The primary objective in cutting and packing problems is trim loss or material input minimization (in stock cutting) or value maximization (when packing into a knapsack). However, in real-life production we usually have many other objectives (costs) and constraints. Probably the most complex auxiliary criteria of a solution are the number of different cutting patterns (setups) and the maximum n...

We extend the concept of packing dimension profiles, due to Falconer and Howroyd (1997) and Howroyd (2001), and use our extension in order to determine the packing dimension of an arbitrary image of a general Lévy process.

An equivalent definition of packing dimension is given for a set in d-dimensional Euclidean space by using its component sets as packings. It is applied to determine the packing dimensions of a class of subsets with prescribed relative group frequencies. c © 2008 Elsevier Ltd. All rights reserved.

Let X = {X(t), t ∈ RN} be a Gaussian random field with values in Rd defined by X(t) = ( X1(t), . . . , Xd(t) ) , ∀ t ∈ R , where X1, . . . , Xd are independent copies of a centered real-valued Gaussian random field X0. We consider the case when X0 is anisotropic and study the packing dimension of the range X(E), where E ⊆ RN is a Borel set. For this purpose we extend the original notion of pack...

introduction: controversy remains as to the advantages and disadvantages of pharyngeal packing during septorhinoplasty. our study investigated the effect of pharyngeal packing on postoperative nausea and vomiting and sore throat following this type of surgery or septorhinoplasty.   materials and methods: this clinical trial was performed on 90 american society of anesthesiologists (asa) i or ii...

brass ferrules have been used as packing in a laboratory- scale glass distillation column approaching pilot plant size because of their availability in all sizes and low cost. the available size range is such that these ferrules could also be used in industry and the results of this study could be scaled up. the performance of the new packing has been compared with the performance of glass pack...

A vertex v of a graph G is domination null in G if g(v) = 0 for every minimum fractional dominating function g on G. Packing nullity is defined analogously, with reference to fractional closed neighborhood packings. We give classes of examples and examine graph operations that produce or preserve such vertices; several open problems are posed.

Using probabilistic ideas, we prove that if μ is a mean porous measure on R, then the packing dimension of μ is strictly smaller than n. Moreover, we give an explicit bound for the packing dimension, which is asymptotically sharp in the case of small porosity. This result was stated in [D. B. BELIAEV and S. K. SMIRNOV, “On dimension of porous measures”, Math. Ann. 323 (2002) 123-141], but the p...

The bin packing problem is a well-studied problem in combinatorial optimization. In the classical bin packing problem, we are given a list of real numbers in (0, 1] and the goal is to place them in a minimum number of bins so that no bin holds numbers summing to more than 1. The problem is extremely important in practice and finds numerous applications in scheduling, routing and resource alloca...