Sentence examples for functions of the independent from inspiring English sources

As a simple example, note dy/dx + Py = Q, in which P and Q can be constants or may be functions of the independent variable, x, but do not involve the dependent variable, y.

where and are all functions of the independent discrete variable.

For linear, Riccati, Bernoulli and Abel components its coefficients are functions of the independent variable x.

Second order polynomial (SOP) models as functions of the independent variables generated response surface and contour plots.

In order to eliminate the possible sources of prediction bias, both the standardised and pure residuals were inspected using scatterplots that were obtained for the candidate models as functions of the independent variables and with and without the estimated random coefficients.

Since the interferers are assumed to be independent of, but not identical to, each other, it can therefore be observed from (7) that the characteristic function of ({z_{m}^{l}}) will be the product of N characteristic functions of the independent random variables ({U_{n}^{l}}), that is, {Phi_{Z} omega)=prod_{n=1}^{N}Phi_{U_{n}} omega)=prod_{n=1}^{N}frac{1}{omega^{2}sigma_{U_{n}}^{2}+1}} (10).

But it goes to the core of the functioning of the independent media in our society.

Unknown complex function of the independent variables.

Let us assume deterministic value of PWV is expressed as a function of the independent variables (ϕ, λ and t).

If the body exhibits orthotropic symmetry, these roots are explicitly given as a function of the independent components of the elasticity tensor.

In addition, computational fluid dynamics (CFD) was used to predict the flow field in the reactor as a function of the independent variables, and relate it to the reaction yield.