Veech groups are discrete subgroups of $\mathrm{SL}(2,\mathbb{R})$ which play an important role in the theory translation surfaces. For a special class surfaces called origamis or square-tiled surfaces, their finite index $\mathrm{SL}(2,\mathbb{Z})$. We show that each stratum space contains infinitely many whose group is totally non-congruence group, i.e., it surjects to $\mathrm{SL} (2,\mathbb...

accurate calculation of reliability index is very important for the reliability analysis of structures. in some limit state functions with nonlinear characteristic and several local optimum design points, the computational reliability methods may not appropriately determine the failure probability, and iterative reliability approaches may be converged to local optimum design points. in this pap...

The Video Projection-based Stereolithography (VP-SL) is a fast, low-cost, and high-resolution additive manufacturing (AM) process. However, critical issues, including defects such as holes in the solid geometry constraints limited size, have been reported. To successfully print part, light exposure intensity needs to be carefully controlled. In this paper, gradient video projection-based stereo...