We prove that in Orlicz spaces endowed with Orlicz norm the uniformly normal structure is equivalent to the reflexivity.

Given a set S of n points in the plane, the reflexivity of S, ρ(S), is the minimum number of reflex vertices in a simple polygonalization of S. Arkin et al. [4] proved that ρ(S) ≤ ⌈n/2⌉ for any set S, and conjectured that the tight upper bound is ⌊n/4⌋. We show that the reflexivity of any set of n points is at most 3 7n+ O(1) ≈ 0.4286n. Using computer-aided abstract order type extension the upp...

This article examines how individuals are reflexive beings who interpret the world in relation to things that matter to them, and how charitable acts are evaluated and embedded in their lives with different degrees of meaning and importance. Rather than framing the discussion of charitable practices in terms of an altruism/egoism binary or imputing motivations and values to social structures, t...

A Declarative Subtyping 6 A.1 Properties of Well-Formedness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1 Proposition (Weakening) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Proposition (Substitution) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 A.2 Reflexivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

Reflexivity lies at the heart of this thesis: I seek to understand to have knowledge of a particular way of knowing. There are echoes of this reflexivity in my literature review of embodied cognition, where I discussed attempts to think about how we think. This reflexive circle need not be 'vicious', in the sense of tying me into a knot of self-reference, if I apply the tools of phenomenology a...

We prove James’s sequential characterization of (compact) reflexivity in set-theory ZF+DC, where DC is the axiom of Dependent Choices. In turn, James’s criterion implies that every infinite set is Dedekind-infinite, whence it is not provable in ZF. Our proof in ZF+DC of James’ criterion leads us to various notions of reflexivity which are equivalent in ZFC but are not equivalent in ZF. We also ...