The test ideal τ(R) of a ring R of prime characteristic is an important object in the theory of tight closure. In this paper, we study a generalization of the test ideal, which is the ideal τ(a) associated to a given ideal a with rational exponent t ≥ 0. We first prove a key lemma of this paper (Lemma 2.1), which gives a characterization of the ideal τ(a). As applications of this key lemma, we ...

The theory for the constant rate of crack closure was investigated. The aim of this theory is to explain why the rate of crack closure is constant during the wetting stage of healing. Assuming that a surface crack in a material is treated by compression or with solvent, its crack closes up at a constant rate and its shape is independent of time. This approach was based on the Gibbs energy of an...

Through this hermeneutic-phenomenological qualitative study, 10 supervisors of a CACREP accredited program identified emergent themes and challenges of triadic supervision: relationship dynamics, feedback, time management, contextual learning, and matching of supervisees. The researchers offer specific methods to approach these challenges within triadic supervision to maximize effectiveness. Au...

We provide a (mostly) self-contained treatment of Hochster and Huneke’s theorem characterizing Hilbert-Kunz multiplicity in terms of tight closure. This is not a new proof, just an elaboration of the one given in [3].

The detection of triadic subgraph motifs is a common methodology in complexnetworks research. The procedure usually applied in order to detect motifs evaluates whether a certain subgraph pattern is overrepresented in a network as a whole. However, motifs do not necessarily appear frequently in every region of a graph. For this reason, we recently introduced the framework of Node-Specific Patter...

This paper presents a formalisation of Peirce’s notion of ‘sign’ using a triadic relation with a functional dependency. The three sign components are then modelled as concepts in lattices which are connected via a semiotic mapping. We call the study of relationships relating to semiotic systems modelled in this manner a semiotic-conceptual analysis. It is argued that semiotic-conceptual analyse...

In a product market with price-sensitive demand, we examine supply chain consisting of one manufacturer and capital-constrained retailer. The retailer may purchase by borrowing securing confirmed warehouse financing (CWF) from competitive bank or the manufacturer's trade credit (TCF), provided that it is also to latter's benefit extend TCF. We obtain optimal pricing decision in two modes under ...

It has often been taken as a working assumption that directed links in information networks are frequently formed by “short-cutting” a two-step path between the source and the destination — a kind of implicit “link copying” analogous to the process of triadic closure in social networks. Despite the role of this assumption in theoretical models such as preferential attachment, it has received ve...