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@@ -42,8 +42,9 @@
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<h1>Mathematics</h1>
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- <section id="topics">
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- <h2>Research topics</h2>
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+ <section>
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+ <a class="anchor" id="topics"></a>
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+ <h2>Research topics</h2>
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<p>
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I deal with
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mathematical <a href="https://en.wikipedia.org/wiki/Inverse_problem">inverse
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@@ -86,14 +87,24 @@
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- <section id="publications">
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+ <section>
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+ <a class="anchor" id="publications"></a>
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<h2>List of
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Publications <a href="pdf/blasten_publications.pdf">PDF</a></h2>
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+ <ul class="navsubbar">
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+ <li><a href="#pubs_submitted">Submitted</a></li>
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+ <li><a href="#pubs_accepted">Accepted</a></li>
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+ <li><a href="#pubs_proceedings">Proceedings</a></li>
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+ <li><a href="#pubs_theses">Theses</a></li>
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+ <li><a href="#pubs_others">Others</a></li>
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+ </ul>
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- <p>
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+ <p style="clear:left">
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+ <a class="anchor" id="pubs_submitted"></a>
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<h3>Submitted</h3>
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<ol reversed>
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- <li id="Blasten-Li-Liu_Wang-2018">
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+ <li>
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+ <a class="anchor" id="Blasten-Li-Liu-Wang-2018"></a>
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<span class="ref-authors">E. Blåsten, H. Li, H. Liu, Y. Wang,</span>
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<span class="ref-title">Localization and
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geometrization in plasmon resonances and geometric
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@@ -104,7 +115,8 @@
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<a href="https://arxiv.org/abs/1809.08533">Preprint</a>
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</div>
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</li>
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- <li id="Blasten-Vesalainen-2018">
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+ <li>
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+ <a class="anchor" id="Blasten-Vesalainen-2018"></a>
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<span class="ref-authors">E. Blåsten, E. V. Vesalainen,</span>
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<span class="ref-title">Non-Scattering Energies and Transmission Eigenvalues in
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<i>H<sup>n</sup></i>.</span>
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@@ -113,7 +125,8 @@
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<a href="http://arxiv.org/abs/1809.04426/">Preprint</a>
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</div>
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</li>
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- <li id="Blasten-Liu-2018">
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+ <li>
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+ <a class="anchor" id="Blasten-Liu-2018"></a>
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<span class="ref-authors">E. Blåsten, H. Liu,</span>
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<span class="ref-title">Scattering by curvatures,
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radiationless sources, transmission eigenfunctions and
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@@ -123,17 +136,8 @@
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<a href="https://arxiv.org/abs/1808.01425">Preprint</a>
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</div>
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</li>
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- <li id="Blasten2018">
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- <span class="ref-authors">E. Blåsten,</span>
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- <span class="ref-title">Nonradiating sources and
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- transmission eigenfunctions vanish at corners and
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- edges.</span>
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- <div class="ref-links">
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- <a href="#desc_Blasten2018">Description</a>
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- <a href="http://arxiv.org/abs/1803.10917/">Preprint</a>
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- </div>
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- </li>
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- <li id="BlastenLiu2017b">
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+ <li>
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+ <a class="anchor" id="BlastenLiu2017b"></a>
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<span class="ref-authors">E. Blåsten, H. Liu,</span>
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<span class="ref-title">Recovering piecewise constant
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refractive indices by a single far-field
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@@ -143,7 +147,8 @@
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<a href="https://arxiv.org/abs/1705.00815">Preprint</a>
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</div>
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</li>
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- <li id="BlastenTzouWang2017">
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+ <li>
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+ <a class="anchor" id="BlastenTzouWang2017"></a>
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<span class="ref-authors">E. Blåsten, L. Tzou,
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J. Wang,</span>
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<span class="ref-title">Uniqueness for the inverse
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@@ -154,7 +159,8 @@
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<a href="https://arxiv.org/abs/1704.06397">Preprint</a>
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</div>
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</li>
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- <li id="BlastenLiu2016">
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+ <li>
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+ <a class="anchor" id="BlastenLiu2016"></a>
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<span class="ref-authors">E. Blåsten, H. Liu,</span>
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<span class="ref-title"> On corners scattering stably
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and stable shape determination by a single far-field
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@@ -168,9 +174,23 @@
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</p>
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<p>
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+ <a class="anchor" id="pubs_accepted"></a>
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<h3>Accepted in Peer-Reviewed Journals</h3>
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<ol reversed>
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- <li id="Pipes1">
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+ <li>
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+ <a class="anchor" id="Blasten2018"></a>
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+ <span class="ref-authors">E. Blåsten,</span>
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+ <span class="ref-title">Nonradiating sources and
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+ transmission eigenfunctions vanish at corners and
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+ edges.</span>
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+ <div class="ref-links">
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+ <a href="#desc_Blasten2018">Description</a>
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+ <a href="https://doi.org/10.1137/18M1182048">Publication</a>
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+ <a href="http://arxiv.org/abs/1803.10917/">Preprint</a>
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+ </div>
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+ </li>
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+ <li>
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+ <a class="anchor" id="Pipes1"></a>
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<span class="ref-authors">F. Zouari, E. Blåsten,
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M. Louati, and M. S. Ghidaoui,</span>
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<span class="ref-title">Internal pipe area
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@@ -178,12 +198,13 @@
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detection.</span>
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<span class="ref-journal">Journal of Hydraulic
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Engineering, ASCE,</span>
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- <span class="ref-year">accpeted 2018.</span>
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+ <span class="ref-year">accepted 2018.</span>
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<div class="ref-links">
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<a href="#desc_Pipes1">Description</a>
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</div>
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</li>
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- <li id="BlastenLin2018">
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+ <li>
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+ <a class="anchor" id="BlastenLin2018"></a>
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<span class="ref-authors">E. Blåsten, Y.-H. Lin</span>
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<span class="ref-title">Radiating and non-radiating
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sources in elasticity.</span>
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@@ -195,7 +216,8 @@
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<a href="http://arxiv.org/abs/1807.07225/">Preprint</a>
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</div>
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</li>
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- <li id="Blasten2017">
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+ <li>
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+ <a class="anchor" id="Blasten2017"></a>
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<span class="ref-authors">E. Blåsten,</span>
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<span class="ref-title">Well-posedness of the Goursat
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problem and stability for point source inverse
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@@ -211,7 +233,8 @@
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<a href="https://arxiv.org/abs/1705.09442">Preprint</a>
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</div>
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</li>
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- <li id="BlastenLiu2017a">
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+ <li>
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+ <a class="anchor" id="BlastenLiu2017a"></a>
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<span class="ref-authors">E. Blåsten, H. Liu,</span>
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<span class="ref-title">On vanishing near corners of
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transmission eigenfunctions,</span>
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@@ -227,7 +250,8 @@
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<a href="https://arxiv.org/abs/1701.07957">Preprint</a>
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</div>
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</li>
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- <li id="BlastenLiLiuWang2017">
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+ <li>
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+ <a class="anchor" id="BlastenLiLiuWang2017"></a>
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<span class="ref-authors">E. Blåsten, X. Li, H. Liu,
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Y. Wang,</span>
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<span class="ref-title"> On vanishing and localizing
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@@ -244,7 +268,8 @@
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<a href="https://arxiv.org/abs/1704.01885">Preprint</a>
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</div>
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</li>
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- <li id="BlastenSylvester2016">
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+ <li>
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+ <a class="anchor" id="BlastenSylvester2016"></a>
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<span class="ref-authors">E. Blåsten, J. Sylvester,</span>
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<span class="ref-title">Translation-Invariant
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Estimates for Operators with Simple
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@@ -261,7 +286,8 @@
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<a href="http://arxiv.org/abs/1607.06214">Preprint</a>
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</div>
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</li>
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- <li id="BlastenImanuvilovYamamoto2015">
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+ <li>
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+ <a class="anchor" id="BlastenImanuvilovYamamoto2015"></a>
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<span class="ref-authors">E. Blåsten,
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O. Yu. Imanuvilov, M. Yamamoto,</span>
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<span class="ref-title">Stability and uniqueness for a
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@@ -279,7 +305,8 @@
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<a href="http://arxiv.org/abs/1504.02207">Preprint</a>
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</div>
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</li>
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- <li id="BlastenPaivarintaSylvester2014">
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+ <li>
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+ <a class="anchor" id="BlastenPaivarintaSylvester2014"></a>
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<span class="ref-authors">E. Blåsten, L. Päivärinta,
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J. Sylvester,</span>
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<span class="ref-title">Corners Always Scatter,</span>
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@@ -295,7 +322,8 @@
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<a href="http://arxiv.org/abs/1211.1848">Preprint</a>
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</div>
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</li>
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- <li id="BlastenPaivarinta2013">
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+ <li>
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+ <a class="anchor" id="BlastenPaivarinta2013"></a>
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<span class="ref-authors">E. Blåsten,
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L. Päivärinta,</span>
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<span class="ref-title">Completeness of generalized
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@@ -315,9 +343,34 @@
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</p>
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<p>
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+ <a class="anchor" id="pubs_proceedings"></a>
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+ <h3>Conference Proceedings</h3>
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+ <ol reversed>
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+ <li>
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+ <a class="anchor" id="PipesProceedings1"></a>
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+ <span class="ref-authors">F. Zouari, M. Louati,
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+ E. Blåsten, and M. S. Ghidaoui,</span>
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+ <span class="ref-title">Multiple defects detection and
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+ characterization in pipes.</span>
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+ <span class="ref-journal">13<sup>th</sup> International Conference on
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+ <span style="font-variant: small-caps">Pressure
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+ Surges</span>,</span>
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+ <span class="ref-year">Bordeaux, France,
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+ 14<sup>th</sup>–16<sup>th</sup> November
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+ 2018.</span>
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+ <div class="ref-links">
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+ <a href="#desc_PipesProceedings1">Description</a>
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+ </div>
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+ </li>
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+ </ol>
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+ </p>
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+
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+ <p>
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+ <a class="anchor" id="pubs_theses"></a>
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<h3>Theses</h3>
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<ol reversed>
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- <li id="Blasten2013">
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+ <li>
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+ <a class="anchor" id="Blasten2013"></a>
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<span class="ref-authors">E. Blåsten,</span>
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<span class="ref-title">On the Gel’Fand-Calderón
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inverse problem in two dimensions,</span>
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@@ -331,7 +384,8 @@
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<a href="http://arxiv.org/abs/1307.4870">Preprint</a>
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</div>
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</li>
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- <li id="Blasten2010">
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+ <li>
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+ <a class="anchor" id="Blasten2010"></a>
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<span class="ref-authors">E. Blåsten,</span>
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<span class="ref-title">The Inverse Problem of the
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Schrödinger Equation in the Plane: A Dissection of
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@@ -345,7 +399,8 @@
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<a href="http://arxiv.org/abs/1103.6200">arXiv version</a>
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</div>
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</li>
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- <li id="Blasten2008">
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+ <li>
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+ <a class="anchor" id="Blasten2008"></a>
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<span class="ref-authors">E. Blåsten,</span>
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<span class="ref-title">Distribuutioteorian alkeet ja
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sovellutuksia,</span>
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@@ -362,6 +417,7 @@
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</p>
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<p>
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+ <a class="anchor" id="pubs_others"></a>
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<h3>Other publications</h3>
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<ol reversed>
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<li>
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@@ -395,10 +451,35 @@
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- <section id="descriptions">
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+ <section>
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+ <a class="anchor" id="descriptions"></a>
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<h2>Description of projects</h2>
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<dl>
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- <dt id="desc_Blasten-Li-Liu-Wang-2018">
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+ <dt>
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+ <a class="anchor" id="desc_PipesProceedings1"></a>
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+ <a href="#PipesProceedings1">
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+ <span class="ref-authors">F. Zouari, M. Louati,
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+ E. Blåsten, and M. S. Ghidaoui,</span>
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+ <span class="ref-title">Multiple defects detection and
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+ characterization in pipes.</span>
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+ </a>
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+ </dt>
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+ <dd>
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+ <p>
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+ This is a continuation and generalization of the work
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+ done for pipe <a href="#Pipes1">area
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+ reconstruction</a>. We extend that method to the
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+ detection of leaks and discrete blockages. Because of
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+ a mathematical non-uniqueness to this one-dimensional
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+ inverse problem, certain configurations of defects
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+ cannot be uniquely identified from certain others. We
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+ propose a solution to this problem: measure the
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+ impulse-response function from both ends of the pipe.
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+ </p>
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+ </dd>
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+
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+ <dt>
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+ <a class="anchor" id="desc_Blasten-Li-Liu-Wang-2018"></a>
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<a href="#Blasten-Li-Liu-Wang-2018">
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<span class="ref-authors">E. Blåsten, H. Li, H. Liu, Y. Wang</span>
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<span class="ref-title">Localization and
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@@ -425,7 +506,8 @@
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large particles!
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</p>
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</dd>
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- <dt id="desc_Blasten-Vesalainen-2018">
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+ <dt>
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+ <a class="anchor" id="desc_Blasten-Vesalainen-2018"></a>
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<a href="#Blasten-Vesalainen-2018">
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<span class="ref-authors">E. Blåsten, E. V. Vesalainen</span>
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<span class="ref-title">Non-Scattering Energies and
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@@ -447,7 +529,8 @@
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into the setting of hyperbolic manifolds.
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</p>
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</dd>
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- <dt id="desc_Blasten-Liu-2018">
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+ <dt>
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+ <a class="anchor" id="desc_Blasten-Liu-2018"></a>
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<a href="#Blasten-Liu-2018">
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<span class="ref-authors">E. Blåsten, H. Liu</span>
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<span class="ref-title">Scattering by curvatures,
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@@ -489,7 +572,8 @@
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and <a href="https://doi.org/10.1137/130908658">2013b</a>.
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</p>
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</dd>
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- <dt id="desc_BlastenLin2018">
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+ <dt>
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+ <a class="anchor" id="desc_BlastenLin2018"></a>
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<a href="#BlastenLin2018">
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<span class="ref-authors">E. Blåsten, Y.-H. Lin</span>
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<span class="ref-title">Radiating and non-radiating
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@@ -523,7 +607,8 @@
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far-field.
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</p>
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</dd>
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- <dt id="desc_Blasten2018">
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+ <dt>
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+ <a class="anchor" id="desc_Blasten2018"></a>
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<a href="#Blasten2018">
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<span class="ref-authors">E. Blåsten,</span>
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<span class="ref-title">Nonradiating sources and
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@@ -533,13 +618,13 @@
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</dt>
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<dd>
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<p>
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- This paper consider the inverse source problem, namely
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- we do not send an incident wave, and are instead using
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- data provided by the unknown source itself. We show
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- that so called <em>nonradiating sources</em> cannot
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- have sharp corner or edge jumps on their
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- boundary. This also implies a simpler proof for the
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- result of <a href="#BlastenLiu2017a">Blåsten, Liu
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+ This paper considers the inverse source problem,
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+ namely we do not send an incident wave, and are
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+ instead using data provided by an unknown source
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+ itself. We show that so called <em>nonradiating
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+ sources</em> cannot have sharp corner or edge jumps on
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+ their boundary. This also implies a simpler proof for
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+ the result of <a href="#BlastenLiu2017a">Blåsten, Liu
|
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2017a</a> assuming that the transmission
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eigenfunctions are smooth enough. Furthermore it gives
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uniqueness for the shape determination of convex
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@@ -555,9 +640,8 @@
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in all directions except the branch cut.
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</p>
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</dd>
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- </dl>
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- <dl>
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- <dt id="desc_Pipes1">
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+ <dt>
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+ <a class="anchor" id="desc_Pipes1"></a>
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<a href="#Pipes1">
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<span class="ref-authors">F. Zouari, E. Blåsten,
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M. Louati, and M. S. Ghidaoui,</span>
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@@ -591,18 +675,17 @@
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irregular shape.
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</p>
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</dd>
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-
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- <dl>
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- <dt id="desc_Blasten2017">
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- <a href="#Blasten2017">
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+ <dt>
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+ <a class="anchor" id="desc_Blasten2017"></a>
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+ <a href="#Blasten2017">
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<span class="ref-authors">Blåsten,</span>
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<span class="ref-title">Well-posedness of the Goursat
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problem and stability for point source inverse
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backscattering</span>
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- </a>
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+ </a>
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</dt>
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<dd>
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- <p>
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+ <p>
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The topic of this paper is on the inverse
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backscattering method by Rakesh and Uhlmann, which
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they use both for
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@@ -613,14 +696,14 @@
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controlled</em>. Our primary goal is to prove
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stability for their uniqueness result of point-source
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inverse backscattering.
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- </p>
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- <p>
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+ </p>
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+ <p>
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A difficulty arising in the proof relates to required
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norm-estimates. It is very difficult to find suitable
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estimates for the direct point-source problem, or a
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related problem which is called the Goursat problem.
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- </p>
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- <p>
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+ </p>
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+ <p>
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The Goursat problem is the wave equation with boundary
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data given on a characteristic cone. Some call it
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the <em>characteristic initial value problem</em>. We
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@@ -630,10 +713,11 @@
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depends continuously on the inputs. This then leads to
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the well-posedness of the point-source problem for the
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wave equation.
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- </p>
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+ </p>
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</dd>
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- <dt id="desc_BlastenLiu2017b">
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+ <dt>
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+ <a class="anchor" id="desc_BlastenLiu2017b"></a>
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<a href="#BlastenLiu2017b">
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<span class="ref-authors">Blåsten, Liu,</span>
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<span class="ref-title">Recovering piecewise constant
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@@ -674,7 +758,8 @@
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</p>
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</dd>
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- <dt id="desc_BlastenTzouWang2017">
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+ <dt>
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+ <a class="anchor" id="desc_BlastenTzouWang2017"></a>
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<a href="#BlastenTzouWang2017">
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<span class="ref-authors">Blåsten, Tzou, Wang,</span>
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<span class="ref-title">Uniqueness for the inverse
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@@ -705,7 +790,8 @@
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</p>
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</dd>
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- <dt id="desc_BlastenLiLiuWang2017">
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+ <dt>
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+ <a class="anchor" id="desc_BlastenLiLiuWang2017"></a>
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<a href="#BlastenLiLiuWang2017">
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<span class="ref-authors">Blåsten, Li, Liu, Wang,</span>
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<span class="ref-title"> On vanishing and localizing
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@@ -744,7 +830,8 @@
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|
</p>
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</dd>
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- <dt id="desc_BlastenLiu2017a">
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+ <dt>
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+ <a class="anchor" id="desc_BlastenLiu2017a"></a>
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<a href="#BlastenLiu2017a">
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<span class="ref-authors">Blåsten, Liu,</span>
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|
<span class="ref-title"> On vanishing near corners of
|
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@@ -779,7 +866,8 @@
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|
</p>
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</dd>
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- <dt id="desc_BlastenLiu2016">
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+ <dt>
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|
+ <a class="anchor" id="desc_BlastenLiu2016"></a>
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|
<a href="#BlastenLiu2016">
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|
<span class="ref-authors">Blåsten, Liu,</span>
|
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|
<span class="ref-title">On corners scattering stably
|
|
@@ -817,7 +905,8 @@
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|
</p>
|
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|
</dd>
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- <dt id="desc_BlastenSylvester2016">
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|
+ <dt>
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|
+ <a class="anchor" id="desc_BlastenSylvester2016"></a>
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|
<a href="#BlastenSylvester2016">
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|
<span class="ref-authors">Blåsten, Sylvester,</span>
|
|
|
<span class="ref-title">Translation-Invariant
|
|
@@ -842,7 +931,8 @@
|
|
|
</p>
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|
|
</dd>
|
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|
- <dt id="desc_BlastenImanuvilovYamamoto2015">
|
|
|
+ <dt>
|
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|
+ <a class="anchor" id="desc_BlastenImanuvilovYamamoto2015"></a>
|
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|
<a href="#BlastenImanuvilovYamamoto2015">
|
|
|
<span class="ref-authors">Blåsten, Imanuvilov, Yamamoto,</span>
|
|
|
<span class="ref-title">Stability and uniqueness for a
|
|
@@ -873,7 +963,8 @@
|
|
|
</p>
|
|
|
</dd>
|
|
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|
|
- <dt id="desc_BlastenPaivarintaSylvester2014">
|
|
|
+ <dt>
|
|
|
+ <a class="anchor" id="desc_BlastenPaivarintaSylvester2014"></a>
|
|
|
<a href="#BlastenPaivarintaSylvester2014">
|
|
|
<span class="ref-authors">Blåsten, Päivärinta,
|
|
|
Sylvester,</span>
|
|
@@ -908,7 +999,8 @@
|
|
|
</p>
|
|
|
</dd>
|
|
|
|
|
|
- <dt id="desc_BlastenPaivarinta2013">
|
|
|
+ <dt>
|
|
|
+ <a class="anchor" id="desc_BlastenPaivarinta2013"></a>
|
|
|
<a href="#BlastenPaivarinta2013">
|
|
|
<span class="ref-authors">Blåsten, Päivärinta,</span>
|
|
|
<span class="ref-title">Completeness of generalized
|
|
@@ -945,7 +1037,8 @@
|
|
|
</p>
|
|
|
</dd>
|
|
|
|
|
|
- <dt id="desc_Blasten2013">
|
|
|
+ <dt>
|
|
|
+ <a class="anchor" id="desc_Blasten2013"></a>
|
|
|
<a href="#Blasten2013">
|
|
|
<span class="ref-authors">Blåsten,</span>
|
|
|
<span class="ref-title">On the Gel’Fand-Calderón
|
|
@@ -974,7 +1067,8 @@
|
|
|
</p>
|
|
|
</dd>
|
|
|
|
|
|
- <dt id="desc_Blasten2010">
|
|
|
+ <dt>
|
|
|
+ <a class="anchor" id="desc_Blasten2010"></a>
|
|
|
<a href="#Blasten2010">
|
|
|
<span class="ref-authors">Blåsten,</span>
|
|
|
<span class="ref-title">The Inverse Problem of the
|
|
@@ -997,7 +1091,8 @@
|
|
|
</p>
|
|
|
</dd>
|
|
|
|
|
|
- <dt id="desc_Blasten2008">
|
|
|
+ <dt>
|
|
|
+ <a class="anchor" id="desc_Blasten2008"></a>
|
|
|
<a href="#Blasten2008">
|
|
|
<span class="ref-authors">Blåsten,</span>
|
|
|
<span class="ref-title">Distribuutioteorian alkeet ja
|
|
@@ -1022,7 +1117,8 @@
|
|
|
|
|
|
|
|
|
|
|
|
- <section id="talks">
|
|
|
+ <section>
|
|
|
+ <a class="anchor" id="talks"></a>
|
|
|
<p>
|
|
|
<h2>Conference and Seminar Talks</h2>
|
|
|
<ol reversed>
|