Sentence examples for method of invariant from inspiring English sources

Exact(7)

In order to apply the method of invariant set of descending flow (see [6]), we need the following concepts and conclusions given by Liu and Sun [6].

(1.5) By the method of invariant set of descending flow, the result on the existence of sign-changing solutions was built.

Additionally, there are also other methods proving the Hyers-Ulam stability of some functional equations [16], for example, the method using the property of shadowing [17], the method of invariant means [18], the method based on sandwich theorems [19].

In this paper, we review the construction of low-dimensional manifolds of reduced description for equations of chemical kinetics from the standpoint of the method of invariant manifold (MIM).

The low-energy return method was investigated using the method of invariant manifold calculations for a Lissajous orbit, the method of direct libration-point orbit transfer and injection, and the control strategy used for a low-energy trajectory.

For a general bounded smooth domain Ω, by the method of invariant sets of the descending flow, the authors in [7] have shown that (1.1) with p = 2 has infinitely many sign-changing solutions when N ≥ 7 and λ > 0, which extends the main result in [4].

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During the late 1940s, the need to treat neutron transfer in complex geometries led to an interest in applying these methods to nuclear reactors, using methods of invariant imbedding.

For instance, Takahashi [2] proved the ergodic theorem for right reversible semigroups of nonexpansive mappings in a Hilbert space by using the methods of invariant means.

To verify these criteria the functional method of compact invariant sets localization is used.

By using iterative method of -adic invariant integral on in the sense of fermionic, we define twisted -Euler numbers as follows (cf. [55]): (2.11).

In this paper, we use the method of Riemann invariants to develop a system of recurrence relations for the one-dimensional elastic impact problem in which a semi-infinite flyer collides with (and adheres to) a stationary Goupillaud-type layered elastic target plate of finite thickness that is bonded to a semi-infinite half-space.

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