For every fixed graph H, we determine the H-covering number of Kn, for all n > n0(H). We prove that if h is the number of edges of H, and gcd(H) = d is the greatest common divisor of the degrees of H, then there exists n0 = n0(H), such that for all n > n0, C(H,Kn) = d dn 2h dn− 1 d ee, unless d is even, n = 1 mod d and n(n− 1)/d+ 1 = 0 mod (2h/d), in which case C(H,Kn) = d ( n 2 ) h e+ 1. Our m...

Using fibre bundle theory we construct the universal covering group of U(n), Ũ(n), and show that Ũ(n) is isomorphic to the semidirect product SU(n)©s R. We give a bijection between the set of projective representations of U(n) and the set of equivalence classes of certain unitary representations of SU(n) ©s R. Applying Bargmann’s theorem, we give explicit expressions for the liftings of project...

In this paper, we study the covering theory of laura algebras. We prove that if a connected laura algebra is standard (that is, has a standard connecting component), then it has Galois coverings associated to the coverings of the connecting component. As a consequence, the first Hochschild cohomology group of a standard laura algebra vanishes if and only if it has no proper Galois coverings.

Cohen, G.D., S.N. Litsyn, On the covering radius of Reed-Muller codes, Discrete Mathematics 106/107 (1992) 147-155. We present lower and upper bounds on the covering radius of Reed-Muller codes, yielding asymptotical improvements on known results. The lower bound is simply the sphere covering one (not very new). The upper bound is derived from a thorough use of a lemma, the ‘essence of Reed-Mul...

With emergencies being, unfortunately, part of our lives, it is crucial to efficiently plan and allocate emergency response facilities that deliver effective and timely relief to people most in need. Emergency Medical Services (EMS) allocation problems deal with locating EMS facilities among potential sites to provide efficient and effective services over a wide area with spatially distributed ...

We calculate the metric on the D-brane vacuum moduli space for backgrounds of the form C 3 /Γ for cyclic groups Γ. In the simplest procedure — starting with a flat " seed " metric on the covering space — we find that the resulting D-brane metric is not Ricci-flat. We argue that this is likely to be true of the true 0-brane metric at weak string coupling.

A poset can be regarded as a category in which there is at most one morphism between objects, and such that at most one of Hom(c, c′) and Hom(c′, c) is nonempty for c 6= c′. If we keep in place the latter axiom but allow for more than one morphism between objects, we have a sort of generalized poset in which there are multiplicities attached to the covering relations, and possibly nontrivial au...

The goal of this paper is twofold. First, it consists of an introduction to the basic features of hyperbolic geometry, and the geometry of an important class of functions of the hyperbolic plane, isometries. Second, it identifies a group structure in the set of isometries, specifically those that preserve orientation, and deals with the topological properties of their discrete subgroups. In the...