Sentence examples for by using the symmetric from inspiring English sources

We discuss the spatio-temporal patterns of bifurcating periodic oscillations by using the symmetric bifurcation theory of delay differential equations combined with representation theory of Lie groups.

By using the symmetric properties of, (5) can be expanded and rewritten as (8).

Now, we can prove the theorem by using the symmetric mountain pass theorem in [[15] [17]].

In Section 3, by using the symmetric mountain pass theorem we prove Theorem 1.3.

Moreover, establish the existence of infinitely many solutions by using the symmetric mountain pass theorem.

By using the symmetric nature of the filter coefficients, the hardware cost is reduced for the negative filter coefficient implementation.

In this section, we prove Theorem 1.3 by using the following symmetric mountain pass theorem.

In this section, by using the following symmetric mountain pass theorem (see [19]), we give the proof of Theorem 1.1.

Standard ac conductivity and DSC studies have been supplemented by dc polarization measurements using the symmetric cell Zn|polymer electrolyte|Zn.

We achieve the automation assisted by the Boolean polygon operations, specifically using the symmetric difference operation.

Then, an authorized user can decipher the encrypted mark using the symmetric key provided by the owner of the content.