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Then, they are simply considered as multidimensional arrays of numbers, constituting a generalization of vectors and matrices that are first‐ and second‐order tensors, respectively, to orders higher than two.
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Algebraic fibring, described in Subsection 4.3 below, constitutes a generalization of fusion (at the propositional level), and generally solves the question of combining logics.
This theorem constitutes a generalization of Theorem 3.1 of [7] and the results generalized therein when (S=T) and (varepsilon=0).
This approach constitutes a generalization of the beam tracing algorithm proposed by Hanrahan and Heckbert [5].
The algorithm constitutes a generalization of projection-type methods to multi-phase flows and employs a predictor corrector time-marching scheme.
Secondly, the proposed parametric relations between the pressure at the fictive throat and at the primary nozzle outlet constitute a generalization of particular geometries and operating conditions treated in previous studies.
For the analysis of the dams' deformations, ANSYS code proposes the Drucker Prager stress criterion which constitutes a generalization of Von Mises criterion taking into account the first invariant of the stress tensor and the second invariant of the deviatoric stress tensor.
The optimization problem presented in this paper constitutes a generalization of the optimal control problem of parabolic systems with Dirichlet and Neumann boundary conditions, considered by Lions et al. [21, 22], Podlubny [27], Oldham et al. [27], Bahaa et al. [1 4, 13 15] and Kotarski et al. [23, 28 30], to the fractional optimal control problem for second order systems with time delay.
The optimization problem presented in this paper constitutes a generalization of the optimal control problem of parabolic systems with the Dirichlet and Neumann boundary conditions considered in Lions [17], Lions and Magenes [18] to fractional optimal control problem for infinite order systems.
We show that our model can be expressed in energetic terms and constitute a generalization of these approaches by extending the range of systems that can be represented (ie. including energy-consuming systems such as eukaryotic promoters) and the type of metrics that can predicted (ie. including measures of dynamic and stochastic properties).
In a source coding context, the work in [3] constitutes a generalization to sensor trees of Wyner-Ziv's pioneering studies [4].
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