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On the representations for isotropic vector-valued, symmetric tensor- valued and skew-symmetric tensor-valued functions. (English) Zbl 0781.15011

In this paper, all tensors are of second order in a 3-dimensional vector space. A function \(\varphi(A_ i,W_ p,v_ m)\) is said to be isotropic if it is invariant under orthogonal transformation, where \(A_ i\), \(W_ p\) and \(V_ m\) are given symmetric tensors, skew-symmetric tensors and vectors respectively. The functions can be scalar-valued, symmetric or skew-symmetric tensor-valued.
The author gives a new derivation procedure for determining the representations of the isotropic functions, i.e., determining the sets of generators for these isotropic (vector-valued, symmetric or skew- symmetric tensor-valued) functions.

MSC:

15A72 Vector and tensor algebra, theory of invariants
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References:

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