Sentence examples for potential of order from inspiring English sources

Here, (I_{alpha}: {mathbb {R}}^{N}rightarrow {mathbb {R}}) is the Riesz potential of order (alphain 0,p)).

For δ > 0, the Riesz potential of order δ, I δ, with respect to the measure dm α is defined, as in the classical case [13], by.

Likewise, a multibody potential of order n can account for interactions among n-tuples of particles uncaptured by interaction functions of lower orders.

In the sense of Euclidean space (mathbb{R}^{n}), the boundedness of commutator ([b,T]) with (bin Lip_{beta}) acting on Lebesgue spaces, is easily obtained by the inequality (|[b,T]f(x) |leq CI_{beta}(|f|)(x)), where T is a Calderón-Zygmund singular integral operator and (I_{beta}) is the Riesz potential of order β.

In case p − = 1, our strategy is to give an estimate of U α , 9 f by the use of another Riesz-type potentials of order 0, which plays a role of the maximal functions.

In order to avoid the potential of an order effect [ 27, 28], the sequence of the three formats (total six sequences) in the recapitulation were balanced across consecutive participants.

To examine a potential effect of order of application, cromakalim was now applied prior to glibenclamide.

The order of items discussed in each interview was varied to avoid potential bias of order effects.

Here note that is nothing but the Green potential of general order (see [9 11]).

In this work, we apply FC concepts to define, and to evaluate, the electrical potential of fractional order.

We demonstrate considerable computational advantages of the new FC-based method, suggesting a potential of an order of magnitude acceleration over alternatives when extended to fully three-dimensional problems.