A new type of permanent magnet actuator driven by electromagnetic repulsive force in breaking course and electromagnetic attraction force during closing course is presented in this paper, and the static and dynamic characteristics for contactor with this new type actuator are mainly focused on by simulation and experiment simultaneously. Firstly, the static electromagnetic attraction force in c...

Given a graph G, the associahedron is simple convex polytope whose face poset based on connected subgraphs of G. With additional assignment color palette, we define colorful associahedron, show it to be collection abstract polytopes, and explore its properties.

We demonstrate that the topological Helly theorem and the algebraic Auslander-Buchsbaum may be viewed as different versions of the same phenomenon. Using this correspondence we show how the colorful Helly theorem of I.Barany and its generalizations by G.Kalai and R.Meshulam translates to the algebraic side. Our main results are algebraic generalizations of these translations, which in particula...

Let P1, . . . , Pd+1 ⊂ R be d-dimensional point sets such that the convex hull of each Pi contains the origin. We call the sets Pi color classes, and we think of the points in Pi as having color i. A colorful choice is a set with at most one point from each color class. The colorful Carathéodory theorem guarantees the existence of a colorful choice whose convex hull contains the origin. So far,...