$(1)$ Derive the relationship between $\frac{?}{\text{b}\text{a}\text{r}}(U{)}_{i,ig}$ and $U_{i,ig}$ based on $\frac{?}{\text{b}\text{a}\text{r}}(H{)}_{i,ig}$ and $\frac{?}{\text{b}\text{a}\text{r}}(V{)}_{i,ig}.$

By the same principle, derive the relationship between $\frac{?}{\text{b}\text{a}\text{r}}(A{)}_{i,ig}$ and $A_{i,ig}(1)$ Derive the relationship between $\frac{?}{\text{b}\text{a}\text{r}}(U{)}_{i,ig}$ and $U_{i,ig}$ based on $\frac{?}{\text{b}\text{a}\text{r}}(H{)}_{i,ig}$ and $\frac{?}{\text{b}\text{a}\text{r}}(V{)}_{i,ig}.$

By the same principle, derive the relationship between $\frac{?}{\text{b}\text{a}\text{r}}(A{)}_{i,ig}$ and $A_{i,ig}$