Sentence examples for transformations under which from inspiring English sources

A recently developed technique known as analogue transformation acoustics has allowed the extension of the transformational paradigm to general spacetime transformations under which the acoustic equations are not form invariant.

As Tarski and others have pointed out, the permutation invariance criterion for logical constants can be seen as a natural generalization of Felix Klein's (1893) idea that different geometries can be distinguished by the groups of transformations under which their basic notions are invariant.

By determining the transformation group under which a given system is invariant, information about the invariants and symmetries of that equation is obtained.

By determining the transformation group under which the given partial differential equation and its boundary conditions are invariant, we obtain the invariants and the symmetries of this equation.

But the transition ahead hinges on a societal transformation, a transformation which isn't going to catalyse itself.

A closer examination of this transformation process yields conditions under which the constant false alarm rate property can be retained.

Using the analytical results and a diffeomorphic state transformation, a stabilizing condition under which the affine fuzzy system is quadratically stabilizable is derived and can be solved by means of an LMI technique in conjunction with a search for scaling parameters.

The five main categories under which the model transformations are discussed in this chapter are of five types.

The transformation owes much to Plan Colombia, under which the United States has pumped some $4.5 billion in mainly military aid into the country since 2000.

However, it is not obvious under which conditions the transformation of an ODE into a CPN is unique, that is, when a given ODE defines exactly one CPN.

This transformation enables us to design an exponentially stabilizing controller under which the plant behaves as if the delays were absent after a finite time interval.