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<math>E=mc^2</math> | <math>E=mc^2</math> | ||
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| − | We consider, for various values of | + | We consider, for various values of <math>s</math>, the <math>n</math>-dimensional integral |
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\begin{align} | \begin{align} | ||
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W_n (s) | W_n (s) | ||
&:= | &:= | ||
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\left| \sum_{k = 1}^n \mathrm{e}^{2 \pi \mathrm{i} \, x_k} \right|^s \mathrm{d}\boldsymbol{x} | \left| \sum_{k = 1}^n \mathrm{e}^{2 \pi \mathrm{i} \, x_k} \right|^s \mathrm{d}\boldsymbol{x} | ||
\end{align} | \end{align} | ||
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| − | + | <math>\begin{align} | |
| − | \begin{align} | + | \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ |
| − | + | \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\ | |
| − | + | \nabla \cdot \vec{\mathbf{B}} & = 0 | |
| − | \ | + | \end{align}</math> |
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Latest revision as of 14:42, 3 April 2016
\(E=mc^2\)
We consider, for various values of \(s\), the \(n\)-dimensional integral
\begin{align} W_n (s) &:= \int_{[0, 1]^n} \left| \sum_{k = 1}^n \mathrm{e}^{2 \pi \mathrm{i} \, x_k} \right|^s \mathrm{d}\boldsymbol{x} \end{align}
\(\begin{align}
\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\
\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\
\nabla \cdot \vec{\mathbf{B}} & = 0
\end{align}\)