Sentence examples for examples as special from inspiring English sources

Simplified versions of the proposed model, illustrated through numerical examples as special cases, converged over the existing theories.

For example, as a special case of n = 1, (1.1) may be thought to be the discrete analogue of the following forward and backward differential difference equation: c 2 u ″ ( t ) = V ′ ( u ( t + 1 ) − u ( t ) ) − V ′ ( u ( t ) − u ( t − 1 ) ), t ∈ R. (1.4).

No one has the right to edit the history or to remake the site to impose a new meaning of their choosing (for example, as "a special place of healing" as the memorial jury said).

The authors in [18] proposed a class of multi-step fixed point proximity algorithms, including several existing algorithms as special examples, for example the algorithms in [11, 12].

The family includes the usual real and the complex Hermite polynomials as special examples.

Several well-known decomposition theories are contained as special examples and are unified under the aspect of group theory.

may all be illustrated as special examples of Eq. (1.1).

Equation (2) include many well-known nonlinear equations that are with applied background as special examples, such as Newell-Whitehead equation, NLS equation, Fisher equation with degree three.

This paper extends their work to a class of linear operators, which contains Radon, Bessel and Riesz fractional integration transforms as special examples.

On the other hand, Besov spaces contain many classical spaces (e.g., L 2 Sobolev spaces and Hölder spaces) as special examples.

We can view the two forms of III as special examples of conformational and colour polymorphism, both of which have been long known and intermittently revisited [18] [21], and frequently related.