6) is differential equation, with auxiliary equation
Zhang: A generalized new auxiliary equation
method and its application to the (2 + 1)-dimensional breaking soliton equations, Appl.
The auxiliary Equation
(2), coupled with the linearity assumption, Equation (3), on the other hand, estimates the effect of study time alone from boys in the class ([J.
F] to construct such a new kind of auxiliary equation
For each additional variable for which an expectation appears in FRB/US, an auxiliary equation
, which expresses the variable as a function of its own past values and of the set of explanatory variables appearing in the core equations, is added to the forecasting model.
3) The direct comparison of these three models is carried out using true ex ante forecasts of money growth rather than an ex post decomposition of money growth into an anticipated and an unanticipated part by way of the frequently-used auxiliary equation approach.
Then ordinary least squares estimates of the coefficient [Alpha] and the vector b in the auxiliary equation
In the past several decades, many effective methods for obtaining exact solutions of nonlinear PDEs have been presented, such as the inverse scattering method , Hirota's bilinear method , Backlund transformation , homogenous balance method , tanh-function method , Jacobi elliptic function expansion method , Exp-function method , F-expansion method , and auxiliary equation
Following Flavin, I estimate equation (6) jointly with an auxiliary equation
for changes in income, imposing the cross-equation restrictions.
Among his topics are equipment and processes, zero-dimensional models, chemical reactions, auxiliary equations
and basic calculations, and bubbling fluidized-bed simulation program and results.
Therefore, auxiliary equations
should be introduced in order to calculate the equations for refrigerant distribution among the paths, and different auxiliary equations
should be used for different cases.
The auxiliary equations
included in the Wittmer paper are rather ill-conditioned and will not converge at high [Alpha]-MS feed levels.