Questions tagged [symmetry]

Questions about symmetry, in group theory, geometry or elsewhere in mathematics. See https://en.wikipedia.org/wiki/Symmetry

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A square on the equator of a sphere is a critical point of the electrostatic potential

$\newcommand{\S}{\mathbb{S}^2}$ This is a self-answered question. I learned something from spelling out the details, and I hope this could be interesting to others. I would welcome alternative ...
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Space and time inversion of PDEs

I am unsure whether I am reversing the $z$ and $t$ dimensions in the following set of PDEs correctly, \begin{align} &\begin{aligned} \partial_{z} \mathcal{E}(z, t) = i \sqrt{d} P(z, t) ...
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Is this sigmoid function point symmetric?

While the usual sigmoid function $\sigma(x) = \frac{1}{1+e^{-x}}$ is symmetric around the origin, I'm curious as to whether this generalization of the sigmoid is point symmetric around $(\theta, 0.5)$:...
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Reflection = Rotation about a planar axis

For a Dihedral group $D_{2n}$, the operation of reflection about an axis, that is in the same plane as the polygon, can be considered as a rotation in $\mathbb{R}^{3}$. For e.g. for a square, the ...
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Finding the order of rotational symmetry about a given axis

Here is the only example my book gives about rotational symmetry about an axis: I am then asked to find the order of rotational symmetry for the following solids: I think (a) (b) and (c) all have an ...
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Quantum Graphs and the Gross-Pitaevskii equation

I'm a final year mathematical physics student and I've been tasked with researching into the gross-pitaevskii equation and it's solutions on quantum graphs. I have a pretty good understanding but I'm ...
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It makes sense to consider oddness with respect a point which is not $0$?

Let $F$ be a $C^1$ function and consider $$G(x) =ax- F(x+a),$$ with $a\in\mathbb{R}^*_+$. I need $G$ to be even. Clearly, if $F$ is odd in the "usual" sense, so it is $G$. But, actually, I ...
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Is there a 2D shape other than a circle that has infinite number of lines of symmetry? [duplicate]

A circle has an infinite number of lines of symmetry. Is there a 2d polygon that also meets this condition?
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I would like to find a function $f(\theta)$ on the domain $\frac{-\pi}{2} \leqslant \theta \leqslant \frac{\pi}{2}$ for which $$\tan \left( \frac{f(\theta) +f(-\theta))}{2}\right) = \cos \left( \frac{... 0 votes 0 answers 15 views Gaussian complexities with or without absolute value? I am reading the paper Rademacher and Gaussian Complexities: Risk Bounds and Structural Results and I'm struggling with understanding the difference between the (empirical) Gaussian complexity$$ \hat{...
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In Riemannian geometry, when we think of the Ricci tensor merely as $Ric(\vec a, \vec b)$, then it's hard to describe it other than saying it's the contraction of the Riemann tensor. But when we ...