Trying to draw the images
Former-commit-id: 25bf663661f3428ea2a9d7ea0558a479c2a3f50b
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@ -469,9 +469,7 @@ sideways false
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status open
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status open
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\begin_layout Plain Layout
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\begin_layout Plain Layout
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\begin_inset Caption Standard
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\align center
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\begin_layout Plain Layout
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\begin_inset Graphics
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\begin_inset Graphics
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filename figs/beyn_lMax_cutoff_Au_sphere.pdf
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filename figs/beyn_lMax_cutoff_Au_sphere.pdf
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width 100text%
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width 100text%
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@ -479,10 +477,9 @@ status open
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\end_inset
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\end_inset
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\end_layout
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\begin_inset Caption Standard
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\end_inset
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\begin_layout Plain Layout
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Consequences of multipole degree cutoff: Eigenfrequencies found with Beyn's
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Consequences of multipole degree cutoff: Eigenfrequencies found with Beyn's
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algorithm for an infinite square lattice of golden spherical nanoparticles
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algorithm for an infinite square lattice of golden spherical nanoparticles
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with varying particle size.
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with varying particle size.
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@ -498,8 +495,13 @@ name "square lattice var lMax, r at gamma point Au"
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\end_inset
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\end_inset
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\end_layout
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\end_inset
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\begin_inset Note Note
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\begin_inset Note Note
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status open
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status collapsed
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\begin_layout Plain Layout
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\begin_layout Plain Layout
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\begin_inset Float figure
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\begin_inset Float figure
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@ -768,7 +768,16 @@ empty
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\begin_inset Formula $\gamma(z)$
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\begin_inset Formula $\gamma(z)$
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\end_inset
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\end_inset
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as defined in
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if the branch is selected to be continuous for
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\begin_inset Formula $-3\pi/2<\arg\left(z-1\right)<\pi/2$
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\end_inset
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\begin_inset Note Note
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status open
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\begin_layout Plain Layout
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as defined in
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\begin_inset CommandInset ref
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\begin_inset CommandInset ref
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LatexCommand eqref
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LatexCommand eqref
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reference "eq:lilgamma_old"
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reference "eq:lilgamma_old"
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@ -776,6 +785,11 @@ plural "false"
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caps "false"
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caps "false"
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noprefix "false"
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noprefix "false"
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\end_inset
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\end_layout
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\end_inset
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\end_inset
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(blue, circular shape).
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(blue, circular shape).
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@ -1415,11 +1429,11 @@ FP: check sign of
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\begin{multline}
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\begin{multline}
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\sigma_{l,m}^{\left(\mathrm{L},\eta\right)}\left(\vect k,\vect s\right)=-\frac{i^{l+1}}{\kappa^{2}\mathcal{A}}\pi^{3/2}2\left(\left(l-m\right)/2\right)!\left(\left(l+m\right)/2\right)!\times\\
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\sigma_{l,m}^{\left(\mathrm{L},\eta\right)}\left(\vect k,\vect s\right)=-\frac{i^{l+1}}{\kappa^{2}\mathcal{A}}\pi^{3/2}2\left(\left(l-m\right)/2\right)!\left(\left(l+m\right)/2\right)!\times\\
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\times\sum_{\vect K\in\Lambda^{*}}\underbrace{e^{i\vect K\cdot\vect s}}_{\text{nemá tu být \ensuremath{\vect{k\cdot s}?}}}\ush lm\left(\vect k+\vect K\right)\sum_{j=0}^{l-\left|m\right|}\left(-1\right)^{j}\left(\gamma\left(\left|\vect k+\vect K\right|/\kappa\right)\right)^{2j+1}\Delta_{j}\left(\frac{\kappa^{2}\gamma\left(\left|\vect k+\vect K\right|/\kappa\right)^{2}}{4\eta^{2}},-i\kappa\gamma\left(\left|\vect k+\vect K\right|/\kappa\right)s_{\perp}\right)\times\\
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\times\sum_{\vect K\in\Lambda^{*}}\underbrace{e^{i\vect K\cdot\vect s}}_{\text{nemá tu být \ensuremath{\vect{k\cdot s}?}}}\ush lm\left(\vect k+\vect K\right)\sum_{j=0}^{l-\left|m\right|}\left(-1\right)^{j}\left(\gamma\left(\left|\vect k+\vect K\right|/\kappa\right)\right)^{2j+1}\Delta_{j}\left(\frac{\kappa^{2}\gamma\left(\left|\vect k+\vect K\right|/\kappa\right)^{2}}{4\eta^{2}},-i\kappa\gamma\left(\left|\vect k+\vect K\right|/\kappa\right)s_{\perp}\right)\times\\
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\times\sum_{\begin{array}{c}
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\times\sum_{\substack{s\\
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s\\
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j\le s\le\min\left(2j,l-\left|m\right|\right)\\
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j\le s\le\min\left(2j,l-\left|m\right|\right)\\
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l-n+\left|m\right|\,\mathrm{even}
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l-n+\left|m\right|\,\mathrm{even}
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\end{array}}\frac{1}{\left(2j-s\right)!\left(s-j\right)!}\frac{\left(-\kappa s_{\perp}\right)^{2j-s}\left(\left|\vect k+\vect K\right|/\kappa\right)^{l-s}}{\left(\frac{1}{2}\left(l-m-s\right)\right)!\left(\frac{1}{2}\left(l+m-s\right)\right)!}\label{eq:Ewald in 3D long-range part 1D 2D}
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}
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}\frac{1}{\left(2j-s\right)!\left(s-j\right)!}\frac{\left(-\kappa s_{\perp}\right)^{2j-s}\left(\left|\vect k+\vect K\right|/\kappa\right)^{l-s}}{\left(\frac{1}{2}\left(l-m-s\right)\right)!\left(\frac{1}{2}\left(l+m-s\right)\right)!}\label{eq:Ewald in 3D long-range part 1D 2D}
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\end{multline}
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\end{multline}
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\end_inset
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\end_inset
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