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The notation means that the functional is applied to considered as a function of.
A new Lyapunov functional is applied to guaranteed the obtained results.
The paper describes the improvement of the reconstruction when a least-square fit algorithm, which minimizes a distance functional, is applied.
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In this new domain, a new set of functionals is applied, resulting in a descriptor vector which is completely rotation invariant and thus suitable for 3D model matching.
After proper positioning of the 3D objects using translation and scaling, a set of functionals is applied to the 3D model producing a new domain of concentric spheres.
Surrogate functionals are applied; the corresponding strategy is shown to converge in norm and to regularize the problem.
Different types of boundary conditions based on the primary variables of the magneto-elastic enthalpy and internal energy functionals are applied to solve the problem at the micro-scale.
Low-level descriptors (LLD) and their first-order delta (difference) coefficients are computed and statistical functionals are applied to the LLD contours in order to summarise the LLD over time, e. g., the LLD are aggregated over each segment into a number of summary statistics such as the mean value, the standard deviation, etc.
The expression "the functional tradition" is applied to this emphasis on functionalism, which appears and reappears throughout the history of architecture independently of changes in style.
Hence we speculate that the functional effect of the analyzed SH2B1 variants might become detectable when a battery of different functional tests is applied.
A multiscale model, combining elasticity and density functional theory, is applied to the interpretation of observations.
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