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First, by means of Lindstedt-Poincare method[16, 17, 18] we use the transformation τ = ω t which transforms Equation 3.2 into ω 2 u ′′ + u + ε u 3 = 0, Open image in new window (3.2).
This section visualized then that the obtained abstract machine behaves exactly like the transformed Colored Petri Net and keeps all the modeled requirements, which is reinforcing our conclusions to use the transformation rules presented in this paper as a base framework for the construction of all the aspects of the transformation, such as its formalization, formal proof and automation.
In order to derive an outer bound on the rate region, we use the transformation.
For simplicity, we use the transformation of variables to the system (1.2).
and use the transformation u = v + 1 2, Open image in new window (3.29).
We use the transformation η = ( b − a ) ( τ + 1 ) / 2 to map the interval [ a, b ] to [ − 1, 1 ].
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Using the transformation technique, the transformed model can be derived.
The missing data, which twist the bi-scale empirical transformation, make the transformed point pattern much different from using the transformation based on the complete data.
Step 3 Transform the preference relations into HFLTS by using the transformation function (E_{G_H } ).
Using the transformation convert (1.1) to the equation (2.16).
Using the transformation (2.9) yields the required result and completes the proof.
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