Invariants of C1∕2 in terms of the invariants of C
Invariants of C1∕2 in terms of the invariants of C
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C1∕2 的不变量用 C 的不变量表示
DOI：
10.2140/jomms.2007.2.1805
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发表时间：
2007
影响因子：
0.9
通讯作者：
A. Norris
中科院分区：
文献类型：
--
作者：
A. Norris
C$^{1/2}$的三个不变量是将此张量及其逆表示为C中的多项式的关键。给出了分别连接C和C$^{1/2}$的两组不变量$I_1、I_2、I_3 $和$i_1、i_2、i_3 $的简单对称表达式。第一个结果是将$I_1，I_2$关联到$i_1，i_2$的二元函数。当C-不变量的角色颠倒时，$i_1$的函数形式与$i_2$的函数形式相同。第二个结果使用对单个函数的单个调用来表达不变量。这两套表达式强调这四个不变量之间的关系的对称性。
The three invariants of C$^{1/2}$ are key to expressing this tensor and its inverse as a polynomial in C. Simple and symmetric expressions are presented connecting the two sets of invariants $I_1, I_2,I_3$ and $i_1, i_2,i_3 $ of C and C$^{1/2}$, respectively. The first result is a bivariate function relating $I_1, I_2$ to $i_1, i_2$. The functional form of $i_1$ is the same as that of $i_2$ when the roles of the C-invariants are reversed. The second result expresses the invariants using a single call to a single function. The two sets of expressions emphasize symmetries in the relations among these four invariants.