Sentence examples for underlying equation for the from inspiring English sources
Masemola et al. in [22] have recently applied the Lie symmetry method to construct the conservation laws and the exact solutions of the underlying equation for the special cases (m=2) and (alpha=-1).
The underlying equations for the thermomechanical coupling are derived for a crystal plasticity model with gradient hardening.
The underlying equation of the MCTDH method is [ Eq. (1)]: (1) where Q1,.., Q f are the nuclear coordinates, the expansion coefficients and the SPFs for each degree of freedom κ.
This part-1 introduces the structure, principles and the underlying equations of the modular simulation system.
Moreover, in setting up the algorithms, the divisors were arranged one above the other, yielding a place-value notation for the underlying equations: the row in which a number occurred was associated with the power of the unknown whose coefficient it was.
Within several scenarios a satisfying robustness against structural errors in the underlying model equations for the nonlinear control law and the inference algorithm is demonstrated.
Furthermore, the conservation laws for the underlying equation were derived by using two different approaches, namely the new conservation theorem and the multiplier method.
For the underlying equation, subject to a highly oscillatory initial data, a hybrid of the WKB approximation and homogenization leads to the Bloch eigenvalue problem and an associated Hamilton Jacobi system for the phase in each Bloch band, with the Bloch eigenvalue be part of the Hamiltonian.
The outline of the paper is presented in the following way: In Section 2 we present some preliminaries; in Section 3 we present symmetry analysis and reduction; in Section 4 we analyze explicit solution for the reduced equation; in Section 5 we construct Cls for the underlying equation.
Our formulation is independent of the underlying equation of state.
To do so, we use comparison results for fractional equations and an equation (in terms of Mittag-Leffler functions) whose family of solutions includes those of the underlying equation.
