1
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1answer
28 views

Proving that the Moment Tensor is super-symmetric

The Carathéodory theorem in the image bellow is the one about convex hull, isn't it? Would you please explain why can the tensor F be rewritten as that sum? From that representation the author ...
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0answers
142 views

How to prove that symmetric traceless “transverse” tensor rank s in 4 dimensions has 2s + 1 independent components?

How to prove that symmetric traceless "transverse" tensor rank $s$ in 4 dimensions has $ 2s + 1$ independent components? Let's have tensor $$ F^{\mu_{1}\dots \mu_{s}}, \quad {F^{\quad ...
1
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1answer
51 views

Relation of Hodge dual to antisymmetric part of the

I have a question in reaction to an article by M. Born and L. Infeld (cf. [1]) concerning the relation between the hodge dual of the electromagnetic tensor and the antisymmetrization of its ...
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1answer
113 views

How does Kronecker $\delta_{ijkl}$ determined?

Let's have symbol $\delta_{ijkl}$. Is it equal to 1 for $i = j = k = l$ and $0$ in the other cases?
3
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1answer
498 views

What does cubic symmetry mean?

Is it an invariance under rotations around x-, y-, z-axis? Does this invariance separately include rotations around an arbitrary $(x$, $y$, $z)$ axis?
2
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1answer
129 views

Question about stiffness tensor

Let's have a stiffness tensor $$ a^{ijkl}: a^{ijkl} = a^{jikl} = a^{klij} = a^{ijlk}. $$ It has a 21 independent components for anisotropic body. How does body symmetry (cubic, hexagonal etc.) ...