ONLINE BIN STRETCHING is a semi-online variant of bin packing in which the algorithm has to use the same number of bins as an optimal packing, but is allowed to slightly overpack the bins. The goal is to minimize the amount of overpacking, i.e., the maximum size packed into any bin. We give an algorithm for ONLINE BIN STRETCHING with a stretching factor of 1.5 for any number of bins. We build o...

The vector bin packing problem (VBP) is a generalization of bin packing with multiple constraints. In this problem we are required to pack items, represented by p-dimensional vectors, into as few bins as possible. The multiple-choice vector bin packing (MVBP) is a variant of the VBP in which bins have several types and items have several incarnations. We present an exact method, based on an arc...

The main capability of the dual-frequency profiling radar proposed for deployment on the Aerosol/Cloud/Ecosystems (ACE) mission [1] is its ability to allow retrievals of vertical profiles of water content and mean hydrometeor size. At the center of this capability is the notion that measuring the radar reflectivity at two sufficiently different frequencies should allow the retrieval of two wate...

Engineering problems frequently require solving a sequence of dual linear systems. This paper introduces recycling BiCG, that recycles the Krylov subspace from one pair of linear systems to the next pair. Augmented bi-Lanczos algorithm and modified two-term recurrence are developed for using the recycle space. Recycle space is built from the approximate invariant subspace corresponding to eigen...

An electrochemical cell coupled with a recycle loop through a transmission FTIR cell is employed in studies of two free radical organic reactions, the oxidation of allylic alcohols and the trifluoromethylation of heteroarenes. Rapid mixing through the recycle loop allows continuous monitoring of reaction progress. Electrochemical generation of free radicals allows their controlled mediation int...

When we throw out our trash it is burned in an incinerator or buried in a landfill. If we burn our trash, it pollutes the air. If we bury it, it fills up our landfills and gets out of hand. But ifwe recycle things, it will not pollute anything and we can use it over again. By recycling we also save money. Our county has a recycling program. Every Friday, you have a chance to put out your trash ...

Why recycle? The most commonly stated reason for recycling is to reduce burdens associated with the disposal of our never-ending stream of wastes. Waste disposal potentially causes air and water pollution and is costly; moreover, landfi lls compete with other land uses. In addition, recycling can extend our supply of materials to alleviate scarcity and to moderate rising prices of raw materials...

The following online bin packing problem is considered: Items with integer sizes are given and variable sized bins arrive online. A bin must be used if there is still an item remaining which fits in it when the bin arrives. The goal is to minimize the total size of all the bins used. Previously, a lower bound of 5 4 on the competitive ratio of this problem was achieved using jobs of size S and ...

In this paper, we study the following knapsack problem: Given a list of squares with profits, we are requested to pack a sublist of them into a rectangular bin (not a unit square bin) to make profits in the bin as large as possible. We first observe there is a Polynomial Time Approximation Scheme (PTAS) for the problem of packing weighted squares into rectangular bins with large resources, then...