<div dir="ltr"><div><span style="color:rgb(80,0,80)"><div>Dear Colleagues!<br></div><br>You are cordially invited to the </span> <span style="color:rgb(80,0,80)">Weekly </span><span style="color:rgb(80,0,80)">Seminar “Analysis and Applied Mathematics” on</span></div><div> Date: Tuesday, May 16, 2023 </div><div>Time: 12.00-13.00 (Istanbul) = 11.00-12.00 (Ghent) = 15.00-16.00 (Almaty) </div><div>Place: Zoom link: <a href="https://us02web.zoom.us/j/6678270445?pwd=SFNmQUIvT0tRaHlDaVYrN3l5bzJVQT09" target="_blank">https://us02web.zoom.us/j/6678270445?pwd=SFNmQUIvT0tRaHlDaVYrN3l5bzJVQT09</a>, Conference ID: 667 827 0445, Access code: 1</div><div> Speaker:
Dr. Yagub Aliyev </div><div>DA University, Baku - Azerbaijan </div><div>Title: Minimality conditions for Sturm-Liouville problems with a
boundary condition depending affinely or quadratically on an
eigenparameter </div><div>Abstract:
In the talk we will discuss Sturm-Liouville problems with a boundary condition
depending affinely or quadratically on an eigenparameter:
−𝑦′′ + 𝑞(𝑥)𝑦 = 𝜆y, 0 < 𝑥 < 1 (1) 𝑦′
(0) sin 𝛽 = 𝑦(0) cos 𝛽 , 0 ≤ 𝛽 < 𝜋 (2) 𝑦′
(1) = (𝑎𝜆^2 + 𝑏𝜆 + 𝑐)𝑦(1), (3)
where 𝜆 is the spectral parameter, 𝑞(𝑥) is a real valued and continuous function on the interval
[0,1], and 𝑎, 𝑏, 𝑐 are real.
In the papers by Binding, Browne, Watson, and Code the existence and asymptotics of
eigenvalues of (1)-(3) were studied. It was proved that the eigenvalues of (1)-(3) form an infinite sequence, accumulating only at +∞, and the following cases are possible:
(a) All the eigenvalues are real and simple;
(b) All the eigenvalues are simple and all, except a conjugate pair of non-real, are real;
(c) All the eigenvalues are real and all, except one double, are simple;
(d) All the eigenvalues are real and all, except one triple, are simple.
The necessary and sufficient conditions for minimality and completeness of the chosen system of root functions of the corresponding operator were previously given in the form, which
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uses some special associated functions. In the current talk another method with the direct use
of characteristic functions will be discussed. This direct method is known for the affine case
and was extensively discussed in the literature. The aim of the present paper is to develop this
direct method for the quadratic case and to consider the affine and quadratic cases together
in a unified way.</div><div> <br></div><div><div><span style="color:rgb(80,0,80)"><div>Abstracts and forthcoming talks can be found on our webpage<br><a href="https://sites.google.com/view/aam-seminars" target="_blank">https://sites.google.com/view/aam-seminars</a><br>With my best wishes</div></span></div></div><div><div dir="ltr" data-smartmail="gmail_signature"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div style="font-size:12.8px"><b style="font-size:12.8px">Prof. Dr. Allaberen Ashyralyev </b></div><div><span style="font-size:small"><b>Department of Mathematics, Bahcesehir University,</b></span><b>34349</b><span style="font-size:small"><b>, Istanbul, Turkiye</b></span><b style="font-size:12.8px"> and </b><b style="font-size:12.8px">Near East University, Lefkoşa(Nicosia), Mersin 10 Turkiye</b></div><div><div style="font-size:12.8px"><span style="font-size:12.8px"><b>Peoples' Friendship University of Russia (RUDN University),</b></span><b style="color:rgb(51,51,51);font-family:arial,helvetica,sans-serif;font-size:13px"> Ul Miklukho Maklaya 6, Moscow 117198, Russian Federation </b></div><div style="font-size:12.8px"><b style="font-size:12.8px">Institute of Mathematics and Mathematical Modelling, 050010, Almaty, Kazakhstan</b></div><div style="font-size:12.8px"><b style="font-size:12.8px">e-mail: <a href="mailto:allaberen.ashyralyev@neu.edu.tr" style="color:rgb(17,85,204)" target="_blank">allaberen.ashyralyev@eng.bau.edu.tr</a> and </b><b style="font-size:12.8px"><a href="mailto:aallaberen@gmail.com" style="color:rgb(17,85,204)" target="_blank">aallaberen@gmail.com</a> </b></div><div style="font-size:12.8px"><b style="font-size:12.8px"> </b><a href="http://akademik.bahcesehir.edu.tr/web/allaberenashyralyev" style="color:rgb(0,86,179);margin:0px;padding:0px;border:0px;font-stretch:inherit;font-size:14px;line-height:inherit;font-family:Roboto,sans-serif;vertical-align:baseline" target="_blank">http://akademik.bahcesehir.edu.tr/web/allaberenashyralyev</a></div><div><p class="MsoNormal"><a href="https://sites.google.com/view/aam-seminars" target="_blank">https://sites.google.com/view/aam-seminars</a></p></div><div><a href="https://content.sciendo.com/view/journals/ejaam/ejaam-overview.xml" target="_blank">https://content.sciendo.com/view/journals/ejaam/ejaam-overview.xml</a><br></div><div><font color="#1155cc"><span style="font-size:12.8px"><b><u><a href="http://icaam-online.org" target="_blank">icaam-online.org</a></u></b></span></font></div></div><div><font color="#1155cc"><span style="font-size:12.8px"><b><a href="https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1" target="_blank">https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1<br></a></b></span><br></font></div></div></div></div></div></div></div></div></div></div></div></div></div></div>