We discuss a general method of revealing both space-space and space-time noncommuting structures in various models in particle mechanics exhibiting reparametrisation symmetry. Starting from the commuting algebra in the conventional gauge, it is possible to obtain a noncommuting algebra in a nonstandard gauge. The change of variables relating the algebra in the two gauges is systematically deriv...

We discuss a method of revealing noncommuting structures in various models in particle mechanics exhibiting reparametrisation symmetry. Starting from the commuting algebra in the conventional gauge, it is possible to obtain a noncommuting algebra in a nonstandard gauge. The change of variables relating the algebra in the two gauges is systematically derived using gauge/reparametrisation transfo...

In this paper, we introduce a special algebra called EQ-algebra which has three binary operations (meet, product, fuzzy equality) and a top element. The fuzzy equality is reflexive, symmetric and transitive with respect to the product. EQ-algebra is a natural algebra proposed as an algebra of truth values on the basis of which the fuzzy type theory (a higher-order fuzzy logic) should be develop...

In this paper, ellipsoid method for linear programming is derived using only minimal knowledge of algebra and matrices. Unfortunately, most authors first describe the algorithm, then later prove its correctness, which requires a good knowledge of linear algebra.

The aim of this note is to prove that every non characteristically nilpotent filiform algebra is provided with an affine structure. We generalize this result to the class of nilptent algebras whose derived algebra admits non singular derivation.