Digit-recurrence binary dividers are sped up via two complementary methods: keeping the partial remainder in redundant form and selecting the quotient digits in a radix higher than 2. Use of a redundant partial remainder replaces the standard addition in each cycle by a carry-free addition, thus making the cycles shorter. Deriving the quotient in high radix reduces the number of cycles (by a fa...

We define the spectral radius and Ptak’s function on a quotient involutive Banach algebra and we extend certains results of V.Ptak to thes quotients. As an application of functional harmonic calculus we obtain theorem similar to those of K.Fan and Von Neumann.

The purpose of this paper is to present the notion of quotient of supergroups in different categories using the unified treatment of the functor of points and to examine some physically interesting examples.

In this paper we study quotients of posets by group actions. In order to define the quotient correctly we enlarge the considered class of categories from posets to loopfree categories: categories without nontrivial automorphisms and inverses. We view group actions as certain functors and define the quotients as colimits of these functors. The advantage of this definition over studying the quoti...

Suppose a spacetime M is a quotient of a spacetime V by a discrete group of isometries. It is shown how causality conditions in the two spacetimes are related, and how can one learn about the future causal boundary on M by studying structures in V . The relations between the two are particularly simple (the boundary of the quotient is the quotient of the boundary) if both V and M have spacelike...

In this paper we study quotients of posets by group actions. In order to define the quotient correctly we enlarge the considered class of categories from posets to loopfree categories: categories without nontrivial automorphisms and inverses. We view group actions as certain functors and define the quotients as colimits of these functors. The advantage of this definition over studying the quoti...

We study the degree of elimination of imaginaries needed for the three main applications: to have canonical bases for types over models, to define strong types as types over algebraically closed sets and to have a Galois correspondence between definably closed sets B such that A ⊆ B ⊆ acl(A) and closed subgroups of the Galois group Aut(acl(A)/A). We also characterize when the topology of the Ga...