We give a classification of e.a.b. semistar (and star) operations by defining four different (successively smaller) distinguished classes. Then, using a standard notion of equivalence of semistar (and star) operations to partition the collection of all e.a.b. semistar (or star) operations, we show that there is exactly one operation of finite type in each equivalence class and that this operati...

If H is a connected, graded Hopf algebra, then Takeuchi’s formula can be used to compute its antipode. However, there is usually massive cancellation in the result. We show how sign-reversing involutions can sometimes be used to obtain cancellationfree formulas. We apply this idea to the Hopf algebras of polynomials, graphs, and noncommutative symmetric functions.

Explores the problem of minimizing loss of significance when a concept set is considered too complex to be communicated comprehensibly to a particular audience. In such a case the set must be transformed, possibly by collapsing some distinctions, so as to reduce the number of conceptual elements in the set by a factor of 2, 3 or more. If collapsed in an orderly manner, maintaining integrative d...

We deene an extended real-valued metric, , for positional games and prove that this class of games is a topological semigroup. We then show that two games are nitely separated ii they are path-connected and ii two closely related Conway games are equivalent. If two games are at a nite distance then this distance is bounded by the maximum diierence of any two atoms found in the games. We may imp...

We define the orthogonal sum of quadratic pairs and we show that there is no Witt cancellation theorem for this operation in characteristic 2. 1. Introduction. Quadratic pairs on central simple algebras were defined in [5]. They play the same role for quadratic forms as involutions for symmetric or skew-symmetric bilinear forms. In particular, they can be used to define twisted orthogonal group...

A segmentation algorithm based on the Jensen-Shannon entropic divergence is used to decompose longrange correlated DNA sequences into statistically significant, compositionally homogeneous patches. By adequately setting the significance level for segmenting the sequence, the underlying power-law distribution of patch lengths can be revealed. Some of the identified DNA domains were uncorrelated,...