The first part of this paper classifies all purely cubic function fields over a finite field of characteristic not equal to 3. In the remainder, we describe a method for computing the fundamental unit and regulator of a purely cubic congruence function field of unit rank 1 and characteristic at least 5. The technique is based on Voronoi’s algorithm for generating a chain of successive minima in...

One of the fundamental problems in the classic DEA is lack of ability to distinguish unit's performance scores that is considered as a disadvantage. Recently, Parkan et al. [9] tried to address this problem.   They proposed to assess each unit both optimistic and pessimistic views are taken into account. In contrast to traditional evaluation, one index is considered for each unit based on the l...

in this article we review an algebraic definition of the gyrogroup and a simplified version of the gyrovector space with two fundamental examples on the open ball of finite-dimensional euclidean space, which are the einstein and möbius gyrovector spaces. we introduce the structure of gyrovector space and the gyroline on the open convex cone of positive definite matrices and see its interest...

We present an algorithm for solving linear systems involving the probability or rate matrix for a Markov chain. It is based on a UL factorization but works only with a submatrix of the factor U. We demonstrate its utility on Erlang-B models as well as more complicated models of a telephone multiplexing system.

Consider a cubic unit u of positive discriminant. We present a computational proof of the fact that u is a fundamental unit of the order Z[u] in most cases and determine the exceptions. This extends a similar (but restrictive) result due to E. Thomas. Introduction Let f(X) := X + aX + bX ± 1 ∈ Z[X] be irreducible in Z[X] and with three (distinct) real roots. We think of the order R := Z[u], obt...

It is generally assumed, both in common-sense argumentations and scientific concepts, that brains and neurons represent late evolutionary achievements which are present only in more advanced animals. Here we overview recently published data clearly revealing that our understanding of bacteria, unicellular eukaryotic organisms, plants, brains and neurons, rooted in the Aristotelian philosophy is...

Using methods of high performance computing, we have found indications that knotlike structures appear as stable finite energy solitons in a realistic 3+1 dimensional model. We have explicitly simulated the unknot and trefoil configurations, and our results suggest that all torus knots appear as solitons. Our observations open new theoretical possibilities in scenarios where stringlike structur...