The phrase "authors formulated" is correct and usable in written English.
It can be used when discussing how authors have developed or created specific ideas, theories, or texts.
Example: "In their research, the authors formulated a new theory that challenges existing paradigms."
Alternatives: "the authors developed" or "the authors created".
Based on these observations, the authors formulated the hypothesis that behavioural change which improved children's hand hygiene compliance would decrease the spread of infectious diseases.
The authors formulated this problem as a sellers' market competition.
Many authors formulated the divided possibility as follows: 'A standing man can sit at another time'.
The authors formulated a self-assessment version which was not considered in this study.
All aforementioned authors formulated optimization problems to obtain their routing solutions.
The authors formulated a constrained optimal graph partition problem to study sleep/wake scheduling with topology control.
In this paper, the authors formulate and study a strategy to also have the embedding dimension vary, therefore providing full adaptive input space capabilities.
In this paper, the authors formulate a free and forced vibration analysis algorithm for frame structures using the transfer dynamic stiffness coefficient method.
Starting from the properties of volumes enclosed by the minimum number of surfaces, the authors formulate, with little calculus, new simple laws, which enable them to discover a set of configuration factors for caps and various segments of the sphere.
Therefore, the authors formulate this problem as a linear programming optimization problem.
In [26 29], the authors formulate an optimization problem, which balances the trade-off between capacity and fairness among the users.
