Sentence examples for with respect to the transformations from inspiring English sources

Exact(3)

Objects are picked out by the identification of invariants with respect to the transformations relevant to the context.

Moreover, since can be expressed in terms of the maximal invariant statistic, it is invariant with respect to the transformations defined in [26].

Through the identification of horizontally acquired elements, we can better understand the evolution of this genus with respect to the transformations occurring at the genomic level as well as the variations in virulence between the species and strains.

Similar(57)

Clearly, S A, c is the union of all the subsets of Ω invariant with respect to the transformation x ↦ A x + c.

Remark A.1 From Theorem A.1 it follows the well-known result that the function R ( t ) = Q ( t ) − P 2 ( t ) − P ′ ( t ) (A.10). is invariant of (1.6) with respect to the transformation V ( t ) = v ( t ) w ( t ).

Descriptors were treated differently with respect to the transformation of the tails of the CDF (Table 1; [see Additional file 2]).

In addition, every object is symmetric with respect to the transformation that does not change the object, which is called the identity (and is equivalent to a rotation by 360° or two successive reflections about the same axis or plane).

Each conserved moiety corresponds to a particular identifiable molecular substructure that is invariant with respect to the chemical transformations of that network.

Then again, as an upper limiting velocity for physical processes, including gravitational force, the light postulate eliminated the "mysterious absolutism" of Newtonian action-at-a-distance. Natorp regarded the requirement of invariance of laws of nature with respect to the Lorentz transformations as "perhaps the most important result of Minkowski's investigation".

Any disturbance to the elements belonging to this minimal set will lead to different simulation results; and (ii) derive a total minimal element sets by exhaustively examining all reachable states of the HFPNe model with respect to the structural transformations along the time variations.

In addition the experiment shows that our system is fairly robust with respect to the rotational transformation, achieving the desirable property of the rotation invariance.

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