Sentence examples for monotone globally from inspiring English sources

The reliability of iterative techniques for solving nonlinear difference schemes can be essentially improved by using component-wise monotone globally convergent iterations.

In this section, we study mean-field BDSDEs with globally monotone coefficients, which is helpful for the case of locally monotone coefficients.

Then for each m, f m is globally monotone in y and globally Lipschitz in z.

The general activation functions include monotone nondecreasing functions, globally Lipschitz continuous and monotone nondecreasing functions, semi-Lipschitz continuous mixed monotone functions, and Lipschitz continuous functions.

In Section 2, we present the existence and uniqueness results about mean-field BDSDEs with globally monotone coefficients.

As a preliminary step, the existence and uniqueness result for the solutions of mean-field BDSDEs with globally monotone coefficients is also established.

Using similar arguments to [18], one may extend the Poincaré map P to a new one which is a globally monotone twist map and which is guaranteed by the Aubry-Mather theorem [18].

The inputs of the neural networks are required to be time varying and the activation functions to be globally continuous and monotone nondecreasing.

In this paper, we study a new type of BDSDEs, that is, the so called mean-field BDSDEs, under the globally (respectively locally) monotone coefficients.

To relax the Lipschitz conditions, Wu and Zhang studied two kinds of BDSDEs under globally (respectively, locally) monotone assumptions and obtained the uniqueness and existence results of the solutions (see [12]).

Some extensions to biological problems where the drift term is not globally Lipschitz but satisfies the monotone growth condition (Equation 20) were studied in [67].