Sentence examples for conditions for validity from inspiring English sources
By comparing the breakthrough curves for saturation with the appropriate asymptotic solutions the conditions for validity of the 'constant pattern' approximation are obtained.
These conditions certainly sound very restrictive but in reality the effective medium theory has been successfully applied to a wide variety of systems which at first glace do not seem to satisfy the conditions for validity.
The parameters have been chosen in such a way that the condition for validity of the semiclassical approximation, k F d > > 1, will be applicable.
The only condition for validity of this approach is that the detector has a certain minimum size given by Eq. (2).
In another recent work, Sadjadi [30] considered spatially flat Friedmann-Robertson-Walker (FRW) universe in the framework of the modified Gauss-Bonnet gravity and obtained the conditions required for validity of generalized second law (GSL).
The results throw light on the conditions for the validity of Dean's analysis.
The conditions for the validity of the method were identified with reference to practical tablet shapes and failure patterns.
We establish both sufficient and necessary conditions for the validity of the so-called Hardy Sobolev inequalities on open sets of the Euclidean space.
These estimates imply necessary and sufficient conditions for the validity of the classical one-term Weyl formula for the counting function and, under certain restrictions, give an order sharp remainder estimate in this formula.
When the Essential Work of Fracture (EWF) method is used to evaluate the fracture toughness of ductile thin polymer films, buckling phenomenon is very often observed, which may violate the conditions for data validity.
Both parabolicity and stochastic completeness have been the subject of a systematic study which led to discovering not only sharp geometric conditions for their validity but also an incredible rich family of tools, techniques and equivalent concepts ranging from maximum principles at infinity, function theoretic tests (Khasʼminskii criterion), comparison techniques etc.
