Sentence examples for the aid of this function from inspiring English sources

With the aid of this function, we split a function u into two parts.

It is with the aid of this function that subcrt checks whether a user-input chemical reaction is balanced with respect to mass and charge and automatically corrects the reaction if the necessary basis species have been defined.

The wheel/track interaction is formulated by the aid of this function and reduced to an infinite system of linear equations for the Fourier coefficients of the contact force.

With the aid of frequency function methods, we can establish these quantitative estimates (see [2, 6]).

With the aid of Nussbaum function, the unknown control gain sign is effectively handled in the controller design.

In the second model, the dynamic effect of free free microbeam is modeled as a concentrated force and moment, and it is introduced by the aid of Dirac function in the motion equation.

The main purpose of this paper is to derive the expression for the basic reproduction number and further show the global stability of disease-free as well as endemic equilibria by the aid of Lyapunov function and Li Muldowney geometric approach applied to four dimensional systems.

The authors then worked out the modified models with the aid of a crossover function and have obtained better results.

The inner radiative exchange within the cavity is solved with the aid of User Defined Function (UDF).

Solutions are expressed with the aid of a special function called the discrete matrix delayed exponential having between every two adjoining knots the form of a polynomial.

The thermal gradients at both sides of the interface, which are needed to obtain the front velocity, are calculated with the aid of a distance function to the reconstructed interface.