Sentence examples for a certain solution of from inspiring English sources

then exponentially for and where is a certain solution of a logistic equation.

By using a fluctuation lemma, Li and Chen [4] obtained sufficient conditions which ensure the second species will be driven to extinction while the first one will stabilize at a certain solution of a logistic equation.

From the proof of Theorem 3 it follows that if x is a q-periodic solution of (1), then x has the following form x(n)=(c_{1}, c_{2}, dots, c_{q},c_{1}, c_{2}, dots, c_{q}, dots), where ((c_{1}, c_{2}, dots, c_{q})) is a certain solution of system (18).

Those tiny granules are formed by exposing a certain solution to a nanolithographic process (but of course we all knew that already).

At a certain point, increasing the number of rows or columns for a certain solution would not compensate the lose of quality, according to the rest of objectives.

If the arrival of the Germans seemed at first yet one more problem, like extra mildew and blight, it also provided a certain solution: the invaders compulsorily purchased millions of bottles of wine.

This design uses the ion-selective electrode method to measure the pH, or the ion concentration of a certain solution.

The first fitness function f 1 evaluates the coverage for a certain literature capacity of a certain solution and will often be the most important requirement.

end{aligned} Further, there is a certain solution (mathbf{r}_{0}) of (3.7) such that 0< mathbf{r}_{0} leqslantfrac{4-4beta- gamma Vert f_{0} Vert - eta Vert h_{0} Vert }{2gammaeta}.

In the absence of the dispersive term and (m=0), model (1.2) reduces to the wave equation u_{tt}-Delta u-Delta u_{t}-Delta u_{tt}+u_{t}=|u|^{p-2}u. (1.4) Xu and Yang [11] established a blow-up result for certain solutions of (1.4) with arbitrary positive initial energy, where (1< p

We give an explicit integral formula for certain solutions of the equation D=0.