The phrase "are further reformulated" is correct and usable in written English.
It can be used when discussing the process of modifying or adjusting something that has already been formulated or established, often in a more advanced or detailed manner.
Example: "The initial hypotheses are further reformulated to account for new data and insights."
Alternatives: "are additionally revised" or "are subsequently modified".
The relaxed sub-problem for location and service allocation decisions is further reformulated into a second-order conic program.
The resulting model is formulated as a two-stage stochastic mixed-integer bilevel nonlinear program, which can be further reformulated into a tractable single-level stochastic mixed-integer linear program by applying KKT conditions and Glover's linearization method.
Using the Kronecker product, the high-cost MUSIC function is further reformulated as an eigenvector-based optimization problem, and a new low-complexity cost function with spatial aliasing is derived.
Substitute (30) into (18), the maximization problem of secrecy capacity can be further reformulated as begin{aligned} max_{{mathbf{w}}_{R}}quad &frac{{mathbf{w}}_{R}^{H}{widetilde{mathbf{G}}{mathbf{w}}_{R}}}{{mathbf{w}}_{R}^{H}{widetilde{mathbf{H}}{mathbf{w}}_{R}}} mathrm{s.t.} quad&|{mathbf{w}}_{R}|^{2}leq{P_{t}-P_{j}} end{aligned} (31).
To circumvent the problem, the use of a new type of directional cohesive interface element, previously proposed for the simulation of crack propagation in elastic shells, is further developed and reformulated for application to the cutting of elastoplastic thin structures, discretized by solid-shell elements.
The approach was further improved by reformulating the simulation formulas where the order in which the summation operations are executed is imposed.
To investigate whether the rMM model (with affinities in the millimolar range) could be further improved or not, we reformulated the ODE model as an SDE model.
(The rule was later invalidated by the courts, and is now being reformulated).
In our study non- or partial responders from step 1 were further randomised to a controlled study with a reformulated, intensified CBT or SSRI (+ CBT-support as defined).
