Sentence examples for by establishing an explicit from inspiring English sources

3, we prove the existence of TW by establishing an explicit expression of their shape.

We quantify the Prokhorov theorem by establishing an explicit formula for the Hausdorff measure of noncompactness (HMNC) for the parameterized Prokhorov metric on the set of Borel probability measures on a Polish space.

In this work, we have quantified the Prokhorov theorem by establishing an explicit formula for the Hausdorff measure of noncompactness (HMNC) for the parameterized Prokhorov metric on the set of Borel probability measures on a Polish space (Theorem 1.4).

By using intrinsic super Poincaré inequalities and establishing an explicit lower bound estimate for the ground state, we present general criteria for the intrinsic ultracontractivity of (TVt t⩾0.

This is done by establishing a set of more explicit contractual arrangements between different players.

Motivated by the work in [24 27], we establish an explicit and general decay of the solutions to a von Kármán plate model (1.1 - 1.7 1.1 - 1.7xation forctions satisfying (1.11).

By establishing a marketplace, open salary policies establish meritocracy.

Start by establishing a routine.

We establish an explicit and general decay rate result using some properties of the convex functions.

We establish an explicit formula for q-analog of Morley's congruence.

Ablowitz and Zepetella [3] have established an explicit solution of Fisher's equation for a special wave speed.