The phrase "a equivalent form" is not correct.
It should be "an equivalent form." You can use it when discussing different representations or variations of something that hold the same meaning or function.
Example: "In mathematics, an equivalent form of the equation can simplify the problem-solving process."
Alternatives: "a comparable form" or "an equal form."
In elution chromatography, in which the peak develops on a time scale, an equivalent form of the above equation is HETP = L σt2/tr2, in which L is now the column length, tr the time of retention of the peak by the column, and σt the standard deviation of the peak measured in units of time; this form is another expression of the equation HETP = L/N given above (see above Column efficiency).
On the other hand, he proposes a stronger program ("axiomatic basis of a physical theory") which proceeds by considering an equivalent form T* of a theory T in which all T-theoretical concepts are eliminated by explicit definitions.
Other forms of equivalent numerical representation exist, for example, the K-Twin-Pair Code [C, G, A, T] = [-1, -1, j, j] has an equivalent form [C, G, A, T] = [-j, -j, 1, 1].
The solution for the problem in Equation (7) can be obtained by re-writing it in an equivalent form, as a constrained optimization problem, converting it into the dual form, and then solving this dual problem (Tomioka and Sugiyama, 2009).
We rewrite the problem in an equivalent form as an optimal control problem with state constraints for an extended system, and prove that the value function, although possibly discontinuous, is the unique viscosity solution of the constrained boundary value problem for the corresponding Hamilton Jacobi equation.
It is worth mentioning that even though the OFDM signal is not explicitly shaped by a filter, we can still find an equivalent form [25] to represent the virtual pulse-shaping filter.
Note that under symmetry of, the second property of an -distance can be rewritten in an equivalent form by replacing with being -close.
We show how to reduce queries about property persistence, a common type of universally-quantified query, to an equivalent form that does not quantify over situations and so is amenable to existing reasoning techniques.
For convenience, we firstly establish an equivalent form of the original system by applying a suitable variable substitution.
In this section, we first derive an equivalent form for SIF optimization; then, we develop a SIF algorithm to recover the SIV efficiently.
