<div dir="ltr"><br clear="all"><div><div style="min-height:1em;color:rgb(0,0,0);font-family:"Times New Roman";font-size:medium">Sayın Hocalarım,</div><div style="min-height:1em;color:rgb(0,0,0);font-family:"Times New Roman";font-size:medium"><br></div><div style="min-height:1em;color:rgb(0,0,0);font-family:"Times New Roman";font-size:medium">Hacettepe Üniversitesi Matematik Bölümü genel seminerlerimiz kapsamında, 11 Mayıs 2022 tarihinde saat 15:00'te zoom bağlantısı üzerinden gerçekleştirilecek,</div><div style="min-height:1em;color:rgb(0,0,0);font-family:"Times New Roman";font-size:medium">Orta Doğu Teknik Üniversitesi'nden Kostyantyn Zheltukhin'in vereceği ''<b>On Discretization of Darboux Integrable Hyperbolic Equations</b>''</div><div style="min-height:1em;color:rgb(0,0,0);font-family:"Times New Roman";font-size:medium">başlıklı konuşmaya hepinizi bekleriz. Konuşmanın özeti ve zoom bağlantısı aşağıda yer almaktadır.</div><div style="min-height:1em;color:rgb(0,0,0);font-family:"Times New Roman";font-size:medium"><br></div><div style="min-height:1em;color:rgb(0,0,0);font-family:"Times New Roman";font-size:medium">Saygılarımla,</div></div><div style="min-height:1em;color:rgb(0,0,0);font-family:"Times New Roman";font-size:medium">Aslı Pekcan</div><div style="min-height:1em;color:rgb(0,0,0);font-family:"Times New Roman";font-size:medium"><br></div><div style="min-height:1em;color:rgb(0,0,0);font-family:"Times New Roman";font-size:medium"><div style="color:rgb(34,34,34);font-family:Arial,Helvetica,sans-serif;font-size:small"><font face="arial, sans-serif" color="#000000"><b>Seminer Zoom bağlantı linki:</b></font></div><div style="color:rgb(34,34,34);font-family:Arial,Helvetica,sans-serif;font-size:small"><a href="https://www.google.com/url?q=https://zoom.us/j/96402021730?pwd%3DOVpremRkZ0ZlRjZKYXBHYmVidktNdz09&sa=D&source=calendar&usd=2&usg=AOvVaw2WMrBlUbHfamNcB43Wbr13" target="_blank" style="font-family:Roboto,Helvetica,Arial,sans-serif;font-size:14px">https://zoom.us/j/96402021730?pwdOVpremRkZ0ZlRjZKYXBHYmVidktNdz09</a></div><div style="color:rgb(34,34,34);font-family:Arial,Helvetica,sans-serif;font-size:small"><b>Toplantı Kimliği: 

</b><span style="color:rgb(0,0,0);font-family:Roboto,Helvetica,Arial,sans-serif;font-size:14px">964 0202 1730</span><br><b>Parola</b>: <span style="font-family:Roboto,Helvetica,Arial,sans-serif;font-size:14px;color:rgb(0,0,0)">884074</span></div></div><div style="min-height:1em;color:rgb(0,0,0);font-family:"Times New Roman";font-size:medium"><br></div><div style="min-height:1em;color:rgb(0,0,0);font-family:"Times New Roman";font-size:medium"><b>Konuşmacı:</b> Kostyantyn Zheltukhin</div><div style="min-height:1em;font-family:"Times New Roman";font-size:medium"><b style="color:rgb(0,0,0)">Konuşma Özeti:</b><font color="#000000"> <span style="font-family:Montserrat,Cambria,Georgia,sans-serif;font-size:16px;text-align:justify">A hyperbolic equation  </span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:16.8px">u</span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:11.8776px">x</span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:11.8776px">y</span><span style="word-spacing:normal;font-family:MJXc-TeX-main-R,MJXc-TeX-main-Rw;white-space:pre-wrap;font-size:16.8px">=</span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:16.8px">f</span><span style="word-spacing:normal;font-family:MJXc-TeX-main-R,MJXc-TeX-main-Rw;white-space:pre-wrap;font-size:16.8px">(</span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:16.8px">x</span><span style="word-spacing:normal;font-family:MJXc-TeX-main-R,MJXc-TeX-main-Rw;white-space:pre-wrap;font-size:16.8px">,</span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:16.8px">y</span><span style="word-spacing:normal;font-family:MJXc-TeX-main-R,MJXc-TeX-main-Rw;white-space:pre-wrap;font-size:16.8px">,</span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:16.8px">u</span><span style="word-spacing:normal;font-family:MJXc-TeX-main-R,MJXc-TeX-main-Rw;white-space:pre-wrap;font-size:16.8px">,</span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:16.8px">u</span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:11.8776px">x</span><span style="word-spacing:normal;font-family:MJXc-TeX-main-R,MJXc-TeX-main-Rw;white-space:pre-wrap;font-size:16.8px">,</span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:16.8px">u</span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:11.8776px">y</span><span style="word-spacing:normal;font-family:MJXc-TeX-main-R,MJXc-TeX-main-Rw;white-space:pre-wrap;font-size:16.8px">) </span><span style="font-family:Montserrat,Cambria,Georgia,sans-serif;font-size:16px;text-align:justify">is called Darboux integrable if there exist two functions I</span><span style="word-spacing:normal;font-family:MJXc-TeX-main-R,MJXc-TeX-main-Rw;white-space:pre-wrap;font-size:16.8px">(</span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:16.8px">x</span><span style="word-spacing:normal;font-family:MJXc-TeX-main-R,MJXc-TeX-main-Rw;white-space:pre-wrap;font-size:16.8px">,</span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:16.8px">u</span><span style="word-spacing:normal;font-family:MJXc-TeX-main-R,MJXc-TeX-main-Rw;white-space:pre-wrap;font-size:16.8px">,</span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:16.8px">u</span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:11.8776px">x</span><span style="word-spacing:normal;font-family:MJXc-TeX-main-R,MJXc-TeX-main-Rw;white-space:pre-wrap;font-size:16.8px">,</span><span style="word-spacing:normal;font-family:MJXc-TeX-main-R,MJXc-TeX-main-Rw;white-space:pre-wrap;font-size:16.8px">…</span><span style="word-spacing:normal;font-family:MJXc-TeX-main-R,MJXc-TeX-main-Rw;white-space:pre-wrap;font-size:16.8px">) </span><span style="font-family:Montserrat,Cambria,Georgia,sans-serif;font-size:16px;text-align:justify">and </span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:16.8px">J</span><span style="word-spacing:normal;font-family:MJXc-TeX-main-R,MJXc-TeX-main-Rw;white-space:pre-wrap;font-size:16.8px">(</span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:16.8px">x</span><span style="word-spacing:normal;font-family:MJXc-TeX-main-R,MJXc-TeX-main-Rw;white-space:pre-wrap;font-size:16.8px">,</span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:16.8px">u</span><span style="word-spacing:normal;font-family:MJXc-TeX-main-R,MJXc-TeX-main-Rw;white-space:pre-wrap;font-size:16.8px">,</span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:16.8px">u</span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:11.8776px">y</span><span style="word-spacing:normal;font-family:MJXc-TeX-main-R,MJXc-TeX-main-Rw;white-space:pre-wrap;font-size:16.8px">,</span><span style="word-spacing:normal;font-family:MJXc-TeX-main-R,MJXc-TeX-main-Rw;white-space:pre-wrap;font-size:16.8px">…</span><span style="word-spacing:normal;font-family:MJXc-TeX-main-R,MJXc-TeX-main-Rw;white-space:pre-wrap;font-size:16.8px">) </span><span style="font-family:Montserrat,Cambria,Georgia,sans-serif;font-size:16px;text-align:justify">such that </span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:16.8px">D</span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:11.8776px">y</span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:16.8px">I</span><span style="word-spacing:normal;font-family:MJXc-TeX-main-R,MJXc-TeX-main-Rw;white-space:pre-wrap;font-size:16.8px">=</span><span style="word-spacing:normal;font-family:MJXc-TeX-main-R,MJXc-TeX-main-Rw;white-space:pre-wrap;font-size:16.8px">0 </span><span style="font-family:Montserrat,Cambria,Georgia,sans-serif;font-size:16px;text-align:justify">and </span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:16.8px">D</span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:11.8776px">x</span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:16.8px">J</span><span style="word-spacing:normal;font-family:MJXc-TeX-main-R,MJXc-TeX-main-Rw;white-space:pre-wrap;font-size:16.8px">=</span><span style="word-spacing:normal;font-family:MJXc-TeX-main-R,MJXc-TeX-main-Rw;white-space:pre-wrap;font-size:16.8px">0 </span><span style="font-family:Montserrat,Cambria,Georgia,sans-serif;font-size:16px;text-align:justify">on all solutions of the equation. The functions </span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:16.8px">I </span><span style="font-family:Montserrat,Cambria,Georgia,sans-serif;font-size:16px;text-align:justify">and </span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:16.8px">J </span><span style="font-family:Montserrat,Cambria,Georgia,sans-serif;font-size:16px;text-align:justify">are called </span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:16.8px">x</span><span style="font-family:Montserrat,Cambria,Georgia,sans-serif;font-size:16px;text-align:justify">- and </span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:16.8px">y</span><span style="font-family:Montserrat,Cambria,Georgia,sans-serif;font-size:16px;text-align:justify">-integrals respectively. The concept of </span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:16.8px">x</span><span style="font-family:Montserrat,Cambria,Georgia,sans-serif;font-size:16px;text-align:justify">-, </span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:16.8px">y</span><span style="font-family:Montserrat,Cambria,Georgia,sans-serif;font-size:16px;text-align:justify">-integrals can be generalized to semi-discrete and discrete equations of the hyperbolic type. Hence we can define Darboux integrability for semi-discrete and discrete equations. In the present talk we consider the problem of finding semi-discrete analogues of Darboux integrable continuous equations. We require for the obtained  semi-discrete equation to be Darboux integrable as well. To find such semi-dıscrete equations we will use the  </span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:16.8px">x</span><span style="font-family:Montserrat,Cambria,Georgia,sans-serif;font-size:16px;text-align:justify">- or </span><span style="word-spacing:normal;font-family:MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw;white-space:pre-wrap;font-size:16.8px">y</span><span style="font-family:Montserrat,Cambria,Georgia,sans-serif;font-size:16px;text-align:justify">-integrals.</span></font></div></div>