The phrase "alternative is established by" is correct and usable in written English.
It can be used when discussing how a particular alternative or option is determined or defined by certain criteria or factors.
Example: "The alternative is established by the guidelines set forth in the project proposal."
Alternatives: "alternative is determined by" or "alternative is defined by".
The decision to utilise autologous bone or its alternatives was established by the operating surgeon preoperatively and each patient gave informed written consent prior to surgery.
Concerning the existence of solutions for the given problem, two theorems are proved via Schauder's fixed point theorem and the Leray-Schauder nonlinear alternative, while the uniqueness of solutions is established by means of Banach's contraction mapping principle.
The existence of solutions for the system (1.4) is derived from Leray-Schauder's alternative, whereas the uniqueness of the solution is established by the Banach contraction principle.
Gene expression patterns might be stabilized once commitment is established by nuclear factors capable of repressing alternative lineage affiliated genes.
The validity of the results is established by comparison with an analytic perturbation solution (where applicable) and by comparison with results from an alternative, axisymmetric numerical scheme.
The existence and uniqueness of solutions is established by Banach's contraction principle, while the existence of solutions is derived by using Leray-Schauder's alternative.
The existence and uniqueness of solutions is established by Banach's contraction mapping principle, while the existence of solutions is derived by using the Leray-Schauder's alternative.
The alternative panel to be established by Mr. Obama will also come up with recommendations by December to reduce annual budget deficits and slow or reverse the growth of the national debt.
An alternative condition can be established by introducing the function f ( t ) = t 1 + ω t 1 / α ̂ − 1 α, (21).
This means an alternative "banking" channel is being established by mobile wallets.
