Sentence examples for terms we establish from inspiring English sources

In mathematical terms, we establish the following equation as a measure of the periodicity [17]: p ( P ) = ∑ t s A ( t + P ) - s A ( t ) 2 ∑ t s A ( t ) 2 (7).

Analysing statistical measures of inter-annotator agreement between 98 pathways and 993 GOBP terms, we established a graph BipartiteGraphPathwayGOBP with 544 vertices, containing 96 pathways 448 associated GOBPs, and 973 edges.

Then, by exploring only the dissipation given by the memory term, we establish the existence of a global attractor to the corresponding dynamical system.

In Section 3, we write (1.4) as an equivalent integral equation, and then, under some assumptions on the nonlinear term f, we establish three theorems on the existence of nontrivial positive solutions and uniqueness of a solution for FBVP (1.4) by means of the Guo-Krasnoselskii fixed point theorem and the Banach contraction mapping principle, respectively.

Then, in terms of prederivatives, we establish both necessary and sufficient conditions for the existence of Pareto minimal solution of set optimization problems.

To investigate the timing of emergence of RANK+ TECs, we established short-term organ cultures of FoxN1 eGFP E11 and E12 thymus rudiments, in the presence or absence of agonistic RANK antibodies, shown previously to induce mTEC progenitor development 13.

In terms of spherical coordinates, we establish: begin{aligned} f_{r, theta,phi}(r,theta,phi) &=f_{x,y,z}(rsin theta cos phi, r sin theta sin phi,r cos theta) cdot J &= frac{3r^{2} sin theta}{4pi R^{3}}, quad 0< r < R. end{aligned}.

Because there is no inherent order for combining these three terms or any three terms that define a fossa, we establish an arbitrary set of three "primary landmarks" that form a reference plane, "secondary landmarks" that specify the fossa's position with respect to the reference plane, and "tertiary landmarks" that further distinguish the fossa from other neighboring fossae.

If you can feel a quiz question coming on here, hang on a second while we establish the terms.

We establish six terms exact sequences relating the KK-theory groups and the E-theory groups of an amalgamated free product C∗-algebra, A1∗BA2, to the respective groups of the three constituents, A1,A2 and B. In the KK-theory case, we assume that B is finite dimensional, but in the E-theory case only that B is nuclear, or is the range of a conditional expectation in both A1 and A2.

If we establish long-term credibility, people will begin to ask questions.