We denote the numerical range of the normal operator T by W (T). A characterization is given to the points inW (T) that lie on the boundary. The collection of such boundary points together with the interior of the the convex hull of the spectrum of T will then be the set W (T). Moreover, it is shown that such boundary points reveal a lot of information about the normal operator. For instance, s...

In this work, the interaction between the semi-circular space and the neighboring joint with and without the presence of rock bolts was investigated using the particle flow code (PFC) approach. For this purpose, firstly, the calibration of PFC was performed using both the Brazilian experimental test and the uniaxial compression test. Secondly, a numerical model with the dimension of 100 m...

We show that the q-numerical range and the real q-numerical range of the unilateral shift and bilateral shift and their adjoints are the closed unit disc when jqj < 1. We also consider some weighted shifts.