We consider definably compact groups in an o-minimal expansion of a real closed field. It is known that to each such group G is associated a natural exact sequence 1→ G00 → G → G/G00 → 1 where G00 is the “infinitesimal subgroup” of G and G/G00 is a compact real Lie group. We show that given a connected open subset U of G/G00 there is a canonical isomorphism between the fundamental group of U an...

Binate (or unate) covering problems occur at several steps during logic synthesis including two-level minimization and DAG covering. This paper presents a better lower bound computation algorithm and two new pruning techniques that significantly improve the efficiency of binate covering problem solvers. We show that these techniques reduce by up to three orders of magnitude the time required to...

Given a vector space V and a non-singular quadratic form Q on V , the orthogonal group O(Q) is the subgroup of GL(V ) that preserves Q. The special orthogonal group SO(Q) is given by O(Q) ∩ SL(V ). If Q is the standard inner product on R then SO(Q) is denoted SO(n). This is a connected, compact Lie group. For n > 2, the group is semi-simple. In the case that n is odd, SO(n) corresponds to the D...

Much success in finding rational points on curves has been obtained by using Chabauty’s Theorem, which applies when the genus of a curve is greater than the rank of the Mordell-Weil group of the Jacobian. When Chabauty’s Theorem does not directly apply to a curve C, a recent modification has been to cover the rational points on C by those on a covering collection of curves Di, obtained by pullb...

Set covering problem is a classical problem in computer science and complexity theory. It has many applications, such as airline crew scheduling problem, facilities location problem, vehicle routing, assignment problem, etc. In this paper, three different techniques are applied to solve set covering problem. Firstly, a mathematical model of set covering problem is introduced and solved by using...

Given a finite set E and a family F={E1,. . . ,Em} of subsets of E such that F covers E, the famous unicost set covering problem (USCP) is to determine the smallest possible subset of F that also covers E. We study in this paper a variant, called the Large Set Covering Problem (LSCP), which differs from the USCP in that E and the subsets Ei are not given in extension because they are very large...

We describe a method that allows, under some hypotheses, to compute all the rational points of some genus 5 curve defined over a number field. This method is used to solve some arithmetic problems that remained open.

In this article, we introduce the concept of co-covering which is the dual of covering concept. Then, we prove several theorems being similar to the theorems that have been de-veloped for the covering concept. For example, we provide the lifting criterion for co-coverings of a topological space X, which helps us to classify them by subgroups of the group of all homeomorphisms of X.

Recursive constructions for covering arrays employ small ingredient covering arrays to build large ones. At present the most effective methods are “cut–and–paste” (or Roux-type) and column replacement techniques. Both can introduce substantial duplication of coverage; if unnecessary duplication can be avoided then the recursion can yield a smaller array. Two extensions of covering arrays are in...