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<p class="MsoNormal" style="margin-bottom:0.0001pt;text-align:center;line-height:normal;background:none repeat scroll 0% 0% white" align="center"><b style><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)"></span></b><b style><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)"></span></b></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal;background:none repeat scroll 0% 0% white;text-align:left"><font size="4"><span><span style="font-family:"Times New Roman",serif;color:rgb(34,34,34)">Değerli liste üyeleri,</span></span></font></p><p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal;background:none repeat scroll 0% 0% white;text-align:left"><font size="4"><span><span style="font-family:"Times New Roman",serif;color:rgb(34,34,34)"> aşağıda ve ekteki afişte detayları verilen bölüm seminerimize ilgilenenleri bekliyoruz.</span></span></font><b style><span style="font-size:16pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)"></span></b></p><p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal;background:none repeat scroll 0% 0% white;text-align:left"><br><b style><span style="font-size:16pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)"></span></b></p><p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal;background:none repeat scroll 0% 0% white;text-align:left"><font size="4"><span><span style="font-family:"Times New Roman",serif;color:rgb(34,34,34)">En iyi dileklerimle,</span></span></font></p><p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal;background:none repeat scroll 0% 0% white;text-align:left"><font size="4"><span><span style="font-family:"Times New Roman",serif;color:rgb(34,34,34)"></span></span></font></p><p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal;background:none repeat scroll 0% 0% white;text-align:left"><font size="4"><span><span style="font-family:"Times New Roman",serif;color:rgb(34,34,34)">mesut</span></span></font><b style><span style="font-size:16pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)"><br></span></b></p><p class="MsoNormal" style="margin-bottom:0.0001pt;text-align:center;line-height:normal;background:none repeat scroll 0% 0% white" align="center"><b style><span style="font-size:16pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)"><br></span></b></p><p class="MsoNormal" style="margin-bottom:0.0001pt;text-align:center;line-height:normal;background:none repeat scroll 0% 0% white" align="center"><b style><span style="font-size:16pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">HACETTEPE ÜNİVERSİTESİ MATEMATİK BÖLÜMÜ GENEL SEMİNERİ</span></b></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;text-align:center;line-height:normal;background:none repeat scroll 0% 0% white" align="center"><b style><span style="font-size:16pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)"> </span></b></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;text-align:center;line-height:normal;background:none repeat scroll 0% 0% white" align="center"><b style><span style="font-size:16pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">(HACETTEPE MATHEMATICS GENERAL SEMINAR)</span></b></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;text-align:center;line-height:normal;background:none repeat scroll 0% 0% white" align="center"><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)"> </span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal;background:none repeat scroll 0% 0% white"><b style><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">Tarih (Date) :</span></b><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)"> 18.02.2015, Çarşamba
(</span><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">Wednesday</span><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">)<span style>                    </span></span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal;background:none repeat scroll 0% 0% white"><b style><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">Saat (Time):</span></b><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)"> 15:00</span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal;background:none repeat scroll 0% 0% white"><b style><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">Yer (Place):</span></b><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)"> Yaşar ATAMAN Seminer
Salonu</span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal;background:none repeat scroll 0% 0% white"><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)"> </span></p>

<p class="MsoNormal" style="margin-bottom:12pt;line-height:normal"><b style><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">Konuşmacı (Speaker):</span></b><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)"> <font size="4">Doç. </font></span><font size="4"><span style="font-family:"Times New Roman",serif;color:rgb(34,34,34);background:none repeat scroll 0% 0% white">Dr. </span><span style="font-family:"Times",serif" lang="EN-US">Burak Aksoylu</span><span style="font-family:"Times New Roman",serif;color:rgb(34,34,34);background:none repeat scroll 0% 0% white" lang="EN-US"> </span><span style="font-family:"Times New Roman",serif;color:rgb(34,34,34);background:none repeat scroll 0% 0% white"><span></span>(</span><span style="font-family:"Times",serif" lang="EN-US">TOBB ET</span><span style="font-family:"Times New Roman",serif;color:rgb(34,34,34)">Ü </span><span>ve Wayne State University)</span></font><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34);background:none repeat scroll 0% 0% white"></span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal"><b style><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">Başlık (Title) :</span></b><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)"> </span><span style="font-size:12pt;font-family:"Times New Roman",serif">Incorporating local boundary
conditions into nonlocal theories.</span></p>

<p class="MsoNormal" style="margin-bottom:12pt;text-align:justify;line-height:normal"><b style><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">Özet (Abstract) : </span></b><span style="font-size:12pt;font-family:"Times New Roman",serif">We study nonlocal equations from the area of
peridynamics on bounded</span><span style="font-size:12pt;font-family:"Times",serif"> </span><span style="font-size:12pt;font-family:"Times New Roman",serif">domains. In our companion paper, we discover that, on Rⁿ,
the governing operator in peridynamics, which involves a convolution, is a
bounded function of the classical (local) governing operator.  Building on
this, we define an abstract convolution operator on bounded domains which is a
generalization of the standard convolution based on integrals.  The
abstract convolution operator is a function of the classical operator, defined
by a Hilbert basis available due to the purely discretespectrum of the
latter.  As governing operator of the nonlocalequation we use a function
of the classical operator, this allows us to incorporate local boundary
conditions into nonlocal theories. The governing operator is determined by what
we call the regulating function. By choosing different regulating
functions, we can define governing operators tailored to the needs of the
underlying application.</span><span style="font-size:12pt;font-family:"Times",serif" lang="EN-US"></span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><span style="font-size:12pt;font-family:"Times New Roman",serif"> </span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><span style="font-size:12pt;font-family:"Times New Roman",serif">For the
homogeneous wave equation with the considered boundary conditions, we prove
that continuity is preserved by time evolution. Namely, if the initial data is
continuous, then the solution is continuous for real t. This is due to the fact
that the solution has a unique decomposition into two parts.  The first
part is the product of a function of time with the initial data.  The
second part is continuous.  This decomposition is induced by the fact that
the governing operator has a unique decomposition into multiple of the identity
and a Hilbert-Schmidt operator.  The decomposition also implies that
discontinuities remain stationary.</span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><span style="font-size:12pt;font-family:"Times New Roman",serif"> </span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><span style="font-size:12pt;font-family:"Times New Roman",serif">We present a
numerical study of the solutions of the wave equation. For discretization, we
employ a weak formulation based on a Galerkin projection and use piecewise
polynomials on each element which allows discontinuities of the approximate
solution at the element borders. We study convergence order of solutions with
respect to polynomial order and observe optimal convergence.  We depict
the solutions for each boundary condition.</span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;text-align:justify;line-height:normal;background:none repeat scroll 0% 0% white"><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)"> </span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal;background:none repeat scroll 0% 0% white"><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">NOT: Konuşma sonunda çay ve pasta ikramı olacaktır.</span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal;background:none repeat scroll 0% 0% white"><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">(P.S.<span style>  </span>Tea and </span><span style="font-size:14pt;font-family:"Times New Roman",serif">cookies will be
served after the talk</span><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">.)</span></p>

<div><div class="gmail_signature"><div dir="ltr">  <br><br>  Mesut Sahin<div>  Associate Professor<br>  Department of Mathematics<br>  Hacettepe University<br>  TR 06800 Beytepe </div><div>  ANKARA - TURKEY<br> <a href="http://yunus.hacettepe.edu.tr/~mesut.sahin" target="_blank">http://yunus.hacettepe.edu.tr/~mesut.sahin</a></div></div></div></div>
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