Sentence examples for geometric realization from inspiring English sources

The purpose of the paper is to give a geometric realization of the unitarizable modules.

The slow invariant manifold is the geometric realization of a non-linear normal mode, which consists of master and slaved dynamics.

In this paper, we give a geometric realization of discrete series representations for unimodular Lie groups on the spaces of harmonic spinors by using Connes Moscovici'sL2-Index theorem.

Our work is a continuation of Atiyah Schmid's geometric realization of discrete series representations for semisimple Lie groups and Connes Moscovici's realization of square-integrable representations for nilpotent Lie groups.

Connectivity is a homotopy invariant property of separable C⁎-algebras which has three notable consequences: absence of nontrivial projections, quasidiagonality and a more geometric realization of KK-theory for nuclear C⁎-algebras using asymptotic morphisms.

The current design process of resistance microfluidic circuits starts with system specifications and concludes with a geometric realization of a topological graph that describes a 2-dimensional network of mechanical micro-scale channels.

The topics encompass the theory of representations of reductive Lie groups, and especially the determination of the unitary dual, the problem of geometric realizations of representations, harmonic analysis on reductive symmetric spaces, the study of automorphic forms, and results in harmonic analysis that apply to the Langlands program.

Unitary representations of Lie groups in L 2 -spaces of holomorphic functions have been studied intensely, and although the abstract theory of Lie group representations is highly developed, it has been long considered important to provide geometric realizations of these representations.

Closely related to this geometric approach is the realization that epistasis must be studied with respect to a particular reference sequence [ 7- 11], and that the forms of epistatic interactions change when the reference is changed.

Optimal recursive decomposition (or DR-planning) is crucial for analyzing, designing, solving or finding realizations of geometric constraint systems.

In order to generate realizations of geometric imperfections, the estimated covariance kernel is decomposed into an orthogonal series in terms of eigenfunctions with corresponding uncorrelated Gaussian random variables, known as the Karhunen Loéve expansion.