Let a,d be two elements in rings and a∥d the inverse of a along d. When exists, we obtain several characterizations for invertibility aa∥d−a∥da, which is related to expressed by certain functions suitable from center ring. On other hand, some equivalent conditions equality aa∥d=a∥da, as complement previous sense, are given means group inverses ring units, respectively. Then, results obtained ap...

We argue that there are three coherent, nontrivial notions of basic-ness: conceptual basic-ness, biological basic-ness, and psychological basic-ness. There is considerable evidence for conceptually basic emotion categories (e.g., “anger,” “fear”). These categories do not designate biologically basic emotions, but some forms of anger, fear, and so on that are biologically basic in a sense we wil...

Cartesian sti ness is usually described by a 6 6 matrix which is vital in the study of rigid body grasping by multiple robot ngers. In this thesis, a closed form expression is derived for evaluating the grasped object sti ness based on the contact geometry and sti ness properties of individual robot ngers. The kinematics of manipulation by elastic ngers is also developed which describes the in ...