Sentence examples for a fractional set from inspiring English sources

The diameter of a non-empty fractional set E, the subset of a fractional set, is given by | E | : = sup { | x − y | α, x α, y α ∈ E }. (8).

However, data points on the right of the diagonal in figures 2D and 2E also show that for a fractional set of target-probe pairs, substitution with MeC and MeU increased hybridization signal relative to the unmodified control.

For the basic theory of the variational method in a fractional setting, one can see [14].

The above result was later extended to a fractional setting in [18] and to a multisublinear setting in [33].

Recently, inequalities (1.1) and (1.2) were extended to a fractional setting in [18] and to a multisublinear setting in [19].

See also [15] for some concentration phenomena in particular cases, and also [13] and the references therein for related problems about Schrödinger-type equations in a fractional setting.

The results obtained naturally extend well-established results to a fractional setting, including both the commensurate and noncommensurate case, thus providing a framework where H∞ design can be recast along the well-known and fruitful lines of the integer case.

It is important to solve this equation for a better understanding of advection and diffusion phenomena in a fractional setting, and for this purpose, numerical and approximate analytical methods are usually required.

To define the space of ultraBoehmians, let (S_{alpha }) and (D_{alpha }) be the fraction spaces of (F_{alpha }) of all members of (S_{beta }^{tilde{beta }} ( R ) ) and (D_{beta }^{ tilde{beta }} ( R ) ), respectively, and, similarly, let (Delta_{alpha }) be the fractional set of (F_{alpha }) of all sequences in (Delta^{alpha }).

In light of this, a natural question is whether such a result holds in the discrete fractional setting.

Soon several African countries will agree to set aside for development a fractional sum levied on hydro-carbon transactions.