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for all, and is the homotopy operator which can be found in [3].
FPCA relies on the estimation of the eigenelements of the covariance operator which can be seen as nonlinear functionals.
In this section, we establish some theorems on the fractional exponential operator which can be useful for solving PFDEs.
As an example, let us now consider the kinetic energy operator, which can be written as (27).
Unlike hyperviscosity kernels, the SVV approach involves a second-order operator which can be readily implemented in standard finite element codes.
The more recent paper Ren et al. (2016b) established the comparison for fully nonlinear degenerate PPDEs, by introducing a regularization operator which can be viewed as the counterpart of the sup-convolution in the PDE literature.
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A metric tensor allows a definition of Hodge-operator which can be used to express constitutive equations [3].
This paper presents two new ternary operators which can be used in different scrambling crypto algorithms.
The fourth lemma is a norm inequality for the sum of two operators, which can be found in [14].
In 1989, Dunkl [10] constructed for each Coxeter group a family of commutative differential-difference operators, called Dunkl operators, which can be considered as perturbations of the usual partial derivatives by reflection parts.
Fractional calculus allows variable-order of fractional operators, which can be exploited in diverse physical and biological applications where rates of change of the quantity of interest may depend on space and/or time.
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CEO of Professional Science Editing for Scientists @ prosciediting.com