Sentence examples for an example which showed from inspiring English sources

Hoff and Serre [27] presented an example which showed the failure of continuous dependence of weak solution, so it should be noticed that contrary to the case of strong solutions, weak solutions with vacuum need not depend continuously on their initial data.

Finally, the Xi'an highway network- planning program is presented as an example, which shows feasibility and effectiveness of the method.

We detail an example which shows that the Pivotal Conditions are not necessary for boundedness of the Hilbert transform.

Furthermore, we give an example which shows that the conjecture in Anderson (Proc. Amer. Math. Soc.83, No. 2 (1981), 269 275) fails to hold.

It is illustrated with an example, which shows that the robustness generalized distance function approach gives more robust optimal condition on which multiple responses are simultaneously optimized and insensitive to small changes of input variables.

A validation of the method is given and is followed by the resolution of an example which shows the importance of achieving a three-dimensional modelling for the design of an industrial tank.

The developed program is applied to a vibration analysis of a Korean bell as an example, which shows that the program is very efficient and saves much computation time for shell structures slightly deviating from axisymmetry compared to commercial FEM codes.

In this section we present an example which shows the motivation for investigating nonlinear F-contractions.

We start with an example which shows the weakness of Theorem 15.

Also, an example, which shows the validity of the hypotheses of our main results, is given.

In Section 5, we give an example which shows the feasibility of the main results.