We generalize certain parts of the theory of group rings to the twisted case. Let G be a finite group acting (possibly trivially) on a field L of characteristic coprime to the order of the kernel of this operation. Let K ⊆ L be the fixed field of this operation, let S be a discrete valuation ring with field of fractions K, maximal ideal generated by π and integral closure T in L. We compute the...

In very-high-energy nuclear collisions, the initial energy of produced gluons per unit area per unit rapidity, (dE/L2)/deta, is equal to f(g(2)&mgr;L) (g(2)&mgr;)(3)/g(2), where &mgr;(2) is proportional to the gluon density per unit area of the colliding nuclei. For an SU(2) gauge theory, a nonperturbative computation of f(g(2)&mgr;L) shows that it varies rapidly for small g(2)&mgr;L but varies...

A graph G = (V ,E) is list L-colorable if for a given list assignment L = {L(v) : v ∈ V }, there exists a proper coloring c of G such that c(v) ∈ L(v) for all v ∈ V . If G is list L-colorable for every list assignment with |L(v)| k for all v ∈ V , then G is said to be k-choosable. In this paper, we prove that (1) every planar graph either without 4and 5-cycles, and without triangles at distance...

This paper extends the notion of geometric control in algebraic K-theory from additive categories with split exact sequences to other exact structures. In particular, we construct exact categories of modules over a noetherian ring filtered by subsets of a metric space and sensitive to the large scale properties of the space. The algebraic K-theory of these categories is related to the controlle...

Suppose G = (V,E) is a graph and p ≥ 2q are positive integers. A (p,q)-coloring of G is a mapping φ : V → {0,1, . . . ,p − 1} such that for any edge xy of G, q ≤ |φ(x) − φ(y)| ≤ p − q. A color-list is a mapping L : V → P({0,1, . . . ,p − 1}) which assigns to each vertex v a set L(v) of permissible colors. An L-(p,q)-coloring of G is a (p,q)-coloring φ of G such that for each vertex v, φ(v) ∈ L(...

Probabilistic generalizations of classical potential theory have been worked out by J. L. Doob [ l ] and G. A. Hunt [2]. Specialized to discrete processes, this provides a potential theory for transient Markov chains, analogous to the theory of the Newtonian potential. We provide a unified potential theory for all denumerable Markov chains; as applied to recurrent chains, the theory generalizes...