On the complexity of digraph packings

Let be a fixed collection of digraphs. Given a digraph H, a -packing of H is a collection of vertex disjoint subgraphs of H, each isomorphic to a member of . For undirected graphs, Loebl and Poljak have completely characterized the complexity of deciding the existence of a perfect -packing, in the case that consists of two graphs one of which is a single edge on two vertices. We characterize -packing where consists of two digraphs one of which is a single arc on two vertices.     

Optimization designs of the combined Shewhart-CUSUM control charts

This article presents the optimization design of the combined Shewhart chart and CUSUM chart ( chart in short) used in Statistical Process Control (SPC). While the optimization design effectively improves the overall performance of the chart over the entire process shift range, it does not increase difficulties in understanding and implementing this combined chart. A new feature pertaining to an additional charting parameter w (the exponential of the sample mean shift) is also investigated, with the hope of further enhancing the detection effectiveness of the chart. Moreover, this article provides the SPC practitioners with a design table to facilitate the designs of the charts. From this design table, the users can directly find the optimal values of the charting parameters, according to the design specifications. The design table makes the design of an chart as simple as the design of the simplest chart. In general, this article will help to enhance the detection effectiveness of the chart, and facilitate and promote its applications in SPC.     

Gauss-Hermite approximation formula

A multidimensional function defined by a sample of points is approximated by a differentiable function . The problem is solved by using the Gauss-Hermite folding method developed in the nuclear shell correction method by Strutinsky.