Sentence examples for using the representations of from inspiring English sources

The positivity condition is expressed in the non-commutative phase space in terms of the full matrix symbol, which is defined using the representations of the group.

In this paper, we define in an intrinsic way operators on a compact Lie group by means of symbols using the representations of the group.

Using the representation of (5.4), these corresponds to (beta_{4}=2) and (beta_{5}=1).

Thus it will be better to analyze the stability of delay differentia systems by using the representation of the solutions directly.

Using the representation of phasor can explain the reason why the performance of the narrowband ANC systems is degraded for some normalized frequency.

Notice that a similar transfer formula can be written using the representation of the fractional Brownian motion as Wiener integral on a finite interval (see, e.g., Nualart [2]).

When choosing representation, you may wish to consider: Using the representation of the CPA who prepared your income tax return.

Our methods use the representations of the systems on convex coordinates that arise from stoichiometric network analysis.

Proof We want to present here a different proof of the lemma which uses the representations of extremal polynomials in (24).

These approaches, also known as coarse-grained simulations, use the representations of small groups of atoms by beads or particles with specified interaction potentials.

Thus, we can use the representation of Corollary 1.