Identical Transformation

Identical Transformation

 

the replacement of one analytic expression by another that is equal to the first expression but is of different form. Identical transformations are used to put expressions in a form more convenient for carrying out numerical calculations, applying further transformations, taking logarithms, taking antilogarithms, differentiating, integrating, solving equations, and so on. Examples of identical transformations are multiplying out (removing parentheses), factoring, reducing algebraic fractions to a common denominator, decomposing algebraic fractions to sums of simple fractions, and reducing sums of trigonometric functions to a form suitable for taking logarithms (that is, transforming the sums into products).

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Model coordinates were then transformed to the local coordinate system applying identical transformation to the common reference points on the models and in the geodesic data.
At the input surface of our device, we have x' = x = 0, and thus y' = y and z' = z, which means an identical transformation at the input surface of the device.
As the input surface of the second compressor behaves equivalently like a free space (due to the identical transformation at the input surface of our compressor), the concentrated DC magnetic field at the output surface of the first compressor cannot be compressed immediately but diverge first and then converge by the second compressor.
m], where [epsilon] is the identical transformation and [theta] is the null transformation.
For example, we can simply compress a big volume to a small one while keeping the outside an identical transformation to enhance the field (see Figures 1(a) and (b)), as proposed in [7,20].