tidy up blog posts and add new one on LSM

Hadrien-Montanelli · Feb 1, 2024 · ce26bd5 · ce26bd5
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diff --git a/2017-10-09.html b/2017-10-09.html
@@ -155,8 +155,7 @@ <h1>When planets dance</h1>
                     <p>Since the integral of \(K(t)\) does not depend on \(j\) and the integral of \(U(t)\) only depends on \(i-j\), the action can be rewritten
                     $$
                     \begin{align}
-                    A = \, & \frac{n}{2}\int_0^{2\pi} \big\vert q'(t) \big\vert^2 dt \\
-                    & + \frac{n}{2}\sum_{j=1}^{n-1} \int_0^{2\pi} \Big\vert q(t) - q\Big(t + \frac{2\pi j}{n}\Big) \Big\vert^{-1}dt.
+                    A = \frac{n}{2}\int_0^{2\pi} \big\vert q'(t) \big\vert^2 dt + \frac{n}{2}\sum_{j=1}^{n-1} \int_0^{2\pi} \Big\vert q(t) - q\Big(t + \frac{2\pi j}{n}\Big) \Big\vert^{-1}dt.
                     \end{align}
                     $$
                     Choreographies correspond to functions \(q(t)\) which minimize \(A\). Since these are closed curves in the complex plane, these can be represented by 
@@ -170,7 +169,6 @@ <h1>When planets dance</h1>
                     <hr>     
                     <h4>Blog posts about spectral methods</h4>
 
-                    <p>2023 &nbsp; <a href="2023-12-15.html">Nonlocal vector calculus on the sphere</a></p>
                     <p>2020 &nbsp; <a href="2020-05-19.html">Exponential integrators for stiff PDEs</a></p>
                     <p>2018 &nbsp; <a href="2018-12-05.html">Computer-assisted proofs for PDEs</a></p>
                     <p>2018 &nbsp; <a href="2018-02-27.html">Spherical caps in cell polarization</a></p>

diff --git a/2017-10-26.html b/2017-10-26.html
@@ -139,7 +139,6 @@ <h1>Solving PDEs on the sphere</h1>
                     <hr>     
                     <h4>Blog posts about spectral methods</h4>
 
-                    <p>2023 &nbsp; <a href="2023-12-15.html">Nonlocal vector calculus on the sphere</a></p>
                     <p>2020 &nbsp; <a href="2020-05-19.html">Exponential integrators for stiff PDEs</a></p>
                     <p>2018 &nbsp; <a href="2018-12-05.html">Computer-assisted proofs for PDEs</a></p>
                     <p>2018 &nbsp; <a href="2018-02-27.html">Spherical caps in cell polarization</a></p>

diff --git a/2018-01-04.html b/2018-01-04.html
@@ -187,7 +187,6 @@ <h1>Gibbs phenomenon and Cesàro mean</h1>
                     <hr>     
                     <h4>Blog posts about spectral methods</h4>
 
-                    <p>2023 &nbsp; <a href="2023-12-15.html">Nonlocal vector calculus on the sphere</a></p>
                     <p>2020 &nbsp; <a href="2020-05-19.html">Exponential integrators for stiff PDEs</a></p>
                     <p>2018 &nbsp; <a href="2018-12-05.html">Computer-assisted proofs for PDEs</a></p>
                     <p>2018 &nbsp; <a href="2018-02-27.html">Spherical caps in cell polarization</a></p>

diff --git a/2018-02-27.html b/2018-02-27.html
@@ -160,7 +160,6 @@ <h1>Spherical caps in cell polarization</h1>
                     <hr>     
                     <h4>Blog posts about spectral methods</h4>
 
-                    <p>2023 &nbsp; <a href="2023-12-15.html">Nonlocal vector calculus on the sphere</a></p>
                     <p>2020 &nbsp; <a href="2020-05-19.html">Exponential integrators for stiff PDEs</a></p>
                     <p>2018 &nbsp; <a href="2018-12-05.html">Computer-assisted proofs for PDEs</a></p>
                     <p>2018 &nbsp; <a href="2018-02-27.html">Spherical caps in cell polarization</a></p>

diff --git a/2018-12-05.html b/2018-12-05.html
@@ -228,7 +228,6 @@ <h2>An example in 1D</h2>
                     <hr>     
                     <h4>Blog posts about spectral methods</h4>
 
-                    <p>2024 &nbsp; <a href="2023-12-15.html">Nonlocal vector calculus on the sphere</a></p>
                     <p>2020 &nbsp; <a href="2020-05-19.html">Exponential integrators for stiff PDEs</a></p>
                     <p>2018 &nbsp; <a href="2018-12-05.html">Computer-assisted proofs for PDEs</a></p>
                     <p>2018 &nbsp; <a href="2018-02-27.html">Spherical caps in cell polarization</a></p>

diff --git a/2019-03-02.html b/2019-03-02.html
@@ -127,8 +127,7 @@ <h2>Maurey's theorem</h2>
                     <p>In practice, we used Maurey's theorem to show that there exists
                     $$
                     \begin{align}
-                    f_{\epsilon}(\boldsymbol{x}) = \, & \sum_{j=1}^{\lceil 1/\epsilon^2\rceil}b_j\big[\cos(\beta_j)\mathrm{Re}(K(\boldsymbol{w}_j\cdot\boldsymbol{x})) \\
-                    & - \sin(\beta_j)\mathrm{Im}(K(\boldsymbol{w}_j\cdot\boldsymbol{x}))\big],
+                    f_{\epsilon}(\boldsymbol{x}) = \sum_{j=1}^{\lceil 1/\epsilon^2\rceil}b_j\big[\cos(\beta_j)\mathrm{Re}(K(\boldsymbol{w}_j\cdot\boldsymbol{x})) - \sin(\beta_j)\mathrm{Im}(K(\boldsymbol{w}_j\cdot\boldsymbol{x}))\big],
                     \end{align}
                     $$
                     with \(\sum_{j=1}^{\lceil 1/\epsilon^2\rceil}\vert b_j\vert \leq C_F\) and \(\beta_j\in\mathbb{R}\), such that

diff --git a/2020-05-19.html b/2020-05-19.html
@@ -175,7 +175,6 @@ <h2>Results of our numerical experiments and Chebfun</h2>
                     <hr>     
                     <h4>Blog posts about spectral methods</h4>
 
-                    <p>2023 &nbsp; <a href="2023-12-15.html">Nonlocal vector calculus on the sphere</a></p>
                     <p>2020 &nbsp; <a href="2020-05-19.html">Exponential integrators for stiff PDEs</a></p>
                     <p>2018 &nbsp; <a href="2018-12-05.html">Computer-assisted proofs for PDEs</a></p>
                     <p>2018 &nbsp; <a href="2018-02-27.html">Spherical caps in cell polarization</a></p>

diff --git a/2020-11-17.html b/2020-11-17.html
@@ -136,7 +136,7 @@ <h2>Qubits</h2>
                     0 & -1
                     \end{pmatrix}.
                     $$
-					The eigenvalues are \(\pm\frac{\hbar}{2}\), while the eigenvectors are given by
+				The eigenvalues are \(\pm\frac{\hbar}{2}\), while the eigenvectors are given by
                     $$
                     \vert0\rangle=\begin{pmatrix}
                     1 \\
@@ -191,9 +191,9 @@ <h2>Tensor products</h2>
                 	<p>The quantum states of two electrons, with respect to \(z\)-spin, may be described in the <a href='https://en.wikipedia.org/wiki/Tensor_product'>tensor product</a> basis as
                 	$$
                 	\begin{align}
-                	\psi & = \psi_1\vert0\rangle\otimes\vert0\rangle
-                	+ \psi_2\vert0\rangle\otimes\vert1\rangle \\[1.5pt]
-                	& + \psi_3\vert1\rangle\otimes\vert0\rangle 
+                	\psi = \psi_1\vert0\rangle\otimes\vert0\rangle
+                	+ \psi_2\vert0\rangle\otimes\vert1\rangle
+                	+ \psi_3\vert1\rangle\otimes\vert0\rangle 
                     + \psi_4\vert1\rangle\otimes\vert1\rangle,
                 	\end{align}
                 	$$