Hybrid electromechanical actuator and actuation system

A hybrid electromechanical actuator has two different types of electromechanical elements, one that expands in a transverse direction when electric power is applied thereto and one that contracts in a transverse direction when electric power is applied thereto. The two electromechanical elements are (i) disposed in relation to one another such that the transverse directions thereof are parallel to one another, and (ii) mechanically coupled to one another at least at two opposing edges thereof. Electric power is applied simultaneously to the elements

Long Cycles through a Linear Forest

AbstractFor a graph G and an integer k⩾1, let S(G)={x∈V(G):dG(x)=0} and σk(G)=min{∑ki=1dG(vi):{v1, v2, …, vk} is an independent set of G}. The main result of this paper is as follows. Let k⩾3, m⩾0, and 0⩽s⩽k−3. Let G be a (m+k−1)-connected graph and let F be a subgraph of G with |E(F)|=m and |S(F)|=s. If every component of F is a path, then G has a cycle of length ⩾min{|V(G)|, 2kσk(G)−m} passing through E(F)∪V(F). This generalizes three related results known previously