<div dir="ltr"><span style="color:rgb(80,0,80)"><div>Dear Colleagues!<br></div><br>You are cordially invited to the Weekly Online Seminar “Analysis and Applied Mathematics” on<br><br></span>Date: Tuesday, November 15, 2022<span style="color:rgb(80,0,80)"><br><br>Time: 14.00-15.00 (Istanbul) = 13.00-14.00 (Ghent) = 17.00-18.00 (Almaty)<br><br>Zoom link: <a href="https://us02web.zoom.us/j/6678270445?pwd=SFNmQUIvT0tRaH-lDaVYrN3l5bzJVQT09" target="_blank">https://us02web.zoom.us/j/6678270445?pwd=SFNmQUIvT0tRaH-lDaVYrN3l5bzJVQT09</a>, Conference ID: 667 827 0445, Access code: 1<br><br></span>Speaker: 

Prof. Dr. Fadi Awawdeh <div>The Hashemite University, Jordan <div>  Title: 

Regularization of Ill-Posed Inverse Problems

</div><div>Abstract:  <span lang="EN-US">Ill-posed<span style="letter-spacing:-0.25pt">
</span>inverse<span style="letter-spacing:-0.3pt"> </span>problems<span style="letter-spacing:-0.25pt"> </span>are<span style="letter-spacing:-0.3pt"> </span>at<span style="letter-spacing:-0.25pt"> </span>the<span style="letter-spacing:-0.3pt"> </span>core<span style="letter-spacing:-0.25pt"> </span>of<span style="letter-spacing:-0.3pt"> </span>many<span style="letter-spacing:-0.25pt"> </span>challenging<span style="letter-spacing:-0.25pt"> </span>applications<span style="letter-spacing:-0.3pt"> </span>in<span style="letter-spacing:-0.2pt"> </span>the<span style="letter-spacing:-0.3pt"> </span>natural<span style="letter-spacing:-0.3pt"> </span>sciences,<span style="letter-spacing:-2.3pt">
</span>medicine and life sciences, as well as in engineering and industrial
applications. The talk illustrates<span style="letter-spacing:0.05pt"> </span>the<span style="letter-spacing:1.2pt"> </span>potential<span style="letter-spacing:1.15pt">
</span>difficulties<span style="letter-spacing:1.2pt"> </span>with<span style="letter-spacing:1.2pt"> </span>reversing<span style="letter-spacing:1.25pt">
</span>the<span style="letter-spacing:1.2pt"> </span>process;<span style="letter-spacing:1.55pt"> </span>namely,<span style="letter-spacing:1.4pt">
</span>given<span style="letter-spacing:1.2pt"> </span>a<span style="letter-spacing:1.25pt"> </span>measured<span style="letter-spacing:1.2pt"> </span>state<span style="letter-spacing:1.25pt"> </span>of<span style="letter-spacing:1.2pt"> </span>the<span style="letter-spacing:1.2pt"> </span>model,<span style="letter-spacing:-2.25pt">
</span>try to determine what exact equation could have produced this outcome.</span></div><div><span lang="EN-US"> We will primarily consider<span style="letter-spacing:0.05pt"> </span>operator<span style="letter-spacing:1pt"> </span>equations<span style="letter-spacing:1pt"> </span>Au<span style="letter-spacing:1.1pt"> </span></span><span lang="EN-US" style="font-family:Tahoma,"sans-serif"">=<span style="letter-spacing:0.65pt"> </span></span><span lang="EN-US">y,<span style="letter-spacing:1.2pt"> </span>with<span style="letter-spacing:1.1pt"> </span>the<span style="letter-spacing:1pt"> </span>operator<span style="letter-spacing:1pt"> </span>A<span style="letter-spacing:1.1pt"> </span></span><span lang="EN-US" style="font-family:Tahoma,"sans-serif"">:<span style="letter-spacing:0.65pt"> </span></span><span lang="EN-US">E <span style="letter-spacing:0.55pt"> </span>Y <span style="letter-spacing:0.15pt"> </span>mapping<span style="letter-spacing:1.05pt"> </span>between<span style="letter-spacing:1.05pt"> </span>function<span style="letter-spacing:1.05pt"> </span>spaces<span style="letter-spacing:1pt">
</span>E<span style="letter-spacing:-2.4pt"> </span></span><span lang="EN-US">and<span style="letter-spacing:0.55pt"> </span>Y<span style="letter-spacing:0.05pt"> </span>.</span><span lang="EN-US" style="letter-spacing:4.05pt"> </span><span lang="EN-US">We</span><span lang="EN-US" style="letter-spacing:2.6pt"> </span><span lang="EN-US">assume</span><span lang="EN-US" style="letter-spacing:2.6pt"> </span><span lang="EN-US">that</span><span lang="EN-US" style="letter-spacing:2.6pt"> </span><span lang="EN-US">the</span><span lang="EN-US" style="letter-spacing:2.6pt"> </span><span lang="EN-US">operator</span><span lang="EN-US" style="letter-spacing:2.6pt"> </span><span lang="EN-US">equation</span><span lang="EN-US" style="letter-spacing:2.65pt"> </span><span lang="EN-US">is</span><span lang="EN-US" style="letter-spacing:2.6pt"> </span><span lang="EN-US">ill-posed</span><span lang="EN-US" style="letter-spacing:2.65pt"> </span><span lang="EN-US">in</span><span lang="EN-US" style="letter-spacing:2.65pt"> </span><span lang="EN-US">the</span><span lang="EN-US" style="letter-spacing:2.6pt"> </span><span lang="EN-US">sense</span><span lang="EN-US" style="letter-spacing:2.6pt"> </span><span lang="EN-US">that</span><span lang="EN-US" style="letter-spacing:2.6pt"> </span><span lang="EN-US">small</span><span lang="EN-US" style="letter-spacing:2.55pt"> </span><span lang="EN-US">perturbations<span style="letter-spacing:0.05pt"> </span></span><span lang="EN-US">of y can lead to arbitrarily large
perturbations on u (or even lead to non-existence of a solution).<span style="letter-spacing:0.05pt"> </span></span><span lang="EN-US">To obtain a stable
estimate of the solution of such problems, it is often necessary to implement a<span style="letter-spacing:0.05pt"> </span>regularization<span style="letter-spacing:0.85pt"> </span>strategy.<span style="letter-spacing:2.4pt"> </span>This<span style="letter-spacing:0.85pt"> </span>requires<span style="letter-spacing:0.85pt">
</span>the<span style="letter-spacing:0.85pt"> </span>solution<span style="letter-spacing:0.9pt"> </span>approach<span style="letter-spacing:0.85pt">
</span>to<span style="letter-spacing:0.85pt"> </span>satisfy<span style="letter-spacing:0.9pt"> </span>some<span style="letter-spacing:0.85pt"> </span>regularizing<span style="letter-spacing:0.9pt"> </span>properties,</span><span lang="EN-US" style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;text-align:center">i.e.,<span style="letter-spacing:2.05pt"> </span>be<span style="letter-spacing:1.95pt"> </span>stable<span style="letter-spacing:1.95pt">
</span>even<span style="letter-spacing:1.95pt"> </span>for<span style="letter-spacing:1.9pt"> </span>noisy<span style="letter-spacing:1.95pt"> </span>data<span style="letter-spacing:1.95pt"> </span>y</span><sup style="font-family:"Microsoft Sans Serif","sans-serif";text-align:center"><span lang="EN-US" style="font-family:"Lucida Sans Unicode","sans-serif"">б</span></sup><span lang="EN-US" style="font-size:9pt;text-align:center;font-family:"Lucida Sans Unicode","sans-serif";letter-spacing:2.2pt"> </span><span lang="EN-US" style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;text-align:center">with</span><span lang="EN-US" style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;text-align:center;letter-spacing:2.55pt"> </span><span lang="EN-US" style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;text-align:center;letter-spacing:2.6pt"> </span><span lang="EN-US" style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;text-align:center">y</span><sup style="font-family:"Microsoft Sans Serif","sans-serif";text-align:center"><span lang="EN-US" style="font-family:"Lucida Sans Unicode","sans-serif"">б</span></sup><span lang="EN-US" style="font-size:9pt;text-align:center;font-family:"Lucida Sans Unicode","sans-serif";letter-spacing:0.35pt"> </span><span lang="EN-US" style="font-size:9pt;text-align:center;font-family:"Lucida Sans Unicode","sans-serif"">—<span style="letter-spacing:-0.45pt"> </span></span><span lang="EN-US" style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;text-align:center">y</span><span lang="EN-US" style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;text-align:center;letter-spacing:2.6pt"> </span><span lang="EN-US" style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;text-align:center;letter-spacing:2.65pt"> </span><span lang="EN-US" style="font-size:9pt;text-align:center;font-family:"Lucida Sans Unicode","sans-serif"">≤<span style="letter-spacing:1.3pt"> </span></span><span lang="EN-US" style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;text-align:center">б<span style="letter-spacing:2.2pt"> </span>in<span style="letter-spacing:2pt"> </span>place<span style="letter-spacing:1.95pt"> </span>of<span style="letter-spacing:1.9pt"> </span>y<span style="letter-spacing:2.2pt"> </span>and<span style="letter-spacing:1.95pt"> </span>yield<span style="letter-spacing:2pt"> </span>reconstructions<span style="letter-spacing:1.95pt"> </span>y</span><sup style="font-family:"Microsoft Sans Serif","sans-serif";text-align:center"><span lang="EN-US" style="font-family:"Lucida Sans Unicode","sans-serif"">б </span></sup><span lang="EN-US">that<span style="letter-spacing:0.1pt"> </span>converge<span style="letter-spacing:0.15pt">
</span>to<span style="letter-spacing:0.15pt"> </span>the<span style="letter-spacing:0.1pt"> </span>exact<span style="letter-spacing:0.1pt"> </span>solution<span style="letter-spacing:0.15pt"> </span>u</span>^{<span lang="EN-US" style="font-family:"Lucida Sans Unicode","sans-serif"">†</span>}<span lang="EN-US" style="font-family:"Lucida Sans Unicode","sans-serif";letter-spacing:-0.05pt"> </span><span lang="EN-US">as б</span><span lang="EN-US" style="font-family:"Times New Roman","serif"">          </span><span lang="EN-US" style="font-family:Tahoma,"sans-serif"">0</span><span lang="EN-US">.<span style="letter-spacing:0.6pt"> </span>Regularization<span style="letter-spacing:1.05pt"> </span>techniques<span style="letter-spacing:1.05pt"> </span>are<span style="letter-spacing:1.05pt"> </span>the<span style="letter-spacing:1.05pt"> </span>subject<span style="letter-spacing:1.05pt">
</span>of<span style="letter-spacing:1pt"> </span>this<span style="letter-spacing:-2.25pt"> </span>talk<span style="letter-spacing:1.15pt"> </span>and<span style="letter-spacing:1.2pt"> </span>we<span style="letter-spacing:1.2pt"> </span>will<span style="letter-spacing:1.1pt"> </span>attempt<span style="letter-spacing:1.15pt"> </span>to<span style="letter-spacing:1.2pt"> </span>highlight<span style="letter-spacing:1.15pt"> </span>two<span style="letter-spacing:1.2pt"> </span>approaches<span style="letter-spacing:1.1pt"> </span>that<span style="letter-spacing:1.15pt"> </span>are<span style="letter-spacing:1.2pt"> </span>wide-spread<span style="letter-spacing:1.2pt"> </span>in<span style="letter-spacing:1.15pt"> </span>the<span style="letter-spacing:1.2pt"> </span>literature: </span></div><div><span lang="EN-US"><span style="letter-spacing:0.5pt"></span>(i) </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">Variational</span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;letter-spacing:0.65pt"> </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">methods</span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;letter-spacing:0.65pt"> </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">are</span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;letter-spacing:0.7pt"> </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">based</span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;letter-spacing:0.7pt"> </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">on</span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;letter-spacing:0.7pt"> </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">minimizing</span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;letter-spacing:0.7pt"> </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">a</span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;letter-spacing:0.7pt"> </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">weighted</span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;letter-spacing:0.7pt"> </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">sum</span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;letter-spacing:0.8pt"> </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">of</span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;letter-spacing:0.65pt"> </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">a</span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;letter-spacing:0.7pt"> </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">discrepancy</span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;letter-spacing:0.7pt"> </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">term</span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;letter-spacing:0.8pt"> </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">and</span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;letter-spacing:0.7pt"> </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">a</span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;letter-spacing:0.7pt"> </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">suitable</span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;letter-spacing:-2.25pt"> </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">regularization</span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;letter-spacing:0.5pt"> </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">term</span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;letter-spacing:0.6pt"> </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">(Tikhonov</span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;letter-spacing:0.5pt"> </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">regularization)</span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;letter-spacing:0.5pt"> </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">or</span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;letter-spacing:0.45pt"> </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">on</span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;letter-spacing:0.55pt"> </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">minimizing</span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;letter-spacing:0.45pt"> </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">one</span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;letter-spacing:0.5pt"> </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">of</span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;letter-spacing:0.4pt"> </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">these</span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;letter-spacing:0.5pt"> </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">terms</span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;letter-spacing:0.45pt"> </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">under</span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;letter-spacing:0.5pt"> </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">a</span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt;letter-spacing:0.45pt"> </span><span style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">constraint </span><span lang="EN-US" style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">on<span style="letter-spacing:0.05pt"> </span>the
other (Ivanov<span style="letter-spacing:0.05pt"> </span>or Morozov<span style="letter-spacing:0.05pt"> </span>regularization,<span style="letter-spacing:0.05pt"> </span>respectively);<span style="letter-spacing:0.05pt"> </span></span></div><div><span lang="EN-US" style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">(ii)
Iterative methods construct a<span style="letter-spacing:-2.4pt"> </span>sequence<span style="letter-spacing:0.45pt"> </span>of<span style="letter-spacing:0.4pt"> </span>iterates<span style="letter-spacing:0.5pt"> </span>approximating<span style="letter-spacing:0.45pt"> </span>the<span style="letter-spacing:0.45pt"> </span>solution<span style="letter-spacing:0.55pt"> </span>u</span><sup style="font-family:"Microsoft Sans Serif","sans-serif""><span lang="EN-US" style="font-family:"Lucida Sans Unicode","sans-serif"">†</span></sup><span lang="EN-US" style="font-family:"Microsoft Sans Serif","sans-serif";font-size:9pt">.</span><p style="margin:0.5pt 30.75pt 0.0001pt;line-height:92%;font-size:9pt;font-family:"Microsoft Sans Serif","sans-serif""><span lang="EN-US"></span></p>

<p style="margin:4.95pt 0cm 0.0001pt 20.8pt;font-size:9pt;font-family:"Microsoft Sans Serif","sans-serif""><span lang="EN-US">Keywords— Regularization,<span style="letter-spacing:0.05pt"> </span>Ill-posed<span style="letter-spacing:0.15pt"> </span>Problems,<span style="letter-spacing:0.1pt"> </span>Variational<span style="letter-spacing:0.05pt"> </span>Methods,<span style="letter-spacing:0.1pt"> </span>Iterative<span style="letter-spacing:0.1pt"> </span>Methods</span><span lang="EN-US"></span></p>

<p style="margin:0cm 0cm 0.0001pt;font-size:9pt;font-family:"Microsoft Sans Serif","sans-serif""><span lang="EN-US"> </span></p>

<p style="margin:0cm 0cm 0.0001pt;font-size:9pt;font-family:"Microsoft Sans Serif","sans-serif""><span lang="EN-US"> </span></p>

<p class="MsoNormal" style="margin:6.05pt 0cm 0.0001pt 5.85pt;font-size:11pt;font-family:"Microsoft Sans Serif","sans-serif""><span lang="EN-US" style="font-size:14pt;font-family:Verdana,"sans-serif"">References</span></p>

<p style="margin:8.6pt 5.9pt 0.0001pt 20.55pt;line-height:107%;font-size:11pt;font-family:"Microsoft Sans Serif","sans-serif""><span lang="EN-US" style="font-size:9pt;line-height:107%">[1]<span style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:7pt;line-height:normal;font-family:"Times New Roman"">   
</span></span><span lang="EN-US" style="font-size:9pt;line-height:107%">Hofmann,<span style="letter-spacing:2pt"> </span>B.,<span style="letter-spacing:2pt"> </span>Kaltenbacher,<span style="letter-spacing:2pt"> </span>B.,<span style="letter-spacing:2pt"> </span>Pöschl,<span style="letter-spacing:2pt"> </span>C.,<span style="letter-spacing:2pt"> </span>Scherzer,<span style="letter-spacing:2pt"> </span>O.<span style="letter-spacing:1.7pt"> </span>2007:<span style="letter-spacing:1.5pt"> </span>A<span style="letter-spacing:1.75pt"> </span>convergence<span style="letter-spacing:1.75pt"> </span>rate<span style="letter-spacing:1.75pt">
</span>result<span style="letter-spacing:1.7pt"> </span>for<span style="letter-spacing:1.75pt"> </span>Tikhonov<span style="letter-spacing:0.05pt">
</span>regularization<span style="letter-spacing:0.55pt"> </span>in<span style="letter-spacing:0.6pt"> </span>Banach<span style="letter-spacing:0.55pt"> </span>spaces<span style="letter-spacing:0.55pt"> </span>with<span style="letter-spacing:0.55pt"> </span>non-smooth<span style="letter-spacing:0.6pt"> </span>operators.<span style="letter-spacing:0.45pt">
</span>Inverse<span style="letter-spacing:0.55pt"> </span>Problems,<span style="letter-spacing:0.5pt"> </span>23(3)<span style="letter-spacing:0.5pt"> </span>987–1010.</span></p>

<p style="line-height:107%;margin:3.9pt 5.9pt 0.0001pt 20.55pt;font-size:11pt;font-family:"Microsoft Sans Serif","sans-serif""><span lang="EN-US" style="font-size:9pt;line-height:107%">[2]<span style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:7pt;line-height:normal;font-family:"Times New Roman"">    </span></span><span lang="EN-US" style="font-size:9pt;line-height:107%">Kaltenbacher,<span style="letter-spacing:0.65pt"> </span>B.,<span style="letter-spacing:0.65pt"> </span>Neubauer,<span style="letter-spacing:0.65pt"> </span>A.,<span style="letter-spacing:0.65pt"> </span>Scherzer,<span style="letter-spacing:0.7pt"> </span>O.<span style="letter-spacing:0.65pt"> </span>2008:<span style="letter-spacing:1.65pt"> </span>Iterative<span style="letter-spacing:0.65pt"> </span>Regularization<span style="letter-spacing:0.7pt"> </span>Methods<span style="letter-spacing:0.7pt"> </span>for<span style="letter-spacing:0.65pt"> </span>Nonlinear<span style="letter-spacing:0.65pt"> </span>Ill-Posed<span style="letter-spacing:0.05pt">
</span>Problems.<span style="letter-spacing:0.65pt"> </span>Radon<span style="letter-spacing:0.8pt"> </span>Series<span style="letter-spacing:0.7pt"> </span>on<span style="letter-spacing:0.8pt"> </span>Computational<span style="letter-spacing:0.65pt"> </span>and<span style="letter-spacing:0.8pt"> </span>Applied<span style="letter-spacing:0.75pt"> </span>Mathematics.<span style="letter-spacing:0.7pt"> </span>de<span style="letter-spacing:0.7pt"> </span>Gruyter,<span style="letter-spacing:0.7pt"> </span>Berlin,<span style="letter-spacing:0.65pt"> </span>2008.</span></p>

<p style="margin:3.9pt 5.8pt 0.0001pt 20.55pt;line-height:107%;font-size:11pt;font-family:"Microsoft Sans Serif","sans-serif""><span lang="EN-US" style="font-size:9pt;line-height:107%">[3]<span style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:7pt;line-height:normal;font-family:"Times New Roman"">   
</span></span><span lang="EN-US" style="font-size:9pt;line-height:107%">Kaltenbacher, B., Rundell, W. 2019:<span style="letter-spacing:0.05pt"> </span>Regularization of a backwards parabolic
equation by fractional operators.<span style="letter-spacing:-2.25pt"> </span>Inverse<span style="letter-spacing:0.7pt"> </span>Problems<span style="letter-spacing:0.75pt">
</span>and<span style="letter-spacing:0.75pt"> </span>Imaging,<span style="letter-spacing:0.7pt"> </span>(13)<span style="letter-spacing:0.7pt"> </span>401–430.</span></p>

<p style="margin:3.9pt 5.85pt 0.0001pt 20.55pt;line-height:107%;font-size:11pt;font-family:"Microsoft Sans Serif","sans-serif""><span lang="EN-US" style="font-size:9pt;line-height:107%">[4]<span style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:7pt;line-height:normal;font-family:"Times New Roman"">   
</span></span><span lang="EN-US" style="font-size:9pt;line-height:107%">Werner, F. 2015:<span style="letter-spacing:0.05pt"> </span>On convergence rates for iteratively
regularized Newton-type methods under a Lipschitz Type <span style="letter-spacing:-2.25pt"> </span>nonlinearity<span style="letter-spacing:0.75pt"> </span>condition.<span style="letter-spacing:0.75pt"> </span>Journal<span style="letter-spacing:0.75pt">
</span>of<span style="letter-spacing:0.75pt"> </span>Inverse<span style="letter-spacing:0.8pt"> </span>and<span style="letter-spacing:0.8pt"> </span>ILL-posed<span style="letter-spacing:0.85pt"> </span>Problems,<span style="letter-spacing:0.75pt">
</span>(23)<span style="letter-spacing:0.8pt"> </span>75–84.</span></p><div><span style="color:rgb(80,0,80)">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><br>Kind regards,</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 style="font-size:12.8px"><span style="font-size:small"><b>Department of Mathematics, Bahcesehir University, 34353, Istanbul, Turkey</b></span><b style="font-size:12.8px">  and </b><b style="font-size:12.8px">Near East University, Lefkoşa(Nicosia), Mersin 10 Turkey</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><br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Thu, 2 Jun 2022 at 16:13, Allaberen Ashyralyev <<a href="mailto:Allaberen.Ashyralyev@listweb.bilkent.edu.tr" target="_blank">Allaberen.Ashyralyev@listweb.bilkent.edu.tr</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><span style="color:rgb(80,0,80)"><div>Dear Colleagues!<br></div><br>You are cordially invited to the Weekly Online Seminar “Analysis and Applied Mathematics” on<br><br></span>Date: Tuesday, June 07, 2022<span style="color:rgb(80,0,80)"><br><br>Time: 14.00-15.00 (Istanbul) = 13.00-14.00 (Ghent) = 17.00-18.00 (Almaty)<br><br>Zoom link: <a href="https://us02web.zoom.us/j/6678270445?pwd=SFNmQUIvT0tRaH-lDaVYrN3l5bzJVQT09" target="_blank">https://us02web.zoom.us/j/6678270445?pwd=SFNmQUIvT0tRaH-lDaVYrN3l5bzJVQT09</a>, Conference ID: 667 827 0445, Access code: 1<br><br></span>Speaker:

Prof. Dr. Yusif Gasimov<div> Azerbaijan University, Baku, Azerbaijan  <div> Title: In this talk an inverse spectral problem is considered with respect to the domain
for the Schrödinger equation. Using the introduced space of the pairs of the convex domains
a new definition of the domain variation is given. The first variation of the eigenvalues with
respect to domain is calculated, a new formula for the eigenvalues of the Schrödinger operator
is proved. A definition of s-function is introduced and a scheme is proposed to reconstruct the
domain by the given set of the s-functions. Some particular cases are also considered.</div><div><span style="color:rgb(80,0,80)"><br>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><br>Kind regards,</span></div><div><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 dir="ltr"><div style="font-size:12.8px"><b style="font-size:12.8px">Prof. Dr. Allaberen Ashyralyev </b></div><div style="font-size:12.8px"><span style="font-size:small"><b>Department of Mathematics, Bahcesehir University, 34353, Istanbul, Turkey</b></span><b style="font-size:12.8px">  and </b><b style="font-size:12.8px">Near East University, Lefkoşa(Nicosia), Mersin 10 Turkey</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></div>
_______________________________________________<br>
Turkmath mailing list<br>
<a href="mailto:Turkmath@listweb.bilkent.edu.tr" target="_blank">Turkmath@listweb.bilkent.edu.tr</a><br>
<a href="http://yunus.listweb.bilkent.edu.tr/cgi-bin/mailman/listinfo/turkmath" rel="noreferrer" target="_blank">http://yunus.listweb.bilkent.edu.tr/cgi-bin/mailman/listinfo/turkmath</a><br>
</blockquote></div>