A nonempty subset A of {1, 2, . . . , n} is relatively prime if gcd(A) = 1. Let f(n) and fk(n) denote, respectively, the number of relatively prime subsets and the number of relatively prime subsets of cardinality k of {1, 2, . . . , n}. Let Φ(n) and Φk(n) denote, respectively, the number of nonempty subsets and the number of subsets of cardinality k of {1, 2, . . . , n} such that gcd(A) is rel...

We study a class of discrete-time bidirectional ring neural network model with delay. We discuss the asymptotic stability of the origin and the existence of Neimark-Sacker bifurcations, by analyzing the corresponding characteristic equation. Employing M-matrix theory and the Lyapunov functional method, global asymptotic stability of the origin is derived. Applying the normal form theory and the...

It is a standard assumption that subordinate clauses like relative, embedded declarative, and interrogative clauses in natural language vary according to their morphosyntactic and semantic characteristics. Their morphosyntactic variation is expressed in the presence/absence of a wh-word, a relative pronoun, or an overt complementizer; syntactic transparency (embedded declaratives) or opacity (e...

Relatively few experiments have measured the time course of free recall from episodic or semantic memory. Of those that have, most report that cumulative recall is a negatively accelerated exponential (or hyperbolic) function that is characterized by two properties: asymptotic recall and rate of approach to asymptote. The most common measure of free recall performance (viz., the number of items...