Necessary and sufficient conditions are given for a quantummechanical system to possess a coordinate system with respect to which its behaviour at discrete times is that of a universal digital computer . The form of the diagonal representation for the unitary time evolution operator for quantum universal computers is derived ; aspects of the transformation between the diagonal representation an...

We give necessary and sufficient conditions for an operator on a separable Hilbert space to satisfy the hypercyclicity criterion.

Given a propositional theory T and a proposition q, a suucient condition of q is one that will make q true under T , and a necessary condition of q is one that has to be true for q to be true under T. In this paper , we propose a notion of strongest necessary and weakest suucient conditions. Intuitively, the strongest necessary condition of a proposition is the most general consequence that we ...

The paper treats functions which are defined on closed subsets of [0, 1] and which are k times Peano differentiable. A necessary and sufficient condition is given for the existence of a k times Peano differentiable extension of such a function to [0, 1]. Several applications of the result are presented. In particular, functions defined on symmetric perfect sets are studied.

In 1971, a salesman first brought an Eyetone, the earliest commercial blood glucose meter to the diabetes clinic at Jacobi Hospital in the Bronx. As a third-year medical student I was fascinated by the technology, but, because it was difficult to use, it was classified as a physician device. Blood glucose meters today are small, virtually pain free, and reasonably accurate. The process of monit...

Causation has been the issue of philosophic debate since Hippocrates. Recent work defines actual causation in terms of Pearl/Halpern’s causality framework, formalizing necessary causes (IJCAI’15). This has inspired causality notions in the security domain (CSF’15), which, perhaps surprisingly, formalize sufficient causes instead. We provide an explicit relation between necessary and sufficient ...