CINXE.COM

<!DOCTYPE html><html lang="en-US"><head><title>Just a moment...</title><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta http-equiv="X-UA-Compatible" content="IE=Edge"><meta name="robots" content="noindex,nofollow"><meta name="viewport" content="width=device-width,initial-scale=1"><style>*{box-sizing:border-box;margin:0;padding:0}html{line-height:1.15;-webkit-text-size-adjust:100%;color:#313131;font-family:system-ui,-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Helvetica Neue,Arial,Noto Sans,sans-serif,Apple Color Emoji,Segoe UI Emoji,Segoe UI Symbol,Noto Color Emoji}body{display:flex;flex-direction:column;height:100vh;min-height:100vh}.main-content{margin:8rem auto;max-width:60rem;padding-left:1.5rem}@media (width <= 720px){.main-content{margin-top:4rem}}.h2{font-size:1.5rem;font-weight:500;line-height:2.25rem}@media (width <= 720px){.h2{font-size:1.25rem;line-height:1.5rem}}#challenge-error-text{background-image:url(data:image/svg+xml;base64,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);background-repeat:no-repeat;background-size:contain;padding-left:34px}@media (prefers-color-scheme:dark){body{background-color:#222;color:#d9d9d9}}</style><meta http-equiv="refresh" content="120"></head><body class="no-js"><div class="main-wrapper" role="main"><div class="main-content"><noscript><div class="h2"><span id="challenge-error-text">Enable JavaScript and cookies to continue</span></div></noscript></div></div><script>(function(){window._cf_chl_opt={cvId: '3',cZone: "publications.waset.org",cType: 'non-interactive',cRay: '91356e327e998819',cH: 'VK4iidGWPOvCX2qQrByJloXoYSmakhHIjxZj0FTm4GM-1739791670-1.2.1.1-bCEIMOuBZwID1kJQYrGeIr0u3i9OnGyBsOlZyFIlELAvYKouDYY2iKIZuZJdmwXL',cUPMDTk: "\/abstracts\/search?q=eigenvalues&__cf_chl_tk=hgOqv0DEgmHDKNVnIp0B9kFCjCFbksKc0vee3jUh1xU-1739791670-1.0.1.1-4jNGrn6ZENs0zdeFEIwUgFGoaTmBPsoPieqlTq9xkvI",cFPWv: 'b',cITimeS: '1739791670',cTTimeMs: '1000',cMTimeMs: '120000',cTplC: 0,cTplV: 5,cTplB: 'cf',cK: "",fa: "\/abstracts\/search?q=eigenvalues&__cf_chl_f_tk=hgOqv0DEgmHDKNVnIp0B9kFCjCFbksKc0vee3jUh1xU-1739791670-1.0.1.1-4jNGrn6ZENs0zdeFEIwUgFGoaTmBPsoPieqlTq9xkvI",md: "Lqb0hj.rNuGw4c.k5Er_5V3EjzS2rBV03ems5ylPK9U-1739791670-1.2.1.1-uVluaeuQ7AOiEDwUAs7mBOXNHsZlwK.KTimnvddDpfcKo6rgnVAgoNlBHIiByvr3VAysQZ9un0QRDgF5a_VgSYmyz6aa19Q16OUYNGUrgyxY3j0NiqDsPYnEgr3GX2v93m15Ktd_IgnxEqeXtcHSrrVJdWK3XQB1..R.Wvlruivcku8o_oNbbp1xybHSZ2LS4NWD7fW4fV7sC6L3EGP8yCuNOQ1Nrw3bqfV8p0dmpkxlhE6eWh5ErYHOYEaAYvf1T3rst1vwvL9W8uA19rkRVDu0EN2mFmE1yZQ.TUGOn1IA1mpEY7SMXXV7kw0XUKoJ.aAi6Yf870kP.371z1u6mURiqmkjaWlYvlspnYlMI1eYpJx6EPxL6kJt83xBLBJLkMu0TxlLKSTiAz__RlmMSSJPZ9URbCRMK10mGmSK1HmKTN.SQIoF4dm90jeSpGOxukD.kggbBjmCouwYbM3JDJFsAQQTFXzgVTLc1AKdwqqxi3FfRD9MyuXZeZLmd4I3sR53sZut5SPT8E1QHfg2xkT08URFZ3ZZuLHYiq777H14xi4iY.S3aNi1prw_UhEOUyZXQAIJXq37j01s9_i1b7nSN6QTKR4fCO.eA3yc4m1.Tx617G6ZvyE34A0rwueE35LewoQ3wZPfTyvsDuJ_uIkmQMlI.PNaSAPMs5EGFUVQH0Qfl1xh2fDZMP.HUUeUknnh732g4h92.LJARCIfLGaT3qKlilBKKvpeXl9iunzt40pd98FXmMHkfriu8nTyqMWgaZiwlXOt7bzToJ6D7K9TjUCn3aUDt2ZnwDcXxLpCoD4bBwGVHU1diwCrfDXyeBtw..e5nIFZQHP1dUSdVN6gpboPzrDxhI6DSLUz0.RXbVKcPcxx62HcRpL04YMmh.80nW.MwxQxOgtjSCDdsj7yObFyO6sr7Kbj8ugr6USXz5KG5A4x9RXosYHcOpOh4dUGs8YtV8vV3P0msEGc_SgIzy7PysKXbC_SrapWuRenlPcKuzOW8wXanca8o6P5GRjQ8Suy_q5H3QVzdMKeirZwnIjVZeQ0AN.091oWjEz6xEQZTqAlLGrtXLLmDbPZ81QZxVVSV.apsRtkT5OlfYBD.k4hDIY34zHV0m6AYJGB7rzTeP4iJT0xV_edssGxQQhIAruU7myLNSi6VzMG0dkkNpmZkzEVzQh2R5F3ujftm9u4PWbS4WdnUlK10wLpTGALubfVgOctrgt15QNnAXkZpxfZRsQRRcoO3asFMhCM1ONuCH49rDGcku0uog6GSfYGg9BTJGRVqSSZN1b.oIufG3Qt_FgqVqA_HwjmIEqrv87XVEjhfeChF8EWzGf0XMpqjWpwkwU4kwr0wtIKTDJprdsJHNIKcGptp8fMtHUgeuLqk0N9F.KyvF_Xbn1ug9R8Q5U8uyYbGX7OLcJhLMsD_xz5aJ0e2b8xD9IaROrFh95.dL9Fgqk9mHOE.BUqJEK6x9VsX4MpPvTqLSgtzIZVp.NiL1l2Q0OGJz5ud1RTkmqpjNd7Vbl8GO95a7MU1gHhKm2bxlOsmHOARhzzKFwveWDFNgrBAm9u2YVzVqaLaKufKbqhRnm7TY1y.v._OkDpVnRA91uUV2Acpb9zFifu7oxPfgMZoMhY8Icp9KygEj5QsEuPPrrJ4xPjiPJRCFkrdin_Qva1ko_Zf.uK1HAS39x_jC93CPBlf_dORgXwtXQyKOlglaP2Q90RJOm4KryxyiIaArguqIk1byT2L.sI1B1IxZPRdeawH.1Isoqx1VD3NtEwAvycH_2.0qvGoZctUDkclFs0FD0MRw9S.zs2yOML5m203xeJUhQ..sIkBfrJDDALp6RiJ3SPaWVRDZZtnqkWZt24KEdiVRGktKFdvLsMKfa5JAtHMGxm_yflLPNbGn435xbgv1p4cBijkCjaaD_zway4yXfrkS2wow",mdrd: "dQqYDGGyhF3z2pHRzEmx.2BQngca6bEVV56KPfgnOkQ-1739791670-1.2.1.1-NOSEs4_XYUwLs6NpGJgeHeHtbY3Unlgdw7ntmcpnKQURk3g7pLrUVGzSL9qXr9A4g.86cZBTQaqY6NVjCpvxZszR.cbk3YpDTrIS_P9YVbHxaR7BaRLX1YGp23Voyt7fezyf8U2wxh2.ZI518xS0o7.89iQmcZxIrR6..L6GD6dtdD0JHWlR.Ua97P.zoLycLz49zUnW_PnMKywFNSRMMoHxLB34k7lCbEP92oyP8rxCgxsDVva_BRrqIsv3zmhMgBoUiFr1J0eIuCl9wKT8BS0W7RAKISrk45EDxjKhnzB69EkgLuXkL.Pan4zkHQBhKgM7m5wN3EAkAqS30Jv1k8FLKoinajK2Q0BVd24lrBvmRCcQieOVzEoRRUoGFgcE1_dknxNUdOPjeMZlkR0nidHG.GcdLMoD4xErTom.2KCeo0KPkSyLV1.Ag1efgxUTU7elSA7qb.4xwFByr.HBfDOvNcCG23S5u70e_xt2_K2RAOMgFhj5AbxgaEjOhUIvlj1Q6.f90v6G25Kau28gRuLSGFmIm9B3WuHb9Um_WgvPNux_K5YyUGpRMsxUFrXceQLLxj64ftjaVCn8daBWB2Yxff.GMAzBAVfeZFs8Sc8gbqnwQvHK79Hzcj.mko8q7KbLbp7xxqHth0J2VqSZ5t8OAyUAccLmPQLbhrZCox7Ta_9VjeSLDv6_SR93p6YAfgkhjTSEtdkKkePorKP5X3GC.IOy8Qu6ZzJnKpRlO_vcZhrs9Y6OrrKsKZrf3IbtUu23bB4XcILvin9tPrSqH6h3asYZmGrofWWcnDP_PEKw1.bXSC7i4HuEVRZqK3E5UWnutsU0b.kJANPOqKgGoMV.SjJpSSRVZzkPblX4gon9Ru9JODOM84wpAGhwYJCvMEuW2uoCVFgNDiCE.SQFIvJ7Kuqii2IltzVSEkC6_jF6vC5ik0b28pf1kMtThljru7tZRf177.BNIwSZ0xk6HYiFymey776aHmclAcKh8S.hjnGgGttUQCVU8YO0OFUWWzw5ZjSPhxNoVIrw98DMt8HnxCpT_0eUhsYFm.YG2mpE59TiBGRKfFMx6.IVdqLH_02T6jygB7oTZsKYpyuFf_wofD.qtdf.RSMz9dVpzpSd8hQVe293ilgjsSU1hKXH3EReW34bwKlNGfdgi2EJWTLHExf81sB.uUJbcsi3yL4uscx1lbqO6e86Vlx3AoTDbGuN40RgiSBPQ5woCu_6j61hzrdycpRetjqI5.smre21EJqwjdzVCHwIXxPVBgxhAsXfBO8dXGyY0qk2lWPPsy3X50E4o4BT6QBmeKLxYOTr54lxQwRGLeO6aPksux9h5ZC2M.DFNQKCtSwJ0sz_7n2sAIL1V1Er.rfD9zYSI6qGnjYQtzw358GAdvXe22hYZ8nZY2XKB5LlF71CMYqXv0T0j.l1CtMFLG2ckiffTZL.wjyW1ACEpg4euH7mwoLWk5DX40oHpRxnKhi5TIo6F96w3saJxQJs5I0rO_xWlacTfeFa9g.jLjivlK.vtVYRyaf5jU_xb_l4c5WGl5qxiQ_mjhStf.4jqUOzXAGCb3msxnuBViSFZqaMsjFeJKPST0R_q3MHCIVG8sztO1N9b3GWWN7whYr00rNCxF4WsIyBiAy6Mlvczqp3fFd_R7XedzdUpya1zIeGNht5LjTroXuwWc_cJVG34mH8CNrszngZBQ1Ubx5VXWUDyCHJnh8F1rOiodFwFdE1hUZiTOPqQGg.V6RlKXYkAVIX.40rYnlK0qdR4tRmP6unjzw7toQAo.5jfFX.qSy0oSSbqpAP.zzVRzyDyvanntFWzj9rsVz2ltU6.vczv59phnip9YT_VrbgTW443PGle_7k2Hs1pUyhRejQYpEYy48logKyajxWHMlp4HFcrpqWScKt1nvhDCU1O0clHIyAleSDoQFbPUm8MLlbTjnlCZUcTqul4IKzK2aPvCCUPOnw4FGzvNPs"};var cpo = document.createElement('script');cpo.src = '/cdn-cgi/challenge-platform/h/b/orchestrate/chl_page/v1?ray=91356e327e998819';window._cf_chl_opt.cOgUHash = location.hash === '' && location.href.indexOf('#') !== -1 ? '#' : location.hash;window._cf_chl_opt.cOgUQuery = location.search === '' && location.href.slice(0, location.href.length - window._cf_chl_opt.cOgUHash.length).indexOf('?') !== -1 ? '?' : location.search;if (window.history && window.history.replaceState) {var ogU = location.pathname + window._cf_chl_opt.cOgUQuery + window._cf_chl_opt.cOgUHash;history.replaceState(null, null, "\/abstracts\/search?q=eigenvalues&__cf_chl_rt_tk=hgOqv0DEgmHDKNVnIp0B9kFCjCFbksKc0vee3jUh1xU-1739791670-1.0.1.1-4jNGrn6ZENs0zdeFEIwUgFGoaTmBPsoPieqlTq9xkvI" + window._cf_chl_opt.cOgUHash);cpo.onload = function() {history.replaceState(null, null, ogU);}}document.getElementsByTagName('head')[0].appendChild(cpo);}());</script></body></html>