Sentence examples for without the classical from inspiring English sources

It is shown that the main properties of Dirichlet spaces can be proved without the classical local compacity hypothesis.

Results about norm-Borel measurable selectors for multi-functions satisfying stronger measurability properties but without the classical requirement of the range Banach space being separable are also obtained.

Information on chemical reaction apparent orders and on kinetic regimes prevailing is thus available without the classical requirement of a mechanism assumption.

Transformations of (1.3), (1.4) make it possible to add the initial vector function, to nonhomogeneity, thus generating an additive and homogeneous operation not depending on, and without the classical assumption regarding the continuous connection of solution with the initial function at.

However, the study by Odd et al. clearly showed cognitive deficits in cohorts suffering from asphyxia and requiring resuscitation without the classical diagnosis of HIE [17].

General population data are also needed to better understand certain approaches to screening (e.g., genomics), where the variability in expression of mutations is not entirely clear until individuals without the classical presentation of a condition are tested.

Without it, the classical dancer is completely exposed.

"I turn the piece truly into a jazz composition without negating the classical tune itself".

He was not alone: other Russians like Michel Fokine, Alexander Gorsky, Kasyan Goleizovsky and Fyodor Lopukhov had all set out to re-invent ballet without forsaking the classical idiom.

Smolensky, for instance, is very explicit in his rejection of premise (vi): "…distributed connectionist architectures, without implementing the Classical architecture, can nonetheless provide structured mental representations and mental processes sensitive to that structure" (1990a: 21990a

Other examples include trajectories of a harmonic oscillator in equilibrium with a thermal bath, and trajectories of particles in a gas (without which the classical derivation of thermodynamics from statistical mechanics would make no sense; see below Section 4).