Sentence examples for by introducing some function from inspiring English sources

In our model, this component has been represented by introducing some function (10) and the parameter α.

In order to generalize Yamazaki et al. (2008), we represent the non-hydrostatic component of the pressure by introducing some function as hat qleft({x,y,z,t} right) = qleft({x,y, - h,t} right)fleft z right), (10).

It is shown that a better payoff allocation mechanism can be computed by introducing some clearing functions in the model.

By introducing some auxiliary functions and using maximum principles, they established some conditions on nonlinearities to guarantee the existence of blow-up solution or global solution.

We start by introducing some notations and functions used in the algorithm.

By introducing some appropriate auxiliary functions and technically using maximum principles, we establish conditions to guarantee that the solution blows up in some finite time or remains global.

The proposed fuzzy controller is developed by introducing some non-negative switching functions, and novel parameter adaptation learning laws are designed using the σ-modification method.

This difficulty is overcome by introducing some special type Lyapunov functions and taking advantage of the mean-value theorem, the backstepping design method and the approximation property of the fuzzy systems.

Two classes of new inequalities similar to Hardy-Hilbert inequality are showed by introducing some parameters and two real functions and.

end{cases} (6) In the next section, we present our main results by introducing some new types of Green's functions.

By introducing some parameters and estimating the weight functions, we build a new Hilbert's inequality with the homogeneous kernel of 0 order and the integral in whole plane.