Isotopes—Terminology, Definitions and Properties

Distinguishable Entities: Definitions and Properties

Many studies in natural language processing are concerned with how to generate definite descriptions that evoke a discourse entity already introduced in the context. A solution to this problem has been initially proposed by Dale (1989) in terms of distinguishing descriptions and distinguishable entities. In this paper, we give a formal definition of the terms “distinguishable entity” in non tri...

Geometric partial differential equations: Definitions and properties

Nonlinear partial differential equations are defined as fibred submanifolds of a jet bundle. The definitions of prolongation and symbol are given and given interpretations. Projections, formal properties, and linearisation are also discussed. Almost no attempt is made to maintain notational consistency with the standard literature.

Block Orthogonal Polynomials: I. Definitions and Properties

Constrained orthogonal polynomials have been recently introduced in the study of the HohenbergKohn functional to provide basis functions satisfying particle number conservation for an expansion of the particle density. More generally, we define block orthogonal (BO) polynomials which are orthogonal, with respect to a first Euclidean scalar product, to a given i-dimensional subspace Ei of polyno...

Definitions and Properties of Monotone Functions

Sense of direction: Definitions, properties, and classes

An extensive body of evidence exists of the impact that specific edge labelings have on the communication complexity of distributed problems. It has been long suspected that these very different labelings share a common property, named sense of direction. In spite of the large number of investigations, and of the obvious practical importance, a formal characterization of this property did not e...