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="390"></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: 'managed',cRay: '91e884b42dae9e38',cH: 'NL58UkSJaXKp6yvNOuWVUkgUyoIItOiB4r70m5yjlQU-1741669543-1.2.1.1-.rlMivjDkX81B1p.PXs8_1qx3Vj05TO1iZ49u2CmNQqCS0QMzAZJQQUhDsSbuaMZ',cUPMDTk: "\/abstracts\/search?q=fractional%20curl%20operators&__cf_chl_tk=9rpjfhzhRmH._2ZrLbTM0G0aC8cagX13PLognHRY3VY-1741669543-1.0.1.1-LkHb9obM5gAiBXFYm9go8.YT2m8pm2Nc7Q8Y_D_K6RE",cFPWv: 'g',cITimeS: '1741669543',cTTimeMs: '1000',cMTimeMs: '390000',cTplC: 0,cTplV: 5,cTplB: 'cf',cK: "",fa: "\/abstracts\/search?q=fractional%20curl%20operators&__cf_chl_f_tk=9rpjfhzhRmH._2ZrLbTM0G0aC8cagX13PLognHRY3VY-1741669543-1.0.1.1-LkHb9obM5gAiBXFYm9go8.YT2m8pm2Nc7Q8Y_D_K6RE",md: "P1R51WNrTpMQBcaXhiubqMVNGjpNgRBuABtU0F3zWk8-1741669543-1.2.1.1-Shlqbay3Y1JiujY2CREWPgfN572I7nKzb0.piHThEVUYuV6qlvBo8qS7qy2A.PwY1mzViwqtfpoN87E19efvTjBm2QSqJGFRQnH0lIJANkinJnP67CR7OGLZrBYh7OSlmSk7AEhw.s82TAyY5amSq60yVO0TKmQA3Axm4djt7Ox1atd4fPAwi4KPzdZYliu0u.RsX16Tj19z4wrXXtGoAQEl3GzYyrpDSPv0jBqNsMlf7xVHw4IFyftqdXbLwRS6TXgTFx2XtzAcVb9pdQxQnog1Em8aiRrWp6ntNPQ8QckWYLHlbAGw5MMhQruCRY1WksrMgRDZcwZ5wOFfmfUPoMhXY_M2qXiUJ3cbT9vEtZZyuUG0D2qWP4teZFlPzHdmrI1s6If_mMmLvdIQZ7wSZfbCiTK8WzSpXxShikaW_dk1zar_Wpx2U95d3klPcvtjKiuQS121IFoOuLhFaP5kJ_SnEaylm0Fjz2CLU4EjAZXo28qqR.AxnzXq8v5tNbOOfiOQs2fJJBaLO9wbwAc2EQcY1OewQvNpBedYCAR7j0T_EW7J9YU4ntvOJEF8D1kpyVrL2ox3IfHsk7f2pqzMFeVdZE6xPduy4FMNUDDniGmSMgYhCcvAn7gXoBTrD1OQnuUvJWPbQwsu7wddNDvmQjV8VlTrikEooynz1RITGeUGtiN8TbmEwTLa735755omRXe8kVWhRhvI2g9rPisKVe8UhDYMXIEF0_gp4XvN9zLz.Nf681m7dzfRN6lBlHM86ds_OgXsSIaFzirauYgm6JEjw_k7WjQfXgYzMqDyZ4rczcnwBdK128sHn8mY5gtOYcTGA.pwUhSkrf5WXB6J9c4qTJIgDKVxQIbPxeyjm1blVD2_Qu48S_JleDU3pYT7QweHvBOqngNbvmRgPAgGVniSet3wjo0AXe6TPjHuI1Na8DD.O0.sjrWwDvYfsfuWQYZCvHnH0if71XYQemCn.Q73.TmUhuNVzgYnzC.SrwfzzRcXBNWptufKM.asW_aft98AKUBVfeylEUwMgEOXD.Spp0UHpYDaZ2KBQaoss8lNULVMTC0Crf_hdnx.MmeHzrKNxuCaWIyqBBKJ8ABZWhgCLq0d5AS7WkAxGtxCDIa7ySI.tht_3Gq2UO_.ogYTASKayFXS5L9X8EQIYpTbUJ2dLkzhEF4r1zmVNAn6l_CyLCqIW6.zG9zZ7kAhG1x3u8_LxgRrxPuYuJbaf6SiyHq.smnJ2ciaNL5HN.GnpkAi0GTgXyEiFEZ1cIqTZ9k7jwMqJR4EunnG46ZJTSHCaKZod9A8tcssDYgr3q04VdHzeEN7paLLOLowQWhfOzt7",mdrd: "Pvq4Q1OrvhdEV3Dhq.b.4byw1pT64ysDoa0KU4yT_80-1741669543-1.2.1.1-Tcmh9n7gDxVI4.gnobPD71LpYFT8uliC.jvHHs3FJIgn416g5ztr3X7QVnVA0a4ePKrBOQ0JuwLwlKLBroaQxn5nteHi8tavpVoTgs5VoS.D8V8CeBZ6RQ_VF4yRHihc_gr0Evo.swNDtNwece99hbahwSA.4BG5Wsr9ug6ILePdMdhwIU87hJa2xl5vTCiAe95_cugjrBfwooouGqk8DhLC7pTuKZM8XlHrAFmbT6qrEFshj5jOskCmthQPsMFZOLJ_wqjLKieuZpIzwvjaZv837aXuKuuaZ3wCb0Q.3koAd4hGHsQ_aOH2FaN6tIfYqo8DEczxmg38wAuDWfs74J1zcf5g65NEPCN6XeN_ndOO2ds1yD5dWg0kPUoPhVhYlBobCJvhn6ByCM5vfXfYsltD7l0Ng63r0OFApdLmoMoxU808.n.Zgq9J41g1LdrotH6YP3Hv_2q70sA_73QGCWPy6owUjiH.5wzfr97aXOf4e.0hYmJtmWNZrtrHJ2TlJpKk0knieFsJKny4CX6djcQo3NgAo7pq5ivEiX564JzfDyh_OaGLDfGwyKna4MbMYj4nXZOSVKLZ.LCQLWrLZ7JEhIt8ow4x4ooCcbvUEOQ7FcWoWYoNCflOkiRm0xMFIGJ56B8MIsv5Xz82iaO6CQAfjxVX1gETFJfG7oCxfpIvQ0DM0648UawaNirleyrki20aDD3kKUgc63UYByno2f.KcyPWdFVr4elCgG8uA1vrNRyW_eSDilfb6TVDcYVy0ChJT_jl2OLSVowoz8fasS1qLzbmJ.YBf97OzoKpfORomvHO5dmEGQdray7gPqWixUgUrmUuauO9PkmWy4HO5MTZg103fREug5uVW_htDSLc.F_HoRwH8NTT.U3tO8PjnhnXq6s2.M.n6wbqiO8cmVxW9LtAJo8DV6El_0qhbVAI.t4AGA97_SePfsJl3N5sEUYlVjThMjpUq.dvGX5AZIDcMdNMRtWbIFYXLyHvKHP.AQ8tzQfAknbbiSlhjuVtynaqNfVIRsuoB7IYEAy_jJQUbvxzO7rQv.k513xKWStqRTbshdHKJdTla3MNWSRFDz2V.t5Z2R9sHeV9vRby_rWfS6fNd5f4v9urfFiU4kiBP8EXm76nRT3LelI3Mt2QxRBRgKk2JZ..ehKTnm7BprKDAdxV0hgyvqmoyWPVLozCUcJvA9nD08CON00wXtT93nsD7CzbHQAbqFEGWa_0bV4kbgzOYvs0XJ8pR8MhXJdMxZ9jJzZN6nYzsfwNrEQTy0.T8oPJx1y1Px6zHDLFAHtXQvm4HHI6ZRBMNkmMb0uAXpcoCxj4VB850Yf1WmyuW9js8bRUU0iAjWFnEdPqn6MksdubUkHNbQ1WeLRKT3_aKenG.5sgqt8N2pbJBQm2KicXBNrIxk3DjCIdiLJ.Tm4NNOMXCJP7FV_Rkagg_o3WZAzeAeAmOXz9Ybukn.PGx4KCs62E7k1mh9Cf4ao730_AEei_ZmtRphj3M316l_CeTDUhM9QIiil0Rh_1koWB_CaYjYPU1ZrgLe4kOk7wbSJYPkL_cWlUBRLketmS6IRd5mcTL.9HMic8GPpxmzWc.V2EbBoErGCSb5apcov8sSQE2IO78tARDgR25ScDi8cyWzuT0sTSLw_hZaxucSHfyFm33ZEhH3qyhywEXmUrLdaOWSa7blaO2_s5j2bW8ZLZhMAiijVcfSN9DaJptEfF64SWeBJKBdjtP4e9de9H4JUoIc.jip_spoAj_nKKoNlpW4cyjSz8YMFJK006N0izhu7N.4Wm6srjGo64WVq8zjnmYn1xJ4X0g3vbi7bIFhoYRD0ZMAW_VqyXUHdc7cy3FtJGVeqv_Swk1s0yUBi5_cNKcPdlyas5r8NVtEzZOqmPzA_CGqDBNvTIPFBE1lxNE6liIZgmeTSkfA6STscYuDgyeoK4D_gph1qqBrG837bzVHiqA9eCzjHtic8HWX2B"};var cpo = document.createElement('script');cpo.src = '/cdn-cgi/challenge-platform/h/g/orchestrate/chl_page/v1?ray=91e884b42dae9e38';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=fractional%20curl%20operators&__cf_chl_rt_tk=9rpjfhzhRmH._2ZrLbTM0G0aC8cagX13PLognHRY3VY-1741669543-1.0.1.1-LkHb9obM5gAiBXFYm9go8.YT2m8pm2Nc7Q8Y_D_K6RE" + window._cf_chl_opt.cOgUHash);cpo.onload = function() {history.replaceState(null, null, ogU);}}document.getElementsByTagName('head')[0].appendChild(cpo);}());</script></body></html>