Sentence examples for using this characterization from inspiring English sources

By using this characterization, particular properties of fractional optimal control are proved.

Using this characterization of functions, Hengartner and Schober proved the following theorem.

A sufficient optimality theorem is given by using this characterization and E-convexity conditions.

Using this characterization we derive new polynomial decay rates which depend on the geometry of the underlying space.

Using this characterization we construct a family of examples which establishes and illustrates the gap between k-hyponormality and (k+1 -hyponormality for each k+1 -hyponormality

Using this characterization they prove the existence of free boundary minimal surfaces in the unit ball of R 3 of genus 0 with boundary having k connected components, for any finite k ≥ 1.

(Mackie (2006, p. 1) provides an example of someone who does explicitly use this characterization).

Then, we use this characterization to develop the concept of co-utile protocol and study under which circumstances co-utility arises.

I end by examining how, after 1297, Philip himself used this characterization of Louis' sanctity to defend himself and his policies.

The paper uses this characterization to design a versatile protocol that, given intervals defined by a daemon whose behavior is unpredictable, breaks them (in a nontrivial manner) in order to produce an abstraction satisfying the IC criterion.

Additionally, we use this characterization to provide a geometric (i.e. coordinate-free) definition of a (CMC- linear momentum and prove its CMC- linearty with the linear momentum defined by andowitt–Deser–Misner.