Sentence examples for arbitrary provided from inspiring English sources

where ν(=ν1 + i ν2) can be arbitrary provided that cos ( ν, n ) ≥ 0 Open image in new window on Γ, n is the outward normal vector onΓ and a0=1.

Recently we have realized that for a given sample size (number of genotyped individuals), the choice of IBD scale parameter for values ≥2 is somewhat arbitrary, provided that appropriate compensatory adjustment is made to the threshold for significance of the fastIBD score or the Refined IBD LOD score (data not shown).

Shannon's showed that a message can always be reproduced at another point in space with arbitrary precision provided noise is below some threshold level.

The method presented here can be used to determine the induced velocity from smooth blob functions of arbitrary form, provided that the vorticity length scale associated with the blob is much less in one direction than in orthogonal directions.

The final far-field noise formula can be used to predict trailing-edge noise in an arbitrary configuration, provided that a minimum statistical description of the aerodynamic pressure fluctuations on the airfoil surface close to the trailing edge is available.

If the denominator of (a_{i}) in (2.2) is zero, then (a_{i}) can be arbitrary constant provided the numerator is also zero.

Practically, the input seeds X 0 can be arbitrary files provided manually by the tester; they may not even be valid with regard to the input format of the program under test.

(1.2) The vector (F x)) in (1.1) is arbitrary convex provided begin{aligned} {f_{i}}bigl(lambda{x}+ 1-lambda){y}+ 1-lambdaambda{y}bigr(x)+(1-leqbda ){f}(y)quad foralambda{f_{i}ts,n end{aligned} (1.3) for each (lambdain[0,1]) and all x, y belongs to (mathbb{R}).

Hence, one can benefit from extracting an adequate sample size (or other properties) for arbitrary applications, provided all underlying reactions are unimolecular.

The methodology is based on multi-body techniques: arbitrary surfaces, providing an accurate surface description, are attached to rigid bodies.

A design is presented for a set of VLSI building blocks that permit the construction of high-bandwidth networks of arbitrary topology, providing the modularity needed for incremental expansibility.