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The gas flow in the matrix system can be ignored.
Ignoring the infinitely small quantity in the iterative process, the numerical model of the matrix system can be obtained.
The transfer functions that describe fluid exchange between the fracture and matrix system can be implemented easily within the framework of the current single-porosity streamline models.
And there exists heterogeneity in the fracture system: the horizontal permeability and vertical permeability of the fracture system are different (k_{text{fh}} ne k_{text{fv}}); Free shale gas exists in the fracture system and can be described using Darcy law; Free gas and adsorption gas coexist in the matrix system; The gas flow in the matrix system can be ignored.
Fibroblasts-derived 3D matrix system can avoid the flat surface of a tissue culture dish which impose an artificially rigid environment onto the cell [ 44].
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Thereafter the dynamic stiffness matrix for the system is defined, from which the multivariable frequency response matrix for system can be established.
The drug is usually confined within a membrane or a matrix system and can also be adsorbed, dissolved, or dispersed from the system [49].
The basic numerical kernel is the preconditioned conjugate gradient method for symmetric, positive-definite, sparse matrix systems, which can be efficiently implemented on the architectures of vector and parallel processing supercomputers.
For the case considered in this work, the total transfer matrix of the system can be written as a product of matrices of the type [36]: M jμ = cos ( ϕ j ) − i sin ( ϕ j ) / q jμ − i q jμ sin ( ϕ j ) cos ( ϕ j ) (2).
In the present paper, it has been shown that the arising quadratic matrix system polynomial factors can be handled in parallel and each of them can be solved efficiently with a preconditioning method, resulting in very few iterations.
(1)–(3) is not identified because for any (rtimes r) non-singular matrix H, the system can be expressed in terms of a new loading matrix and a new set of common factors as follows: Y_t = P^F^_t + varepsilon_t (4) F^_t = F_{t-1}^ + eta_t^, (5 where (P^=PH), (F^_t = H^{-1}F_t), and (eta_t^ = H^{-1}eta_t).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com