Sentence examples for without any derivations from inspiring English sources

These results were mostly written up without any derivations.

(b): The results for fluctuation in the order parameter and for residence time are presented without any derivation with [ 16] to unpublished work.

"My basic faith, is in the random competence of people in all walks of life, at any level of income, of any derivation," he said.

I know a lot of people who never utter any derivation of the word "occupy" unless it refers to a bathroom, and that's all right with me.

Then any derivation in is in.

One of the advantages of the bootstrap methods is that they can be used without analytical derivations.

We have briefly provided the proof of this theorem in [28] without formal derivations.

The proposed method is capable of solving the plate problems with different boundary conditions via a step-by-step derivation without any trial solutions.

The geometry of tribo pairs can be cylindrical or cuboid which can be as simple as the samples in SHPB experiments, and the time-resolved interfacial friction coefficient can be directly calculated without any assumptions or theoretical derivation.

Thus they are presented here without derivations.

Without resorting to derivations developed in the context of ET, one may consider that, as for pure ET (see also section 5.3), the energy gap between diabatic free energy surfaces in eq 11.12 measures the departure from the transition-state coordinate for the PCET reaction.