Any line bundle L on a smooth curve C of genus g with degL ≥ 2g+1 is normally generated, i.e., φL(C) ⊆ PH(C,L) is projectively normal. However, it has known that more various line bundles of degree d failing to be normally generated appear on multiple coverings of genus g as d becomes smaller than 2g+1. Thus, investigating the normal generation of line bundles on multiple coverings can be an ef...

We will discuss some relations among values, i.e., global/overall importance of each single element of the object to be considered, interaction indices, i.e., simultaneous interaction among the elements in a coalition, and inclusion-exclusion coverings, i.e., decomposability of non-additive measures and/or of the Choquet integral. So, we show that inclusion-exclusion coverings are characterized...

In this paper we show that all 3-manifolds of a family introduced by M. J. Dunwoody are cyclic coverings of lens spaces (eventually S), branched over genus one 1-bridge knots. As a consequence, we give a positive answer to the Dunwoody conjecture that all the elements of a wide subclass are cyclic coverings of S branched over a knot. Moreover, we show that all branched cyclic coverings of a 2-b...

Gilles L a c h a u d 1 S u m m a r y I n t r o d u c t i o n 1. The equation Tq-T = a 2. The equation yq-y = f 3. The genus of coverings 4. Exponential sums and L functions 5. Bounds for traces of exponential sums, for n u m b e r of points of coverings, and for trace equations 6. Examples : coverings of the line 7. The Carlitz-Uchiyama bound for geometric BCH codes Bibliography Introduction

Eliminating unwanted noise in passenger compartments of vehicles is important to automobile manufacturers. The ability to reduce noise inside the vehicle enhances the perceived value of the vehicle to the consumer, and offers a competitive advantage to the manufacturer. Several methods are presently employed to reduce noise and its sources, one of which uses soundabsorbing materials attached to...

In [M.R. Casali, Computing Matveev’s complexity of non-orientable 3-manifolds via crystallization theory, Topology Appl. 144(1–3) (2004) 201–209], a graph-theoretical approach toMatveev’s complexity computation is introduced, yielding the complete classification of closed non-orientable 3-manifolds up to complexity six. The present paper follows the same point-of view, making use of crystalliza...

We introduce and study certain notions which might serve as substitutes for maximum density packings and minimum density coverings. A body is a compact connected set which is the closure of its interior. A packing P with congruent replicas of a body K is n-saturated if no n− 1 members of it can be replaced with n replicas of K, and it is completely saturated if it is n-saturated for each n ≥ 1....

A rectifier network is a directed acyclic graph with distinguished sources and sinks; it is said to compute a Boolean matrix M that has a 1 in the entry (i, j) iff there is a path from the jth source to the ith sink. The smallest number of edges in a rectifier network that computes M is a classic complexity measure on matrices, which has been studied for more than half a century. We explore two...