Sentence examples for comparison relations from inspiring English sources

We show that a number of naturally occurring comparison relations on positive elements in a C⁎-algebra are equivalent to natural comparison properties of their corresponding open projections in the bidual of the C⁎-algebra.

These sections are mutually closely connected since we analyze some comparison relations linking the different functional spaces defined in each paragraph.

Relation is one of the comparison relations between semantic references presented above: Identical, Near, VeryNear, MoreGeneric, MoreSpecific, Stronger Weaker or any consistent combination of these relations.

In this section, we show how we use the competency comparison relations into the rule conditions of the recommendation/adaptation software agents.

Simpler solutions exist such as an outline/tree editor that is available in any text editor, but it would have to be extended to provide the structural parts of a competency on which competency comparison relations can be computed.

The latter corresponds to a well-known comparison relation on positive elements defined by Blackadar.

In particular we show that Cuntz comparison of positive elements corresponds to a comparison relation on open projections, that we call Cuntz comparison, and which is defined in terms of and is weaker than a comparison notion defined by Peligrad and Zsidó.

Comparison: relation between comparative events.

Also, if there is a comparison relation defined between a matrix/vector and a scalar, the relations are defined against every element in the matrix or a vector to the vector.

A comparison relation ⊳ is defined for two collections (mathcal {D}={mathcal {D}_{1},mathcal {D}_{2},dots,mathcal {D}_{s}}) and (mathcal {F}={mathcal {F}_{1},mathcal {F}_{2},dots,mathcal {F}_{w}}) that satisfy (mathop cup limits _{m=1}^{s}mathcal {D}_{m}=mathop cup limits _{n=1}^{w}mathcal {F}_{n}=mathcal {H}subseteq mathcal {N}).

This comparison yields relations between the macroscopic continuum parameters and the microscopic lattice parameters.