The phrase "a different formulation of" is correct and usable in written English.
You can use it when discussing an alternative way of expressing or presenting an idea, concept, or theory.
Example: "The researchers proposed a different formulation of the existing theory to better explain the observed phenomena."
Alternatives: "an alternative expression of" or "a revised version of".
The following corollaries are different formulations of the above inequalities of Jensen's type.
She mentions them only in passing, and shows no curiosity about a different formulation of the struggle (though it would be legitimate to point out that white women with influential husbands could take risks impossible for others).
Although it is not a novel product and represents a different formulation of the old Soviet vaccine, it is currently in clinical trials at several locations around the country.
(P′) now is simply a different formulation of the (IC): if we accept the (IC) then we should accept (P′).
A different formulation of the PHD method with linear programming approach (refer to Section 2.2 for description of linear programming) for array processing is studied in [121].
These proposed general noise SVR models use a different cost function and hence a different formulation of the optimization problem from the one applied in classical (epsilon -SVR.
The American version of Clear has a different formulation and only one of the 11 varieties in the women's line is anti-dandruff.
A slightly different formulation of the GSK/NIH vaccine was tested on 20 volunteers in the United States.
Caloric restriction experiments employed a slightly different formulation of SC medium [88] compared to the formulation employed in other experiments [87].
The problems arising from these three curses of dimensionality however can be overcome by using aggregation and a slightly different formulation of Bellmanns' equation around the post-decision state variable, two approaches that will be described in more detail below.
