Sentence examples for model are proved from inspiring English sources

The existence and the uniqueness of the solution of the model are proved.

The accuracy and reliability of proposed model are proved by comparison with previous research and analytical solutions.

Using the energy estimates and Gagliardo-Nirenberg-type inequalities, the existence and uniform boundedness of global solutions for the model are proved.

In addition, the global stability, the finite-time convergence and the denoising ability of the VRNN model are proved by rigorous mathematical results in theory.

By using the embedding theorem, the higher-order energy estimates and bootstrap arguments, the condition of chemotaxis-driven instability and the nonlinear evolution near an unstable positive constant equilibrium for this chemotaxis model are proved.

A multitude of experiments demonstrate three aspects: a) results of attribute reduction using GCRS model are proved to be of higher classification accuracies; b) attribute reduction based on GCRS model for big data manifests faster speed; c) results of rough self-learning experiments illustrate the validity of the proposed theory.

After that, and once the economics of the model are proven, Supr Daily will look to other tier-one cities in India.

The advantages of this model are proven by comparing its results against those predicted by the maximum value based model.

The model is proved to be a convex nonlinear program.

Finally, the statistical significance of the model was proved.

A uniqueness theorem for this model is proved.