Given a finite nonempty sequence S of integers, write it as XY k, where Y k is a power of greatest exponent that is a suffix of S: this k is the curling number of S. The curling number conjecture is that if one starts with any initial sequence S, and extends it by repeatedly appending the curling number of the current sequence, the sequence will eventually reach 1. The conjecture remains open. ...

Many thinning algorithms for 2D binary images, or modifications of existing ones, have been proposed in recent years. The one given herein is surprisingly simple compared to most of them, and still it has theoretically favorable properties. Actually, it provides a connected single-pixel in width whenever possible well-centered homototic skeleton that allows shapes to be nearly reconstructed. In...

After pre-processing and segmenting suspicious masses in mammographies based on the Top-Hat and Markov Random Fields methods, we developed a mass-detection algorithm that uses gray level cooccurrence matrices, gray level difference statistics, gray level run length statistics, shape descriptors and intensity parameters as the entry of a vector support machine classifier. During the classificati...

For an improved monitoring of process parameters, it is generally desirable to have ef?cient designs of control charting structures. The addition of Shewhart control limits to the cumulative sum (CUSUM) control chart is a simple monitoring scheme sensitive to wide range of mean shifts. To improve the detection ability of the combined Shewhart–CUSUM control chart to off-target processes, we deve...