The phrase "approximations to the same" is correct and usable in written English.
It can be used when discussing estimates or near values that relate to a specific reference point or standard.
Example: "The calculations yielded several approximations to the same, indicating a consistent trend in the data."
Alternatives: "estimates of the same" or "near values to the same".
Individuals sampled from classes E, I, and P are assumed (as an approximation) to have the same antibody titer as the class R10.
Hence, both phase- and frequency-response-oriented approximations will lead to the same solution.
We begin with recalling the definition of approximation to the identity, which plays the same role as the heat kernel (H s,x,y)) does in [11].
Hence, the Gamma-Ap (also including the Nakagami approximation, as they belong to the same family) represents a versatile approximation approach, which may find applications for a lot of problems in practice, including a lot of performance analysis problems in wireless communications.
A first approximation would likely lead to the same conclusion as the outsiders' hypothesis; i.e., the first protein component to be "tinkered" with probably was the OM channel Tom40 because protein sorting to inside the organelle requires that host proteins could first cross an open gate in the OM.
For the same K, the approximation to the 3-D integrals under M1 is poorer than the approximation to the 2-D integrals under M0.
We apply the same three node subgraph approximation to the routing problem in mesh networks.
The NN application in the study is not a function approximation problem where same input must always lead to the same output.
Comparing the result to stochastic simulation also shown in Figure 4 (a) we see that both approximations yield the same qualitative result but the IOS coefficient is slightly more accurate in predicting the position and value of the minimum.
The decoupled external source versus ground response approach is valid because, excluding regions close to strong conductivity anomalies, to a good approximation, the same magnetospheric-ionospheric source current will produce similar horizontal magnetic field variations at regions with different ground conductivity structures.
