This paper presents three new systematic approaches for computing coefficient matrices of the Heffron-Phillips multi-machine model (K1, …, K6). The amount of computations needed for conventional and three new approaches are compared by counting number of multiplications and divisions. The advantages of new approaches are: (1) their computation burdens are less than 73 percent of that of convent...

We describe a method to perform per pixel divisions using graph ics hardware with a simple iterative algorithm In the worst case the number of rendering passes is for approximate divisions and for accurate divisions The algorithm can be used for D vec tor normalization evaluating complex lighting models and image reconstruction Introduction and Previous Work Graphics hardware can act as a power...

Abstract This introductory article examines early modern letter-writing in its ambiguous state between private and public communication by providing a few historical systematic perspectives. From point of view, it can be shown how several humanists tried to outline some characteristics the letter with regard traditional distinction speech conversation. The new opportunities marked printing pres...

Buchberger’s algorithm for computing a Gröbner basis solves the ideal membership problem over commutative polynomial rings. In the early 1990’s, an alternative to this algorithm was found, namely the involutive basis algorithm, which provides a Gröbner basis with extra combinatorial properties. Buchberger’s work was generalised to noncommutative polynomial rings by Bergman and Mora during the 1...

Divisions of labor are ubiquitous in nature and can be found at nearly every level of biological organization, from the individuals of a shared society to the cells of a single multicellular organism. Many different types of microbes have also evolved a division of labor among its colony members. Here we review several examples of microbial divisions of labor, including cases from both multicel...

An arrangement of hyperplanes in E'' is a "plaid" provided its hyperplanes form no multiple flats of intersection and lie in parallel families that are in general position. We develop some geometrically natural formulas for the number of r-faces that are formed by such an arrangement.