Sorting suffixes of two-pattern strings

Recently, several authors presented linear recursive algorithms for sorting suffixes of a string. All these algorithms employ a similar three-step approach, based on an initial division of the suffixes of x into two sets: in step 1 sort the first set using recursive reduction of the problem, in step 2 determine the order of the suffixes in the second set based on the order of the suffixes in the first set, and in step 3 merge the two sets together. To optimize such analgorithm either for space or time, it may not be sufficient to optimize one of the three steps, since in doing so, one might increase the resources required for the others to an unacceptable extent. Franek, Lu, and Smyth introduced two-pattern strings as a generalization of Sturmian strings. Like Sturmian strings, two-pattern strings are generated by iterated morphisms, but they exhibit a much richer structure. In this paper we show that the suffixes of two-pattern strings can be sorted in linear time using a variant of the three step approach outlined above. It turns out that, given the order of the suffixes in a two-pattern string, one can almost directly list in linear time all the suffixes of its expansion under a two-pattern morphism

Algorithms to Compute the Lyndon Array

We first describe three algorithms for computing the Lyndon array that have been suggested in the literature, but for which no structured exposition has been given. Two of these algorithms execute in quadratic time in the worst case, the third achieves linear time, but at the expense of prior computation of both the suffix array and the inverse suffix array of x. We then go on to describe two variants of a new algorithm that avoids prior computation of global data structures and executes in worst-case n log n time. Experimental evidence suggests that all but one of these five algorithms require only linear execution time in practice, with the two new algorithms faster by a small factor. We conjecture that there exists a fast and worst-case linear-time algorithm to compute the Lyndon array that is also elementary (making no use of global data structures such as the suffix array)

Abrasion resistance of selected commercially available polymer materials

The aim of this investigation was to examine several types of commercially available polymers for potential application in machine elements that are exposed to abrasion. Selected materials were evaluated on a rubber and steel wheel abrasion test rig according to the standard ASTM G65, using as abrasive quartz sand (SiO2) as abrasive, with a particle grain size in the range of 0.8 – 1.6 mm. Tests were performed under dry conditions and at room temperature. Applied load was 50 N, within testing times of 1½, 3, 4½, and 6 hours respectively. Results of testing revealed influence on wear behavior of polymer hardness as well as influence of abrasive particle embedment

k-Dirac operator and parabolic geometries

The principal group of a Klein geometry has canonical left action on the homogeneous space of the geometry and this action induces action on the spaces of sections of vector bundles over the homogeneous space. This paper is about construction of differential operators invariant with respect to the induced action of the principal group of a particular type of parabolic geometry. These operators form sequences which are related to the minimal resolutions of the k-Dirac operators studied in Clifford analysis