The no-three-in-line problem is one of unsolved problems in number theorem. The goal of the no-three-in-line problem is to locate 2N points on an N X N squares array where no three points are in line. The proposed algorithm uses N* hysteresis McCulloch-Pitts neurons as the processing elements for the N X N array problem. Our neural network algorithm has discovered several different solutions fo...

While developing a method for reasoning about programs, Pitts defined the ⊤⊤-closed relations as an alternative to the standard admissible relations. This paper reformulates and studies Pitts’s operational concept of ⊤⊤-closure in a semantic framework. It investigates the nontrivial connection between ⊤⊤-closure and admissibility, showing that ⊤⊤-closure is strictly stronger than admissibility ...

BENJAMIN A. CAMPBELL, MARTIN GANCO, APRIL M. FRANCO, and RAJSHREE AGARWAL* 1 Fisher College of Business, Ohio State University, Columbus, Ohio, U.S.A. 2 Carlson School of Management, University of Minnesota, Minneapolis, Minnesota, U.S.A. 3 Rotman School of Management, University of Toronto, and Department of Management, University of Toronto at Scarborough, Toronto, Ontario, Canada 4 Robert H....

We give a shorter proof of the existence of nontrivial closed minimal hypersurfaces in closed smooth (n + 1)–dimensional Riemannian manifolds, a theorem proved first by Pitts for 2 ≤ n ≤ 5 and extended later by Schoen and Simon to any n.

Are all subcategories of locally finitely presentable categories that are closed under limits and λ-filtered colimits also locally presentable? For full subcategories the answer is affirmative. Makkai and Pitts proved that in the case λ = א0 the answer is affirmative also for all iso-full subcategories, i. e., those containing with every pair of objects all isomorphisms between them. We discuss...

Abstract. We combine the notion of norming algebra introduced by Pop, Sinclair and Smith with a result of Pisier to show that if A1 and A2 are operator algebras, then any bounded epimorphism of A1 onto A2 is completely bounded provided that A2 contains a norming C ∗-subalgebra. We use this result to give some insights into Kadison’s Similarity Problem: we show that every faithful bounded homomo...