Sentence examples for explicit bound from inspiring English sources

Using the theory of martingale transforms we prove that these operators are bounded in Lp Rd) for 1<p<∞ and we obtain the same explicit bound for their norm as the one known for the second order Riesz transforms.

Agarwal et al. [2] obtained the explicit bound to the unknown function of the following retarded integral inequality (1.2).

In 2009, Kim [12] obtained the explicit bound of the unknown function of the following inequality: (1.7).

We derive an explicit bound for the resulting input and discuss the influence of the controller parameters.

Since the inequality (1.2) provides an explicit bound of the unknown function it furnishes a handy tool in the study of various properties of solutions of differential equations.

The main objective of this paper is to establish a new retarded nonlinear integral inequality with two variables, which provide explicit bound on unknown function.

We then look at the case of a planar domain bounded by two closed curves and obtain an explicit lower bound in terms of the geometry of the domain.

As an application of his theory of lower bounds for linear forms in logarithms, Baker [11] gave an explicit upper bound for the size of integral solutions of hyperelliptic curves.

The CFVP gives us the explicit upper bound for the L2 norm of the approximation error.

In [10], an improved completely explicit upper bound were proved combining ideas from [15, 19 25].

We give a more explicit lower bound on E s2) than Bulutoglu and Ryan (2008).