"Gusev, A.A., Gerdt, V.P., Vinitsky, S.I., Derbov, V.L., G\u00f3\u017ad\u017a, A., P\u0229drak, A.: Symbolic algorithm for generating irreducible bases of point groups in the space of SO(3) group. In: Gerdt, V.P., Koepf, W., Seiler, W.M., Vorozhtsov, E.V. (eds.) CASC 2015. LNCS, vol. 9301, pp. 166\u2013181. Springer, Cham (2015). https:\/\/doi.org\/10.1007\/978-3-319-24021-3_13","DOI":"10.1007\/978-3-319-24021-3_13"},{"key":"12_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"228","DOI":"10.1007\/978-3-319-45641-6_15","volume-title":"Computer Algebra in Scientific Computing","author":"AA Gusev","year":"2016","unstructured":"Gusev, A.A., et al.: Symbolic algorithm for generating irreducible rotational-vibrational bases of point groups. In: Gerdt, V.P., Koepf, W., Seiler, W.M., Vorozhtsov, E.V. (eds.) CASC 2016. LNCS, vol. 9890, pp. 228\u2013242. Springer, Cham (2016). https:\/\/doi.org\/10.1007\/978-3-319-45641-6_15"},{"key":"12_CR24","doi-asserted-by":"crossref","unstructured":"Varshalovitch, D.A., Moskalev, A.N., Hersonsky, V.K.: Quantum Theory of Angular Momentum, Nauka, Leningrad (1975) (also World Scientific, Singapore (1988))","DOI":"10.1142\/0270"},{"key":"12_CR25","doi-asserted-by":"publisher","first-page":"901","DOI":"10.1063\/1.1666074","volume":"13","author":"M Moshinsky","year":"1972","unstructured":"Moshinsky, M., Seligman, T.H., Wolf, K.B.: Canonical transformations and the radial oscillator and Coulomb problems. J. Math. Phys. 13, 901\u2013907 (1972)","journal-title":"J. Math. Phys."},{"key":"12_CR26","volume-title":"Handbook of Mathematical Functions","author":"M Abramowitz","year":"1972","unstructured":"Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. Dover, New York (1972)"},{"key":"12_CR27","doi-asserted-by":"publisher","first-page":"373","DOI":"10.1016\/0029-5582(59)90226-3","volume":"10","author":"DR Bes","year":"1959","unstructured":"Bes, D.R.: The $$\\gamma $$-dependent part of the wave functions representing $$\\gamma $$-unstable surface vibrations. Nucl. Phys. 10, 373\u2013385 (1959)","journal-title":"Nucl. Phys."},{"issue":"2","key":"12_CR28","first-page":"304","volume":"14","author":"AP Budnik","year":"1971","unstructured":"Budnik, A.P., Gay, E.V., Rabotnov, N.S., et al.: Basis wave functions and operator matrices of collective nuclear model. Soviet J. Nuclear Phys. 14(2), 304\u2013314 (1971)","journal-title":"Soviet J. Nuclear Phys."},{"key":"12_CR29","unstructured":"Strang, G.: Linear Algebra and its Applications. Academic press, N. Y. (1976)"},{"key":"12_CR30","unstructured":"Weisstein, E.W.: Gram-Schmidt Orthonormalization. From MathWorld - A Wolfram WebResource. http:\/\/mathworld.wolfram.com\/Gram-SchmidtOrthonormalization.html"},{"key":"12_CR31","unstructured":"MathWorld - A Wolfram WebResource. http:\/\/mathworld.wolfram.com"},{"key":"12_CR32","doi-asserted-by":"crossref","unstructured":"Dvornik, J., Jaguljnjak Lazarevic, A., Lazarevic, D., Uros, M.: Exact arithmetic as a tool for convergence assessment of the IRM-CG method. Heliyon. 6, e03225 (2020). https:\/\/doi.org\/10.1016\/j.heliyon.2020.e03225","DOI":"10.1016\/j.heliyon.2020.e03225"}],"container-title":["Lecture Notes in Computer Science","Computer Algebra in Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-60026-6_12","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,24]],"date-time":"2021-04-24T11:33:13Z","timestamp":1619263993000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-60026-6_12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020]]},"ISBN":["9783030600259","9783030600266"],"references-count":32,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-60026-6_12","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020]]},"assertion":[{"value":"2 October 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"CASC","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Workshop on Computer Algebra in Scientific Computing","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Linz","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Austria","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2020","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14 September 2020","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"18 September 2020","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"casc2020","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/www.casc-conference.org\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"41","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"34","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"83% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3.17","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"5.6","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"The conference was held virtually due to the COVID-19 pandemic. Two invited talks are also included.","order":10,"name":"additional_info_on_review_process","label":"Additional Info on Review Process","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}