Iterating lowering operators

Iterating Lowering Operators

For an algebraically closed base field of positive characteristic, an algorithm to construct some non-zero GL(n − 1)-high weight vectors of irreducible rational GL(n)-modules is suggested. It is based on the criterion proved in this paper for the existence of a set A such that Si,j(A)fμ,λ is a non-zero GL(n − 1)-high weight vector, where Si,j(A) is Kleshchev’s lowering operator and fμ,λ is a no...

Iterating Octagons

In this paper we prove that the transitive closure of a nondeterministic octagonal relation using integer counters can be expressed in Presburger arithmetic. The direct consequence of this fact is that the reachability problem is decidable for flat counter automata with octagonal transition relations. This result improves the previous results of Comon and Jurski [7] and Bozga, Iosif and Lakhnec...

Iterating Transducers

Iterating Definiteness

A central concept in the study of vagueness is the concept of a borderline case. This concept has its most basic application when we are faced with a question of the form ‘Is x F?’, but are unwilling to answer ‘Yes’ or ‘No’ for a certain distinctive kind of reason. Wanting to be co-operative, we need to say something; by saying ‘It’s a borderline case’, we excuse our failure to give a straightf...

Iterating Bregman Retractions

The notion of a Bregman retraction of a closed convex set in Euclidean space is introduced. Bregman retractions include backward Bregman projections, forward Bregman projections, as well as their convex combinations, and are thus quite flexible. The main result on iterating Bregman retractions unifies several convergence results on projection methods for solving convex feasibility problems. It ...