{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T00:02:56Z","timestamp":1772150576193,"version":"3.50.1"},"reference-count":75,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,4,14]],"date-time":"2020-04-14T00:00:00Z","timestamp":1586822400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The influence of a spherical boundary on the vacuum fluctuations of a massive scalar field is investigated in the background of a     ( D + 1 )    -dimensional Milne universe, assuming that the field obeys Robin boundary conditions on the sphere. The normalized mode functions are derived for the regions inside and outside the sphere and different vacuum states are discussed. For the conformal vacuum, the Hadamard function is decomposed into boundary-free and sphere-induced contributions and an integral representation is obtained for the latter in both the interior and exterior regions. As important local characteristics of the vacuum state, the vacuum expectation values (VEVs) of the field squared and of the energy-momentum tensor are investigated. It is shown that the vacuum energy-momentum tensor has an off-diagonal component that corresponds to the energy flux along the radial direction. Depending on the coefficient in Robin boundary conditions, the sphere-induced contribution to the vacuum energy and the energy flux can be either positive or negative. At late stages of the expansion and for a massive field the decay of the sphere-induced VEVs, as functions of time, is damping oscillatory. The geometry under consideration is conformally related to that for a static spacetime with negative constant curvature space and the sphere-induced contributions in the corresponding VEVs are compared.<\/jats:p>","DOI":"10.3390\/sym12040619","type":"journal-article","created":{"date-parts":[[2020,4,15]],"date-time":"2020-04-15T04:01:46Z","timestamp":1586923306000},"page":"619","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["The Casimir Densities for a Sphere in the Milne Universe"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6576-9895","authenticated-orcid":false,"given":"Aram A.","family":"Saharian","sequence":"first","affiliation":[{"name":"Department of Physics, Yerevan State University, 1 Alex Manoogian Street, 0025 Yerevan, Armenia"},{"name":"Institute of Applied Problems in Physics NAS RA, 25 Nersessian Street, 0014 Yerevan, Armenia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tigran A.","family":"Petrosyan","sequence":"additional","affiliation":[{"name":"Department of Physics, Yerevan State University, 1 Alex Manoogian Street, 0025 Yerevan, Armenia"},{"name":"Institute of Applied Problems in Physics NAS RA, 25 Nersessian Street, 0014 Yerevan, Armenia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Birrell, N.D., and Davies, P.C.W. (1982). Quantum Fields in Curved Space, Cambridge University Press.","DOI":"10.1017\/CBO9780511622632"},{"key":"ref_2","unstructured":"Grib, A.A., Mamayev, S.G., and Mostepanenko, V.M. (1994). Vacuum Quantum Effects in Strong Fields, Friedmann Laboratory Publishing."},{"key":"ref_3","unstructured":"Fulling, S.A. (1996). Aspects of Quantum Field Theory in Curved Space-Time, Cambridge University Press."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Parker, L., and Toms, D. (2009). Quantum Field Theory in Curved Spacetime: Quantized Fields and Gravity, Cambridge University Press.","DOI":"10.1017\/CBO9780511813924"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1016\/0003-4916(74)90304-2","article-title":"Quantization on spacetime hyperboloids","volume":"84","author":"Sommerfield","year":"1974","journal-title":"Ann. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/0550-3213(74)90551-3","article-title":"Field quantization on the surface X2 = constant","volume":"75","author":"Gromes","year":"1974","journal-title":"Nucl. Phys. B"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1892","DOI":"10.1063\/1.1666554","article-title":"Quantization on hyperboloids and full space-time field expansion","volume":"15","author":"DiSessa","year":"1974","journal-title":"J. Math. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1098\/rspa.1977.0056","article-title":"Quantum vacuum energy in two dimensional space-times","volume":"354","author":"Davies","year":"1977","journal-title":"Proc. R. Soc. Lond. A"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1844","DOI":"10.1103\/PhysRevD.18.1844","article-title":"Stress tensor of massless conformal quantum fields in hyperbolic universes","volume":"18","author":"Bunch","year":"1978","journal-title":"Phys. Rev. D"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"4435","DOI":"10.1103\/PhysRevD.18.4435","article-title":"Massive quantum field theory in two-dimensional Robertson-Walker space-time","volume":"18","author":"Bunch","year":"1978","journal-title":"Phys. Rev. D"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2968","DOI":"10.1103\/PhysRevD.51.2968","article-title":"Particle spectrum created through bubble nucleation and quantum field theory in the Milne universe","volume":"51","author":"Yamamoto","year":"1995","journal-title":"Phys. Rev. D"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"6061","DOI":"10.1103\/PhysRevD.55.6061","article-title":"Quantized gravitational waves in the Milne universe","volume":"55","author":"Tanaka","year":"1997","journal-title":"Phys. Rev. D"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"083531","DOI":"10.1103\/PhysRevD.96.083531","article-title":"Entanglement of the vacuum between left, right, future, and past: The origin of entanglement-induced quantum radiation","volume":"96","author":"Higuchi","year":"2017","journal-title":"Phys. Rev. D"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3905","DOI":"10.1103\/PhysRevD.10.3905","article-title":"Conformal energy-momentum tensor in curved spacetime: Adiabatic regularization and renormalization","volume":"10","author":"Fulling","year":"1974","journal-title":"Phys. Rev. D"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1103\/PhysRevD.16.251","article-title":"Path-integral quantization and cosmological particle production: An example","volume":"16","author":"Chitre","year":"1977","journal-title":"Phys. Rev. D"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1143\/PTP.58.560","article-title":"On a quantized scalar field in some Bianchi-type I universe","volume":"58","author":"Nariai","year":"1977","journal-title":"Prog. Theor. Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"842","DOI":"10.1143\/PTP.58.842","article-title":"On a quantized scalar field in some Bianchi-type I universe. II: DeWitt\u2019s two vacuum states connected causally","volume":"58","author":"Nariai","year":"1977","journal-title":"Prog. Theor. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1143\/PTP.59.296","article-title":"On the creation of scalar particles in an isotropic universe","volume":"59","author":"Nariai","year":"1978","journal-title":"Prog. Theor. Phys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1143\/PTP.63.324","article-title":"Canonical approach to the creation of scalar particles in the Chitre-Hartle model-universe","volume":"63","author":"Nariai","year":"1980","journal-title":"Prog. Theor. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1007\/BF00756617","article-title":"Application of the propagator method to pair production in the Robertson-Walker metric","volume":"12","author":"Mensky","year":"1980","journal-title":"Gen. Rel. Grav."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"892","DOI":"10.1143\/PTP.66.892","article-title":"The renormalized energy-momentum tensor in a Robertson-Walker universe","volume":"66","author":"Azuma","year":"1981","journal-title":"Prog. Theor. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3023","DOI":"10.1103\/PhysRevD.24.3023","article-title":"Uniqueness of the propagator in spacetime with cosmological singularity","volume":"24","author":"Charach","year":"1981","journal-title":"Phys. Rev. D"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3367","DOI":"10.1103\/PhysRevD.26.3367","article-title":"Feynman propagators and particle creation in linearly expanding Bianchi type-I universes","volume":"26","author":"Charach","year":"1982","journal-title":"Phys. Rev. D"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1007\/BF00761454","article-title":"Low-energy behavior of a quantized scalar field in the linearly expanding universe","volume":"14","author":"Azuma","year":"1982","journal-title":"Gen. Rel. Grav."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1298","DOI":"10.1103\/PhysRevD.28.1298","article-title":"Feynman propagator in a linearly expanding universe","volume":"28","author":"Calzetta","year":"1983","journal-title":"Phys. Rev. D"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1088\/0264-9381\/4\/3\/028","article-title":"The Green functions in curved spacetime","volume":"4","author":"Buchbinder","year":"1987","journal-title":"Class. Quantum Grav."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"124017","DOI":"10.1103\/PhysRevD.60.124017","article-title":"Physical distinction among alternative vacuum states in flat spacetime geometries","volume":"60","author":"Redmount","year":"1999","journal-title":"Phys. Rev. D"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"106005","DOI":"10.1103\/PhysRevD.66.106005","article-title":"Quantum fields in a big-crunch-big-bang spacetime","volume":"66","author":"Tolley","year":"2002","journal-title":"Phys. Rev. D"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1850177","DOI":"10.1142\/S0219887818501773","article-title":"Scalar Casimir effect in a linearly expanding universe","volume":"15","author":"Saharian","year":"2018","journal-title":"Int. J. Geom. Methods Mod. Phys."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Elizalde, E., Odintsov, S.D., Romeo, A., Bytsenko, A.A., and Zerbini, S. (1994). Zeta Regularization Techniques with Applications, World Scientific.","DOI":"10.1142\/9789812779342"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Mostepanenko, V.M., and Trunov, N.N. (1997). The Casimir Effect and Its Applications, Clarendon.","DOI":"10.1093\/oso\/9780198539988.001.0001"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Milton, K.A. (2002). The Casimir Effect: Physical Manifestation of Zero-Point Energy, World Scientific.","DOI":"10.1142\/9789812810526"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Parsegian, V.A. (2005). Van der Vaals Forces: A Handbook for Biologists, Chemists, Engineers, and Physicists, Cambridge University Press.","DOI":"10.1017\/CBO9780511614606"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Bordag, M., Klimchitskaya, G.L., Mohideen, U., and Mostepanenko, V.M. (2009). Advances in the Casimir Effect, Oxford University Press.","DOI":"10.1093\/acprof:oso\/9780199238743.001.0001"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Dalvit, D., Milonni, P., Roberts, D., and da Rosa, F. (2011). Casimir Physics, Springer.","DOI":"10.1007\/978-3-642-20288-9"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"846","DOI":"10.1016\/S0031-8914(53)80095-9","article-title":"Introductory remarks on quantum electrodynamics","volume":"19","author":"Casimir","year":"1953","journal-title":"Physica"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1764","DOI":"10.1103\/PhysRev.174.1764","article-title":"Quantum electromagnetic zero-point energy of a conducting spherical shell and the Casimir model for a charged particle","volume":"174","author":"Boyer","year":"1968","journal-title":"Phys. Rev."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1324","DOI":"10.1063\/1.1666141","article-title":"Quantum electromagnetic zero-point energy of a conducting spherical shell","volume":"13","author":"Davies","year":"1972","journal-title":"J. Math. Phys."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/0003-4916(78)90083-0","article-title":"Electromagnetic waves near perfect conductors. II. Casimir effect","volume":"112","author":"Balian","year":"1978","journal-title":"Ann. Phys."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1016\/0003-4916(78)90161-6","article-title":"Casimir self-stress on a perfectly conducting spherical shell","volume":"115","author":"Milton","year":"1978","journal-title":"Ann. Phys."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"085009","DOI":"10.1103\/PhysRevD.82.085009","article-title":"Casimir effect of the electromagnetic field in D-dimensional spherically symmetric cavities","volume":"82","author":"Teo","year":"2010","journal-title":"Phys. Rev. D"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"081701(R)","DOI":"10.1103\/PhysRevD.84.081701","article-title":"Exact solution for the Casimir stress in a spherically symmetric medium","volume":"84","author":"Leonhardt","year":"2011","journal-title":"Phys. Rev. D"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"064005","DOI":"10.1103\/PhysRevD.85.064005","article-title":"Casimir densities for a spherical boundary in de Sitter spacetime","volume":"85","author":"Milton","year":"2012","journal-title":"Phys. Rev. D"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/0550-3213(81)90201-7","article-title":"Electromagnetic vacuum fields in a spherical cavity","volume":"192","author":"Olaussen","year":"1981","journal-title":"Nucl. Phys. B"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1016\/0370-2693(81)90613-4","article-title":"Chromomagnetic vacuum fields in a spherical bag","volume":"100","author":"Olaussen","year":"1981","journal-title":"Phys. Lett. B"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/0003-4916(83)90196-3","article-title":"Electromagnetic Casimir densities in dielectric spherical media","volume":"149","author":"Brevik","year":"1983","journal-title":"Ann. Phys."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"805","DOI":"10.1139\/p84-111","article-title":"Casimir stress in spherical media when \u03b5\u03bc = 1","volume":"62","author":"Brevik","year":"1984","journal-title":"Can. J. Phys."},{"key":"ref_48","first-page":"28","article-title":"Casimir effect for a perfectly conducting spherical surface","volume":"83","author":"Grigoryan","year":"1986","journal-title":"Dokl. Akad. Nauk Arm. SSR"},{"key":"ref_49","first-page":"3","article-title":"Photon vacuum in a spherical layer between perfectly conducting surfaces","volume":"22","author":"Grigoryan","year":"1987","journal-title":"Izv. Akad. Nauk. Arm. SSR Fiz."},{"key":"ref_50","unstructured":"Saharian, A.A. (2008). The Generalized Abel\u2013Plana Formula. Applications to Bessel Functions and Casimir Effect, Yerevan State University Publishing House. Report No. ICTP\/2007\/082."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"125007","DOI":"10.1103\/PhysRevD.63.125007","article-title":"Scalar Casimir effect for D-dimensional spherically symmetric Robin boundaries","volume":"63","author":"Saharian","year":"2001","journal-title":"Phys. Rev. D"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"3765","DOI":"10.1088\/0264-9381\/20\/16\/315","article-title":"Casimir densities for a spherical shell in the global monopole background","volume":"20","author":"Saharian","year":"2003","journal-title":"Class. Quantum Grav."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"4301","DOI":"10.1142\/S0217751X04019378","article-title":"Casimir densities for two concentric spherical shells in the global monopole space-time","volume":"19","author":"Saharian","year":"2004","journal-title":"Int. J. Mod. Phys. A"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1023\/B:ASYS.0000031841.59310.c2","article-title":"Quantum vacuum effects in the gravitational field of a global monopole","volume":"47","author":"Saharian","year":"2004","journal-title":"Astrophysics"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"3543","DOI":"10.1088\/0305-4470\/37\/10\/017","article-title":"Spinor Casimir densities for a spherical shell in the global monopole spacetime","volume":"37","author":"Saharian","year":"2004","journal-title":"J. Phys. A Math. Gen."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"4673","DOI":"10.1088\/0264-9381\/23\/14\/008","article-title":"Spinor Casimir effect for concentric spherical shells in the global monopole spacetime","volume":"23","author":"Saharian","year":"2006","journal-title":"Class. Quantum Grav."},{"key":"ref_57","first-page":"049","article-title":"Vacuum polarization by a global monopole with finite core","volume":"10","author":"Saharian","year":"2006","journal-title":"J. High Energy Phys."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"065019","DOI":"10.1103\/PhysRevD.75.065019","article-title":"Polarization of the fermionic vacuum by a global monopole with finite core","volume":"75","author":"Saharian","year":"2007","journal-title":"Phys. Rev. D"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1016\/j.nuclphysb.2005.07.011","article-title":"Casimir densities for a spherical brane in Rindler-like spacetimes","volume":"724","author":"Saharian","year":"2005","journal-title":"Nucl. Phys. B"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1016\/j.physletb.2006.04.037","article-title":"Surface Casimir densities on a spherical brane in Rindler-like spacetimes","volume":"637","author":"Saharian","year":"2006","journal-title":"Phys. Lett. B"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"089","DOI":"10.1088\/1126-6708\/2007\/02\/089","article-title":"Casimir densities for two spherical branes in Rindler-like spacetimes","volume":"02","author":"Saharian","year":"2007","journal-title":"J. High Energy Phys."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"2331","DOI":"10.1088\/0264-9381\/18\/12\/308","article-title":"Casimir effect for a spherical shell in de Sitter space","volume":"18","author":"Setare","year":"2001","journal-title":"Class. Quantum Grav."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"4823","DOI":"10.1088\/0264-9381\/18\/22\/308","article-title":"Casimir stress for concentric spheres in de Sitter space","volume":"18","author":"Setare","year":"2001","journal-title":"Class. Quantum Grav."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"415203","DOI":"10.1088\/1751-8113\/41\/41\/415203","article-title":"A summation formula over the zeros of the associated Legendre function with a physical application","volume":"41","author":"Saharian","year":"2008","journal-title":"J. Phys. A Math. Theor."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"465210","DOI":"10.1088\/1751-8113\/42\/46\/465210","article-title":"A summation formula over the zeros of a combination of the associated Legendre functions with a physical application","volume":"42","author":"Saharian","year":"2009","journal-title":"J. Phys. A Math. Theor."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"3047","DOI":"10.1140\/epjc\/s10052-014-3047-4","article-title":"Wightman function and the Casimir effect for a Robin sphere in a constant curvature space","volume":"74","author":"Bellucci","year":"2014","journal-title":"Eur. Phys. J. C"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"105006","DOI":"10.1103\/PhysRevD.89.105006","article-title":"Casimir densities from coexisting vacua","volume":"89","author":"Bellucci","year":"2014","journal-title":"Phys. Rev. D"},{"key":"ref_68","unstructured":"Abramowitz, M., and  Stegun, I.A. (1972). Handbook of Mathematical Functions, Dover."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"085005","DOI":"10.1103\/PhysRevD.69.085005","article-title":"Energy-momentum tensor for a scalar field on manifolds with boundaries","volume":"69","author":"Saharian","year":"2004","journal-title":"Phys. Rev. D"},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"038","DOI":"10.1007\/JHEP02(2013)038","article-title":"Entanglement entropy in de Sitter space","volume":"02","author":"Maldacena","year":"2013","journal-title":"J. High Energy Phys."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"072","DOI":"10.1007\/JHEP07(2014)072","article-title":"Entanglement entropy of \u03b1-vacua in de Sitter space","volume":"07","author":"Kanno","year":"2014","journal-title":"J. High Energy Phys."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1140\/epjc\/s10052-017-5503-4","article-title":"Entangled de Sitter from stringy axionic Bell pair I: An analysis using Bunch-Davies vacuum","volume":"78","author":"Choudhury","year":"2018","journal-title":"Eur. Phys. J. C"},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"114606","DOI":"10.1016\/j.nuclphysb.2019.03.018","article-title":"Quantum entanglement in de Sitter space from stringy axion: An analysis using \u03b1 vacua","volume":"943","author":"Choudhury","year":"2019","journal-title":"Nucl. Phys. B"},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1140\/epjc\/s10052-019-7582-x","article-title":"Spectrum of cosmological correlation from vacuum fluctuation of stringy axion in entangled de Sitter space","volume":"80","author":"Choudhury","year":"2020","journal-title":"Eur. Phys. J. C"},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"2979","DOI":"10.1103\/PhysRevD.51.2979","article-title":"Euclidean vacuum mode functions for a scalar field on open de Sitter space","volume":"51","author":"Sasaki","year":"1995","journal-title":"Phys. Rev. D"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/4\/619\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:21:08Z","timestamp":1760361668000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/4\/619"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,14]]},"references-count":75,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,4]]}},"alternative-id":["sym12040619"],"URL":"https:\/\/doi.org\/10.3390\/sym12040619","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,4,14]]}}}