In this paper we study the reflexive subobject lattices and reflexive endomorphism algebras in a concrete category. For the category Set of sets and mappings, a complete characterization for both reflexive subobject lattices and reflexive endomorphism algebras is obtained. Some partial results are also proved for the category of abelian groups.

We introduce reflexive polytopes of index l as a natural generalisation of the notion of a reflexive polytope of index 1. These l-reflexive polytopes also appear as dual pairs. In dimension two we show that they arise from reflexive polygons via a change of the underlying lattice. This allows us to efficiently classify all isomorphism classes of l-reflexive polygons up to index 200. As another ...

The present study examines the uses of the reflexive marker in Lusaamia, a Bantu language of Kenya. In addition to being a true reflexive, the reflexive verbal prefix is also used in indirect reflexive constructions, as a middle voice / stative marker, and also to indicate when an action is being done for no particular purpose (when used in conjunction with a causative marker). I show that unac...

Of concern is the Cauchy problem du dt ∈ Au, u(0) = u0, t > 0, where u : [0,∞) → X, X is a real Banach space, and A : D(A) ⊂ X → X is nonlinear and multi-valued. It is showed by the method of lines, combined with the Crandall–Liggett theorem that this problem has a limit solution, and that the limit solution is a unique strong one if A is what is called embeddedly quasi-demi-closed. In the case...

Let K be a nonempty closed convex and bounded subset of a reflexive Banach space X. Let [Formula: see text] be N-variables monotone demi-continuous mappings from [Formula: see text] into X. Then: (1) the system of multivariate variational inequalities [Formula: see text] has a solution [Formula: see text]; (2) the set of solutions of this system of multivariate variational inequalities is close...

Answering an old problem in nonlinear theory, we show that c0 cannot be coarsely or uniformly embedded into a reflexive Banach space, but that any stable metric space can be coarsely and uniformly embedded into a reflexive space. We also show that certain quasi-reflexive spaces (such as the James space) also cannot be coarsely embedded into a reflexive space and that the unit ball of these spac...