{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T06:06:48Z","timestamp":1775023608609,"version":"3.50.1"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T00:00:00Z","timestamp":1680307200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,4,17]],"date-time":"2023-04-17T00:00:00Z","timestamp":1681689600000},"content-version":"vor","delay-in-days":16,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100006690","name":"Politecnico di Milano","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100006690","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2023,4]]},"abstract":"Abstract<\/jats:title>Given a positive operator A<\/jats:italic> on some Hilbert space, and a nonnegative decreasing summable function $$\\mu $$<\/jats:tex-math>\n \u03bc<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, we consider the abstract equation with memory $$\\begin{aligned} \\ddot{u}(t)+ A u(t)- \\int _0^t \\mu (s)Au(t-s) ds=0 \\end{aligned}$$<\/jats:tex-math>\n \n \n \n \n \n \n u<\/mml:mi>\n \u00a8<\/mml:mo>\n <\/mml:mover>\n \n (<\/mml:mo>\n t<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n +<\/mml:mo>\n A<\/mml:mi>\n u<\/mml:mi>\n \n (<\/mml:mo>\n t<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n -<\/mml:mo>\n \n \u222b<\/mml:mo>\n 0<\/mml:mn>\n t<\/mml:mi>\n <\/mml:msubsup>\n \u03bc<\/mml:mi>\n \n (<\/mml:mo>\n s<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n A<\/mml:mi>\n u<\/mml:mi>\n \n (<\/mml:mo>\n t<\/mml:mi>\n -<\/mml:mo>\n s<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n d<\/mml:mi>\n s<\/mml:mi>\n =<\/mml:mo>\n 0<\/mml:mn>\n <\/mml:mrow>\n <\/mml:mtd>\n <\/mml:mtr>\n <\/mml:mtable>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:disp-formula>modeling the dynamics of linearly viscoelastic solids. The purpose of this work is to provide numerical evidence of the fact that the energy $$\\begin{aligned} {{\\textsf{E}}}(t)=\\Big (1-\\int _0^t\\mu (s)ds\\Big )\\Vert u(t)\\Vert ^2_1+\\Vert \\dot{u}(t)\\Vert ^2 +\\int _0^t\\mu (s)\\Vert u(t)-u(t-s)\\Vert ^2_1ds \\end{aligned}$$<\/jats:tex-math>\n \n \n \n \n \n E<\/mml:mi>\n \n (<\/mml:mo>\n t<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n =<\/mml:mo>\n \n (<\/mml:mo>\n <\/mml:mrow>\n 1<\/mml:mn>\n -<\/mml:mo>\n \n \u222b<\/mml:mo>\n 0<\/mml:mn>\n t<\/mml:mi>\n <\/mml:msubsup>\n \n \n \u03bc<\/mml:mi>\n \n (<\/mml:mo>\n s<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n d<\/mml:mi>\n s<\/mml:mi>\n \n )<\/mml:mo>\n <\/mml:mrow>\n \u2016<\/mml:mo>\n u<\/mml:mi>\n \n (<\/mml:mo>\n t<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n \u2016<\/mml:mo>\n <\/mml:mrow>\n 1<\/mml:mn>\n 2<\/mml:mn>\n <\/mml:msubsup>\n \n +<\/mml:mo>\n \u2016<\/mml:mo>\n <\/mml:mrow>\n \n u<\/mml:mi>\n \u02d9<\/mml:mo>\n <\/mml:mover>\n \n \n \n (<\/mml:mo>\n t<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n \u2016<\/mml:mo>\n <\/mml:mrow>\n 2<\/mml:mn>\n <\/mml:msup>\n +<\/mml:mo>\n \n \u222b<\/mml:mo>\n 0<\/mml:mn>\n t<\/mml:mi>\n <\/mml:msubsup>\n \u03bc<\/mml:mi>\n \n (<\/mml:mo>\n s<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n \n \n \u2016<\/mml:mo>\n u<\/mml:mi>\n \n (<\/mml:mo>\n t<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n -<\/mml:mo>\n u<\/mml:mi>\n \n (<\/mml:mo>\n t<\/mml:mi>\n -<\/mml:mo>\n s<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n \u2016<\/mml:mo>\n <\/mml:mrow>\n 1<\/mml:mn>\n 2<\/mml:mn>\n <\/mml:msubsup>\n d<\/mml:mi>\n s<\/mml:mi>\n <\/mml:mrow>\n <\/mml:mtd>\n <\/mml:mtr>\n <\/mml:mtable>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:disp-formula>of any nontrivial solution cannot decay faster than exponential, no matter how fast might be the decay of the memory kernel $$\\mu $$<\/jats:tex-math>\n \u03bc<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. This will be accomplished by simulating the integro-differential equation for different choices of the memory kernel $$\\mu $$<\/jats:tex-math>\n \u03bc<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and of the initial data.<\/jats:p>","DOI":"10.1007\/s00211-023-01351-1","type":"journal-article","created":{"date-parts":[[2023,4,17]],"date-time":"2023-04-17T11:05:02Z","timestamp":1681729502000},"page":"611-633","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Lack of superstable trajectories in linear viscoelasticity: a numerical approach"],"prefix":"10.1007","volume":"153","author":[{"given":"Paola F.","family":"Antonietti","sequence":"first","affiliation":[]},{"given":"Lorenzo","family":"Liverani","sequence":"additional","affiliation":[]},{"given":"Vittorino","family":"Pata","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,4,17]]},"reference":[{"key":"1351_CR1","doi-asserted-by":"publisher","first-page":"491","DOI":"10.1080\/00207169908804871","volume":"72","author":"A Aky\u00fcz","year":"1999","unstructured":"Aky\u00fcz, A., Sezer, M.: A Chebyshev collocation method for the solution of linear integro-differential equations. Int. J. Comput. Math. 72, 491\u2013507 (1999)","journal-title":"Int. J. Comput. Math."},{"key":"1351_CR2","first-page":"269","volume":"50","author":"VV Chepyzhov","year":"2006","unstructured":"Chepyzhov, V.V., Pata, V.: Some remarks on stability of semigroups arising from linear viscoelasticity. Asymptot. Anal. 50, 269\u2013291 (2006)","journal-title":"Asymptot. Anal."},{"key":"1351_CR3","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1103\/RevModPhys.33.239","volume":"33","author":"BD Coleman","year":"1961","unstructured":"Coleman, B.D., Noll, W.: Foundations of linear viscoelasticity. Rev. Mod. Phys. 33, 239\u2013249 (1961)","journal-title":"Rev. Mod. Phys."},{"key":"1351_CR4","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1016\/j.jfa.2022.109422","volume":"282","author":"M Conti","year":"2022","unstructured":"Conti, M., Dell\u2019Oro, F., Pata, V.: Some unexplored questions arising in linear viscoelasticity. J. Funct. Anal. 282, 10 (2022)","journal-title":"J. Funct. Anal."},{"key":"1351_CR5","doi-asserted-by":"publisher","first-page":"6","DOI":"10.1007\/s00033-019-1229-5","volume":"71","author":"M Conti","year":"2020","unstructured":"Conti, M., Pata, V.: General decay properties of abstract linear viscoelasticity. Z. Angew. Math. Phys. 71, 6 (2020)","journal-title":"Z. Angew. Math. Phys."},{"key":"1351_CR6","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1353\/ajm.2018.0008","volume":"140","author":"M Conti","year":"2018","unstructured":"Conti, M., Danese, V., Giorgi, C., Pata, V.: A model of viscoelasticity with time-dependent memory kernels. Am. J. Math. 140, 349\u2013389 (2018)","journal-title":"Am. J. Math."},{"key":"1351_CR7","doi-asserted-by":"publisher","first-page":"1687","DOI":"10.1353\/ajm.2018.0049","volume":"140","author":"M Conti","year":"2018","unstructured":"Conti, M., Danese, V., Pata, V.: Viscoelasticity with time-dependent memory kernels, II: asymptotic behavior of solutions. Am. J. Math. 140, 1687\u20131729 (2018)","journal-title":"Am. J. Math."},{"key":"1351_CR8","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1142\/S0218202508002590","volume":"18","author":"M Conti","year":"2008","unstructured":"Conti, M., Gatti, S., Pata, V.: Uniform decay properties of linear Volterra integro-differential equations. Math. Models Meth. Appl. Anal. 18, 21\u201345 (2008)","journal-title":"Math. Models Meth. Appl. Anal."},{"key":"1351_CR9","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1142\/S0219199712500125","volume":"14","author":"M Conti","year":"2012","unstructured":"Conti, M., Marchini, E., Pata, V.: Approximating infinite delay with finite delay. Commun. Contemp. Math. 14, 13 (2012)","journal-title":"Commun. Contemp. Math."},{"key":"1351_CR10","doi-asserted-by":"publisher","first-page":"554","DOI":"10.1016\/0022-0396(70)90101-4","volume":"7","author":"CM Dafermos","year":"1970","unstructured":"Dafermos, C.M.: An abstract Volterra equation with applications to linear viscoelasticity. J. Differ. Equ. 7, 554\u2013569 (1970)","journal-title":"J. Differ. Equ."},{"key":"1351_CR11","doi-asserted-by":"publisher","first-page":"361","DOI":"10.2528\/PIER07090403","volume":"78","author":"M Dehghan","year":"2008","unstructured":"Dehghan, M., Shakeri, F.: Solution of an integro-differential equation arising in oscillating magnetic fields using he\u2019s homotopy perturbation method. Prog. Electromagn. Res. 78, 361\u2013376 (2008)","journal-title":"Prog. Electromagn. Res."},{"key":"1351_CR12","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1007\/BF00251609","volume":"37","author":"CM Dafermos","year":"1970","unstructured":"Dafermos, C.M.: Asymptotic stability in viscoelasticity. Arch. Ration. Mech. Anal. 37, 297\u2013308 (1970)","journal-title":"Arch. Ration. Mech. Anal."},{"key":"1351_CR13","doi-asserted-by":"publisher","first-page":"2388","DOI":"10.1002\/mana.201700212","volume":"291","author":"F Dell\u2019Oro","year":"2018","unstructured":"Dell\u2019Oro, F.: On the spectrum of the equation of linear viscoelasticity. Math. Nachr. 291, 2388\u20132396 (2018)","journal-title":"Math. Nachr."},{"key":"1351_CR14","doi-asserted-by":"publisher","first-page":"641","DOI":"10.1007\/s00245-016-9365-1","volume":"76","author":"F Dell\u2019Oro","year":"2017","unstructured":"Dell\u2019Oro, F., Pata, V.: On the Moore-Gibson-Thompson equation and its relation to linear viscoelasticity. Appl. Math. Optim. 76, 641\u2013655 (2017)","journal-title":"Appl. Math. Optim."},{"key":"1351_CR15","volume-title":"One-Parameter Semigroups for Linear Evolution Equations","author":"KJ Engel","year":"2000","unstructured":"Engel, K.J., Nagel, R.: One-Parameter Semigroups for Linear Evolution Equations. Springer, New York (2000)"},{"key":"1351_CR16","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1007\/s00205-010-0300-3","volume":"198","author":"M Fabrizio","year":"2010","unstructured":"Fabrizio, M., Giorgi, C., Pata, V.: A new approach to equations with memory. Arch. Ration. Mech. Anal. 198, 189\u2013232 (2010)","journal-title":"Arch. Ration. Mech. Anal."},{"key":"1351_CR17","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/BF00375589","volume":"116","author":"M Fabrizio","year":"1991","unstructured":"Fabrizio, M., Lazzari, B.: On the existence and asymptotic stability of solutions for linear viscoelastic solids. Arch. Ration. Mech. Anal. 116, 139\u2013152 (1991)","journal-title":"Arch. Ration. Mech. Anal."},{"key":"1351_CR18","volume-title":"Mathematical Problems in Linear Viscoelasticity. SIAM Studies in Applied Mathematics No. 12","author":"M Fabrizio","year":"1992","unstructured":"Fabrizio, M., Morro, A.: Mathematical Problems in Linear Viscoelasticity. SIAM Studies in Applied Mathematics No. 12. SIAM, Philadelphia (1992)"},{"key":"1351_CR19","doi-asserted-by":"publisher","first-page":"1245","DOI":"10.1080\/0003681021000035588","volume":"81","author":"M Fabrizio","year":"2002","unstructured":"Fabrizio, M., Polidoro, S.: Asymptotic decay for some differential systems with fading memory. Appl. Anal. 81, 1245\u20131264 (2002)","journal-title":"Appl. Anal."},{"key":"1351_CR20","doi-asserted-by":"publisher","first-page":"659","DOI":"10.1090\/qam\/1486541","volume":"55","author":"C Giorgi","year":"1997","unstructured":"Giorgi, C., Lazzari, B.: On the stability for linear viscoelastic solids. Q. Appl. Math. 55, 659\u2013675 (1997)","journal-title":"Q. Appl. Math."},{"key":"1351_CR21","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1006\/jmaa.2001.7437","volume":"260","author":"C Giorgi","year":"2001","unstructured":"Giorgi, C., Mu\u00f1oz Rivera, J.E., Pata, V.: Global attractors for a semilinear hyperbolic equation in viscoelasticity. J. Math. Anal. Appl. 260, 83\u201399 (2001)","journal-title":"J. Math. Anal. Appl."},{"key":"1351_CR22","first-page":"155","volume-title":"Evolution Equations, Semigroups and Functional Analysis, Progress in Nonlinear Differential Equations and Their Applications, No. 50","author":"M Grasselli","year":"2002","unstructured":"Grasselli, M., Pata, V.: Uniform attractors of nonautonomous systems with memory. In: Lorenzi, A., Ruf, B. (eds.) Evolution Equations, Semigroups and Functional Analysis, Progress in Nonlinear Differential Equations and Their Applications, No. 50, pp. 155\u2013178. Birkh\u00e4user, Boston (2002)"},{"key":"1351_CR23","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1007\/BF00253942","volume":"11","author":"ME Gurtin","year":"1962","unstructured":"Gurtin, M.E., Sternberg, E.: On the linear theory of viscoelasticity. Arch. Ration. Mech. Anal. 11, 291\u2013356 (1962)","journal-title":"Arch. Ration. Mech. Anal."},{"key":"1351_CR24","doi-asserted-by":"publisher","first-page":"392","DOI":"10.1016\/j.cpc.2013.09.008","volume":"185","author":"A Gelmi","year":"2014","unstructured":"Gelmi, A., Jorquera, H.: IDSOLVER: a general purpose solver for nth-order integro-differential equations. Comp. Phys. Commun. 185, 392\u2013397 (2014)","journal-title":"Comp. Phys. Commun."},{"key":"1351_CR25","first-page":"1","volume-title":"Handbuch der Physik","author":"MJ Leitman","year":"1973","unstructured":"Leitman, M.J., Fisher, G.M.C.: The linear theory of viscoelasticity. In: Fl\u00fcgge, S. (ed.) Handbuch der Physik, vol. VIa\/3, pp. 1\u2013123. Springer, Berlin (1973)"},{"key":"1351_CR26","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF00917570","volume":"47","author":"K Liu","year":"1996","unstructured":"Liu, K., Liu, Z.: On the type of $$C_0$$-semigroup associated with the abstract linear viscoelastic system. Z. Angew. Math. Phys. 47, 1\u201315 (1996)","journal-title":"Z. Angew. Math. Phys."},{"key":"1351_CR27","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1090\/qam\/1373836","volume":"54","author":"Z Liu","year":"1996","unstructured":"Liu, Z., Zheng, S.: On the exponential stability of linear viscoelasticity and thermoviscoelasticity. Q. Appl. Math. 54, 21\u201331 (1996)","journal-title":"Q. Appl. Math."},{"key":"1351_CR28","volume-title":"Semigroups Associated with Dissipative Systems. Chapman & Hall\/CRC Research Notes in Mathematics, No. 398","author":"Z Liu","year":"1999","unstructured":"Liu, Z., Zheng, S.: Semigroups Associated with Dissipative Systems. Chapman & Hall\/CRC Research Notes in Mathematics, No. 398. Chapman & Hall, Boca Raton (1999)"},{"key":"1351_CR29","volume-title":"A Treatise on Mathematical Theory of Elasticity","author":"AH Love","year":"1944","unstructured":"Love, A.H.: A Treatise on Mathematical Theory of Elasticity. Dover, New York (1944)"},{"key":"1351_CR30","doi-asserted-by":"publisher","first-page":"629","DOI":"10.1090\/qam\/1306041","volume":"52","author":"JE Mu\u00f1oz Rivera","year":"1994","unstructured":"Mu\u00f1oz Rivera, J.E.: Asymptotic behaviour in linear viscoelasticity. Q. Appl. Math. 52, 629\u2013648 (1994)","journal-title":"Q. Appl. Math."},{"key":"1351_CR31","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1007\/BF00042192","volume":"44","author":"JE Mu\u00f1oz Rivera","year":"1996","unstructured":"Mu\u00f1oz Rivera, J.E., Lapa, E.C., Barreto, R.: Decay rates for viscoelastic plates with memory. J. Elast. 44, 61\u201387 (1996)","journal-title":"J. Elast."},{"key":"1351_CR32","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1090\/S0033-569X-06-01010-4","volume":"64","author":"V Pata","year":"2006","unstructured":"Pata, V.: Exponential stability in linear viscoelasticity. Q. Appl. Math. 64, 499\u2013513 (2006)","journal-title":"Q. Appl. Math."},{"key":"1351_CR33","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1007\/s00032-009-0098-3","volume":"77","author":"V Pata","year":"2009","unstructured":"Pata, V.: Stability and exponential stability in linear viscoelasticity. Milan J. Math. 77, 333\u2013360 (2009)","journal-title":"Milan J. Math."},{"key":"1351_CR34","doi-asserted-by":"publisher","first-page":"721","DOI":"10.3934\/cpaa.2010.9.721","volume":"9","author":"V Pata","year":"2010","unstructured":"Pata, V.: Exponential stability in linear viscoelasticity with almost flat memory kernels. Commun. Pure Appl. Anal. 9, 721\u2013730 (2010)","journal-title":"Commun. Pure Appl. Anal."},{"key":"1351_CR35","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5561-1","volume-title":"Semigroups of Linear Operators and Applications to Partial Differential Equations","author":"A Pazy","year":"1983","unstructured":"Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer, New York (1983)"},{"key":"1351_CR36","doi-asserted-by":"publisher","DOI":"10.1007\/b98885","volume-title":"Numerical Mathematics","author":"A Quarteroni","year":"2007","unstructured":"Quarteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics, 2nd edn. Springer, Berlin (2007)","edition":"2"},{"key":"1351_CR37","volume-title":"Mathematical Problems in Viscoelasticity","author":"M Renardy","year":"1987","unstructured":"Renardy, M., Hrusa, W.J., Nohel, J.A.: Mathematical Problems in Viscoelasticity. Wiley, New York (1987)"},{"key":"1351_CR38","volume-title":"Functional Analysis","author":"W Rudin","year":"1973","unstructured":"Rudin, W.: Functional Analysis. McGraw-Hill, New York (1973)"},{"key":"1351_CR39","volume-title":"Computer Solution of Ordinary Differential Equations: The Initial Value Problem","author":"LF Shampine","year":"1975","unstructured":"Shampine, L.F., Gordon, M.K.: Computer Solution of Ordinary Differential Equations: The Initial Value Problem. W.H. Freeman, San Francisco (1975)"},{"key":"1351_CR40","doi-asserted-by":"publisher","first-page":"3175","DOI":"10.1016\/j.camwa.2008.07.020","volume":"56","author":"A Yildirim","year":"2008","unstructured":"Yildirim, A.: Solution of BVPs for fourth-order integro-differential equations by using homotopy perturbation method. Comput. Math. Appl. 56, 3175\u20133180 (2008)","journal-title":"Comput. Math. Appl."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-023-01351-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00211-023-01351-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-023-01351-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,11]],"date-time":"2023-05-11T13:02:13Z","timestamp":1683810133000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00211-023-01351-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4]]},"references-count":40,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2023,4]]}},"alternative-id":["1351"],"URL":"https:\/\/doi.org\/10.1007\/s00211-023-01351-1","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,4]]},"assertion":[{"value":"6 October 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 February 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 April 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 April 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}