Let us fix an ordering of the vertex set V. Then the notation 〈σ〉 means the oriented simplex which belongs to the equivalent class of a natural ordering.
Therefore, D defines an equivalent relation on (mathbb{R}times Xtimes X), where the equivalent class of ((t,a,b)) is [toverrightarrow{ab}] = bigl{ soverrightarrow{uv} : tlangle overrightarrow{ab},overrightarrow{xy}rangle= slangleoverrightarrow {uv}, overrightarrow{xy}rangle, forall x, y in X bigr}.
The term PQ,Low= V L ·I Q is the quiescent power dissipation of an equivalent class-AB LD continuously working at V L. The additional quiescent power dissipation of the LD when working at the high voltage supply is defined as P Q, High = ( V H − V L ) · I Q · μ cp ( P u ) · ρ. (12).
where PLow,CP is the LD power consumption value of an equivalent class-AB LD running continuously at the low voltage supply, and PHigh,CP refers to the additional power consumption when the LD is switching to the high voltage supply.
Evidently this fundamental principle of infinitesimal geometry is not satisfied for a structure which is merely a conformal structure, since the conformal structure only determines an equivalence class of conformally equivalent symmetric connections.
However, a conformal structure by itself does not determine a unique symmetric linear connection; it only determines an equivalence class of conformally equivalent connections \(K = [\Gamma]\), namely, connections which preserve the conformal structure \(C\) during parallel transport.
Since the conformal structure determines only an equivalence class of conformally equivalent symmetric linear connections \(K = [\Gamma]\), the affine connection in this type of geometry is not uniquely determined, and the parallel transport of vectors is not generally well defined.
Ignoring this knowledge may result in a Bayesian network that captures the statistical relationships between the states of phosphoproteins perfectly but does not make any biological sense--a phenomenon referred to as equivalent classes of Bayesian networks in the machine learning field [ 30, 31].
The result of meta analysis is represented as the Hasse Diagram structure of meta relations by classifying equivalent classes of fuzzy relational structures.
We use the marketing classification of the retail company to aggregate equivalent classes of products.
