Sentence examples for split equation from inspiring English sources

We can further split Equation 5 into real and imaginary parts as shown in Equation 6: T ε ω = ∑ m = 0 M - 1 Re K m H ˜ NYQ ω - ω m - Re S ω + j ∑ m = 0 M - 1 Im K m H ˜ NYQ ω - ω m - Im S ω (6).

To avoid calculating non-minimal solutions we split equation (6) into two constraints, (7a) ∑ i ∈ B x i ≤ | B | − 1, (7b) ∑ i ∈ N x i ≥ 1.

The split equations are closed and coupled through the concept of impedance at domain boundaries.

The consistent boundary conditions on the tentative velocity and pressure have been determined by a procedure that consists of approximation of the split equations and the boundary limit of the result.

The method splits equation (1) into two ordinary differential equations with the separation constant a as follows: begin{aligned}& frac{d^{2}G}{{deta}^{2}}+ (a-2qcos2eta )G=0, end{aligned} (2) begin{aligned}& frac{d^{2}F}{{dxi}^{2}}- (a-2qcosh2xi )F=0, end{aligned} (3) where (q=k^{2}c^{2}/4>0).

The formula in Equation 49 states that the operator °∇can be considered on spaces provided with the N-connection structure but this linear connection is not adapted to the N-connection splitting (Equation 71), i.e., it is not a d-connection, see definition 7 (so, we do not use a boldfaced symbol for the Levi-Civita connection).

In coordinate form, we can characterize such objects (linear connections, metrics or any tensor field) by certain group and coordinate transforms adapted to the global space splitting (Equation 71) into z- and v-subspaces (z-projections on L π E Open image in new window play the role of h-projections on E).

Equations (10 - 13 10 - 13lled the splitting equareons (see [13]).

The method reduces high-dimensional problems to a series of uncoupled one-dimensional problems in each time step interval, in which one-dimensional ELLAM is used to solve the one-dimensional splitting equations.

(c) Integrate the split reaction equation by a half timestep Δ t k /2.

(b) Integrate the split diffusion equation by a full timestep Δ t k.