The phrase "are formulated using a" is correct and usable in written English.
It can be used when describing how something is created or developed, particularly in a technical or academic context.
Example: "The theories in this paper are formulated using a combination of empirical data and theoretical frameworks."
Alternatives: "are developed with a" or "are constructed using a".
The equations of motion are formulated using a coupled piezoelectric formulation solving for strain and electric charge.
Sufficient conditions of global synchronization are formulated using a poly-quadratic stability concept.
A control-like problem and a structural optimization problem are formulated using a common framework.
The failure criteria are formulated using a von Mises, a modified von Mises and a maximum stress failure criterion.
The stress and strain partitioning into the austenite and martensite phases are formulated using a mean-field homogenization approach.
To conduct a meaningful comparison, the optimal design problems for both systems are formulated using a same analytical framework based on the continuous approximation approach.
Limit states are formulated using an incremental load formulation in differential form considering both random strengths and stiffnesses.
The equilibrium equations of a straight beam element are formulated using an updated Lagrangian (UL) incremental description.
The uncertainties of the time-delay and system gain, which imply the nonlinearities and the variable dynamic characteristics, are formulated using an uncertainty polytope.
In this work, single-objective optimization and multiobjective optimization problems are formulated using an algorithm known as "strawberry optimization" and tested with actual reservoir data.
The structure of the FIS consists of fuzzy sets and fuzzy rules which are formulated using an Ad-Hoc Data Driven Learning (ADDL) process and the algorithm by [87, 88].
