Sentence examples for is continuous by using the from inspiring English sources

Proof Noticing that f : [ 0, 1 ] × R n → R is continuous, by using the Ascoli-Arzela theorem and standard arguments, the result can easily be shown.

Consequently, is completely continuous by using the Arzela-Ascoli theorem [3].

Very recently, Zhu et al.[26] obtain the existence results when a nonlocal item g is Lipschitz continuous by using the Hausdorff measure of noncompactness and operator transformation.

Thus (widetilde{T}: X rightarrow X) is completely continuous, by using the Schauder fixed point theorem, T̃ has at least a fixed point ((u^, v^ )) such that ((u^, v^ )=widetilde{T} u^, v^)).

The problem of active protection of continuous structure domains is developed by using the well known results of optimal control theory.

First, the optimal policy is provided by using the continuous time stochastic dynamic programming.

Thus basically first the continuous distribution function is exponentiated and the resulting exponentiated continuous distribution is then discretized by using the methodology-IV.

Normally distributed continuous variables were compared by using the Student t test with unequal variances, whereas continuous non-parametric variables were compared by using Kruskall-Wallis and Mann-Whitney U tests.

Continuous simulations are performed by using the high-resolution rainfall data series for the 'doo nothing'' and DRWH scenarios.

Continuous variables were analyzed by using the Mann–Whitney U test and discrete variables were analyzed by using the Chi squared test.

Continuous variables were dichotomised by using the median split method.