Sentence examples for scaling transformation from inspiring English sources

Furthermore, the control parameterization method and the time scaling transformation are adjusted to transform the original optimal control problem into a normal nonlinear programming problem, which can be solved by the existing gradient-based method.

First, the time scaling transformation is utilized to project the impulsive moments (t=0,tau_{1}, tau_{2},ldots, tau_{n}) into (s=0,1,2,ldots,n) in a new time horizon.

This permits general expressions of performance indices to be derived for any scaling transformation.

A scaling transformation is used to resolve the initial development of the singularity.

Therefore, we infer from the scaling transformation that lim t → ∞ ∥ t 1 m − 1 u ( t ) − f ∥ ∞ = 0. (3.24).

Thus, we infer from the scaling transformation that lim t → ∞ ∥ t 1 m − 1 u ( t ) − f 0 ∥ ∞ = 0. (3.29).

The SIFT descriptor is invariant to translations, rotations and scaling transformations in the image domain and robust to moderate perspective transformations and illumination variations.

Thus, the synthesized training images can be generated by applying various combination of translation, rotation, and scaling transformations within a predefined range.

For analysis of discontinuous data such as urinalysis, the data was subjected to scale transformation, which expresses the data as the severity of the signs (Table  1).

The foregoing argument relates to scale transformations in the sense of order-preserving adjustments in the metric used to assign numbers to an individual utility function.

The researchers found that the six Geospiza finches and their ancestor the Black-faced Grassquit matched up with scaling transformations alone.