The Runge0Lenz Vector (continued)

We continue our discussion of the Runge-Lenz vector in a quantum mechanical context. The traditional form of the Runge-Lenz vector is obtained, and the commutation relations between the Runge-Lenz vector, the Hamiltonian, and the Angular Momentum are obtained using Maple.

Finite Characterizations and Paretian Preferences

A characterization of a property of binary relations is of finite type if it is stated in terms of ordered T-tuples of alternatives for some positive integer T. A characterization of finite type can be used to determine in polynomial time whether a binary relation over a finite set has the property characterized. Unfortunately, Pareto representability in R2 has no characterization of finite type (Knoblauch, 2002). This result is generalized below Rl, l larger than 2. The method of proof is applied to other properties of binary relations.

Joint Attention in Young Children with Autism

Autism spectrum disorders (ASDs) are classified as pervasive developmental disorders characterized by social, communicative, and behavioral impairments. According to formal and informal reports, children with ASD present with receptive and expressive language delay. Joint attention (JA: the behavior that occurs when two individuals focus on the same object or event) has been identified as a possible marker of delayed language development in children with ASD. In this study, the JA behaviors in children with ASD were contrasted with initially language-matched typically developing (TYP) children across three visits. Measures of language, the frequency, duration, and source of initiation of JA episodes, and the choice of toy during those episodes, were coded. Across visits and groups, mothers initiated more JA episodes than children; however, typical children also initiated more JA episodes than ASD children at visits 1 and 2. Also, the total duration of typically developing children’s JA episodes was generally longer than that of the ASD children’s, significantly so at Visit 2. Significant associations emerged between children’s vocabulary and two measures of JA: frequency and number of maternal initiations. Teaching parents to incorporate JA training in their interactions with their children may likely help children with ASD acquire language.