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Again, the risk-adjusted PV can be rewritten using the law of geometric sequences (ESM of Appendix C.3).

The second term in the LP criterion (13), which is due to the noise, can be rewritten using the Parceval theorem as follows: (23).

The error equation can be rewritten using the MRRE in the error term to find the maximum output error caused by reduced-precision.

This equation can be rewritten using the fluxomer variable introduced by [ 29].

This statement can be rewritten using the clusteredness measure of the regions i.e. the probability that the minimum clusteredness degree of all sectors is less than a certain threshold value (in our case 0.9) is less than 0.05.

This last equation can be rewritten using the two-cluster approximation as: Substitution in the expression for p(a i| a i -1) then yields the expression for the first-order root distribution probabilities.

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Therefore, the equations of motion are derived for each monoclinic anisotropic layer of both walls of double-walled laminated composite cylindrical shell; then, these equations are rewritten using the state space method.

At the Communications layer, IPC were originally implemented using the Simple Object Access Protocol (SOAP), 23 but for performance reasons have been rewritten using the Java Native Interface (JNI lib).

We first show that if the views subsume the query from the point of view of the information content, then the query can be rewritten using only the views, but the resulting query might be extremely inefficient.

The set of eqs. 1 and 2 (see main text) describing the rate of variation in the size of protein classes X and Y can be rewritten using a more convenient pair of variables, i.e., the total number of evolving proteins, N = X + Y Y, and the number of essential proteins, Y.

In the case of a monophonic audio signal, the downsampling factor can be rewritten using (2): (59).

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