Sentence examples for and therefore the ordered from inspiring English sources

Exact(1)

As a matter of fact, if an ordered vector space ( X, ≽ K ) is induced by a closed convex cone K in X, then from (1), d ( u, v ) ∈ K if and only if d X ( u, v ) ≽ K 0 ; and therefore, the ordered metrics on sets extend the concept of cone metrics.

Similar(59)

Respondents may use various heuristics to complete the tasks, and therefore the order of the dimensions may impact on the importance assigned to particular states.

However, in the presence of higher amounts of MAs, both compounds improve the phospholipid packing and, therefore, the order of the lipid surfactant monolayer.

However, the order of the particle distribution and therefore, the order in which the addition is executed is changed when comparing Sapporo1 and Sapporo2.

Saturation metrics score is changing in each iteration step due to the continuous process of the assigning frequencies to the SUs, and therefore, the order of the SUs also dynamically changes.

At this point, the reader needs to bear in mind that the sample consists of members of 'Flinkster' and 'Multicity' and, therefore, the order of the operators is not representing early adopters in general.

As the phylogeny is unrooted, the position of this ancestral KAP-β remains unknown, and therefore the order of events involved in elaboration of this gene family is unclear.

The particle in Figure 1, however, is off a zone axis highlighting this alternating intensity and, therefore, the ordering is not obvious.

From assumption A2, S F ( b ) is inductive; and therefore the totally ordered subset (chain) C of S F ( b ) has an upper bound in S F ( b ), say c, with c ∈ S F ( b ).

It is notable that the WBGT reached the critical level of 32° for just one match and therefore the FIFA Medical Officer ordered a cooling break.

Nucleation processes correspond to second-order reactions and therefore the rate of protein aggregation is strongly dependent on the initial protein concentration.

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