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].

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...

BACKGROUND Ecological intervention programs are recommended to prevent overweight and obesity in children. The National Institute of Public Health (INSP) in Mexico implemented a successful ecological intervention program to promote healthy lifestyle behaviors in school age children. This study assessed the integration of ecological principles and Social Cognitive Theory (SCT) constructs in this...

We present foundations for triadic concept analysis of data with graded attributes. Triadic concept analysis departs from the dyadic case by taking into account modi, such as time instances or conditions, under which objects have attributes. That is, instead of a two-dimensional table filled with 0s and 1s (equivalently, binary relation or two-dimensional binary matrix), the input data in triad...

Two experiments used a mutual imitation paradigm to assess 9-, 14-, and 18-month-old infants’ developing understanding of intentions in others. In the first study, 1 experimenter imitated the infants’ actions, and another experimenter performed contingent but different actions on an identical toy. From 9 months of age, infants show discrimination between the mimicking and the contingent experim...

For a set Ω an unordered relation on Ω is a family R of subsets of Ω . If R is such a relation we let G(R) be the group of all permutations on Ω that preserve R, that is g belongs to G(R) if and only if x ∈R implies x ∈R. We are interested in permutation groups which can be represented as G= G(R) for a suitable unordered relation R on Ω . When this is the case, we say that G is defined by the r...