Sentence examples for restricted fractional from inspiring English sources

In this paper, we consider the following problem involving fractional Laplacian operator:(1)αu="|u|2α⁎−2−εu+λuinΩ,u="0on ∂Ω, where Ω is a smooth bounded domain in RN, ε∈[0,2⁎α−2), 0<α<1, 2α⁎="2NN−2α, and α is either the spectral fractional Laplacian or the restricted fractional Laplacian.

In [8], Section 4.1, Mingione studied the boundedness of the restricted fractional maximal operator M β, B M β, B f ( x ) = sup B ( x, t ) ⊂ B | B ( x, t ) | β n − 1 ∫ B ( x, t ) | f ( y ) | d y, x ∈ R n, in the restricted Lorentz-Morrey spaces L p, q ; λ ( B ), where B is any ball.

The same argument can also be used to obtain the same result for the restricted fractional Laplacian.

Various approaches can be considered to address non-linearity within the regression framework, including restricted cubic splines and fractional polynomials [ 15, 26].

Indeed, it is well known that super-directivity can greatly restrict the array fractional bandwidth, defined as the ratio between the actual bandwidth and the array nominal center frequency.

As an illustration of our approach, we deduce optimal convergence rates in classical approximation formulas for C0-semigroups restricted to the domains of fractional powers of their generators.

We create a new, functional calculus, approach to approximation formulas for C0-semigroups on Banach spaces restricted to the domains of fractional powers of their generators.

The important phenomenon observed in all figures is that the solution of any of the considered functions in the fractional theory is restricted in a bounded region.

Nonlinear association between pretransplant, time-averaged HbA1c and posttransplant outcomes was assessed using fractional polynomials and restricted cubic splines.

The functional form (in particular, nonlinearity) of continuous variables in the final model was explored by both fractional polynomials and restricted cubic splines (7).

δ phase pinning of grain boundaries restricted grain growth and hence the fractional increase of special grain boundaries.