\begin{subequations}\label{eqnsimple}
\begin{align}
 g_x(a_i,b_j,0)&=k_1\;\sqrt{(i-k_2)^2+(j-k_2)^2}&  \beta_y(a_i,b_j,0)&=k_3   \\
g_x(a_i,b_j,0)&=k_1\;\sin({\frac{\pi \; i}{k_2}})&  \beta_y(a_i,b_j,0)&=k_3    \\
g_x(a_i,b_j,0)&=k_1\;\sin({\frac{i}{k_2}})\;\sin{(\frac{j}{k_2})}&  \beta_y(a_i,b_j,0)&=k_3   
\end{align}
\end{subequations}
