Sentence examples for under the usual condition from inspiring English sources

under the usual condition of having the sum of weights equal to one.

In [10 13] the authors showed exponential and polynomial decay for a viscoelastic wave equation under the usual condition -c_{1} g(t) leq g' (t) leq-c_{2} g(t quad mbox{and}quad 0 leq g" (t) leq c_{3} g(t) for some (c_{i}), (i=1,2,3).

Two molecules of H2 add to the triple bond to give an alkane under the usual conditions of catalytic hydrogenation.

He will have to qualify for the 2004 European Championship, and from a group containing newly potent Turkey, under the usual conditions.

Once cleaned from the pipe walls the layers re-accumulate under the usual conditions within the system.

Corollary 18 below shows that, under the usual conditions, for these we have the existence of fixed points.

Such a type of crystallization occurs most commonly when flexible polymers are crystallized under the usual conditions.

As a consequence, PRRS has a complex epidemiologic profile and has been especially difficult to control under the usual conditions of commercial swine production.

We show that, with this metric, the standard k-nearest neighbor regression estimate is asymptotically consistent under the usual conditions on k, and minimal requirements on the input data.

Initially, we prepared a typical peracetylated (β-d-glucopyranosyl thiosemicarbazone 4a from 4-formyl-3-phenylsydnone 2a (R=H) and thiosemicarbazide 3 under the usual conditions in our procedure for synthesis of these thiosemicarbazones (Scheme 2).

In both approaches the continuous homo-polymer is transformed into a quasi-regular cellular solid that is much more capable of undergoing large local plastic flow by ligament stretching between cavitated particles and is less susceptible to the propagation of brittle cracks under the usual conditions of tensile straining.