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This solution was found by using a decomposition technique developed by Amundson and Ramkrishna which transforms an inseparable, non-self-adjoint equation into a separable, self-adjoint equation.
As a main result, the strong direct inequality of approximation by the operator is established by using a decomposition technique.
By means of K-functional and modulus of smoothness defined in [5], we will extend (1.4) to the case of higher dimension by using a decomposition technique.
Additional quantitative information was obtained by using a decomposition algorithm.
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During preprocessing the residual water signal was subtracted by using a decomposition-fitting algorithm.
Yue and Zhong [13] studied the long time behavior of the three-dimensional NSV model of viscoelastic incompressible fluid for system (1.1) by using a useful decomposition method.
The retail strategy problem is formulated as an MINLP problem which is transformed into MILP by jointly using a decomposition and the disjunctive constraints and solved using CPLEX 12.5.1 solver in GAMS 24.1.2 software [44] on Intel Pentium CPU at 2 GHz and 1 GB of RAM.
The model parameters have been tuned by hand using a decomposition of the model (see Materials and Methods section).
The long transient phenomenon in nonlinear structural vibrations is examined in detail by using a signal decomposition and processing method based on the empirical mode decomposition, Hilbert–Huang transform (HHT), and nonlinear dynamic characteristics derived from perturbation analysis.
The background meshes ares constructed with quadrilateral elements on three-dimensional surfaces by using a domain decomposition method.
The time integration is performed by using a domain decomposition time-splitting technique combined with multiterm fractional step diagonally implicit Runge Kutta methods.
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