"as already defined" is grammatically correct and commonly used in written English.
It is typically used when referencing a term or concept that has already been defined or explained earlier in the text. Here is an example: "The concept of 'sustainability', as already defined in the introduction, refers to meeting the needs of the present without compromising the ability of future generations to meet their own needs."
where Φ2 and Φ are as already defined, γ j contains all non-zero elements of β j and likely to also contain some zeros in the positions of variables that appear in only one of the two equations, and j = 1, 2.
However, were the term to be defined, the term "transaction" should include a "transfer" as already defined in § 1(16) and "obligation" which itself is not defined but instead must be understood in its ordinary sense.
As already defined in the previous section, a homomorphic cryptosystem allows to carry out some basic algebraic operations on encrypted data by translating them into corresponding operations in the plaintext domain.
Since matrices Φ jk a, Φ jk av, Φ jk va, and Φ jk v, and vector μ jk a, have been pre-computed in the training stage, the computation in (7) for a sequence of length T-frames, takes on the order of M N2T operations [48], where, as already defined, N is the number of states of the AV-HMM, and M is the number of mixtures.
If necessary, quantitative cultures of tracheobronchial secretions or bronchoalveolar lavage were performed and interpreted as already defined [ 12].
As already defined in the previous section, 〈 P2(cos β)〉 takes a range of values from a minimum of 0 (isotropic) to a maximum of 1.0 (perfect orientation).
As we have already defined the likelihood function p(D| θ, M) to combine mathematical models with RNA-seq data, the statistical tools provided by Bayesian methodology are available for us in their full power.
Just as important, Mr. Cash had already defined his persona as one of popular music's most incorrigible wild men, an amphetamine-fueled hellcat who had no patience for either country music's pieties or rock 'n' roll's teen-pop sentimentality.
To improve the classification, after defining areas that are comprised of healthy crypts, the probability score for a unit to be classified as pathological is decreased if it is adjacent to an area that is already defined as healthy.
Classical economics had already defined this as "opportunity cost," which is just as accurate but less tear-jerking.
