Sentence examples for by using the solutions from inspiring English sources

The following theorem establishes that the Fibonacci numbers can be obtained by using the solutions of (7).

propose a new technique to find the exact solutions of problem (1.1) by using the solutions of interval integer order delay differential equation.

A new technique is proposed to find the exact solutions of IFDDE by using the solutions of interval integer order delay differential equation.

In particular, by using the solutions and methods for PR problems and PH problems one can effectively solve a number of periodic problems in plane elasticity [11 13].

This can be done by using the solutions of a set of 2D models for a coherent line source for real andimaginarywavenumbers.

Let us consider the (forward) Cauchy problem (9); we construct a positive lower solution by using the solutions to begin{cases} y'= betafrac{sqrt{y 2-y)}}{1-y}, y(0) = 0, end{cases} (13) in dependence of (betafrac{sqrt{y 2-y

We solve the second system by using the solution of specific dual q-integral equations.

Consequently, ŝ 1 R is obtained by using the solution ŝ 2 R in (21).

By using the solution of one population, a new population is formed.

The transport performances of (permeability, selectivity and partition coefficients) are evaluated by using the solution-diffusion model.

We also construct explicit formulas for the curve deformations by using the solution of linear diffusion differential/difference equations.