Random Process Theory Approach to Geometric Heterogeneous Surfaces: Effective Fluid–Solid Interaction

A Geometric Approach to Standard Monomial Theory

We obtain a geometric construction of a “standard monomial basis” for the homogeneous coordinate ring associated with any ample line bundle on any flag variety. This basis is compatible with Schubert varieties, opposite Schubert varieties, and unions of intersections of these varieties. Our approach relies on vanishing theorems and a degeneration of the diagonal; it also yields a standard monom...

A Geometric Approach to Classical Galois Theory

A geometric approach to saddle points of surfaces

We outline an alternative approach to the geometric notion of a saddle point for real-valued functions of two real variables. It is argued that our treatment is more natural than the usual treatment of this topic in standard texts on calculus.

Obstacle Detection on Heterogeneous Surfaces Using Color and Geometric Cues

Autonomous navigation is one of the most essential capabilities of autonomous robots. In order to navigate autonomously, robots need to detect obstacles. While many approaches achieve good results tackling this problem with lidar sensor devices, vision based approaches are cheaper and richer solutions. This paper presents an algorithm for obstacle detection using a stereo camera pair that overc...

Effective field theory approach to Casimir interactions on soft matter surfaces