Sentence examples for applied to the arbitrary from inspiring English sources

Suppose that L is a linear functional applied to the arbitrary function h ( x ), and then consider the following special function: H ( x ; h, λ ) = h ( x ) + λ L ( h ) ( λ ∈ R ∖ { 0 } ).

The proposed circuit can also be applied to the design of arbitrary logic function in a multilevel threshold network.

The principle of minimum total energy, i.e. the sum of the potential and fracture energies, which stems directly from the Griffith's theory of cracks, is applied to the problem of arbitrary crack growth in 2D.

The method is applied to the governing equations in arbitrary Lagrangian Eulerian (ALE) form, and results in a prescription for computing integrated grid speed terms along with the requirement of higher-order quadrature rules in both space and time.

The proposed synchronization method can be applied to the synchronization of an arbitrary fractional-order chaotic system.

The formulated optimization problem to realize the constrained scheme could be applied to the systems with an arbitrary number of multiplexed data streams and with different antenna selection criteria.

Rather than applying an arbitrary cut-off value for fold-changes, two standard deviations from the control pair (CN CN) was applied to the list of proteins of each experimental pair (CN T21) to identify proteins with potentially significant differential expression.

Moreover, we present new analytical upper and lower bounds for the ergodic capacity of the system, which apply to the system with arbitrary number of antennas, CCI and feedback delay at any SIRs.

However, the methods proposed there do not apply to the general case of arbitrary weights, for reasons that will become clear in Section 3.3.

This simple numerical solution method can be easily applied to any arbitrary shape and the unsteady solidification problem.

This theory is applied to an arbitrary geometry of the polymer sample and an arbitrary initial penetrant content in the polymer.