Sentence examples for functional fails from inspiring English sources
Local approximation GGA functional fails to yield the accuracy band gaps.
The corresponding energy functional fails to satisfy the classical Palais-Smale ((PS)) condition in (W^{1,p}_{0}(Omega)).
The corresponding energy functional fails to satisfy the classical Palais-Smale ((PS) for short) condition in (W^{1,p}_{0}(Omega)).
However, the widely used semi-local LDA and GGA functionals fail to give accurate electronic structures in molecules and semiconductors due to lack of long-range nonlocal Hartree-Fock exchange interaction in the KSDFT calculations.
In fact, it enabled the treatment of many cases where conventional approximate DFT functionals failed badly, including dimers [9,10], polymers [11], molecular crystals [12,13], and molecules adsorbed on surfaces [14 17].
In our DFT-based study, we found that hybrid-exchange correlation functionals withybrid-exchange correlationion ofunctionalsock exchange are able to capture both the FCT mechanism for the Cu/TCNE and the ICT mechanism for Cu/NaCl/TCNE, withe (semi)local functionalsufficientlye latter scenario.
Results indicate that altering assumptions about one cornerstone of ecological modeling (i.e., functional response) fails to produce qualitative differences in survival extinction outcomes even in conjunction with a wide range of capture efficiency permutations.
Due to the presence of the critical exponent in the second equation of (1.1), the functional J fails to satisfy the Palais-Smale condition.
As we know, under the general singular assumption (f) or (f0), the functional J fails to be Fréchet differentiable because of the singular term.
The camera usage allows detection of problems arising in the circuits between the TV memory and the screen, i.e., when the image on the screen does not correspond to the image in the TV memory and when the TV functional operation fails.
As a consequence, the non-functional DSC2 R203C fails to localize at the desmosomes of ID structures, whereas only a proportion of the partly functional DSC2 T275M protein is still incorporated into the desmosomes.
