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The quasi-steady treatment through the junction yields a system of nonlinear balance equations.
The penalty method yields a system of linear equations that is Symmetric Positive Definite (SPD).
The implicit function theorem yields a system of linear equations from the discretized Navier-Stokes equations.
The transformation yields a system of four nonlinear ordinary differential equations (ODEs).
Application of diffuse interface models (DIM) yields a system of partial differential equations (PDEs) that generally requires a numerical solution.
Inertia effects are included in our previous static model which yields a system of partial differential equations.
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The local mechanical and charge equilibrium equations yield a system of partial differential equations for the characteristic functions that are solved using the finite element method.
The applied tractions are expanded in Fourier Bessel series and boundary conditions are used to yield a system of simultaneous equations.
The model combines principles of thermodynamics, heat and mass transfer applied to the system components with empirical correlations, assigning thermodynamic control volumes to each component, which yield a system of ordinary differential equations with respect to time that is integrated explicitly and accurately with low computational time.
The use of 0.1 equivalents of benzylamine A1 yielded a system of constituents 1– 4. Here, compound 2 constituted nearly 43 % of the total imine content, which indicated a preferred systemic expression of 2 over the other constituents under these conditions.
Since q(c) is a polynomial of order 2, the derivatives with respect to c im and λ i yield a system of N × (Nclust + 1) linear equations of the form: (9) (S 0 0 S ⋯ ⋯ 0 I N 0 I N ⋯ ⋯ ⋯ ⋯ ⋯ 0 0 I N I N ⋯ ⋯ S I N I N 0 ) · (c 1 c 2 ⋯ c N c l u s t λ ) = (0 0 ⋯ 0 1 ) with I N being N × N identity matrix and c m = (c1 m,…, c Nm ).
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