<div dir="ltr"><div><span style="color:inherit;font-style:inherit;font-variant:inherit;font-weight:inherit;margin:0px;padding:0px;border:0px;font-stretch:inherit;line-height:normal;font-family:"Times New Roman",Times,serif;vertical-align:baseline">Sayın Liste Üyeleri,</span><span style="color:inherit;font-style:inherit;font-variant:inherit;font-weight:inherit;margin:0px;padding:0px;border:0px;font-stretch:inherit;line-height:normal;font-family:"Times New Roman",Times,serif;vertical-align:baseline"> </span><br></div><div><span style="color:inherit;font-style:inherit;font-variant:inherit;font-weight:inherit;margin:0px;padding:0px;border:0px;font-stretch:inherit;line-height:normal;font-family:"Times New Roman",Times,serif;vertical-align:baseline"><br></span></div><div><p style="margin:0cm 0cm 8pt;line-height:22px"><span style="color:inherit;font-family:"Times New Roman",Times,serif;margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;vertical-align:baseline">Gebze Teknik Üniversitesi (GTÜ) Matematik Bölümü Genel Seminerleri kapsamında, 12 Mart Cuma günü saat 14:00'te<span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;color:inherit"> </span></span><span style="color:inherit;font-family:"Times New Roman",Times,serif;margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-stretch:inherit;line-height:normal;vertical-align:baseline"><b> Dr. Öğr. Üyesi Nagehan Alsoy-Akgün </b><span style="font-weight:inherit"> (Van Yüzüncü Yıl Üniversitesi</span></span><span style="color:inherit;font-family:"Times New Roman",Times,serif;margin:0px;padding:0px;border:0px;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;vertical-align:baseline"><span style="font-style:inherit">)</span><span style="margin:0px;padding:0px;border:0px;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;color:inherit"><i>  </i></span></span><span style="color:inherit;margin:0px;padding:0px;border:0px;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;vertical-align:baseline"><i><font face="Times New Roman, Times, serif">“</font></i></span><span style="color:inherit;margin:0px;padding:0px;border:0px;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;vertical-align:baseline"><i> </i></span> <span style="color:rgb(0,0,0)"><i style=""><font face="times new roman, serif">The numerical solution of 2D sine-Gordon equation using DRBEM</font></i></span> <font color="#201f1e"> </font><span style="color:inherit;font-variant:inherit;font-weight:inherit;margin:0px;padding:0px;border:0px;font-stretch:inherit;line-height:normal;vertical-align:baseline"><i style="font-family:"Times New Roman",Times,serif">”  </i></span><span style="color:inherit;font-style:inherit;font-variant:inherit;font-weight:inherit;font-family:"Times New Roman",Times,serif;margin:0px;padding:0px;border:0px;font-stretch:inherit;line-height:normal;vertical-align:baseline">başlıklı bir seminer verecektir. Seminerin detayları aşağıda olup tüm ilgilenenler davetlidir. </span><span style="color:inherit;font-style:inherit;font-variant:inherit;font-weight:inherit;font-family:"Times New Roman",Times,serif;margin:0px;padding:0px;border:0px;font-stretch:inherit;line-height:normal;vertical-align:baseline"> </span></p><p style="font-family:Calibri,sans-serif;margin:0cm 0cm 8pt;color:rgb(32,31,30);line-height:22px"><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:inherit">Seminer için Microsoft Teams platformu kullanılacaktır. Seminere katılmak için aşağıdaki linki kullanabilirsiniz:</span></p><p style="font-family:Calibri,sans-serif;margin:0cm 0cm 8pt;line-height:22px"><b><u><a href="https://teams.microsoft.com/l/meetup-join/19%3a0ae91f7b86a24e8fa1d818a6f74b22a1%40thread.tacv2/1615194140427?context=%7b%22Tid%22%3a%22066690f2-a8a6-4889-852e-124371dcbd6f%22%2c%22Oid%22%3a%22a343f6fd-86f8-4abe-95cf-3c7f4ad5f0ca%22%7d">https://teams.microsoft.com/l/meetup-join/19%3a0ae91f7b86a24e8fa1d818a6f74b22a1%40thread.tacv2/1615194140427?context=%7b%22Tid%22%3a%22066690f2-a8a6-4889-852e-124371dcbd6f%22%2c%22Oid%22%3a%22a343f6fd-86f8-4abe-95cf-3c7f4ad5f0ca%22%7d</a></u></b><br style="font-size:15px"></p><p style="font-family:Calibri,sans-serif;margin:0cm 0cm 8pt;color:rgb(32,31,30);line-height:22px"><span style="color:black;font-family:"Times New Roman",Times,serif;font-style:inherit;font-variant-ligatures:inherit;font-variant-caps:inherit;font-weight:inherit">Seminere bağlanırken aşağıdaki pencereyi görürseniz,  </span><br></p><div><div style="margin:0px;padd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;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:inherit">Konuşmadığınız sürece lütfen mikrofonunuzu kapalı tutunuz.</span></font></p><br style="color:rgb(32,31,30)"><p style="margin-top:0px;margin-bottom:0px;color:rgb(32,31,30)"></p><p style="font-family:Calibri,sans-serif;margin:0cm 0cm 8pt;color:rgb(32,31,30);line-height:22px"><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:inherit">Saygılarımızla.</span><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:inherit"> </span></p><p style="font-family:Calibri,sans-serif;margin:0cm 0cm 8pt;color:rgb(32,31,30);line-height:22px"><br></p><p style="font-family:Calibri,sans-serif;margin:0cm 0cm 8pt;color:rgb(32,31,30);line-height:22px"><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:inherit">Dear all,</span><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:inherit"> </span></p><p style="margin:0cm 0cm 8pt;color:rgb(32,31,30);line-height:22px"><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-stretch:inherit;line-height:normal;vertical-align:baseline;color:inherit"><span style="color:rgb(34,34,34)"><font face="times new roman, serif" style=""><b>Dr. Öğr. Üyesi Nagehan Alsoy-Akgün</b></font></span><span style="font-weight:inherit;font-family:Arial,Helvetica,sans-serif;color:rgb(34,34,34)"> </span><font face="Times New Roman, Times, serif" style="font-weight:inherit">from Van Yüzüncü Yıl University will give a talk titled</font><span style="font-weight:inherit;font-family:inherit;margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-stretch:inherit;line-height:inherit;vertical-align:baseline;color:inherit"> </span></span><span style="color:inherit;font-variant:inherit;font-weight:inherit;margin:0px;padding:0px;border:0px;font-stretch:inherit;line-height:normal;vertical-align:baseline"><span style="font-family:"Times New Roman",Times,serif;font-style:inherit">  </span><span style="font-style:inherit;margin:0px;padding:0px;border:0px;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;vertical-align:baseline;color:inherit"><i><font face="Times New Roman, Times, serif">“</font></i></span><span style="margin:0px;padding:0px;border:0px;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;vertical-align:baseline;color:inherit"><span style="color:inherit;margin:0px;padding:0px;border:0px;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;vertical-align:baseline"><i> </i></span> <span style="color:rgb(0,0,0)"><i><font face="times new roman, serif">The numerical solution of 2D sine-Gordon equation using DRBEM</font></i></span>  <span style="font-family:"Times New Roman",Times,serif;font-style:inherit"><font face="times new roman, serif"> </font></span><span style="font-family:"Times New Roman",Times,serif;font-style:inherit">”  </span></span><span style="font-family:"Times New Roman",Times,serif;font-style:inherit">on March 12th , at 14:00.</span></span><span style="font-family:"Times New Roman",Times,serif;color:inherit;font-style:inherit;font-variant:inherit;font-weight:inherit;margin:0px;padding:0px;border:0px;font-stretch:inherit;line-height:normal;vertical-align:baseline"> All interested are invited.</span></p><p style="margin:0cm 0cm 8pt;color:rgb(32,31,30);line-height:22px"><font face="times new roman, serif"><span style="color:inherit;font-style:inherit;font-variant:inherit;font-weight:inherit;margin:0px;padding:0px;border:0px;font-stretch:inherit;line-height:normal;vertical-align:baseline"><span style="color:rgb(0,0,0)">Abstract: </span></span></font><span style="color:rgb(0,0,0)"><font face="times new roman, serif" style="">In this study two-dimensional sine-Gordon equation is solved by using the </font></span><span style="font-family:"times new roman",serif;color:rgb(0,0,0)">dual reciprocity boundary element method (DRBEM). At the beginning of </span><span style="font-family:"times new roman",serif;color:rgb(0,0,0)">the solution procedure, central difference approximations are used for both f</span><span style="font-family:"times new roman",serif;color:rgb(0,0,0)">irst and second order time derivatives. After inserting the finite difference approximations into the governing equation, the form of the modified Helmholtz equation is obtained. The fundamental solution of modified </span>Helmholtz<span style="font-family:"times new roman",serif;color:rgb(0,0,0)"> equation is employed in the integral equation formulation. The </span><font face="times new roman, serif">inhomogeneous<span style="color:rgb(0,0,0)"> </span></font><span style="font-family:"times new roman",serif;color:rgb(0,0,0)">terms of the equation cause a domain integral in the integral equation formulation which leads to loss of advantage of the method. </span><span style="font-family:"times new roman",serif;color:rgb(0,0,0)">The DRBEM provides to transform the domain integral into the boundary </span><span style="font-family:"times new roman",serif;color:rgb(0,0,0)">integral by approximating the inhomogeneous term of the </span><span style="font-family:"times new roman",serif;color:rgb(0,0,0)">with thin </span><font face="times new roman, serif" style="color:rgb(0,0,0)">plate spline ($r^2ln\,r$).  First, code validation of the method is done using a </font><span style="color:rgb(0,0,0);font-family:"times new roman",serif">test problem and then proposed method is applied for several cases involving </span><span style="color:rgb(0,0,0);font-family:"times new roman",serif">line and ring </span>solitons<span style="color:rgb(0,0,0);font-family:"times new roman",serif"> to show its capability to </span>treat of the<span style="color:rgb(0,0,0);font-family:"times new roman",serif"> problem. Presented numerical results are observed to be in good agreement with other </span><span style="font-family:"times new roman",serif;color:rgb(0,0,0)">numerical results available in the literature.</span></p><p style="font-family:Calibri,sans-serif;margin:0cm 0cm 8pt;color:rgb(32,31,30);line-height:22px"><span style="color:inherit;font-style:inherit;font-variant:inherit;font-weight:inherit;margin:0px;padding:0px;border:0px;font-stretch:inherit;line-height:normal;font-family:"Times New Roman",Times,serif;vertical-align:baseline"><br></span></p><p style="font-family:Calibri,sans-serif;margin:0cm 0cm 8pt;color:rgb(32,31,30);line-height:22px"><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:inherit">Microsoft Teams platform will be used for the seminar. To join the seminar, please use the following link:</span></p><p style="font-family:Calibri,sans-serif;margin:0cm 0cm 8pt;color:rgb(32,31,30);line-height:22px"><b><u><a href="https://teams.microsoft.com/l/meetup-join/19%3a0ae91f7b86a24e8fa1d818a6f74b22a1%40thread.tacv2/1615194140427?context=%7b%22Tid%22%3a%22066690f2-a8a6-4889-852e-124371dcbd6f%22%2c%22Oid%22%3a%22a343f6fd-86f8-4abe-95cf-3c7f4ad5f0ca%22%7d">https://teams.microsoft.com/l/meetup-join/19%3a0ae91f7b86a24e8fa1d818a6f74b22a1%40thread.tacv2/1615194140427?context=%7b%22Tid%22%3a%22066690f2-a8a6-4889-852e-124371dcbd6f%22%2c%22Oid%22%3a%22a343f6fd-86f8-4abe-95cf-3c7f4ad5f0ca%22%7d</a>  </u></b></p><p style="font-family:Calibri,sans-serif;margin:0cm 0cm 8pt;color:rgb(32,31,30);line-height:22px">  <br style="font-size:15px"></p><p style="font-family:Calibri,sans-serif;margin:0cm 0cm 8pt;color:rgb(32,31,30);line-height:22px"><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;color:inherit"><span lang="EN-US" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:black">If you see the following window when connecting to the seminar,  </span></span><br></p><div><img src="cid:ii_kfs6ydpv1" alt="image.png" width="327" height="165" class="gmail-CToWUd gmail-a6T" tabindex="0" style="cursor: pointer; outline: 0px;"><br></div><p align="center" style="font-family:Calibri,sans-serif;margin:0cm 0cm 0pt;color:rgb(32,31,30);background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;text-align:center"><b><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;color:inherit"></span><span lang="EN-US" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",serif;vertical-align:baseline;color:black"></span><span lang="EN-US" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:black"> </span></b></p><p style="font-family:Calibri,sans-serif;margin:0cm 0cm 0pt;color:rgb(32,31,30);background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><span lang="EN-US" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:black">please select</span><span lang="EN-US" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:bold;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",serif;vertical-align:baseline;color:black"><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:inherit"> </span></span><span lang="EN-US" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:bold;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:black"><b>Allow</b></span><span lang="EN-US" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:black"><b>.<span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;color:inherit"> </span></b>Then you will be able to use your microphone and camera during the seminar. </span></p><p style="font-family:Calibri,sans-serif;margin:0cm 0cm 0pt;color:rgb(32,31,30);background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><span lang="EN-US" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:black"><br></span></p><p style="margin-top:0px;margin-bottom:0px;color:rgb(32,31,30)"></p><p style="font-family:Calibri,sans-serif;margin:0cm 0cm 8pt;color:rgb(32,31,30);line-height:22px"><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:rgb(0,0,0)">Please use your real and complete name when you enter the system.</span></p><p style="font-family:Calibri,sans-serif;margin:0cm 0cm 8pt;color:rgb(32,31,30);line-height:22px"><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:inherit">Please switch your microphone off unless you are speaking.</span></p><p style="font-family:Calibri,sans-serif;margin:0cm 0cm 8pt;color:rgb(32,31,30);line-height:22px"><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:inherit"><br></span></p><p style="font-family:Calibri,sans-serif;margin:0cm 0cm 8pt;color:rgb(32,31,30);line-height:22px"><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:inherit">Sincerely</span></p></div></div>