<div dir="ltr"><div><font size="4" 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">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;vertical-align:baseline"> </span></font></div><div><font size="4" 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"><br></span></font></div><div><font face="times new roman, serif" size="4" style="text-align:justify"><span style="color:inherit;margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;vertical-align:baseline">3 Haziran Cuma günü saat 14:00'da<span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;vertical-align:baseline;color:inherit"> </span></span><span style="color:inherit;margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-stretch:inherit;line-height:normal;vertical-align:baseline"><b>Doç Dr. Onur Baysal </b><span style="font-weight:inherit">(University of Malta- Malta</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"><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;vertical-align:baseline;color:inherit"><i>"</i></span></span></font><span style="text-align:justify"> </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"> <font face="times new roman, serif" size="4"><i>A Numerical Method for Source Identification Problem Related to Dynamical Kirchoff Plate Equation</i></font> <i style="font-size:large;font-family:"Times New Roman",Times,serif">”  </i></span><font face="times new roman, serif" size="4" style="text-align:justify"><span style="font-style:inherit;font-variant:inherit;font-weight:inherit;color:inherit;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="font-style:inherit;font-variant:inherit;font-weight:inherit;color:inherit;margin:0px;padding:0px;border:0px;font-stretch:inherit;line-height:normal;vertical-align:baseline"> </span></font></div><div><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-weight:inherit;font-stretch:inherit;line-height:normal;vertical-align:baseline;color:inherit"><font size="4" face="times new roman, serif">Seminer için Microsoft Teams platformu kullanılacaktır. Seminere katılmak için aşağıdaki linki kullanabilirsiniz:</font></span></p><p style="margin:0cm 0cm 8pt;color:rgb(32,31,30);line-height:22px"><span style="font-family:"times new roman",serif;font-size:large"><a href="https://teams.microsoft.com/l/meetup-join/19%3a0ae91f7b86a24e8fa1d818a6f74b22a1%40thread.tacv2/1653904979472?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.tacv2/1653904979472?context=%7b%22Tid%22%3a%22066690f2-a8a6-4889-852e-124371dcbd6f%22%2c%22Oid%22%3a%22a343f6fd-86f8-4abe-95cf-3c7f4ad5f0ca%22%7d</a></span><font face="times new roman, serif" size="4"><br></font></p><p style="margin:0cm 0cm 8pt;color:rgb(32,31,30);line-height:22px"><font face="times new roman, serif" size="4"><span style="color:black;font-style:inherit;font-variant-ligatures:inherit;font-variant-caps:inherit;font-weight:inherit">Seminere bağlanırken aşağıdaki pencereyi görürseniz,  </span><br></font></p><div><div style="margin:0px;padding:0px 0px 20px;width:1292.01px"><div><div id="gmail-m_-1833613292872292077gmail-m_8395606941996739994gmail-m_4130259175706602100m_2562651738967369373gmail-m_-4297721377384934555gmail-m_-8518595497998456552gmail-m_2551662775674340865gmail-m_4872606395496930393gmail-m_6442542691571764390gmail-m_-5579924115673701571gmail-m_-9192166314807377313gmail-m_-6564398631029376806gmail-m_2738258699330394105gmail-m_-9113426807227295895gmail-m_7854396500508507239m_-3169123720609391510gmail-m_6495276165393011454gmail-m_-4484010747638358063gmail-m_2336171309765023997gmail-m_-5290101658690503534gmail-m_15064305376630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rgin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;vertical-align:baseline;color:black"><font size="4" face="times new roman, serif">Seminere giriş yaparken lütfen gerçek ve tam adınızı kullanınız.</font></span></p><p style="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;vertical-align:baseline;color:black"><font size="4" face="times new roman, serif"><br></font></span></p><p style="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"><font color="#000000" size="4" face="times new roman, serif"><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;vertical-align:baseline;color:inherit">Konuşmadığınız sürece lütfen mikrofonunuzu kapalı tutunuz.</span></font></p><font face="times new roman, serif" size="4"><br style="color:rgb(32,31,30)"></font><p style="margin-top:0px;margin-bottom:0px;color:rgb(32,31,30)"></p><p style="margin:0cm 0cm 8pt;color:rgb(32,31,30);line-height:22px"><font size="4" face="times new roman, serif"><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;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;vertical-align:baseline;color:inherit"> </span></font></p><p style="margin:0cm 0cm 8pt;color:rgb(32,31,30);line-height:22px"><font size="4" face="times new roman, serif"><br></font></p><p style="margin:0cm 0cm 8pt;color:rgb(32,31,30);line-height:22px"><font size="4" face="times new roman, serif"><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;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;vertical-align:baseline;color:inherit"> </span></font></p><p style="margin:0cm 0cm 8pt;line-height:22px"><span style="color:inherit;font-style:inherit;font-variant:inherit;font-family:"times new roman",serif;font-size:large;margin:0px;padding:0px;border:0px;font-stretch:inherit;line-height:normal;vertical-align:baseline"><span style="font-style:inherit;font-variant:inherit;color:inherit;text-align:justify;margin:0px;padding:0px;border:0px;font-stretch:inherit;line-height:normal;vertical-align:baseline"><b>Assoc.Prof.Dr. Onur Baysal </b></span></span><span style="color:inherit;font-style:inherit;font-variant:inherit;margin:0px;padding:0px;border:0px;font-stretch:inherit;line-height:normal;vertical-align:baseline"><span style="font-weight:inherit"><font face="times new roman, serif" size="4">from University of Malta </font></span></span><font face="times new roman, serif" size="4" style="color:rgb(32,31,30)">(Malta<span style="color:rgb(34,34,34)">) </span><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"><font style="font-weight:inherit">will give a talk titled</font></span></font><font face="times new roman, serif" size="4" style="text-align:justify"><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"><span style="font-style:inherit"> </span></span></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"><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">

<font face="times new roman, serif" size="4" style="text-align:justify"><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"><span style="margin:0px;padding:0px;border:0px;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;vertical-align:baseline;color:inherit"><i>"</i></span></span></font><span style="text-align:justify"> </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"> <font face="times new roman, serif" size="4"><i>A Numerical Method for Source Identification Problem Related to Dynamical Kirchoff Plate Equation</i></font> <i style="font-size:large;font-family:"Times New Roman",Times,serif">” </i></span> </span></span><font face="times new roman, serif" size="4" style="color:rgb(32,31,30)"><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-style:inherit">on June 3rd at 14:00. </span></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;vertical-align:baseline">All interested are invited.</span></font></p><p style="margin:0cm 0cm 8pt;color:rgb(32,31,30);line-height:22px"><font size="4"><font face="times new roman, serif"><span style="color:inherit;font-style:inherit;font-variant: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></font><font face="times new roman, serif" size="4"><span style="text-align:justify;text-indent:0.5in;color:rgb(34,34,34)">Kirchoff Plate model is an integral part of most
engineering fields including plate and shell</span><span style="text-align:justify;text-indent:0.5in;color:rgb(34,34,34);letter-spacing:0.05pt">
</span><span style="text-align:justify;text-indent:0.5in;color:rgb(34,34,34)">structures [1]. In [2], some important identification problems are
stated and some properties are analyzed</span><span style="text-align:justify;text-indent:0.5in;color:rgb(34,34,34);letter-spacing:0.05pt"> </span><span style="text-align:justify;text-indent:0.5in;color:rgb(34,34,34)">such
as stability and uniqueness. In this work we study the inverse problem of
identifying the unknown</span><span style="text-align:justify;text-indent:0.5in;color:rgb(34,34,34);letter-spacing:0.05pt"> </span><span style="text-align:justify;text-indent:0.5in;color:rgb(34,34,34)">load</span><span style="text-align:justify;text-indent:0.5in;color:rgb(34,34,34);letter-spacing:0.1pt"> </span><span style="text-align:justify;text-indent:0.5in;color:rgb(34,34,34)">distribution </span><span style="text-align:justify;text-indent:0.5in;color:rgb(34,34,34);line-height:98%">𝑓<span style="top: -0.5pt;">(</span>𝑥,<span style="letter-spacing:-0.7pt"> </span>𝑦<span style="top: -0.5pt;">) </span></span><span style="text-align:justify;text-indent:0.5in;color:rgb(34,34,34)">in</span><span style="text-align:justify;text-indent:0.5in;color:rgb(34,34,34);letter-spacing:0.1pt"> </span><span style="text-align:justify;text-indent:0.5in;color:rgb(34,34,34)">the
rectangular</span><span style="text-align:justify;text-indent:0.5in;color:rgb(34,34,34);letter-spacing:0.05pt"> </span><span style="text-align:justify;text-indent:0.5in;color:rgb(34,34,34)">domain</span><span style="text-align:justify;text-indent:0.5in;color:rgb(34,34,34);letter-spacing:0.15pt"> </span><span style="text-align:justify;text-indent:0.5in;color:rgb(34,34,34);line-height:98%">𝛺:<span style="letter-spacing:-0.65pt"> </span>=<span style="letter-spacing:0.6pt"> </span><span style="top: -0.5pt;">(</span>0,<span style="letter-spacing:-0.65pt"> </span>𝑘<span style="top: -0.5pt;">)<span style="letter-spacing:0.05pt"> </span></span>×<span style="letter-spacing:0.05pt">
</span><span style="top: -0.5pt;">(</span>0,<span style="letter-spacing:-0.65pt"> </span>𝑙<span style="top: -0.5pt;">)<span style="letter-spacing:-0.2pt"> </span></span></span><span style="text-align:justify;text-indent:0.5in;color:rgb(34,34,34)">such</span><span style="text-align:justify;text-indent:0.5in;color:rgb(34,34,34);letter-spacing:0.05pt"> </span><span style="text-align:justify;text-indent:0.5in;color:rgb(34,34,34)">that</span></font></p>

<p class="MsoNormal" style="text-align:left;margin:0in 99.5pt 0in 0in;line-height:14pt"><font face="times new roman, serif" size="4">  𝑢_𝑡𝑡<span style="letter-spacing:1.2pt"> </span>+<span style="letter-spacing:0.35pt"> </span>𝐷𝛥²𝑢<span style="letter-spacing:1.35pt"> </span>=<span style="letter-spacing:1.15pt"> </span>𝑔<span style="top: -0.5pt;">(</span>𝑡<span style="top: -0.5pt;">)</span>𝑓<span style="top: -0.5pt;">(</span>𝑥,<span style="letter-spacing:-0.3pt"> </span>𝑦<span style="top: -0.5pt;">)<span style="letter-spacing:0.4pt"> </span></span>in<span style="letter-spacing:0.25pt"> </span>𝛺_𝑡:<span style="letter-spacing:-0.4pt"> </span>=<span style="letter-spacing:1pt"> </span>𝛺<span style="letter-spacing:0.7pt"> </span>×<span style="letter-spacing:0.4pt"> </span><span style="top: -0.5pt;">(</span>0,<span style="letter-spacing:-0.45pt"> </span>𝑇<span style="top: -0.5pt;">)</span></font></p><p class="MsoNormal" style="text-align:left;margin:0in 99.5pt 0in 0in;line-height:14pt"><span style="font-family:"times new roman",serif;font-size:large">  𝑢</span><span style="font-family:"times new roman",serif;font-size:large">(</span><span style="font-family:"times new roman",serif;font-size:large">𝑥,</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:-0.4pt"> </span><span style="font-family:"times new roman",serif;font-size:large">𝑦,</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:-0.6pt"> </span><span style="font-family:"times new roman",serif;font-size:large">0</span><span style="font-family:"times new roman",serif;font-size:large">)<span style="letter-spacing:1pt"> </span></span><span style="font-family:"times new roman",serif;font-size:large">=</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:1pt">
</span><span style="font-family:"times new roman",serif;font-size:large">0,</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:-0.55pt"> </span><span style="font-family:"times new roman",serif;font-size:large">𝑢</span><sub style="font-family:"times new roman",serif">𝑡</sub><span style="font-family:"times new roman",serif;font-size:large">(</span><span style="font-family:"times new roman",serif;font-size:large">𝑥,</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:-0.4pt"> </span><span style="font-family:"times new roman",serif;font-size:large">𝑦,</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:-0.4pt"> </span><span style="font-family:"times new roman",serif;font-size:large">0</span><span style="font-family:"times new roman",serif;font-size:large">)<span style="letter-spacing:0.9pt"> </span></span><span style="font-family:"times new roman",serif;font-size:large">=</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:1pt">
</span><span style="font-family:"times new roman",serif;font-size:large">0,</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:0.25pt"> </span><span style="font-family:"times new roman",serif;font-size:large">for</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:0.1pt"> </span><span style="font-family:"times new roman",serif;font-size:large">(</span><span style="font-family:"times new roman",serif;font-size:large">𝑥,</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:-0.55pt"> </span><span style="font-family:"times new roman",serif;font-size:large">𝑦</span><span style="font-family:"times new roman",serif;font-size:large">)<span style="letter-spacing:0.9pt"> </span></span><span style="font-family:"times new roman",serif;font-size:large">∈</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:0.9pt"> </span><span style="font-family:"times new roman",serif;font-size:large">𝛺, </span></p><p class="MsoNormal" style="text-align:left;margin:0in 99.5pt 0in 0in;line-height:14pt"><span style="font-family:"times new roman",serif;font-size:large">  𝑢</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:0.95pt"> </span><span style="font-family:"times new roman",serif;font-size:large">=</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:0.8pt"> </span><span style="font-family:"times new roman",serif;font-size:large">0,</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:-0.7pt"> </span><span style="font-family:"times new roman",serif;font-size:large">𝜕</span><sub style="font-family:"times new roman",serif">𝑛</sub><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:1.35pt"> </span><span style="font-family:"times new roman",serif;font-size:large">=</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:0.8pt"> </span><span style="font-family:"times new roman",serif;font-size:large">0,</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:0.1pt"> </span><span style="font-family:"times new roman",serif;font-size:large">on</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:0.05pt"> </span><span style="font-family:"times new roman",serif;font-size:large">𝜕𝛺</span><sub style="font-family:"times new roman",serif">𝑖</sub><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:0.9pt"> </span><span style="font-family:"times new roman",serif;font-size:large">× </span><span style="font-family:"times new roman",serif;font-size:large">[</span><span style="font-family:"times new roman",serif;font-size:large">0,</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:-0.7pt"> </span><span style="font-family:"times new roman",serif;font-size:large">𝑇</span><span style="font-family:"times new roman",serif;font-size:large">]</span><span style="font-family:"times new roman",serif;font-size:large">,</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:0.1pt"> </span><span style="font-family:"times new roman",serif;font-size:large">for 𝑖</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:1pt"> </span><span style="font-family:"times new roman",serif;font-size:large">=</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:0.8pt"> </span><span style="font-family:"times new roman",serif;font-size:large">1,2,3,4,</span></p><p class="MsoNormal" style="text-align:left;margin:1pt 101.45pt 0.0001pt 0in;line-height:17.55pt"><font face="times new roman, serif" size="4"><span style="letter-spacing:0.0666667px">  </span>𝑢<span style="letter-spacing:1.85pt"> </span>=<span style="letter-spacing:1.55pt"> </span>0,<span style="letter-spacing:-0.25pt"> </span>−𝐷(𝜈𝑢_𝑥𝑥<span style="letter-spacing:1.45pt"> </span>+<span style="letter-spacing:0.6pt"> </span>𝑢_𝑦𝑦)<span style="letter-spacing:1.45pt"> </span>=<span style="letter-spacing:1.35pt"> </span>0<span style="letter-spacing:0.7pt"> </span>on<span style="letter-spacing:0.6pt"> </span>𝜕𝛺₁<span style="letter-spacing:1.15pt"> </span>×<span style="letter-spacing:0.65pt"> </span><span style="top: -0.5pt;">[</span>0,<span style="letter-spacing:-0.25pt"> </span>𝑇<span style="top: -0.5pt;">]</span>.</font></p>

<p class="MsoNormal" style="text-align:left;margin:0.2pt 5.3pt 0.0001pt 5.6pt;line-height:97%"><font face="times new roman, serif" size="4"><span style="line-height:97%"><br></span></font></p><p class="MsoNormal" style="text-align:left;margin:0.2pt 5.3pt 0.0001pt 5.6pt;line-height:97%"><font face="times new roman, serif" size="4"><span style="line-height:97%">Here<span style="letter-spacing:2.5pt"> </span></span><span style="line-height:97%">𝑢<span style="top: -0.5pt;">(</span>𝑥, 𝑦,
𝑡<span style="top: -0.5pt;">) </span>or
(𝑢<span style="top: -0.5pt;">(</span>𝑥,
𝑦, 𝑡; 𝑓<span style="top: -0.5pt;">)</span>)<span style="letter-spacing:2.6pt"> </span></span><span style="line-height:97%">is<span style="letter-spacing:2.5pt"> </span>the<span style="letter-spacing:2.5pt"> </span>displacement<span style="letter-spacing:2.5pt"> </span>at<span style="letter-spacing:2.5pt"> </span>a<span style="letter-spacing:2.5pt"> </span>point<span style="letter-spacing:2.55pt"> </span></span><span style="line-height:97%">(</span><span style="line-height:97%">𝑥, 𝑦<span style="top: -0.5pt;">) </span>∈ </span></font><font face="times new roman, serif" size="4"><span style="line-height:97%">𝛺 </span><span style="line-height:97%">and<span style="letter-spacing:2.5pt"> </span>a<span style="letter-spacing:2.5pt"> </span>time<span style="letter-spacing:2.55pt"> </span></span><span style="line-height:97%">𝑡<span style="letter-spacing:2.65pt"> </span>∈<span style="letter-spacing:-2.5pt"> </span><span style="top: -0.5pt;">[</span>0,<span style="letter-spacing:-0.5pt"> </span>𝑇<span style="top: -0.5pt;">]</span></span><span style="line-height:97%">,<span style="letter-spacing:-1.4pt">
</span></span><span style="line-height:97%">𝜕_𝑛𝑢<span style="letter-spacing:-1.2pt"> </span></span><span style="line-height:97%">denotes<span style="letter-spacing:2.25pt"> </span>the<span style="letter-spacing:2.3pt"> </span>normal<span style="letter-spacing:2.3pt"> </span>derivative<span style="letter-spacing:2.3pt"> </span>of<span style="letter-spacing:1.3pt"> </span></span><span style="line-height:97%">𝑢<span style="letter-spacing:-1.2pt"> </span></span><span style="line-height:97%">,<span style="letter-spacing:1.2pt">
</span></span><span style="line-height:97%">𝑔<span style="letter-spacing:1.05pt"> </span>∈<span style="letter-spacing:1px"> </span>𝐿²<span style="top: -0.5pt;">(</span>0,<span style="letter-spacing:-0.6pt"> </span>𝑇<span style="top: -0.5pt;">)<span style="letter-spacing:-1.55pt"> </span></span></span><span style="line-height:97%">is<span style="letter-spacing:2.25pt"> </span>the<span style="letter-spacing:2.3pt"> </span>(known)<span style="letter-spacing:2.35pt"> </span>temporal<span style="letter-spacing:2.3pt">
</span>load,<span style="letter-spacing:1.25pt"> </span></span><span style="line-height:97%">𝐷:<span style="letter-spacing:-0.6pt"> </span>= </span></font><span style="font-family:"times new roman",serif;font-size:large">𝐸</span><span style="font-family:"times new roman",serif;font-size:large">⁄(</span><span style="font-family:"times new roman",serif;font-size:large">1 −</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:0.1pt"> </span><span style="font-family:"times new roman",serif;font-size:large">𝑣</span><sup style="font-family:"times new roman",serif">2</sup><span style="font-family:"times new roman",serif;font-size:large">) </span><span style="font-family:"times new roman",serif;font-size:large">is</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:1.25pt"> </span><span style="font-family:"times new roman",serif;font-size:large">the</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:1.3pt"> </span><span style="font-family:"times new roman",serif;font-size:large">bending</span></p><p class="MsoNormal" style="text-align:left;margin:0.2pt 5.3pt 0.0001pt 5.6pt;line-height:97%"><span style="font-family:"times new roman",serif;font-size:large"><br></span></p><p class="MsoNormal" style="text-align:left;margin:0.2pt 5.3pt 0.0001pt 5.6pt;line-height:97%"><span style="font-family:"times new roman",serif;font-size:large">stiffness,</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:0.15pt"> </span><span style="font-family:"times new roman",serif;font-size:large">𝑣</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:1.25pt"> </span><span style="font-family:"times new roman",serif;font-size:large">∈</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:0.75pt"> </span><span style="font-family:"times new roman",serif;font-size:large">(</span><span style="font-family:"times new roman",serif;font-size:large">0,1</span><span style="font-family:"times new roman",serif;font-size:large">)</span><span style="font-family:"times new roman",serif;font-size:large">is</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:1.25pt"> </span><span style="font-family:"times new roman",serif;font-size:large">the</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:1.3pt"> </span><span style="font-family:"times new roman",serif;font-size:large">Poisson’s</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:1.3pt"> </span><span style="font-family:"times new roman",serif;font-size:large">ratio,</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:0.05pt"> </span><span style="font-family:"times new roman",serif;font-size:large">𝐸 is</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:1.25pt"> </span><span style="font-family:"times new roman",serif;font-size:large">the</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:1.35pt"> </span><span style="font-family:"times new roman",serif;font-size:large">elasticity</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:1.35pt"> </span><span style="font-family:"times new roman",serif;font-size:large">modulus</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:1.25pt"> </span><span style="font-family:"times new roman",serif;font-size:large">and </span><span style="font-size:large;font-family:"times new roman",serif">𝜕𝛺</span><span style="font-size:large;font-family:"times new roman",serif;letter-spacing:1.05pt"> </span><span style="font-size:large;font-family:"times new roman",serif">= </span><span style="font-size:large;font-family:"times new roman",serif"><span style="font-size:12pt;font-family:"Cambria Math",serif">∑</span></span><span style="font-size:large;font-family:"times new roman",serif"><span style="font-size:12pt;font-family:"Cambria Math",serif"> </span></span><span style="font-size:large;font-family:"times new roman",serif">(</span><span style="font-family:"Cambria Math",serif;font-size:16px">i=1 to 4 ) </span><span style="font-size:large;font-family:"times new roman",serif">𝜕𝛺</span><sub style="font-family:"times new roman",serif">𝑖 </sub><span style="font-size:large;font-family:"times new roman",serif">where </span><span style="font-size:large;font-family:"times new roman",serif">𝜕𝛺</span><sub style="font-family:"times new roman",serif">1</sub><span style="font-size:large;font-family:"times new roman",serif;letter-spacing:1.35pt"> </span><span style="font-size:large;font-family:"times new roman",serif">=</span><span style="font-size:large;font-family:"times new roman",serif;letter-spacing:0.8pt"> </span><span style="font-size:large;font-family:"times new roman",serif">(</span><span style="font-size:large;font-family:"times new roman",serif">0,</span><span style="font-size:large;font-family:"times new roman",serif;letter-spacing:-0.6pt"> </span><span style="font-size:large;font-family:"times new roman",serif">𝑘</span><span style="font-size:large;font-family:"times new roman",serif">)<span style="letter-spacing:0.25pt"> </span></span><span style="font-size:large;font-family:"times new roman",serif">×</span><span style="font-size:large;font-family:"times new roman",serif;letter-spacing:0.2pt"> </span><span style="font-size:large;font-family:"times new roman",serif">{0},</span><span style="font-size:large;font-family:"times new roman",serif;letter-spacing:-0.6pt"> </span><span style="font-size:large;font-family:"times new roman",serif">𝜕𝛺</span><sub style="font-family:"times new roman",serif">2</sub><span style="font-size:large;font-family:"times new roman",serif;letter-spacing:1.4pt"> </span><span style="font-size:large;font-family:"times new roman",serif">=</span><span style="font-size:large;font-family:"times new roman",serif;letter-spacing:0.95pt"> </span><span style="font-size:large;font-family:"times new roman",serif">{𝑘}</span><span style="font-size:large;font-family:"times new roman",serif;letter-spacing:0.15pt"> </span><span style="font-size:large;font-family:"times new roman",serif">×</span><span style="font-size:large;font-family:"times new roman",serif;letter-spacing:0.1pt"> </span><span style="font-size:large;font-family:"times new roman",serif">(</span><span style="font-size:large;font-family:"times new roman",serif">0,</span><span style="font-size:large;font-family:"times new roman",serif;letter-spacing:-0.6pt"> </span><span style="font-size:large;font-family:"times new roman",serif">𝑙</span><span style="font-size:large;font-family:"times new roman",serif">)</span><span style="font-size:large;font-family:"times new roman",serif">,</span><span style="font-size:large;font-family:"times new roman",serif;letter-spacing:-0.6pt"> </span><span style="font-size:large;font-family:"times new roman",serif">𝜕𝛺</span><sub style="font-family:"times new roman",serif">3</sub><span style="font-size:large;font-family:"times new roman",serif;letter-spacing:1.4pt"> </span><span style="font-size:large;font-family:"times new roman",serif">=</span><span style="font-size:large;font-family:"times new roman",serif;letter-spacing:0.95pt"> </span><span style="font-size:large;font-family:"times new roman",serif">(</span><span style="font-size:large;font-family:"times new roman",serif">0,</span><span style="font-size:large;font-family:"times new roman",serif;letter-spacing:-0.6pt"> </span><span style="font-size:large;font-family:"times new roman",serif">𝑘</span><span style="font-size:large;font-family:"times new roman",serif">)<span style="letter-spacing:0.05pt"> </span></span><span style="font-size:large;font-family:"times new roman",serif">×</span><span style="font-size:large;font-family:"times new roman",serif;letter-spacing:0.25pt"> </span><span style="font-size:large;font-family:"times new roman",serif">{𝑙},</span><span style="font-size:large;font-family:"times new roman",serif;letter-spacing:-0.7pt"> </span><span style="font-size:large;font-family:"times new roman",serif">𝜕𝛺</span><sub style="font-family:"times new roman",serif">4</sub><span style="font-size:large;font-family:"times new roman",serif;letter-spacing:1.45pt"> </span><span style="font-size:large;font-family:"times new roman",serif">=</span><span style="font-size:large;font-family:"times new roman",serif;letter-spacing:0.8pt"> </span><span style="font-size:large;font-family:"times new roman",serif">{0}</span><span style="font-size:large;font-family:"times new roman",serif;letter-spacing:0.15pt"> </span><span style="font-size:large;font-family:"times new roman",serif">×</span><span style="font-size:large;font-family:"times new roman",serif;letter-spacing:0.2pt"> </span><span style="font-size:large;font-family:"times new roman",serif">(</span><span style="font-size:large;font-family:"times new roman",serif">0,</span><span style="font-size:large;font-family:"times new roman",serif;letter-spacing:-0.55pt"> </span><span style="font-size:large;font-family:"times new roman",serif">𝑙</span><span style="font-size:large;font-family:"times new roman",serif">)</span><span style="font-size:large;font-family:"times new roman",serif">. </span><span style="font-family:"times new roman",serif;font-size:large">In</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:0.05pt"> </span><span style="font-family:"times new roman",serif;font-size:large">determination</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:0.05pt"> </span><span style="font-family:"times new roman",serif;font-size:large">of</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:0.05pt"> </span><span style="font-family:"times new roman",serif;font-size:large">𝑓we</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:0.05pt"> </span><span style="font-family:"times new roman",serif;font-size:large">have the following</span></p><p class="MsoNormal" style="text-align:left;margin:0.2pt 5.3pt 0.0001pt 5.6pt;line-height:97%"><span style="font-family:"times new roman",serif;font-size:large"><br></span></p><p class="MsoNormal" style="text-align:left;margin:0.2pt 5.3pt 0.0001pt 5.6pt;line-height:97%"><span style="font-family:"times new roman",serif;font-size:large">boundary </span><span style="font-family:"times new roman",serif;font-size:large">observation</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:0.05pt"> </span><span style="font-family:"times new roman",serif;font-size:large">on</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:0.2pt"> </span><span style="font-family:"times new roman",serif;font-size:large">𝜕𝛺</span><sub style="font-family:"times new roman",serif">1</sub><span style="font-family:"times new roman",serif;font-size:large">: </span><span style="font-family:"times new roman",serif;font-size:large">𝜃</span><span style="font-family:"times new roman",serif;font-size:large">(</span><span style="font-family:"times new roman",serif;font-size:large">𝑥,</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:-0.55pt"> </span><span style="font-family:"times new roman",serif;font-size:large">𝑡</span><span style="font-family:"times new roman",serif;font-size:large">)</span><span style="font-family:"times new roman",serif;font-size:large">:</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:-0.45pt"> </span><span style="font-family:"times new roman",serif;font-size:large">=</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:1.05pt"> </span><span style="font-family:"times new roman",serif;font-size:large">𝑢</span><sub style="font-family:"times new roman",serif">𝑦</sub><span style="font-family:"times new roman",serif;font-size:large">(</span><span style="font-family:"times new roman",serif;font-size:large">𝑥,</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:-0.55pt"> </span><span style="font-family:"times new roman",serif;font-size:large">0,</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:-0.5pt"> </span><span style="font-family:"times new roman",serif;font-size:large">𝑡</span><span style="font-family:"times new roman",serif;font-size:large">)</span><span style="font-family:"times new roman",serif;font-size:large">,</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:0.3pt"> </span><span style="font-family:"times new roman",serif;font-size:large">for</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:0.15pt"> </span><span style="font-family:"times new roman",serif;font-size:large">𝑥</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:1.4pt"> </span><span style="font-family:"times new roman",serif;font-size:large">∈</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:0.95pt"> </span><span style="font-family:"times new roman",serif;font-size:large">[</span><span style="font-family:"times new roman",serif;font-size:large">0,</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:-0.5pt"> </span><span style="font-family:"times new roman",serif;font-size:large">𝑙</span><span style="font-family:"times new roman",serif;font-size:large">]</span><span style="font-family:"times new roman",serif;font-size:large">,</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:-0.55pt"> </span><span style="font-family:"times new roman",serif;font-size:large">𝑡</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:1.2pt"> </span><span style="font-family:"times new roman",serif;font-size:large">∈</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:0.95pt"> </span><span style="font-family:"times new roman",serif;font-size:large">[</span><span style="font-family:"times new roman",serif;font-size:large">0,</span><span style="font-family:"times new roman",serif;font-size:large;letter-spacing:-0.5pt"> </span><span style="font-family:"times new roman",serif;font-size:large">𝑇</span><span style="font-family:"times new roman",serif;font-size:large">]</span></p>

<p class="gmail-MsoBodyText" style="text-align:left;margin:1.3pt 5.25pt 0.0001pt 5.6pt;text-indent:0.5in"><font face="times new roman, serif" size="4">The<span style="letter-spacing:0.05pt"> </span>conjugate<span style="letter-spacing:0.05pt"> </span>gradient<span style="letter-spacing:0.05pt">
</span>algorithm<span style="letter-spacing:0.05pt"> </span>(CGA)<span style="letter-spacing:0.05pt"> </span>is<span style="letter-spacing:0.05pt"> </span>designed<span style="letter-spacing:0.05pt"> </span>for<span style="letter-spacing:0.05pt"> </span>the<span style="letter-spacing:0.05pt"> </span>numerical<span style="letter-spacing:0.05pt">
</span>solution<span style="letter-spacing:0.05pt"> </span>of<span style="letter-spacing:0.05pt"> </span>the<span style="letter-spacing:0.05pt"> </span>identification
problem. The proposed approach is based on weak solution theory for PDEs,
Tikhonov<span style="letter-spacing:0.05pt"> </span>regularization combined with
the adjoint method. Computational results, obtained for noisy output data,<span style="letter-spacing:0.05pt"> </span>are illustrated to show an efficiency and
accuracy of the proposed approach, for typical classes of source<span style="letter-spacing:0.05pt"> </span>functions.</font></p>

<p class="gmail-MsoBodyText" style="margin:0.55pt 0in 0in"><font face="times new roman, serif" size="4"> </font></p>

<h1 style="margin:0in 0in 0in 5.6pt"><font face="times new roman, serif" size="4">References</font></h1>

<p class="gmail-MsoListParagraph" style="text-indent:0in;margin:0.05pt 23.3pt 0in 5.6pt"><font face="times new roman, serif" size="4">1.<span style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal"> 
</span>L.<span style="letter-spacing:-0.15pt"> </span>Fryba,<span style="letter-spacing:-0.05pt"> </span>Vibrations<span style="letter-spacing:-0.15pt"> </span>of<span style="letter-spacing:-0.1pt"> </span>the<span style="letter-spacing:-0.2pt"> </span>Solids<span style="letter-spacing:-0.15pt">
</span>and<span style="letter-spacing:-0.05pt"> </span>Structures<span style="letter-spacing:-0.15pt"> </span>under<span style="letter-spacing:-0.05pt">
</span>Moving<span style="letter-spacing:-0.05pt"> </span>Loads,<span style="letter-spacing:-0.1pt"> </span>Thomas<span style="letter-spacing:-0.15pt">
</span>Telford<span style="letter-spacing:-0.15pt"> </span>Publishing<span style="letter-spacing:-2.35pt"> </span>House, 1999.  </font></p>

<font face="times new roman, serif" style="" size="4">  2.  M.<span style="letter-spacing:-0.05pt"> </span>Yamamoto,<span style="letter-spacing:-0.05pt"> </span>Determination<span style="letter-spacing:-0.05pt"> </span>of<span style="letter-spacing:-0.15pt"> </span>forces<span style="letter-spacing:-0.1pt"> </span>in<span style="letter-spacing:-0.2pt"> </span>vibrations<span style="letter-spacing:-0.2pt"> </span>of<span style="letter-spacing:-0.05pt"> </span>beams<span style="letter-spacing:-0.15pt"> </span>and plates<span style="letter-spacing:-0.1pt"> </span>by<span style="letter-spacing:-0.15pt"> </span>point<span style="letter-spacing:-0.1pt"> </span>wise<span style="letter-spacing:-0.15pt"> </span>and<span style="letter-spacing:-0.05pt"> </span>line<span style="letter-spacing:-2.35pt">
</span>observations,<span style="letter-spacing:-0.05pt"> </span>J. Inv.
Ill-Posed<span style="letter-spacing:-0.05pt"> </span>Problems, Vol.4, No.5,<span style="letter-spacing:-0.1pt"> </span>pp.437-457<span style="letter-spacing:-0.1pt"> </span>1996.</font></div><div><font face="times new roman, serif" style="" size="4"><br></font></div><div><font face="times new roman, serif" style="" size="4"><br></font></div><div><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-weight:inherit;font-stretch:inherit;line-height:normal;vertical-align:baseline;color:inherit"><font size="4" face="times new roman, serif">Microsoft Teams platform will be used for the seminar. To join the seminar, please use the following link:</font></span></p><p style="margin:0cm 0cm 8pt;color:rgb(32,31,30);line-height:22px"><font face="times new roman, serif" size="4"><a href="https://teams.microsoft.com/l/meetup-join/19%3a0ae91f7b86a24e8fa1d818a6f74b22a1%40thread.tacv2/1653904979472?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.tacv2/1653904979472?context=%7b%22Tid%22%3a%22066690f2-a8a6-4889-852e-124371dcbd6f%22%2c%22Oid%22%3a%22a343f6fd-86f8-4abe-95cf-3c7f4ad5f0ca%22%7d</a></font><font face="times new roman, serif" size="4"><br></font></p><p style="margin:0cm 0cm 8pt;color:rgb(32,31,30);line-height:22px"><font size="4" face="times new roman, serif"><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height: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;vertical-align:baseline;color:black">If you see the following window when connecting to the seminar,  </span></span><br></font></p><div><font size="4" face="times new roman, serif"><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></font></div><p align="center" style="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><font size="4" face="times new roman, serif"><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height: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;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;vertical-align:baseline;color:black"> </span></font></b></p><p style="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"><font size="4" face="times new roman, serif"><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;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;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;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;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;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;vertical-align:baseline;color:inherit"> </span></b>Then you will be able to use your microphone and camera during the seminar. </span></font></p><p style="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;vertical-align:baseline;color:black"><font size="4" face="times new roman, serif"><br></font></span></p><p style="margin-top:0px;margin-bottom:0px;color:rgb(32,31,30)"></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-weight:inherit;font-stretch:inherit;line-height:normal;vertical-align:baseline;color:rgb(0,0,0)"><font size="4" face="times new roman, serif">Please use your real and complete name when you enter the system.</font></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-weight:inherit;font-stretch:inherit;line-height:normal;vertical-align:baseline;color:inherit"><font size="4" face="times new roman, serif">Please switch your microphone off unless you are speaking.</font></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-weight:inherit;font-stretch:inherit;line-height:inherit;vertical-align:baseline;color:inherit"><font size="4" face="times new roman, serif"><br></font></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-weight:inherit;font-stretch:inherit;line-height:inherit;vertical-align:baseline;color:inherit"><font size="4" face="times new roman, serif">Sincerely</font></span></p></div></div>