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Here and below in similar situations, we write an operator to the right of an operand, because the action of the operator involves noncommutative matrix multiplication in such order.
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In the particular case when ϕ ( x, t ) = | t | p ( x ) − 2, the operator involved in (B) is the p ( x ) -Laplacian.
The harmonic -fields are defined by for some The orthogonal complement of in is defined by for all The harmonic projection operator is the operator involved in the Poisson's equation where is the Green's operator.
As far as the authors know, there are no results concerned with the eigenvalue problem for a more general p ( x ) -Laplacian type problem in the whole space R N. When ϕ ( x, t ) = | t | p ( x ) − 2, the operator involved in (E) is called the p ( x ) -Laplacian, i.e., Δ p ( x ) u : = div ( | ∇ u | p ( x ) − 2 ∇ u ).
Based on the dynamic operator precedence table, the precedence of the operators involved in the change expression are verified.
Among the operators involved in urban transport, public ownership remains dominant in various forms (commercialised, communalised, or budgetary units).
The investigation of these Hilbert Schmidt norms requires us to calculate the integral kernels of the operators involved.
It considers two issues: (1) Is it possible to apply local rationality to get "inside the head" of the operators involved in the incident at Buncefield.
Particular attention is payed to the accuracy-related issues arising from the use of the low-latency approximations of some of the operators involved.
As previously discussed, the operators involved in forward model (10) are a cropping operator, a one-dimensional convolution, and a projector.
In Section 2, we recall our recent study for the design of all the operators involved in a 2D non separable lifting structure [36, 37].
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