I want to prove $\lambda_j>\mu_j$ where $\lambda_j=\dfrac{\sigma^2}{4} j^2\Delta \tau (\ln x_j)^2$ and $\mu_j=\dfrac{j\Delta \tau }{4}\left(\frac{1}{T}-r\ln x_j+\dfrac{\sigma^2}{2} (\ln x_j)^2\right)$ and $0 ≤ j ≤ N_x$. $N_x$ is taken arbitrary and $r,\sigma$ and $T$ are some constants. $\Delta \tau={T}/{N_\tau}$, where $N_\tau$ is the number of points in $[0,T]$ and $\Delta x={1}/{N_x}$, where $N_x$ is the number of points in the interval $[0,1]$.
Is there any condition this imposes on $r,\sigma$ and $T$ ?