Sentence examples for define representations from inspiring English sources

We define representations D ± of the cyclic group Z d which map the k th power of the generator g ∈ Z d of degree d to D ± ( g k ) : = U ± k.

In the case of the ∗-algebras with quadratic involutions, analytically defined representations are introduced, and irreducible analytically defined representations are described up to unitary equivalence using dynamical systems.

In the case of the ∗-algebras with involutions of the first order all analytically defined representations are shown to be one- dimensional.

However, adopting user defined representations is clearly suboptimal, as it is desirable to learn descriptors specific to the scene of interest.

The importance of spatially explicit and geographically defined representations of the network in urban and regional planning and design is stressed, and appropriate, context-dependent visualizations of these are suggested based on experience from real-world planning cases.

Additionally, in contrast to the well-defined categorical representation in control subjects, unsupervised clustering indicated poorly defined representation of semantic categories in patients.

Each structural mode has a defined representation in these directions up to the fourth bending mode.   4.

BioPAX offers a standard, well defined representation of biological pathway data using OWL and it has been widely used in biological data integration [15, 31].

Dysfunctional anger is a major mood disorder which merits a more prominent and better defined representation in psychiatric nomenclature.

However, this format does not impose a uniquely defined representation for a given single tree topology, as the same biological information can be saved and loaded in the shape of various text strings and tree representations.

The key issue in these applications is to define appropriate representations that can efficiently support motion estimation with the required accuracy.