Sentence examples for symmetry relations from inspiring English sources

Also, we suppose that the symmetry relations (5) are satisfied.

Theorem 4 Assume that the symmetry relations (5) are satisfied.

Lemma 1 Assume that the symmetry relations (5) are satisfied.

Wang et al. in [1, 20, 21] gave some symmetry relations for the Apostol-Bernoulli polynomials.

After we use the symmetry relations (5), this equality takes on the form (18).

In many applications, the complex-valued data obeys additional symmetry relations that can be exploited to enhance resolution and accuracy.

Firstly, Yang [22] proved symmetry relation for Bernoulli polynomials.

In the framework, we first define symmetry matrices to characterize the geometric symmetry relation among image features, and then develop two methods to discover such symmetry.

Our main results are a symmetry relation for the dwell time distributions in reversible motors, and a relation between certain relative step frequencies and the free energy per cycle.

Here, by a comparative study of two MPB systems of BaZr0.2Ti0.8O3-PbTiO3 (BZT-PT) and Bi0.5Na0.5TiO3-PbTiO3 (BNT-PT), we find that the symmetry relation between the two ferroelectric phases at MPB plays a crucial role in piezoelectric activity.

We show that the system matrix exhibits a particular physics-based symmetry relation that allows us to efficiently construct the time- and frequency-domain reduced-order models via a Lanczos-type reduction algorithm.