论文标题
在代表标量，向量和张量的各向同性功能的最少数量的功能上
On the Smallest Number of Functions Representing Isotropic Functions of Scalars, Vectors and Tensors
论文作者
论文摘要
在本文中，我们解决了与同性恋函数的表征不可约性的不可约性有关的开放问题。 In particular, we prove that for isotropic functions that depend on $P$ vectors, $N$ symmetric tensors and $M$ non-symmetric tensors (a) the number of irreducible invariants for a scalar-valued isotropic function is $3P+9M+6N-3$ (b) the number of irreducible vectors for a vector-valued isotropic function is $3$ （c）张张值的各向同性功能的不可减至的张量最多为$ 9 $。给定的（a），（b）和（c）中的不可还原数远低于文献中获得的数字。不可还原标量/矢量/张量值函数的大幅减少具有基本简化建模复杂性的潜力。
In this paper, we address the open problem (stated in Pennisi and Trovato, 1987. Int. J. Engng Sci., 25(8), 1059-1065) associated with the irreducibility of representations for isotropic functions. In particular, we prove that for isotropic functions that depend on $P$ vectors, $N$ symmetric tensors and $M$ non-symmetric tensors (a) the number of irreducible invariants for a scalar-valued isotropic function is $3P+9M+6N-3$ (b) the number of irreducible vectors for a vector-valued isotropic function is $3$ and (c) the number of irreducible tensors for a tensor-valued isotropic function is at most $9$. The irreducible numbers in given (a), (b) and (c) are much lower than those obtained in the literature. This significant reduction in the number of irreducible scalar/vector/tensor-valued functions have the potential to substantially simplify modelling complexity.
