We study the set S = {(x, y) ∈ + × Zn : x + Bjyj ≥ bj, j = 1, . . . , n}, where Bj , bj ∈ +−{0}, j = 1, . . . , n, and B1| · · · |Bn. The set S generalizes the mixed-integer rounding (MIR) set of Nemhauser and Wolsey and the mixing-MIR set of Günlük and Pochet. In addition, it arises as a substructure in general mixed-integer programming (MIP), such as in lot-sizing. Despite its importance, a n...

In this paper we consider a class of economies with a nite number of divisible commodities, linear production technologies, and indivisible goods, and a nite number of agents. This class contains several well-known economies with indivisible goods and money as special cases. It is shown that if the utility functions are continuous on the divisible commodities and are weakly monotonic both on on...

the convention on the prevention and punishment of the crime of genocide was adopted by the un general assembly in december 1948. in former yugoslavia and rwanda occurred many heinous crimes and majority ruling powers tried to destroy molem and totsi minority groups. the un security council established the international criminal tribunal for the former yugoslavia (icty) and rwanda (ictr). the u...

Classical list scheduling is a very popular and efficient technique for scheduling jobs in parallel and distributed platforms. It is inherently centralized. However, with the increasing number of processors in new parallel platforms, the cost for managing a single centralized list becomes too prohibitive. A suitable approach to reduce the contention is to distribute the list among the computati...

In this paper, we establish an asymptotic existence theorem for group divisible designs of type mn with block sizes in any given set K of integers greater than 1. As consequences, we will prove an asymptotic existence theorem for frames and derive a partial asymptotic existence theorem for resolvable group divisible designs. © 2006 Elsevier Inc. All rights reserved.

Despite widespread acceptance that their emissions accelerate climate change and its disastrous ecological effects, new fossil fuel extraction projects continue apace, further entrenching dependence, thereby enacting particular futures. In this article, we examine how is occurring in the case of a proposed onshore shale gas “fracking” industry remote Northern Territory Australia, drawing on pol...

At present, the filter theory of $BL$textit{-}algebras has been widelystudied, and some important results have been published (see for examplecite{4}, cite{5}, cite{xi}, cite{6}, cite{7}). In other works such ascite{BP}, cite{vii}, cite{xiii}, cite{xvi} a study of a filter theory inthe more general setting of residuated lattices is done, generalizing thatfor $BL$textit{-}algebras. Note that fil...

We study the global structure of moduli spaces of quasi-isogenies of p-divisible groups introduced by Rapoport and Zink. We determine their dimensions and their sets of connected components and of irreducible components. If the isocrystals of the p-divisible groups are simple, we compute the cohomology of the moduli space. As an application we determine which moduli spaces are smooth.

Recently Hagis and McDaniel have studied the largest prime factor of an odd perfect number. Using their results, we begin the study here of the second largest prime factor. We show it is at least 139. We apply this result to show that any odd perfect number not divisible by eight distinct primes must be divisible by 5 or 7.