Sentence examples for the existing bounds from inspiring English sources
The example shows that the bound in Theorem 3.2 is better than the existing bounds in Theorem 4 in [11] and Theorem 4 in [10] in some cases.
The example shows that the bound in Theorem 3.3 is better than the existing bounds in Theorem 4 in [11], Theorem 4 in [10] and Theorems 2.1, 2.2 in [9].
The example shows that the bounds in Theorem 2.1 and Theorem 2.2 are better than the existing bounds.
The example shows that the bounds in Theorem 4.1 are better than the existing bounds in Theorem 1 in [2] and Theorem 1 in [3].
Additionally, the derivatives of (B_{N}(x;f)) also satisfy the existing bounds of the corresponding derivatives of f (see [26]) and possess the same convergence properties (see [16]).
Some related issues were already considered in the literature for the 2-dimensional case S2; our results are new or improve the existing bounds even in these special circumstances.
Using this condition and the existing bounded real lemma, we develop systematic design methods for H2 and mixed H2/H∞ control of 2-D systems, and an application of the controller design methods to the control problem of a metal rolling process is demonstrated in this paper.
This illustration compares the proposed lower bound with the existing lower bounds from [3] and [4], showing that the proposed lower bound is tighter.
Then, a new definition for uncertainty bounds is presented in order to eliminate the type-reduction process in IT2 FLSs and to increase accuracy of the existing uncertainty bounds in the literature.
More precisely, we show the usefulness of both theories to improve the existing automata bounds on the work of Neyman (1998) Finitely repeated games with finite automata, Mathematics of Operations Research, 23 (3), 513 552.
To improve forecasting accuracy, this paper focuses on two aspects: ①proposing a novel hybrid method using Boosting algorithm and a multi-step forecast approach to improve the forecasting capacity of traditional ARMA model; ②calculating the existing error bounds of the proposed method.
