Introduction. In classical algebraic geometry the adjoint curves to an irreducible plane curve are an essential tool in the study of the geometry on the curve. In this paper we shall give an algebro-arithmetic development of the theory of adjoint curves, and shall extend the classical results to irreducible plane curves with arbitrary singularities defined over arbitrary ground fields. Our defi...

An important goal in the fuzzy relation equations framework is to obtain the whole set of solutions. This paper introduces algebraic properties in the multi-adjoint concept lattice setting. Moreover, using the relationship between these concept lattices and multi-adjoint relation equations, the complete set of solutions of these general equations is characterized and computed, avoiding the nece...

We give the number of nilpotent orbits in the Lie algebras of orthogonal groups under the adjoint action of the groups over F(2(n)). Let G be an adjoint algebraic group of type B, C, or D defined over an algebraically closed field of characteristic 2. We construct the Springer correspondence for the nilpotent variety in the Lie algebra of G.

In this paper we show that there is no left adjoint to the inclusion functor from the full subcategory C 0 of Scott domains (i.e., consistently complete ! algebraic cpo's) to SFP, the category of SFP-objects and Scott-continuous maps. We also show there is no left adjoint to the inclusion functor from C 0 to any larger category of cpo's which contains a simple ve-element domain. As a corollary,...

The adjoint method is an elegant approach for the computation of the gradient of a cost function to identify a set of parameters. An additional set of differential equations has to be solved to compute the adjoint variables, which are further used for the gradient computation. However, the accuracy of the numerical solution of the adjoint differential equation has a great impact on the gradient...