Practicing Hope

In this chapter, DeYoung considers how the theological virtue of hope might be practiced. She first explains Thomas Aquinas’s account of this virtue, including its structural relation to the passion of hope, its opposing vices, and its relationship to the friendship of charity. Then, using narrative and character analysis from the film The Shawshank Redemption, she examines a range of hopeful and proto-hopeful practices concerning both the goods one hopes for and the power one relies on to attain those goods. In particular, she shows how the film’s picture of the role friends and friendship play in catalyzing hope is a compelling metaphor for Christian hope’s reliance on God.

An Overview of the Foundations of the Hypergroup Theory

This paper is written in the framework of the Special Issue of Mathematics entitled “Hypercompositional Algebra and Applications”, and focuses on the presentation of the essential principles of the hypergroup, which is the prominent structure of hypercompositional algebra. In the beginning, it reveals the structural relation between two fundamental entities of abstract algebra, the group and the hypergroup. Next, it presents the several types of hypergroups, which derive from the enrichment of the hypergroup with additional axioms besides the ones it was initially equipped with, along with their fundamental properties. Furthermore, it analyzes and studies the various subhypergroups that can be defined in hypergroups in combination with their ability to decompose the hypergroups into cosets. The exploration of this far-reaching concept highlights the particularity of the hypergroup theory versus the abstract group theory, and demonstrates the different techniques and special tools that must be developed in order to achieve results on hypercompositional algebra.