We present two infinite families of sequences that are analogous to the Stern sequence. Sequences in the first family enumerate the set of positive rational numbers, while sequences in the second family enumerate the set of positive rational numbers with either an even numerator or an even denominator.

The word “quantum” means a single share or portion. In quantum mechanics, this means that energy comes in discrete chunks, or quanta, rather than a continuous flow. But it also means that particles have other properties that are discrete in a way that’s deeply counterintuitive. Today I want to tell you about one such property, called spin, and the experiment that discovered it: the Stern-Gerlac...

The problem of finding the minimum-energy configuration of particles on a lattice, subject to a generic short-ranged repulsive interaction, is studied analytically. The study is relevant to charge ordered states of interacting fermions, as described by the spinless Falicov–Kimball model. For a range of particle density including the half-filled case, it is shown that the minimum-energy states c...

Douglas Stern, DO, will discuss the symptoms, signs and types of migraines that may occur. Learn about the warning signs leading up to these painful headaches. Discuss treatments and pain relief. Learn simple lifestyle changes and medications that can ease the pain. Douglas Stern, DO, joined UPMC Bedford’s Emergency Department in November of 2010. Dr. Stern is a graduate of the Pennsylvania Sta...

Perceiving Systematically, Not Just Differently: Calling for Perceptual Models With Explanatory Power Emily Balcetis, Chadly Stern & Shana Cole To cite this article: Emily Balcetis, Chadly Stern & Shana Cole (2016) Perceiving Systematically, Not Just Differently: Calling for Perceptual Models With Explanatory Power, Psychological Inquiry, 27:4, 275-280, DOI: 10.1080/1047840X.2016.1215215 To lin...

Adaptive and intelligent Web-based educational systems (AIWBES) provide an alternative to the traditional “just-put-it-on-the-Web” approach in the development of Web-based educational courseware (Brusilovsky & Miller, 2001). AIWBES attempt to be more adaptive by building a model of the goals, preferences and knowledge of each individual student and using this model throughout the interaction wi...